stem-haadf nanotomography: application to …docinsa.insa-lyon.fr/these/2009/benlekbir/these.pdfn...
TRANSCRIPT
N° 2009-ISAL-0025 Year 2009
Thesis
STEM-HAADF nanotomography:
application to nanomaterials
Submitted to
L’institut national des sciences appliquées de Lyon
To obtain
the degree of doctor
By
Samir BENLEKBIR
Defence on march 30th, 2009
Jury
Rapporteur P. DONNADIEU Director of research CNRS (SIMAP Grenoble)
Rapporteur J. WERCKMANN Engineer of research CNRS (IPCMS Strasbourg)
Supervisor T. EPICIER Director of research CNRS (MATEIS INSA Lyon)
Examiner C. GEANTET Director of research CNRS (IRCELYON, University of Lyon I)
Examiner S. MARCO C.R. INSERM (Institut Curie Paris)
Examiner F. DANOIX C.R. CNRS (GPM Rouen)
Laboratory Materials: Engineering and Science (MATEIS)
2
3
4
5
STEM-HAADF nanotomography: application to nanomaterials
Abstract: Electron tomography is a technique used to characterise 3D structure and chemistry of the
observed samples, with a nanometer resolution when applied in a Transmission Electron
Microscope. The chosen imaging mode is STEM-HAADF (Scanning Transmission Electron
Microscopy in the High Angle Annular Dark Field imaging mode) because it is well-adapted
to a quantitative tomography, for both crystalline and amorphous materials. Moreover the
STEM HAADF contrast is related to the chemical nature of elements, and simulation of
images can be undertaken to extract chemical information, such as volume density or atomic
number of particles. The aim of this thesis is threefold: (i) firstly to adapt the transmission
electron microscope of the laboratory to „tilting‟ tomography, (ii) secondly to apply this
approach to the study of heterogeneous nanostructures and nanomaterials, (iii) endly to
explore alternative 3D methods, such as extended stereoscopy, which requires the acquisition
of fewer images as compared to complete „titlitng tomography‟. The experimental work has
consisting in adaptating the tip of the TEM specimen holder in order to reach a tilt range up of
160°, as a tomography experience requires acquisition of hundreds of images at different tilt.
A software has been written to control semi-automatically the microscope and the detector,
and especially to correct the focus in images during the phase of acquisition. The materials
which have been studied are: nanoprecipitates of VC, Pd catalysts, Au@SiOx nanocomposites,
and an AlZnMg alloy.
Keywords: electron microscopy - tomography - STEM-HAADF - stereoscopy -
nanoprecipitates - nancomposites - catalysts - alloys
Nanotomograhie en mode STEM-HAADF : application aux
nanomatériaux
Résumé: La tomographie électronique est une technique utilisée pour caractériser en 3D la
structure et la chimie des matériaux, avec une résolution nanométrique dans le cas d‟un
microscope électronique par transmission. Le mode d‟imagerie choisi est le champ
sombre annulaire à grand angle, car il est adapté à la tomographie quantitative à la fois
pour les échantillons cristallins et amorphes. De plus, le contraste du champ sombre
annulaire dépend de la nature chimique des éléments observés, et la simulation des
images permet d‟extraire des informations chimiques, comme la densité volumique ou le
numéro atomique des espèces chimiques présentes. L‟objectif de cette thèse est triple :
(i) dans un premier temps, adapter le microscope électronique par transmission du
laboratoire à la tomographie par rotation, (ii) ensuite, appliquer cette approche à l‟étude
de nanostructures hétérogènes ainsi que de nanomatériaux, (iii) finalement, explorer des
méthodes 3D alternatives, comme la stéréoscopie, qui nécessite l‟acquisition d‟un
nombre plus faible d‟images qu‟en tomographie électronique. Le travail expérimental a
consisté à adapter l‟embout du porte objet du MET, afin d‟atteindre une plage de tilt au
delà de 160° : une expérience de tomographie nécessite l‟acquisition d‟une centaine
d‟images sur différentes inclinaisons. Un logiciel a été développé pour contrôler semi-
automatiquement le microscope, le détecteur, et surtout pour corriger le focus dans les
images durant la phase d‟acquisition. Les matériaux étudiés sont des nanoprécipités de
carbure de vanadium (VC), des nanoparticules de catalyseurs (Pd), des nanocomposites
de type « Au@SiOx », et un alliage AlZnMg.
Mots-clès: microscopie électronique - tomographie - champ sombre annulaire -
stéréoscopie - nanoprecipitès - nanocomposites - catalyseurs - alliages
6
7
Contents
List of abbreviations………………...………………………...........................11
List of figures………………………………………………………………….13
List of tables…………………………………………………………………...23
Résumé français……………………………….………………………………25
1. Introduction………………………………………………….…………37
1.1. Interest of tomography………………………………………………….…….……39
1.2. Tomography techniques used in material science…………………………….….42
1.2.1. X-rays……………………………………………………………………….42
1.2.2. Electron microscopy………………………………………………………..…46
1.2.2.1. The projection requirement…………………………….………..……46
1.2.2.2. TEM…………………………………………………………………...47
1.2.2.3. STEM-HAADF………………………………….……………………48
1.2.2.4. EFTEM………………………………………………………...……...50
1.2.3. Atom probe……………………………………………………………………52
1.3. 3D analysis different from tomography…………………………………...………56
1.3.1. Difference between 3D analysis and tomography…………………….………56
1.3.2. Introduction to the stereoscopy…………………………………..…………...57
1.4. Results obtained by electron tomography on material science during the last
decade………………………………………………………………………………..58
1.5. Algorithms of reconstruction…………………..……………………………..……66
1.5.1. Back Projection (BP) ……………………..……………….…………….……66
1.5.2. Weighted Back Projection (WBP) …………….………...……………………66
1.5.3. Algebraic Reconstruction Technique (ART) …………...………………….…67
1.5.4. Simultaneous Iterative Reconstruction Technique (SIRT) ……………..….…67
1.6. Practical aspects of tilting tomography…………………………………………...68
1.6.1. Geometry of acquisition………………...……….……………..…………….68
1.6.1.1. Simple tilt axis……………………..………………………………….68
1.6.1.2. Double tilt axis………………………..……………………………….68
1.6.1.3. Conical tomography…………………………………………………..69
1.6.2. Principle of alignment of images…………………………………………...…69
1.6.2.1. Tilt axis…………………………………………………..………...….70
1.6.2.2. Alignment with cross correlation………….....…………………….....71
1.6.2.3. Alignment using fiducial markers…………………………………….72
1.6.2.4. Improving alignment by image stretching…………….………………72
1.6.3. Resolution of tomogram………………………………….…………..….……73
1.6.3.1. Influence of acquisition parameters and sample geometry……………73
1.6.3.2. Spatial dependence of resolution regarding various directions…….…75
References of chapter 1………………………………………………...………………..76
8
2. Experimental procedures………………………………………………83
2.1. Adaptation of tip of holder…………………………………………………………85
2.2. Correction of drift……………………………………………..……………………89
2.3. Correction of focus……………………………………………………….…………91
2.3.1. Linearity of focus with angle of tilt………………………...…………………92
2.3.2. Dynamic focus……………………………………………...…………………94
2.3.3. Examples…………………………………………………...…………………95
2.4. Software…………………………………………………………..…………………96
2.4.1. Aim of the software………………………………………...…………………96
2.4.2. The software „step by step‟................................................................................98
References of chapter 2…………………………………………….…………………100
3. Applications…………………………….…………..…………………101
3.1. VC nanoprecipitates ……………………………………….……………………..103
3.1.1. Experimental background: sample preparation………..…….………………103
3.1.2. Interest of electron tomography characterization…………..…..……………104
3.1.3. Results………………………………………………………..……………...104
3.1.4. Conclusion…………………………………………………...………………108
3.2. Au@SiOx...................................................................................................................109
3.2.1. Synthesis of Au@SiOx nano composites……………...…………………….109
3.2.2. Interest of stereoscopy characterization…………………………..…………111
3.2.3. Discussion of the imaging mode………………………………….…………113
3.2.4. Internal localisation of gold particles in the Au@„homogeneous‟SiO x
nanocomposites……………………………………………………..…………116
3.2.5. External localisation of gold particles in the Au@„core -shell‟SiOx
nanocomposites…………………………………………….………………….125
3.2.6. Chemical quantification of the core-shell structures of silica particles in the
Au@„core-shell‟SiOx nanocomposites……………………………………..….129
3.2.7. Conclusion………………………………………...…………………………132
3.3. Pd (bi-pyramidal, nano-rod)...................................................................................133
3.3.1. Justification of the study..................................................................................133
3.3.2. Synthesis of Palladium nanoparticles….……………………….……………133
3.3.3. Results……………………………………….………………………………134
3.3.3.1. Pentagonal rods……………………………….….………….………134
3.3.3.2. Bipyramids…………………………………….…………….………135
3.3.4. Conclusion………………………………...…………………………………138
3.4. AlZnMg…………………………………………………………...……………..…139
3.4.1. Context of the study………………………………………..………...………139
3.4.2. Literature survey on the characterization of the precipitation state in the Al-Zn-
Mg alloy used in this study…………………………………………………….139
3.4.3. Preparation of AlZnMg specimen for tomography….………………………142
3.4.4. TEM Results…………………………...……………………………………146
3.4.5. Towards a comparison between TEM and APT tomography……………….150
9
3.4.6. Conclusion………………………………………………………...…………153
References of chapter 3……….…………………..……………………………………153
4. Perspectives and general conclusion…………………………………159
4.1. Chemical quantification in STEM tomography………………...….……...……161
4.2. STEM tomography and crystallography……………………...……164
4.3. Correlation of STEM tomography with analytical techniques…..………..…168
4.3.1. Case of EDX…………………………………………………….…………...168
4.3.2. Case of EFTEM…………………………………………………..………….169
4.4. General conclusion…………………………………….…………….………….…170
References of chapter 4………………..…………………………..…….………….….160
Appendix 1…………………………………………………………………...173
10
11
List of abbreviations
APT: Atom Probe Tomography
ART: Algebraic Reconstruction Techniques
BF: Bright Field
BP: Back Projection
DF: Dark Field
DM: Digital Micrograph
EDX: Energy Dispersive X-ray
EELS: Electron Energy Loss Spectroscopy
EFTEM: Energy Filtered Transmission Electron Microscopy
FIB: Focused Ion Beam
HAADF: High Angle Annular Dark Field
SAXS: Small-Angle X-ray Scattering
SEM: Scanning Electron Microscopy
SIRT: Simultaneous Iterative Reconstruction Techniques
STEM: Scanning Transmission Electron Microscopy
WBP: Weighted Back Projection
12
13
List of figures
1. Introduction Figure 13: some dates, events, and names that marked the development of electron tomography in
biological or material science [Ziese2004].
Figure 14: projections are partial representations of the reality, illustrations to highlight errors and no
complete information extracted from projections, a) volume that contains spheres, projected through z
direction, shows error of measure of distance directly from projection, b) 3D geometry made by hands
projected through z direction, shows errors of analyse of morphology directly from projection.
Figure 15: a) Planar section of a beta-quenched sample. The circles mark disjointed clusters of
parallel lamellae having the same orientation. It is not sure if these clusters belong to the same colony,
b) Volume fraction of beta-quenched TA6V (with a voxel size set to 0.7 µm, the scanned volume is of
the order of 7003 µm3). The black line delineates a colony. c) Visualization of the beta phase spatial
distribution within a cube of edge 45 µm. d) Superposition of the initial volume and the limits
determined by the segmentation algorithm. The limits have been thickened for ease of visualization. e)
Example of colony. f) Detail of a colony [Vanderesse2008].
Figure 16: Unloaded interlock reinforcement G1151 (20 µm resolution, rescaled), (a) three successive
slices within warp yarn planes, (b) three successive slices within weft planes, the same yarn is
underlined in black. Pure shear: comparison of simulation with CT scans, (c) deformed shape of the
unit cell, (d) set of yarn cross sections along half a period of the yarn [Badel2008].
Figure 17: series of projections of the same area of VC nanoprecipitates deposited on a carbon
extraction replica obtained from a model FeVC steel. 3 BF micrographs are shown in a), b) and c),
which were acquired at tilts respectively equal to 0, 2 and 4°. Note that the contrast of thickness
fringes at the periphery of the particles changes significantly even within a small tilt range, which does
not fulfil the projection requirement.
Figure 18: Bright and Dark Field mode on Transmission Electron Microscopy. The backbone of this
imaging mode is the special shape of the diaphragm: the central beam is shuttered with an opaque disc
and the image is formed by electrons scattered at high angles that have passed through the annular slit
of the diaphragm. Value of camera length depends on imaging mode and angle of collection.
Figure 19: series of projections of the same area of VC nanoprecipitates deposited on a carbon
extraction replica obtained from a model FeVC steel. 3 HAADF images are shown in a), b) and c),
which strictly correspond to the BF micrographs reported in Figure 1.
Figure 20: principle of EFTEM imaging (case of a „in-column‟ spectrometer or filter inserted in the
microscope [Zeiss]).
Figure 21: (a and b) Carbon atom maps; and corresponding concentration profiles (c and d) across
austenite–ferrite interface in a steel transformed at 325 °C for 1350 s ( b means bainitic ferrite and
austenite) [Caballero2009].
Figure 22: Study of cracks in a stainless steel after stress-corrosion cracking. (a) Nano-SIMS
composite map of the distribution of 56
Fe16
O- (red),
52Cr
16O
- (blue), and
11B
16O2
- (green) showing
oxidized deformation shear bands (arrowed). (b) Bright-field TEM image showing two orientations of
shear bands (arrowed) either side of an advancing crack. APT maps of (c) Cr and (d) CrO species from
a volume taken from the vicinity of a crack tip, showing O diffusion along a serrated, Cr-segregated
shear band [Cerezo2007].
14
Figure 23: SBA15 mesoporous material observed a) along the structural channels after a tilt of -28°
(sample provided by V. Dufaux, ENS-Lyon), b) perpendicularly to the previous projection (tilt +62°).
The first micrograph shows some filled channels edge-on (arrows; the filling material is a non-
crystalline (W,P)-based oxide). On the second micrograph, the length of the „filaments‟ filling the
channels is directly evidenced (MET 2010F; tilting at 90° in this microscope has been made possible
by using a dedicated home-made modified holder tip, see §.2.1).
Figure 24: conventions used to describe the motion of a given particle during a tilt experiment, (a) M
particle at M0(X0, Y0, Z0) position at zero tilt. The angle 0 characterizes the elevation of M, is the
radius of the circular trajectory described by M around the tilt axis Oy, (b) M particle moved from M0
to M (X , Y , Z ).
Figure 25: a typical STEM HAADF image of Pd6Ru6 nanoparticles and an MCM-41 mesoporous
silica support [Midgley2003].
Figure 26: (a) a montage in which each image is a voxel projection of the 3D reconstruction of an
MCM41-Pd6Ru6 catalyst viewed at angles shown in the figure. The 3D structure of the mesopores is
well resolved. The nanoparticles are coloured red to improve clarity [Midgley2003].
Figure 27: an illustration of how an individual nanoparticle can be isolated in the reconstructed data
set to show that it is anchored to a wall of a mesopore of the MCM-41. The mesoporous channels are
about 3 nm in diameter and the single nanoparticle of Pd6Ru6 is about 1 nm in diameter. The scale bar
corresponds to image (c) [Midgley2003].
Figure 28: (a) BF image of a magneto tactic bacterium showing the backbone of magnetite crystals
surrounded by the organism‟s organic „drapery‟. (b) A high magnification STEM HAADF image of a
similar bacterium to that shown in (a), which shows the excellent Z-contrast and spatial resolution of
this technique [Midgley2003].
Figure 29: tomographic reconstruction of a magnetite nanocrystal from a magnetotactic bacterium.
The reconstruction was made from a tilt series of STEM HAADF images. The montage shows the
three-dimensional morphology of the crystal viewed from a range of directions [Midgley2003].
Figure 30: a comparison between (a) an original zero tilt oxygen jump-ratio image taken from a
magnetite chain in a magnetotactic bacterium and (b) the zero tilt projection of the tomographic
reconstruction. Note the dramatic improvement in the signal-to-noise ratio in the reconstruction
[Midgley2003].
Figure 31: two colour sections through the EFTEM reconstructions of the magnetite crystal chain.
The pixel intensity of the oxygen (green) has been rescaled to better compare with the iron (red). The
main image is a section (perpendicular to z) taken approximately midway though the centre crystal.
Sections have also been taken perpendicular to the chain axis from five of the crystals and are
displayed in A–E [Midgley2003].
Figure 32: zero-loss BF image of a stainless steel grain boundary used for EFTEM tomography, the
general direction of which is shown by the arrow. Diffraction contrast obscures most of the carbide
structure, which is complex and irregular both along the length of, and across, the boundary
[Midgley2003].
Figure 33: voxel projections of a tomographic reconstruction using Cr jump-ratio images of the grain
boundary carbide structure seen in Figure 29. The carbides are viewed (a) at 45° from all major axes,
and parallel to (b) the z-axis, (c), the x-axis and (d) the y-axis, respectively. The box edge is 1.5 mm in
length [Midgley2003].
Figure 34: the center panel of the top three images shows the surface rendered visualization of the
reconstructed density of an Au/SBA-15 model catalyst particle (~256 nm × 256 nm × 166 nm). The
size and location of Au particles inside the material can be seen unambiguously (left: virtual cross-
section - thickness 0.64 nm - through the reconstruction, right: surface rendering of gold particles -
15
size 8 nm -) and subjected to statistical evaluation. The slices at the bottom display three of the 151
electron microscopy projection images (−55◦, 0◦ and +55◦ tilt angle) that were used to calculate the
volume. The two-sided arrows indicate the reversible process of projection and back-projection
[Ziese2004].
Figure 35: silica bead topped with a nickel nanocrystal. (a) scanning electron microscopic view of a
2D array of packed silica beads topped with nickel nanocrystals. (b) projection image of a single silica
bead topped with a nickel nanocrystal showing the supporting membrane and the gold nanoparticles
used as spatial reference. (c) a cross-section in the voxel matrix of a silica bead decorated with nickel
nanocrystals. The bead diameter is 300 nm and the volume of the topping metal nanocrystal is 0.7.106
nm3. The dark structures are related to Ni particles while the contribution of the silica shows up as a
large grey disk. (d) 3D modelling of the silica bead (white) and Ni nano-object (blue). The gold
particles that were used for geometric corrections are shown in red [Ersen2007].
Figure 36: illustration of the non-uniform sampling of tomogram brought about by the acquisition of a
tilt series in the Fourier space: the centre is much well-sampled compared to edges .This implies a
greater error in the calculation of the high frequency components in the tomogram than in the low
frequency ones, which results in image degradation [Kak1988].
Figure 37: relationship between a projection P acquired at tilt and Fourier transform of sample f as
described by central slice theorem, a) geometry of acquisition of projection of sample at tilt, t axis is
image of x axis by rotation, b) frequency domain of the sample, which can be fulfilled by all
projections, then a tomogram is obtained by an inverse Fourier transform, Fourier transform of P is a
section oriented by θ with u axis on Fourier space of sample.
Figure 38: Comparison of the single-tilt, double-tilt, and conical tilt geometries used to image
specimens in electron tomography [Lanzavecchia2005]. In Fourier space, each image is represented by
a central plane oriented orthogonal to the viewing direction. The empty regions represent the „„missing
volume‟‟ resulting from limitations in tilt. (A) The stack of central planes obtained in single-tilt with
the missing volume shaped as a double wedge. (B) The stack of planes obtained in double-tilt
geometry with the missing volume shaped as a double pyramid. (C) The layout obtained in conical tilt
geometry. The missing volume is shaped as a double cone, which greatly reduces the anisotropy in the
resolution along the XY plane. The tilt angle was 55° in all three examples.
Figure 39: positioning the tilt axis from a tilt series obtained on a group of Pd nano-particles deposited
on a carbon substrate (see §.3.3). (a) single STEM HAADF image acquired at zero tilt. (b)
Superimposition of all images (about 100 images) from the whole series. The montage is displayed
with artificial colours to highlight the trajectories: their elongation underline the direction
perpendicular to the tilt axis as indicated. Note further that the particles located at the top of the
images exhibit less trajectory „streaking‟, which indicate that they are closer to the exact position of
the tilt axis.
Figure 40: Fourier transform of the summation of the entire (aligned) tilt series in order to determine
the tilt axis [Midgley2003]. (a) A single STEM HAADF image acquired at zero tilt from a catalyst
structure (palladium particles embedded within a carbon matrix). (b) Summation of the entire (aligned)
tilt series showing a distinct movement in one direction at an angle to the horizontal. (c) The power
spectrum allows the positioning of the tilt axis direction.
Figure 41: illustration of the cross-correlation procedure for image alignment. The two first
micrographs (a) and b) are HAADF images of carbide particles observed on a carbon extraction
replica at tilt respectively equal to 27 and 32°; c) shows the cross-correlation: the vector linking the
centre of the image to the peak of maximum intensity (arrow) represents the displacement of the first
image (a) relatively to the second one (b).
Figure 42: illustration of the tilt limitation when using a TEM grid.
16
Figure 43: different projections respectively on (Ox,Oy), (Ox,Oz) and (Oy,Oz) plans, of a tomogram
of a sphere (radius = 50 pixel) reconstructed with WBP method, from different tilt ranges with step
angle of 1°, to illustrate elongation effect: a) tilt range of 180°: no effect of elongation is observed on
projections, b) tilt range varies from -45° to 45°: projections seems to be stretched on Oz direction
because of elongation effect, c) tilt range varies from 0 to 90°: direction of elongation effect, is not
parallel to optical axis, but it‟s oriented by the half of the tilt range from Oz axis.
2. Experimental procedures Figure 44: (a) a rod-shaped specimen, after a tungsten deposition for the purpose of protection
against the gallium ion irradiation, the specimen was first fabricated in a plate form, a prism form next,
and finally a rod form by FIB. (b) A modified molybdenum specimen grid with the fixing position of
the rod-shaped specimen indicated by an arrow. (c) a modified JEM2200FS specimen holder allowing
±90° tilt. The original profile is marked by the dashed line [Kawase2007].
Figure 45: (a) A standard Philips CM single tilt holder, with a width at the specimen of 6mm. (b) A
modified Philips EM400 holder, original profile marked as dashed line, with a width at the specimen
of 4mm allowing complete rotation inside the 5.2 mm gap of the SuperTWIN objective lens
[Midgley2003]. Figure 42: (a) A standard Philips CM single tilt holder, with a width at the specimen
of 6mm. (b) A modified Philips EM400 holder, original profile marked as dashed line, with a width at
the specimen of 4mm allowing complete rotation inside the 5.2mm gap of the SuperTWIN objective
lens [Midgley2003].
Figure 46: a) simple tilt specimen holder provided by JEOL for the 2010F microscope; the original
tip, limiting the tilt capabilities to about 25°, has been removed and replaced by the home-made
commercial tip of holder which allows tilting up to 85°; b) typical sample deposited on a 3 mm
copper grid; c) reduction of the grid size to be mounted on the home-made holder tip.
Figure 47: illustration of the tilt capabilities of the JEOL 2010F with the modified tip of the single tilt
specimen holder: a) -67°, b) 0°, c) +75°.
Figure 48: sample on carbon grid tilted at different angles: a) -67°, b) 0°, c) +75°.
Figure 49: a) successive versions of the holder tip: a-b) rectangular geometry with (a) and without (b)
a notch; c) cylindrical geometry compatible with samples adapted to atom probe tomography. The first
holder in a) was made in copper, b) and c) are in non-magnetic steel.
Figure 50: STEM HAADF images of VNbC nano-precipitates (arrow), acquired at tilt of 0°, and
showing the image shift due to the modification of the "x" excitation of deflector N°6 (excitation value
equal to dix= 9477, 5381, and -507 mA from a) to c) respectively).
Figure 51: same as Figure 47 for the "y" excitation of deflector N°6: diy = 4324, -1052 and -5404 mA
from a) to c).
Figure 52: montage showing the superimposition of series of micrographs from Figure 47 (a) and
Figure 48 (b), to show that the two directions of shift x and y are perpendicular, and related to the X,Y
directions of drift of the image by a rotation angle β (c).
Figure 53: illustration of the poor depth of focus in the STEM image mode; a) the probe is
focussed at the upper part of an inclined flat object (tilt ); b) without any further settings,
the probe is out of focus at the bottom part of the object; c) ideal situation where the probe
is re-focussed at each „height‟ of the object.
Figure 54: VC precipitates on a carbon extraction replica used to illustrate the poor depth of focus in
the STEM-HAADF imaging mode. Whatever the excitation of the objective lens, only a small part of
the image is in focus (top, middle and bottom from a) to c) respectively; the tilt axis is as indicated).
17
Figure 55: geometry of an inclined flat object (tilt angle ).
Figure 56: calibration of the focus variation (excitation of the objective lens) for an indicative tilt
series; a) for each tilt θ, the focus is manually adjusted to get respectively optimal focus on the bottom
and top of image; b) verification of the linear variation of the focus difference focus between top and
bottom of image with tan(θ).
Figure 57: STEM HAADF image acquired with a dynamic focus correction every 10 lines; it is
required to have direction of tilt axis perpendicular to direction of scanning in order to keep
synchronisation between variation of focus and time of scanning of image.
Figure 58: examples of focus corrections applied to STEM-HAADF images of: a) Au@SiOx nano-
composites, b) VNbC nano-precipitates, c) Palladium nano-particles. In each case, the series of 3
images correspond respectively to the „focus top‟, „focus bottom‟ and „dynamic focus‟ conditions.
Figure 59: principal window interface is composed by five pushbuttons: „tilt parameters‟, „save
images‟, „start acquisition‟, „managing files‟, and close interface. All these pushbuttons open further
windows, except „Close interface‟ which closes the „EXT 1‟ communication between the microscope
and the computer.
Figure 60: „Tilt parameters‟ interface allowing the initial tilt, tilt step and number of images to acquire
(or equivalently the final tilt to reach) to be defined. The minimal and maximal tilt angles are lower
and upper limits fixed to protect the pole pieces of microscope.
Figure 61: „Save images‟ (left) and „Managing Files‟ (right) interfaces allowing elementary image
saving and manipulation.
Figure 62: „Start acquisition‟ interface to control iteratively tilting of sample, correction of focus, and
saving images.
3. Applications Figure 63: steps of preparation of carbon replicas. Precipitates on the film of carbon are extracted
from the attacked matrix: (a) sample after mechanical polishing, (b) chemical attack by nital to reveal
precipitates, (c) deposition of a carbon film, (d) chemical attack of the underlying matrix, (e) replica of
extraction ready to be observed [Acevedo-Reyes2007].
Figure 64: aligned series of projections of VC nanoprecipitates acquired at different tilt in the STEM
HAADF imaging mode: (a) -58°, (b) -41.5°, (c) -23.5°, (d) -7°, (e) 9.5°, (f) 27.5°, (g) 44°, (h) 60.5°, (i)
75.5°. Tilt axis is (Oy).
Figure 65: volume rendering of a tomogram of VC nanoprecipitates (Figure 61) reconstructed by the
ART algorithm (number of iterations = 14 and relaxation coefficient t = 0.07) (see §.1.5.3), TOMOJ
[Messaoudi2007]) and visualized by AMIRA software [AMIRA].
Figure 66: projection of the tomogram respectively along (a) xy, (b) yz, and (c) xz.
Figure 67: (a) labelling of VC nanoprecipitates (STEM HAADF image acquired at tilt=0.5°); (b)
results of an automatic segmentation of tomogram in order to measure the real volume and equivalent
radius (sphere approximation) of VC particles.
Figure 68: a) measure of area of VC nanoprecipitates in a projection acquired at 6.5° tilt, in order to
obtain an approximation of equivalent radius of nanoprecipitates; b) superposition of yellow and pink
circles on the projection in a), their radius is calculated respectively from a) and from segmentation of
the tomogram (Figure 62).
18
Figure 69: different magnified views of surface rendering [AMIRA] of tomogram of a VC particle (on
the centre), to highlight its 3D morphology.
Figure 70: two types of geometry of Au@SiOx nanocomposites. (a), (b) and (c) are steps to synthesize
respectively a silica core, then a silica shell and finally gold particles on the surface of the silica shell
(M. Martini, thesis in progress, INSA-Lyon). (d) and (e) are respectively steps to synthesise gold
nanoparticles before the silica ball: in this geometry, gold particles are expected to be inside the silica
sphere.
Figure 71: BF TEM and HAADF imaging of both “external” and “internal” Au@SiOx systems. (a)-
(b): same area of “external” Au@SiOx particles deposited on a holey grid of carbon and visualized at
low magnification, respectively imaged in TEM-BF and STEM-HAADF mode. (c)-(d): respectively,
BF and HAADF images of the “internal” Au@SiOx nanocomposites.
Figure 72: basic illustrations showing the interest of a 3D approach to measure accurately distances,
volume and surface density of nanogold particles with respect to the silica balls, (a) 3D representation
of gold nanoparticles and (b) corresponding 2D projection along the Z direction; (c) 3D representation
of silica and gold nanoparticles, and (d) corresponding Z‟ projection. These examples illustrate the
artefacts visible in both 2D projections. For example in d), the central gold particle could be though to
be inside the silica ball, and the bottom right one at its surface: both particles are in fact outer the silica
sphere as seen in c).
Figure 73: evidence for rapid contamination during STEM observations: (a) HAADF image acquired
at tilt = –65°, (b) HAADF image recorded after 20‟ at tilt = 15°: the halo around the silica particles
arises from contamination, due to a prolonged exposure to the electron beam.
Figure 74: comparison of TEM and HAADF images of the Au@SiOx nanocomposite elaborated by
Diop (thesis in progress, Figure 67d-e). a) TEM bright field micrograph showing some gold
nanoparticles with a high contrast because of strong diffracting conditions (Au „S‟), compared to
others (e.g. „L‟). The inset shows a single gold particle imaged under high resolution conditions along
the [110]fcc direction. b) STEM-HAADF of another area, showing a direct relationship between
contrast and “mass-thickness”.
Figure 75: HAADF imaging of Au@SiOx nanocomposites: a) simplified geometry showing the
volume of interaction of a probe crossing a spherical particle (note that the electron beam is supposed
to be parallel and that no beam spreading throughout the particle is considered). b) display of the
expected contrasts resulting from intensity calculations according to a) for various situations: (1) and
(2): an external 5 nm gold particles at the surface of a 100 nm SiOx „ball‟, (3) gold nanoparticle inside
the SiOx sphere.
Figure 76: a) a DM GUI is developed to load images, then to extract radius and 2D position of
nanoparticles semi-automatically (b); and finally projections can be recalculated at the same
experimental tilt (c).
Figure 77: acquired series of Au@„homogeneous‟SiOx on STEM HAADF imaging mode at different
tilt, images are aligned, then tilt axis is calculated, and images are rotated to make tilt axis parallel to
(Oy) axis: (a) -73.5°, (b) -66°, (c) -58.5°, (d) -51°, (e) -43.5°, (f) -36°, (g) -28.5°,(h) -21°, (i) -13.5°, (j)
For sake of clarity, the first image is enlarged -73.5°.
Figure 78: (a) (x,y) positions of some nanoparticles extracted from aligned projections, tilt axis is
calculated by following trajectory of some nanoparticles, and images are rotated to make tilt axis
parallele to (Oy) axis, (b) in aligned images, x(pixel) coordinate of nanoparticles, is linear with cos(α-
tilt), α is the elevation of the particle at tilt of 0°.
Figure 79: projections of Au@SiOx nanocomposites calculated at the same tilt like experimental
projections in Figure 73: (a) -73.5°, (b) -66°, (c) -58.5°, (d) -51°, (e) -43.5°, (f) -36°, (g) -28.5°,(h) -
21°, (i) -13.5°, (j) -73.5°.
19
Figure 80: superposition of calculated and experimental projections, to show the high precision of the
calculated projections: (a) -73.5°, (b) -66°, (c) -58.5°, (d) -51°, (e) -43.5°, (f) -36°, (g) -28.5°,(h) -21°,
(i) -13.5°, (j) -73.5°.
Figure 81: accuracy of position of two nanogold particles, that have respectively maximal and
minimal error, it‟ is measured from images in Figure 73 by comparing experimental with calculated
projections at different tilt. Triangular and square marks illustrate error of nanogold particle that have
respectively maximal and minimal error.
Figure 82: colored particles on projection series (from Figure 74): blue for gold particles inside the
silica balls, green for gold particles on their surface and red for gold particles „outside‟.
Figure 83: visualization of 3D position of Au@SiOx nanocomposites assuming its spherical geometry.
Some of gold particles are hung in the vacuum, this does not have any physical significance, but in
fact only because silica particles to which they are associated, are not selected.
Figure 84: histogram of distance between gold nanoparticles inside the silica balls for the
Au@„homogeneous‟SiOx nanocomposite.
Figure 85: histogram of volume fraction of gold nanoparticles for the Au@„homogeneous‟SiOx
nanocomposite.
Figure 86: different areas from the same sample of Au@SiOx nanocomposites are characterized by a
stereoscopy approach, results are added in order to obtain 3D statistics, (a) experimental projection
acquired on STEM-HAADF at tilt 0°, (b) superposition of experimental and calculated projection, (c)
classification of gold nanoparticles, (d) experimental projection acquired on STEM-HAADF at tilt 0°,
(e) superposition of experimental and calculated projection, (f) classification of gold nanoparticles.
Figure 87: series of projections of Au@SiOx nanocomposite acquired at different angles of tilt on
STEM HAADF imaging mode, and aligned with tilt axis is parallel to Oy.
Figure 88: series of projections of Au@SiOx nanocomposite acquired at different angles of tilt on
TEM imaging mode, and aligned with tilt axis is parallel to Oy.
Figure 89: a) localisation of gold nanoparticles: blue, green, and red colours correspond to gold
nanoparticles localized respectively inside, on the surface, and outside of the silica sphere; b) distance
between gold nanoparticles and the silica centre.
Figure 90: a) localisation of gold nanoparticles; the green colour corresponds to gold nanoparticles on
the surface of the silica particle; b) distance between gold nanoparticles and the centre of the silica
particle assuming contact with each gold nanoparticle.
Figure 91: different views to show that all nanogold particles analysed in Figure 87, are localized
between two spherical silica particles which have respectively minimal and maximal radius, measured
from projection series in Figure 85.
Figure 92: detail of a silica particle in the Au@„core-shell‟ SiOx nanocomposite. a) STEM HAADF
image, and b) corresponding intensity profile through a diameter line; c) TEM micrograph and d)
corresponding profile as in b).
Figure 93: linear regression between (Iint)1/3
and S0.5
, with Iint is the integrated HAADF intensity of all
pixels within the projected gold particle (crystalline) after a background subtraction, and S is the
projected area of the gold particle (assumed to be spherical).
Figure 94: superposition of the experimental and simulated profile of STEM HAADF intensity
IHAADF through a diameter of the projected sphere of SiOx core-shell.
20
Figure 95: reconstruction of a pentagonal rod; (a): selection of images recorded every 15° from a
HAADF tilted series acquired on a Pd nano-particle between -65 and 65° by step of 1° (tilt axis
parallel to y-axis); (b): volume rendering of the reconstructed particle; (c): nearly edge-on projection:
the dotted line shows a perfect pentagon superimposed for comparison.
Figure 96: Pd nano-particle exhibiting triangular projections (bottom line): selection of images
recorded every 10° from a typical HAADF tilted series acquired between -50 and 71° by step of 1°
(tilt axis parallel to y-axis).
Figure 97: 3D analysis of the Pd particle shown in Figure 93. a): surface rendering of the tomogram.
b): stretched superposition of slices extracted every 6 nm from the tomogram. c): geometrical model
used to describe the particle; the summits of the top and bottom pyramids are labeled A and B
respectively. d): tomogram seen along the [111] axis (horizontal direction = [1-10]); note that the A
summit appears to be flat, i.e. truncated. e): tomogram rotated 54.5° around the [1-10] axis to be seen
along the [001] direction (theoretical tilt angle = 54.44°), showing that both summits are truncated;
two angles of 90° can be measured as expected from crystallography. f): tomogram after a 180°
rotation from position d), thus showing the B summit.
Figure 98: microstructure of an Al-Zn-Mg alloy after welding: (a) schema showing the temperature
gradient, (b) TEM images acquired at different areas, show that size of nano precipitates is slightly
increasing with the temperature, (c) distribution of size of nanoprecipitates measured from TEM
images (adapted from [Nicolas2002]).
Figure 99: typical 3D reconstructed volumes of the T7 state obtained by the atom probe tomography
[Dumont2005].
Figure 100: illustration of the drastic thickness increase at large tilt when using a thin for tilting
tomography in the TEM.
Figure 101: tip of the TEM specimen holder adapted for APT „needles‟.
Figure 102: problems encountered with AlZnMg specimens for the TEM tomography; (a-b) stringly
oxidized tip; (c-d) bent tip; e): nice tip but without any precipitate.
Figure 103: BF and STEM-HAADF projections of the same area of a top showing MgZn2 precipitates
in the aluminium matrix (T7 state). (a) and (b) are respectively TEM images acquired at -29° and -
32.5°, which correspond to HAADF micrographs in (c) and (d) respectively. A clear inspection reveals
the presence of a grain-boundary, as indicated by arrows in b) and (d). Note that the diffraction effects
near the grain-boundary and in the matrix (especially in the top-right grain) degrade significantly the
visibility of the precipitates in the BF images.
Figure 104: series of projections of Al-Zn-Mg alloy acquired at different angles of tilt on STEM
HAADF imaging mode, and aligned with tilt axis is parallel to oy. (a) -67°, (b) -56°, (c) -45°, (d) -33°
, (e) -11°, (f) 11°, (g) 33°, (h) 55°, (i) 75°.
Figure 105: analysis of the HAADF series from Figure 101; (a) volume rendering of the reconstructed
tomogram, using the Amira software [AMIRA], (b) corresponding experimental projection obtained at
a tilt of -1°for comparison: note that the particles are highlighted in the tomogram (a).
Figure 106: illustration of an other area analysed in 3D; (a) typical HAADF STEM image from the tilt
series. Arrows indicate alignments of platelets-like precipitates (see text for details). (b): (xOy), (xOz)
and (yOz) projections of the reconstructed tomogram illustrating the 3D shape of the tip.
Figure 107: histogram of size distribution of Zn-Mg nanoprecipitates as measured by STEM electron
tomography (a) and by (b) TEM [Dumont2005].
21
Figure 108: effect of oxidation observed on the head of TIP, and removed by a FIB cleaning: (a)
STEM image acquired at MATEIS-Lyon, (b) EDX nano-analysis of the tip of sample before FIB
cleaning, (c) image of tip of sample after FIB cleaning performed at GPM-Rouen.
Figure 109: result of a AlZnMg tip reconstruction: experimental HAADF image acquired at zero tilt
(left) and corresponding tomogram viewed in the corresponding projection (right).
Figure 110: comparison of TEM (a) and APT (b) reconstructed volumes of the same AlZnMg tip.
Note that corresponding details (arrows) can be found in both volumes displayed at the same scale.
4. Perspectives Figure 111: a) data describing the particles used for STEM HAADF simulations (note that it was
chosen to use the same atomic density and size); b) calculated STEM HAADF projections of
homogeneous Au, Pd, and Al spheres perfectly centred on a virtual tilt axis, (in this ideal geometry all
projections remain the same whatever the tilt angle); c) intensity profile through the particle diameter
in order to highlight the darkest Al sphere.
Figure 112: a) volume rendering of Al, Pd and Au tomograms reconstructed by the ART algorithm
(number of iterations=14 and relaxation coefficient=0.07, TOMOJ [Messaoudi2007]) and visualized
with the AMIRA software [AMIRA], b) histogram of intensity within the tomogram, c) check of the
linear relationship between intensity and the square of the atomic number.
Figure 113: precipitation microstructure as seen along the [1-10]Al zone-axis (a). Most precipitates
have a spherical shape (circles) but two variants of ‟-platelets lying in {111}Al planes are seen edge-
on (b).
Figure 114: orientation of an Al matrix grain in the AlZnMg alloy: (a) two diffraction patterns
recorded while acquiring the tilt series and consistently indexed using basic operations with the
stereographic projection [Johari1969]; (b) extension of the indexing in order to select a desired zone
axis to be reached, i.e. the [01-1]Al direction; (c) first step of the rotation to be achieved in order to
project the tomogram along the chosen [01-1]Al. (d) tomogram once viewed along the [01-1]Al : two
variants of edge-on ‟-platelets (arrows) appear in the (111) Al and (-111)Al planes (as expected).
Figure 115: (a) visualisation of a round-shape precipitate from a TAP experiment in the AlZnMg
alloy tempered in the T7 state. The (001)Al planes of the matrix are seen edge-on; (b) a Fourier
transform of the image further evidences the (113)Al reflections in addition to the (001)Al one
[Dumont2005].
Figure 116: chemical analysis of Fe-Pt nanoparticles in STEM. Particles encircled on the left HAADF
image were numerically analysed, and their intensity correlated to the Fe/Pt ratio according to EDX
analysis of a few particles. Then, the composition PtxFe1-x of each particle (right) was deduced from
the EDX calibration procedure ((courtesy T. Epicier, unpublished work; sample provided by M.
Delalande, CEA Grenoble, (2005)).
22
23
List of tables
3. Applications Table 1: 3D statistics established from 4 series or areas from the same Au@„homogeneous‟SiOx
nanocomposite: a) per series, b) mean results.
Table 2: Overall composition of the material obtained by APT measurements in the T7 materials
[Dumont2005].
Table 3: Precipitate composition and volume fraction obtained by APT for the T7 state of ageing
[Dumont2005].
24
25
Résumé français
La tomographie est une approche de caractérisation tridimensionnelle de la structure et de la
chimie des objets en biologie ou en science des matériaux, en utilisant des instruments
optiques. Le principe consiste à acquérir une centaine d‟images (projections) sous différents
angles de vue en inclinant l‟échantillon observé. Ces données sont ensuite traitées grâce à des
algorithmes dédiés permettant de reconstruire le volume exploré: on obtient alors un
„tomogramme‟, qui est l‟image tridimensionnelle de l‟échantillon. La tomographie en
microscopie électronique par transmission (TEM) permet d‟atteindre une résolution
nanométrique; elle présente un intérêt majeur pour la nanotechnologie, dans la mesure où les
propriétés optiques, électriques, catalytiques,… des nanomatériaux, dépendent de la taille, la
morphologie et la distribution des nanoparticules [Moriarty2001, El-Sayed2001, El-
Sayed2004, Chen1997, Kelly2003, Henry2005]. Quel que soit le mode d‟imagerie utilisé,
l‟intensité acquise doit varier linéairement avec l’épaisseur massique de l‟échantillon, afin
d‟obtenir des projections fidèlement liées aux différentes régions de l‟objet en volume. Cette
condition est nécessaire pour reconstruire correctement le tomogramme.
La tomographie électronique en „champ clair‟ (BF) est utilisée en biologie pour la
reconstruction de macromolécules dès 1968 [De Rosier1968], car c‟est un mode bien adapté
aux échantillons non-cristallins, ce qui est une caractéristique assez générale des objets
biologiques. L‟intensité en champ clair (transmission conventionnelle), est une combinaison
de la diffusion élastique à faible angle et de la diffusion inélastique des électrons incidents.
Pour des matériaux cristallins, le contraste des images acquises en champ clair est fortement
influencé, voire souvent dominé par le contraste de diffraction qui est non uniforme dans la
mesure où il dépend des conditions de Bragg ainsi que la structure cristalline. L‟intensité du
champ clair n‟est donc plus linéaire avec l‟épaisseur massique des échantillons, et ce mode
n‟est donc pas adapté à la tomographie des matériaux cristallins.
Les premières applications de la tomographie aux matériaux cristallins ont été exposées à
partir de 2001, grâce au développement des modes d‟imagerie spécifiques: champ sombre
annulaire à grand angle (HAADF-STEM) [Koster2000(1), Midgley2003] ou imagerie filtrée
(EFTEM) [Möbus2001, Möbus2003, Midgley2003], qui sélectionnent majoritairement
l‟intensité incohérente, et par conséquent, sont insensibles aux effets des orientations
cristallines rencontrées (contraste de diffraction) dans la majorité des cristaux (Figure 1).
L‟intérêt de ce mode d‟imagerie est qu‟il reste également adapté aux matériaux amorphes.
26
L‟intensité STEM-HAADF dépend du numéro atomique des espèces présentes dans l‟objet,
ainsi que de leur densité: par conséquent, il est possible d‟extraire des informations chimiques
à partir des images acquises dans ce mode [Treacy1999]. L‟imagerie EFTEM permet de
caractériser à la fois la chimie et la morphologie de la zone observée en 3D.
Une expérience de tomographie en TEM nécessite un temps certain, du fait de l‟acquisition
d‟un très grand nombre d‟images sous différents angles de projection (de 1 à quelques
heures). Ceci n‟est donc parfois pas possible dans le cas où l‟échantillon évolue en cours
d‟observation, comme c‟est le cas dans 2 situations classiques en MET: soit l‟exposition au
faisceau électronique provoque des dégâts d‟irradiation, soit l‟objet se „contamine‟ avec le
temps (diffusion de molécules carbonées sur les surfaces exposées aux électrons, qui modifie
le contraste et la forme de l‟échantillon). Dans ce cas, des approches 3D plus rapides, i.e. qui
nécessitent peu d‟images acquises à différents angles peuvent être utilisées (Figure 2), comme
la stéréoscopie, afin d‟effectuer des mesures 3D plus précises et surtout plus fiables par
rapport à celles effectuées directement sur des images 2D (distance, densité volumique,
distribution,..). À la différence de la tomographie, de telles approches 3D ne permettent
cependant pas de reconstruire le volume d‟objets présentant des morphologies complexes.
Une fois les images acquises, le traitement consiste à reconstruire le volume étudié. La
reconstruction du tomogramme est basée sur le théorème de la section centrale, qui stipule
que toute projection acquise est une transformée de Fourier inverse d‟un hyperplan, orienté
par le même angle d‟acquisition dans l‟espace de Fourier [Kak1985](Figure 3). Deux types
d‟algorithmes de reconstruction sont souvent utilisés, le premier est un calcul direct basé sur
la transformée de Fourier (BP, WBP), le deuxième est un calcul itératif (ART, SIRT) qui
converge vers un volume reconstruit optimal. Ces algorithmes de reconstruction ne dépendent
pas de la source ni du mode d‟imagerie utilisé, ils dépendent uniquement de la géométrie
d‟acquisition (notamment l‟axe de rotation – axe de „tilt‟ simple ou „double-tilt‟, géométrie
conique, qui consiste à acquérir plusieurs séries d‟images autour de différents axes de „tilt‟).
27
Figure 1: série de projections de nanoprécipités de carbure de vanadium VC cristallins, acquises en
champ clair BF (a), et en champ sombre annulaire HAADF (b), pour des inclinaisons respectivement
de 0°, 2° et 4°. Le contraste interne des nanoparticules dans les images TEM change beaucoup sur une
plage d‟inclinaisons faible, à cause du contraste de diffraction, contrairement aux images HAADF, en
raison de l‟insensibilité de ce mode à l‟orientation cristalline des précipités.
Figure 2: deux images STEM-HAADF, d‟un matériau mésoporeux (SBA15), acquises selon deux
directions perpendiculaires, respectivement à -28° et 62° (échantillon fourni par V. Dufaux, ENS-
Lyon). Les deux vues permettent d‟avoir une vision 3D des „filaments‟ de matière qui remplissent les
canaux poreux linéaires, en mettant respectivement en évidence a) la section et b) la longueur de ces
filaments.
a)
b)
a) b)
28
Figure 3 : illustration de la relation entre les projections Pθ et le volume reconstruit, d‟après le
théorème de la section centrale: une projection acquise sous un angle θ (a), est la transformée inverse
d‟un hyperplan orienté selon θ dans l‟espace de Fourier du tomogramme (b).
Dans la géométrie du „simple-tilt‟, il est généralement impossible de collecter une information
complète concernant l‟objet observé, pour des raisons liées à la limite de la plage
d‟inclinaison. Une géométrie alternative est celle du „double-tilt‟, qui consiste à acquérir deux
séries autour de deux axes d‟inclinaison perpendiculaires, ce qui réduit l‟information
manquante. Idéalement, la géométrie conique permet d‟acquérir une information complète de
l‟échantillon. Dans le cas du „simple-tilt‟, le manque d‟informations introduit des artefacts
sous forme d‟une élongation du tomogramme dans la direction de l‟axe optique.
La qualité de reconstruction dépend aussi de la précision dans l‟alignement des images.
Généralement celles-ci sont alignées par corrélation croisée, et l‟axe d‟inclinaison est ensuite
calculé en suivant les trajectoires de quelques détails dans la série alignée: en effet cet axe
sera perpendiculaire à la trajectoire de ces détails suivis dans la série d‟images (Figure 4).
Afin d‟améliorer cette procédure d‟alignement, des nanoparticules d‟or (sphériques, de taille
~1 nm) peuvent être déposées pendant ou après la préparation de l‟échantillon, ce qui permet
de disposer des „détails‟ nécessaires à l‟alignement; dans ce cas l‟erreur de positionnement
peut être estimée à 1 nm.
A cause de divers facteurs (comme par exemple l‟élongation évoquée plus haut), la résolution
du tomogramme est généralement anisotrope: elle dépend du mode d‟imagerie utilisé, des
conditions expérimentales d‟acquisition, ainsi que de la géométrie de l‟échantillon. Elle est
souvent estimée à trois fois l‟épaisseur de l‟échantillon divisé par le nombre des images
29
acquises [Ziese2004]. Par conséquent une faible épaisseur et un grand nombre d‟images
améliorent la résolution du tomogramme.
Figure 4 : calcul de la direction de l‟axe de „tilt‟ par analyse des trajectoires de particules présentes
dans les images acquises: (a) image STEM HAADF acquise à 0° de nanoparticules de palladium
déposées sur un film-support mince. (b) montage constituée de la „somme‟ d‟une série de projections
(couleurs artificielles pour mettre en évidence la trajectoire de chaque nanoparticule), qui montre que
ces trajectoires sont rectilignes après alignement: l‟axe de „tilt‟ est ainsi positionné
perpendiculairement à la direction commune des trajectoires.
Afin d‟assurer une qualité acceptable des tomogrammes, c‟est-à-dire de minimiser les
artéfacts et la dégradation de la résolution, on convient généralement qu‟une expérience de
tomographie nécessite l‟acquisition d‟une série d„images sur une plage d‟inclinaison
supérieure à typiquement 120-130°. Dans notre étude, le microscope utilisé est un JEOL
2010F, équipé d‟un détecteur STEM-HAADF et de deux pièces polaires de haute résolution.
La distance entre ces pièces polaires est d‟environ 2 mm, ce qui limite très sévèrement la
plage d‟inclinaison. Le porte-objet „simple-tilt‟ commercial fourni par le constructeur pour
l‟imagerie usuelle „2D‟ permet des inclinaisons de ± 20°, ce qui est incompatible avec une
approche de tomographie sérieuse. Il a donc été nécessaire de procéder à une adaptation du
porte objet, pour atteindre une plage de „tilt‟ suffisante. Ceci a été facilité par le fait qu‟un
embout amovible a pu être remplacé par une partie facilement usinée, qui nous permet
d‟atteindre une plage d‟inclinaison d‟environ 160° (Figure 5).
Pendant la phase d‟acquisition, et après chaque image, de nombreux réglages sont
nécessaires. D‟une part, l‟échantillon peut dériver ou se déplacer du fait de l‟accroissement de
l‟inclinaison pratiqué, et afin de garder la zone observée sous le faisceau, une correction
automatique ou manuelle du déplacement est effectuée. D‟autre part, un inconvénient majeur
du mode d‟imagerie STEM-HAADF est sa faible profondeur de champ: par conséquent, la
particles trajectory
tilt axis direction
50 nm
a) b)
30
mise au point optique dépendant de l‟altitude de l‟objet, il devient impossible d‟acquérir une
image uniformément nette lorsque l‟angle d‟inclinaison est élevé. Nous avons choisi une
solution consistant à corriger le „focus‟ pendant le balayage de l‟image. Cette correction
nécessite une synchronisation entre la variation de l‟excitation de la lentille-objectif
contrôlant la mise au point et la vitesse d‟acquisition (i.e. de balayage) de l‟image (Figure 6).
Un logiciel a été développé pour contrôler ces différentes étapes de la phase d‟acquisition
d‟une manière semi-automatique, et ainsi d‟optimiser le temps de l‟expérience: ce programme
contrôle donc le microscope (par une liaison de type RS232), commande l‟enregistrement des
images sur le détecteur HAADF tout en corrigeant le „focus‟ de façon dynamique. Dans ces
conditions, nous sommes parvenus à un temps d‟acquisition variant de 2 à 3 heures pour une
série d‟environ 150 images.
Figure 5: porte-objet „simple-tilt‟ du microscope JEOL 2010F adapté pour atteindre une plage
d‟inclinaison de 160°: l‟embout modifié (1) remplace l‟embout d‟origine commerciale fourni par le
constructeur (2).
a)
b)
31
Figure 6: illustration de la faible profondeur de champ et de la correction du focus en STEM-HAADF:
a-c) schémas de principe montrant respectivement: (a) la sonde électronique focalisé en haut de
l‟objet, (b) la sonde dans les mêmes conditions de focalisation en bas de l‟objet (donc défocalisée), et
(c) un réglage correct de la sonde à toute altitude de l‟objet. Les valeurs de mise au point correcte en
haut et en bas de l‟objet sont réglées manuellement et sont utilisées par une routine qui corrige le focus
en temps réel pendant le balayage de l‟image: d-f) illustration de la correction du focus appliquée à des
nanocomposites Au@SiOx déposés sur un film de carbone à trou (respectivement : image focalisée
pour rendre nette la partie haute (d), puis la partie basse (e), puis mise au point "dynamique" (f)).
Une fois les aspects matériels sont réglés (porte-objet, logiciel de pilotage de l‟acquisition),
différents systèmes ont été étudiés dans le cadre de cette thèse.
Le premier concerne une problématique de précipitation dans des aciers, étudiée récemment
au laboratoire [Acevedo Reyes2007]. Des nanoprécipités de carbure de vanadium VC ont été
extraits sur des répliques (film-support) en carbone, puis observés en MET. Ces particules ont
été utilisées comme un échantillon „test‟ nous permettant de calibrer les différents réglages
lors de la phase d‟acquisition et de mettre au point les routines informatiques nécessaires à ces
réglages. Une étude „3D‟ a de surcroît pu en être faite, en termes de localisation dans l‟espace,
caractérisation des volumes et des morphologies des nanoprécipités à partir d‟une
segmentation du tomogramme obtenu.
Le deuxième système se réfère à des nanocomposites Au@SiOx constitués de nano-particules
d‟or cristallin associées à des particules plus grossières à base de silice non cristalline.
a) b) c)
1µm
d) e) f)
32
L‟objectif a été d‟étudier précisément et en 3 dimensions la localisation des nanoparticules
d‟or par rapport aux particules de silice, et ce afin d‟estimer la qualité de synthèse de ces
nanoparticules. Pour des raisons liées aux effets de contamination de l‟échantillon en cours
d‟acquisition, il était impossible d‟effectuer une expérience de tomographie, et nous avons dû
procédé à une analyse stéréoscopique, nécessitant peu d‟images et permettant d‟effectuer
suffisamment de mesures pour une localisation précise des particules avec une resolution
d‟environ 3 nm. Par ailleurs, grâce à la sensibilité du contraste HAADF à la chimie des objets
étudiés (en l‟occurrence ici des particules relativement sphériques), il a été possible d‟étudier
finement la structure „cœur-coquille‟ des sphères de silice telle qu‟elle apparaît dans certaines
conditions de synthèse. Des simulations assez élémentaires de l‟intensité des images HAADF
nous ont permis de mesurer la variation de densité volumique entre le centre (cœur) et la
périphérie (coquille) des particules SiOx (Figure 7).
Figure 7 : a-b): images STEM HAADF de nanocomposites Au@SiOx acquises respectivement à -25 et
+25°; c): rendu de surface de la reconstruction de ces nanoparticules par une approche stéréoscopique:
les deux sphères concentriques claire et sombre (rose et rouge) correspondent respectivement au
minimum et au maximum du diamètre (128 et 140 nm) de la particule de silice mesuré à partir des
projections; d): régression linéaire entre l‟intensité intégrée (Iintegrée)1/3
et la racine de la surface projetée
S1/2
des nanoparticules d‟or effectuée à partir de a-b). On obtient une droite conformément à la loi
établie par [Treacy1989]; e): profil expérimental de l‟intensité le long du diamètre de la sphère de la
silice (violet), superposé au profil calculé (bleu) à partir d‟une modélisation de la structure „cœur-
coquille‟ de la particule (voir texte principal du mémoire pour les détails).
Une troisième partie de notre travail a porté sur la caractérisation de morphologies complexes
de nanoparticules de palladium, difficiles à caractériser en imagerie 2D. Nous avons ainsi pu
mettre en évidence des formes de bipyramides (Figure 8), qui ont pu être analysées du point
de vue cristallographique par des mesures angulaires effectuées à partir des tomogrammes
reprojetés dans des directions particulières.
5500 nnmm SiO2
Au
a) b) c)
(Iintegrée)1/3 IHAADF
(S)1/2 distance (pixels)
d) e)
Iint(1/3)
33
Figure 8: a) illustration d‟une série de projections d‟une particule de palladium acquise en mode
STEM-HAADF respectivement à -42°, 6.5°, et 70°: b) rendu de surface du volume reconstruit sous 3
angles de vues à intervalle d‟environ 110°, montrant la morphologie bipyramidale de la particule.
Enfin, un quatrième exemple a concerné une étude quantitative d‟un état de précipitation dans
un alliage industriel Al-Mg-Zn. Une approche mettant en parallèle la tomographie en mode
STEM-HAADF dans le TEM, et la tomographie en sonde atomique a été conduite en
collaboration avec le laboratoire GPM de l‟Université de Rouen. Les échantillons ont été
préparés sous la forme de pointes adaptées à la sonde atomique tomographique, et ces
échantillons ont été examinés dans le microscope grâce à une nouvelle adaptation du porte-
objet. A partir de nos séries d‟images expérimentales acquises en HAADF sur ces pointes,
nous avons pu calculer directement sur les tomogrammes la distribution et la fraction
volumique des nanoprécipités Zn-Mg dans un état donné de précipitation au sein de l‟alliage
d‟aluminium (Figure 9).
20 nm
a)
b)
34
Figure 9 : séries d‟images d‟une pointe AlZnMg: a) image STEM HAADF acquise à 0°, b) projection
du tomogramme reconstruit, affiché en c) après une rotation de 90° autour de l‟axe verticale.
Les résultats obtenus ont été comparées à une étude antérieure menée conjointement en TEM
conventionnelle, sonde atomique et diffusion des rayons-X aux petits angles [Dumont2005].
Un excellent accord a pu être trouvé pour des précipités de taille moyenne 8 nm et en faible
fraction volumique, de l‟ordre de 2 %.
Tout au long de ce travail, nous avons illustré l‟intérêt de la nano-tomographie électronique
en TEM et en particulier en STEM-HAADF, appliquée à différents types de nano-matériaux,
cristallins et non-cristallins. Nous avons également montré que cette approche peut être
complémentaire à d‟autres approches tomographiques, comme en sonde atomique. D‟autres
techniques peuvent également être mise en œuvre en parallèle de la tomographie STEM-
HAADF en TEM: le „FIB‟ (Focused Ion Beam : microscope à faisceau d‟ions focalisé), ou la
la tomographie dans un microscope électronique à balayage. L‟application approfondie de
plusieurs de ces techniques à une problématique unique reste à faire : il serait ainsi possible
d‟améliorer la résolution et la fiabilité des données acquises, mais aussi, en corrélant les
tomogrammes issus des différentes approches, de corriger les artefacts possibles.
Références du résumé
[Acevedo Reyes2007] Acevedo-Reyes D. Evolution de l'état de précipitation au cours de
l'austénitisation d'aciers microalliés au vanadium et au niobium. INSA de Lyon 2007.
[Chen1997] Chen C C, Herhold A B, Johnson C S, Alivisatos A P. Size dependence of structural
metastability in semiconductor nanocrystals. Science (1997) 276: pp. 398-401.
[De Rosier1968] De Rosier D J, Klug A. Reconstruction of Three Dimensional Structures from
Electron Micrographs. Nature (1968) 217: pp. 130-134.
[El-Sayed2001] El-Sayed M A. Some interesting properties of metals confined in time and nanometer
space of different shapes. Accounts of Chemical Research (2001) 34: pp. 257-264.
20 nm
a) b) c)
35
[El-Sayed2004] El-Sayed M A. Small is different: shape-, size-, and composition-dependent properties
of some colloidal semiconductor nanocrystals. Accounts of Chemical Research (2004) 37: pp. 326-
333.
[Henry2005] Henry C R. Morphology of supported nanoparticles. Progress in Surface Science (2005)
80: pp. 92-116.
[Kelly2003] Kelly K L, Coronado E, Zhao L L, Schatz G C. The optical properties of metal
nanoparticles: the influence of size, shape, and dielectric environment. Journal of Physical Chemistry
B (2003) 107: pp. 668-677.
[Koster2000(1)] Koster A J, Ziese U, Verkleij A Y, Janssen A H. Three-Dimensional Transmission
Electron Microscopy: A Novel Imaging and Characterization Technique with Nanometer Scale
Resolution for Materials Science. Journal of Physical Chemistry B (2000) 104: pp. 9368-9370.
[Möbus2001] Möbus G, Inkson B J. Three-dimensional reconstruction of buried nanoparticles by
element-sensitive tomography based on inelastically scattered electrons. Applied Physics Letters
(2001) 79: pp. 1369-1371.
[Möbus2003] Möbus G, Doole R C, Inkson B J. Spectroscopic electron tomography. Ultramicroscopy
(2003) 96: pp. 433-451.
[Midgley2003] Midgley P A, Weyland M. 3D electron microscopy in the physical sciences: the
development of Z-contrast and EFTEM tomography. Ultramicroscopy (2003) 96: pp. 413-431.
[Moriarty2001] Moriarty P. Nanostructured materials. Reports on Progress in Physics (2001) 64: pp.
297-383.
[Kak1985] Kak A C. Tomographic imaging with diffracting and non-diffracting sources. In Haykin S,
Array Signal Processing. Ed. Prentice-Hall Englewood Cliffs (1985): pp. 351-428.
[Treacy1989] Treacy M M J, Rice S B. Catalyst particle sizes from rutherford scattered intensities. J.
Microsc (1989) 156: pp. 211-234.
[Treacy1999] Treacy M M J. Pt agglomeration and entombment in single channel zeolites: Pt/LTL.
Microporous and Mesoporous Materials (1999) 28: pp. 271-292.
[Ziese2004] Ziese U, De Jong K P, Koster A J. Electron tomography: a tool for 3D structural probing
of heterogeneous catalysts at the nanometer scale. Applied Catalysis A: General (2004) 260: pp. 71-
74.
36
37
Introduction
38
39
1.1. Interest of tomography
Tomography1 is an exciting tool for investigating three-dimensional (3D) structures using
optical instruments. It consists in various approaches aiming at reconstructing the 3D volume
of the object from the analysis of series of 2D projections (see below 1.11.1. Projection
requirement), according to mathematical principles first postulated by Radon in 1917
[Radon1917]. Such images can be acquired by tilting the specimen over a large angular range,
as it is currently done in various microscopy techniques, i.e. optical, X-ray, and electron.
Tilting sample allows probing several 3D areas and thus increasing quantity of acquired
information, For that the holder of microscope that bring the sample, is turned iteratively
around a tilt axis (constant during acquisition phase) by a small angle step. Tomography in a
Transmission Electron Microscope (TEM) has been used in biology for the reconstruction of
macromolecules and cell organelles as early as 1968 [De Rosier1968]. However, extension to
material sciences has been difficult owing to the fact that the contrast of crystalline materials
is very sensitive to the orientation because of diffraction effects. First applications were then
reported starting from 2000 by using STEM2-HAADF
3 [Koster2000(1), Midgley2003] or
EFTEM4 [Möbus2001, Möbus2003, Midgley2003], i.e. imaging modes which are largely
insensitive to crystalline orientations, and present a better signal-to-noise ratio than
conventional TEM imaging [Friedrich2005] (Figure 10). It‟s the aim of this first general
chapter to make the reader more familiar with the most relevant features of tomography
techniques especially in the case of methods that can be applied to TEM.
1 Etymology: Greek tomo (slice, section) + Greek Graphos (that describes)
2 Scanning Transmission Electron Microscopy
3 High Angle Annular Dark Field
4 Energy Filtered Transmission Electron Microscopy
40
Development of electron tomography 1960’s : first applications of tomography related technique in electron microscopy in biological sciences (1982 Nobel Prize for Klug). 1990’s: routine application of TEM tomography in biological sciences. 2000: first application of TEM tomography in catalysis by Geus/Janssen/d Jong/Koster [ Koster2000(1)][ Koster2000(2)]. 2001: routine application of TEM tomography in catalysis by Janssen de Jong Koster [Janssen2001(1)][Janssen2001(2)]. 2001: first applications of electron tomography to HAADF-STEM and spectroscopic (EFTEM, EDX) images by Midgley/Weyland [Weyland2001(1)] and Möbus [Möbus2001]. Timeline~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 1917: formulation of mathematical base for tomographic techniques by Radon (Radon Transform). 1960’s: development of X-ray computerized tomography (1979 Noble Prize for Cormack and Haunsfield). 1990’s: development of automated TEM tomography by Agard [Koster1992] and Baumeister [Dierksen1992]. 1990: first commercial systems enable data acquisition in ~4h. 2001: development of pre-calibration electron tomography by Koster/Ziese [Ziese2002]. 2001: commercial systems making use of precalibration enable improved accuracy and data acquisition in ~30-60 min. The timeline focuses on the development and availability of the instrumentation for electron tomography and the application of the technique in heterogeneous catalysis. For the sake of clarity, several major steps, which took place throughout the 1960-1980s and that are the base of modern automated electron tomography, like e.g. the thorough evaluation of the underlying theory as well as the development of CCD cameras for fast image acquisition, are not taken into account.
Figure 10: some dates, events, and names that marked the development of electron tomography in
biological or material science [Ziese2004].
When the thickness size of an object is not negligible in comparison with its lateral
dimension, 3D characterisation is required. Tomography is a useful tool for the accurate 3D
characterisation of various structural features, such as distribution, densities, distance, and
chemistry of heterogeneities in the observed area; it avoids conflicts of information that can‟t
be resolved by conventional 2D imaging techniques. Analysis from 2D images could
introduce errors concerning 3D localization and measure of distance (Figure 11. a).
Transmission electron tomography allows to reconstruct the 3D morphology of the specimen
with a nanometre resolution [Frank1992, Baumeister1999, Marco2004, kübel2005]. It appears
thus well-suited to the study of nanometre-sized objects, and is currently applied to various
fields of nanotechnology. Since the catalytic, electronic and optical properties of
41
nanomaterials [Moriarty2001, El-Sayed2001, El-Sayed2004, Chen1997] strongly depend on
their size, distribution, and shape [Kelly2003, Henry2005], the determination of their exact
3D morphology is of importance in order to understand and control their physical properties
(Figure 11. b).
Figure 11 : projections are partial representations of the reality, illustrations to highlight errors and no
complete information extracted from projections, a) volume that contains spheres, projected through z
direction, shows error of measure of distance directly from projection, b) 3D geometry made by hands
projected through z direction, shows errors of analyse of morphology directly from projection.
Obviously, reasonable estimations of the shape of nanoparticles remains possible using
conventional 2D imaging, assuming simultaneous crystallographic analysis of their structure
and symmetries [Wang2000, Wang2003]. But this approach becomes difficult for objects
with complex shapes and structures, and requires anyway exploring several orientations.
1.2. Tomography techniques used in material science
1.2.1. X-rays
a)
b) x
y
z
x
y
42
The principle of X-ray tomography is explained in details in [Baruchel2000]. This technique
is analogous to the medical scanner and allows from X-ray radiography reconstructing non-
destructively the internal structure of objects, with a size varying from few millimeters to tens
of centimeters, with a resolution of few hundred of nanometer, and to study the behaviour of
materials during mechanical tests (studies in situ) [Eckermann2008, McDonald2009]. X ray
tomography approaches are used for different studies of precipitates, voids or cracks within
matrices, foams or granular materials [Parra Denis2008, Madi2007, Elmoutaouakkil2002].
These cases have in common the presence of phases that show contrast differences, and
segmentation can be achieved through threshold or watershed operations.
Energy of X rays varies from some electron-volts (eV) to some MeV. The experimental
procedure consists of irradiating a sample with a highly energetic, monochromatic X-ray
beam, and projections are acquired by measuring attenuation of transmitted X rays; it contains
absorption and phase contrast [Lengeler2001]. When the sample is heterogeneous, the image
obtained contains contrast, resulting from the variations of the X-ray absorption coefficient
inside the material and from the optical phase shift of the beam as it crosses interfaces. For
transparent objects, the phase contrast is dominant. The distance between the sample and the
detector determines the preponderance of one or the other mechanism. 3D cartography of the
different phases or interfaces can be obtained by recording several radiographies of the
rotated sample. The measured attenuation depends on energy of X rays, masse density and
atomic number of the observed material. Spatial resolution depends on size and shape of X
ray beam and object, resolution of the used detector, magnification, noise, and time of
acquisition [Withers2007].
The beam may be essentially parallel, as delivered by certain synchrotron where the source-
to-object distance is very large (e.g. 145 m on ID19 in the ESRF5 [ESRF] (Grenoble,
France)), or a cone beam where the source-to-object distance can be very small (as little as 1
mm).The spatial resolution images of X-ray tomography may achieve the submicron with
synchrotron radiation. A commercial model of tomography [PHOENIX] is located in the
MATEIS laboratory at Lyon University. It includes a nanofocus transmission X-ray tube (W
target). The size of the focus (and thus the resolution) is tunable from 1 to 5 µm. The setup
used exhibiting cone beam geometry, so it is easy to obtain images at different values of the
magnification. For this purpose, the sample could be simply placed at different distances from
the source.
5 European Synchrotron Radiation Facility
43
The reconstruction involves a computed step and the final image is a 3D map of the local X-
ray attenuation coefficient. Value of voxel on tomogram is proportional to the linear
coefficient of attenuation, which depends on mass density of the object; it‟s calculated as
mean of mass density of different materials present in voxel. With a prior calibration by using
some materials with known density and atomic number, comparison of tomographical data
allows the density and atomic number of the studied material to be deduced. Then local
measurements of the atomic density for example can be performed.
Two examples are described below to illustrate characterisation of 3D structure by X ray
tomography:
The three-dimensional representations of microstructure of beta-quenched titanium alloy were
studied by microtomography at a mesoscopic scale [Vanderesse2008], to understand its
microstructural evolution through various industrial processes. The pure titanium exists in two
phases, namely the beta body-centered cubic phase at high temperature, and the alpha
hexagonal close-packed phase at room temperature. The observed microstructure is
characterized by a complex entanglement of alpha lamellae delimited by residual beta phase.
Two-dimensional observations show clusters of parallel lamellae, all having the same
crystalline orientation, called colonies. The interior of each prior beta grain is partitioned into
several colonies. Individual two-dimensional (2D) observations cannot give access to the
morphology and 3D connectivity of the microstructure (Figure 12. a). 3D representations of
the inside of the material is illustrated in (Figure 12. b), the alpha phase appears dark and the
beta phase in clear. The beta phase is not distributed uniformly along the alpha lamellae, it
forms somewhat irregular layers and, in most cases, it is impossible to identify single lamellae
(Figure 12. c). Thus, the microstructural features of interest are the colonies. Indeed, the beta
layers are, on average, homogeneously oriented inside each colony. Evaluation of these
textures provides a criterion for the extraction of individual colonies from the volume (Figure
12. d). The microstructure was mainly of a parallel plate type, and the colonies form an
intricate aggregate. Typical examples of colonies are shown in Figure 12. e, their shapes
appear somewhat rounded with an effective resolution of about 5 to10 µm. The overall shape
of the colonies is reproduced and it can be seen that they are compact and non-convex (Figure
12. f).
44
The preforming stage of the RTM (Resin Transfer Moulding) composite manufacturing
process leads to fibrous reinforcement deformations. The knowledge of the mesoscopic
deformed geometry is important for damage prediction analyses of the composite. X-ray
tomography is used to obtain experimental undeformed and deformed 3D geometries of the
textile reinforcements [Badel2008]. The information gathered from these experiments is used
to improve and justify the hypotheses made during the development of the mechanical
constitutive model and above all to validate the results obtained from simulation. Preform
deformation at the scale of the composite part (macroscopic scale) corresponds to local
deformation of the fibrous network (mesoscopic scale). This deformation modifies the
mechanical properties and the permeability of the reinforcement. Undeformed and deformed
geometries of the woven composite fabrics (G1151), used as a complex interlock
reinforcement, have been analysed. The interest of an interlock structure is to tie several
layers together. 3D views of this reinforcement underline the complexity of the woven
structure characterized by nontrivial initial geometries (Figure 13. a). From the comparison of
Figure 13. a-b, it can be noticed that the fiber bundle tends to be denser in the deformed state,
though the distribution appears to be at random. The transverse behavior of the yarns is of a
great importance because local crushing of the yarns is significant during the deformation. X-
ray tomography observations support the fact that the behavior of the yarn can be assumed to
be transversely isotropic. In Figure 13. c-d, the mesoscopic deformed geometries of the unit
cell under biaxial tension and large in-plane shear (46°) is compared to the experimental
geometries obtained by tomography. The agreement is good.
45
Figure 12 : a) Planar section of a beta-quenched sample. The circles mark disjointed clusters of
parallel lamellae having the same orientation. It is not sure if these clusters belong to the same colony,
b) Volume fraction of beta-quenched TA6V (with a voxel size set to 0.7 µm, the scanned volume is of
the order of 7003 µm3). The black line delineates a colony. c) Visualization of the beta phase spatial
distribution within a cube of edge 45 µm. d) Superposition of the initial volume and the limits
determined by the segmentation algorithm. The limits have been thickened for ease of visualization. e)
Example of colony. f) Detail of a colony [Vanderesse2008].
a) b)
c) d)
e) f)
46
Figure 13 : Unloaded interlock reinforcement G1151 (20 µm resolution, rescaled), (a) three successive
slices within warp yarn planes, (b) three successive slices within weft planes, the same yarn is
underlined in black. Pure shear: comparison of simulation with CT scans, (c) deformed shape of the
unit cell, (d) set of yarn cross sections along half a period of the yarn [Badel2008].
1.2.2. Electron microscopy
1.2.2.1. The projection requirement
Imaging modes dedicated to electron tomography have been developed and adapted to
optimize conditions of acquisition, in order to respect the requirements of reconstruction
algorithms. The most important problem is that the image intensity at each point must be a
a)
b)
c) d)
47
monotonic function of two quantities, namely, the specimen thickness and the density of
elements along the imaging beam. This condition must be fulfilled in order to insure that in
any projection, the intensity in the image is simply mass-thickness dependent, which is
required for a correct 3D reconstruction. This constraint is called the projection requirement,
and thus tomography reconstruction is based on the assumption that the acquired images are
true projections of the structure.
1.2.2.2. TEM
The usual method of imaging in conventional TEM consists in selecting the transmitted beam
after interaction with the object. This Bright Field (BF) imaging mode produces images, the
intensity of which is a combination of low angle elastic and inelastic scattering of incident
electrons with the atoms of the sample.
For crystalline specimens, BF images contain non uniform contrasts owing to diffraction
effects resulting from elastic scattering at certain tilt angles (Bragg angle orientations). These
effects, which are essentially non-linear with mass-thickness, do not fulfil the projection
requirement.
According to the above, tomography in Bright Field (BF) imaging mode can be applied if the
contrast of the images is not orientation-dependent (except from the effect of the mass-
thickness variation with the tilting of the object). Thus, BF tomography is basically restricted
to amorphous samples or to very weakly scattering samples (sufficiently thin or constituted
with low atomic number elements) [Hawkes1992]. For crystalline specimens with relatively
high atomic number, the intensity in the BF-TEM images is significantly perturbed by phase
contrast effects, such as Fresnel contrast seen at the edges of the specimen, or diffraction
contrast, such as kinematical or dynamical bend contours or thickness fringes. Such features
are illustrated in Figure 1, which concerns a test case which is developed in §.3.1.
It should be noted that Fresnel contrast can be apparent even for non-crystalline specimen,
which may in some cases lead to the breakdown of the projection requirement.
To overcome the problem of Fresnel and diffraction contrast, the acquired signal must be
essentially incoherent as it is the case for HAADF and, to a lesser extent, for EFTEM as
introduced in the two next paragraphs.
It should however be mentioned that BF imaging remains a very fast imaging mode. This
remains a great advantage in the case of biological samples, which are generally very
sensitive to beam damage [Midgley2003].
48
Figure 14: series of projections of the same area of VC nanoprecipitates deposited on a carbon
extraction replica obtained from a model FeVC steel. 3 BF micrographs are shown in a), b) and c),
which were acquired at tilts respectively equal to 0, 2 and 4°. Note that the contrast of thickness
fringes at the periphery of the particles changes significantly even within a small tilt range, which does
not fulfil the projection requirement.
It is important here to make a short comment about the thickness of the sample in TEM. In
order to get a electron signal that can be exploited for imaging, the sample must be
sufficiently thin (nominally of the order of a fraction of micrometer). When starting from a
bulk material, a „thin foil‟ has thus to be prepared. This generally leads to severe restrictions
in the tilting capabilities of that sample, since the projected thickness increases drastically at
large tilts (say > 70°), which reduces considerably the electrons than could cross the matter.
1.2.2.3. STEM-HAADF
High Angle Annular Dark Field (HAADF) imaging in the scanning transmission electron
microscope (STEM) [Pennycook1990, Jesson1995] is capable of providing simultaneous
structural and chemical information with atomic resolution [Nellist1998(1), Nellist1998(2),
James1999].
HAADF imaging consists in acquiring the electrons scattered at high angles, which are
associated with electron interactions close to the nucleus of the atoms within the object. Thus
the cross-section for HAADF scattering approaches the unscreened Rutherford scattering
cross-section. The use of an annular detector allows the intensity to be integrated over a given
range of angular collection. It is recommended to adjust the collection settings in a way that
the inner-angle of the detector is larger than twice the Bragg angle of significant diffracted
beams in order to ensure „true‟ incoherent imaging conditions.
The acquisition is performed in the STEM mode: the incident probe is scanned over the
specimen, as illustrated by Figure 15.
a) b) c)
49
Figure 15: Bright and Dark Field mode on Transmission Electron Microscopy. The backbone of this
imaging mode is the special shape of the diaphragm: the central beam is shuttered with an opaque disc
and the image is formed by electrons scattered at high angles that have passed through the annular slit
of the diaphragm. Value of camera length depends on imaging mode and angle of collection.
In „a large scattering angle‟ hypothesis, each atom of the object can be considered as an
independent scatterer, with a cross-section approaching a Zx dependence, where Z is the
atomic number and x is a constant depending on the collection conditions (1.6 < x < 2)
[Kubel2005, Jesson1995, Nellist1999]. Therefore, the intensity within the HAADF image can
be simply written as:
IHAADF i niZix (1)
where ni is the number of atoms with atomic number Zi contained in the illuminated volume
at the considered probe position [Treacy1999].
This basic relationship shows that high contrast images are expected when structural
heterogeneities imply heavy atoms against light ones. The images are then strongly dependent
on the atomic number of the components (Z contrast imaging). In the case of tomography,
there is a tremendous improvement in contrast, signal to noise ratio (SNR), and clarity in the
reconstruction of heavy atoms in the presence of light ones [Midgley2001]. Finer variations
are obviously encountered for small changes in chemistry, as for example near interfaces or
around precipitates [Midgley2003, Weyland2001(2), Midgley2001, Weyland2004].
The above expression of IHAADF also proves the incoherent nature of the HAADF image:
consequently HAADF imaging does not suffer from diffraction effects as such encountered in
BF imaging in conventional TEM. HAADF is then largely insensitive to the orientation in the
specimen
BF
DF scattered electrons
electron probe
50
case of crystalline materials [Weyland2001, Midgley2001, Bals2004, Ziese2004], thus it is
applicable for imaging quantification for both amorphous and crystalline objects. This is
illustrated by Figure 16, to be compared with Figure 1.
The image resolution in STEM mode is mostly determined by the electron probe size that is
scanned across the specimen surface. Thus the smallest possible probe, with a sufficient
probe-current is generally needed. This can be achieved by de-magnification of the electron
source through the probe-forming lens system [Klie2005]. However, it should be noted that
although the Z-contrast image is mostly incoherent in the image plane, coherent effects along
the electron beam direction could affect slightly the contrast in the image under high
resolution conditions [Nellist1999, Klie2005].
Figure 16 : series of projections of the same area of VC nanoprecipitates deposited on a
carbon extraction replica obtained from a model FeVC steel. 3 HAADF images are shown in
a), b) and c), which strictly correspond to the BF micrographs reported in Figure 1.
In the perspective of tomography, it was already stated that TEM-BF imaging is well-adapted
to biological specimens. It however appears that STEM-HAADF imaging can be a good
alternative for such materials in terms of possible reduction of beam damage. The beam
damage kinetics during STEM mode is very different than for BF-TEM; damage appears to
depend not on the total dose, but on the dose rate. Intriguingly these results also raise the
prospect that STEM may also be well-suited, at least in terms of beam damage, for
application in biological tomography [Weyland2005].
1.2.2.4. EFTEM
Energy-filtered transmission electron microscopy (EFTEM), which can roughly be considered
as an incoherent imaging mode, is used to generate 2D chemical maps of the observed area,
by collecting electrons within a specified energy-loss window [Reimer1995, Thomas2001].
a) b) c)
60 nm
51
This window is defined using an energy selection slit with a typical width of 5-10 eV located
at a given inelastic energy loss, as illustrated in Figure 17.
Figure 17 : principle of EFTEM imaging (case of a „in-column‟ spectrometer or filter inserted in the
microscope [Zeiss]).
The EFTEM resolution is generally limited to 1 to 2 nm due to the chromatic aberration
caused by the electron energy loss range in the images [Krivanek1995]. As a general rule,
EFTEM provide high contrast images; since it removes most of inelastic scattered electrons
(detrimental to resolution), particularly for thick specimens [Grimm1998, Angert2000]. This
is frequently applied in conventional TEM by producing zero-loss images, which simply
collect purely elastically scattered electrons.
In fact the contrast observed in an energy-loss image is derived from a combination of
inelastic scattering (through changes in composition and electronic structure) and elastic
effects (via crystal thickness and orientation). The compositional information from a single
energy-loss image may be isolated by generating either a background subtracted elemental
map (from three or more images) or a jump-ratio map (from two images). Both maps show
pixel intensities related to the amount of the atomic specie defined by the selected energy-loss
(in the case of ionization edges). Diffraction effects can be removed partially by dividing the
map by a zero-loss image, but this can also introduce artefacts associated with changes in the
diffraction contrast itself as a function of energy loss. Jump-ratio images are a useful way of
removing residual diffraction contrast, they can show higher sensitivity than an elemental
map but the intensity values cannot be related in an absolute (quantitative) way to the
composition.
52
EFTEM tomography is based on acquisition of 2D maps of chemical elements at different tilt
[Möbus2003, Boudier2005], then a 3D chemical map is obtained by the same algorithms of
reconstruction used in TEM and STEM tomography. In fact, 2D maps contain background
noise which is due to the electronic of the detector, multiple and non-specific interactions. For
each tilt, this noise is estimated from few acquired images and then subtracted from map. As
indicated above, possible residual diffraction contrast within some elementary 2D maps may
affect the validity of the projection requirement in the same way as it did in the case of the
BF-TEM imaging.
The main drawback of EFTEM imaging for tomography is that EFTEM mapping requires
long exposures and/or high beam currents, since it essentially uses a very small part of the
electron beam (i.e. defined by the energy-loss selected by the energy slit) to produce the
images. This makes EFTEM a difficult technique to apply to biological samples
[Koster1997].
1.2.3. Atom probe
Atom probe tomography (APT) represents the most recent branch of field ion microscopy
(FIM) [Miller1996]. This technique is exceptional, as it allows the detection and localization
of individual atoms with, in the best cases, an Angström accuracy. It is based on the field
evaporation effect discovered by [Muller1941]; as a consequence of the evaporation process,
FIM and APT are destructive techniques. When an electric field of several volts per Angström
is applied on a surface, surface atoms evaporate in the form of ions. Such an electric field can
be obtained by applying a few kV on a specimen prepared in the form of a tip, with an end
radius of 10 to 50 nm. Due to the spherical shape of the specimen apex, ionized atoms are
radially emitted from the surface and collected onto a dedicated detector. APT consists in
using a time resolved position-sensitive detector, which allows to deduce the initial positions
of the collected species, then to reconstruct the 3D structure of the evaporated tip, at the
atomic resolution in the best cases. A further advantage is that the mass analysis of the
detected ions permits a chemical identification. In the conventional 3DAP (3D Atom Probe),
a fraction of the voltage is applied by means of HV pulses (1 ns) in order to control the
moment of ion emission and allow their chemical identification by time-of-flight mass
spectrometry. Thanks to the projection law, removed atoms are positioned in each atomic
layer on a nearly atomic scale. The controlled removal of the material layer after layer
provides a 3D image of the material resolved at the atomic scale [Deconihout2008]. The
advances in the application of atom probe tomography have been made possible by recent
53
developments, in specimen preparation techniques (using focused-ion beam - FIB -
instruments) and the more routine use of laser pulsing. The combination of these two
developments now permits atomic-scale investigation of site-specific regions within
engineering alloys (e.g. at grain boundaries and in the vicinity of cracks) and also the atomic-
level characterization of interfaces in multilayers, oxide films, and semiconductor materials
and devices (see for example [Cerezo2007]).
Two examples related to steels are described below to illustrate the use of APT in 3D
chemical mapping applications.
The first example concerns metallurgical phase transformations [Caballero2009]. Atom probe
tomography is used to analyse the carbon distribution in austenite during isothermal bainite
formation, and the incomplete reaction phenomenon in medium-carbon, high-silicon,
manganese-alloyed steels. The aim of the study was to confirm atom probe investigations
performed in the 1980s on the distribution of carbon in austenite at an atomic scale,
essentially to explain the incomplete reaction phenomenon identified at that time. The
presence of cementite was confirmed as the lower bainite carbide in the steel investigated by
the authors. Carbon atom maps obtained from specimens isothermally transformed at 325 °C
for 1350 s are shown in Figure 18 a-b). The distribution of carbon atoms in the analysis
volume is not uniform, and carbon-enriched and carbon-depleted regions are clearly
distinguishable. In this case, no crystallographic information could be deduced from the
analysis, and the carbon-enriched regions were assumed to represent austenite, as its carbon
content is higher than the average value of 1.32 at.%, and the low carbon (<1 at.%) regions
were assigned to the ferrite phase. From such maps, elementary numerical treatments allow
concentration profiles to be deduced, as presented for the carbon specie in Figure 18 c) and d).
Among valuable metallurgical insights deduced from such 3D analyses, it clearly
demonstrates that Atom probe confirms that finer austenite films accumulate higher amounts
of carbon during bainite formation.
54
Figure 18 : (a and b) Carbon atom maps; and corresponding concentration profiles (c and d) across
austenite–ferrite interface in a steel transformed at 325 °C for 1350 s ( b means bainitic ferrite and
austenite) [Caballero2009].
The second example concerns mechanical properties and especially failure mechanisms in
steels [Cerezo2007]. Study of the crack tip is critical, since it provides information on the
crack advance; cold work is known to harden the material through changes in the
microstructure such as the formation of deformation shear bands. However, the mechanisms
that control crack propagation in cold-worked samples are not yet clear. Figure 19 shows a
combined TEM, nano-SIMS, and APT investigation of a type-304, Japanese-grade stainless
steel widely used in pressurized water reactors (PWRs). Thermomechanical treatments (heat
55
treatments and mechanical testing in order to simulate the working conditions in the reactor)
were shown to produce intergranular cracks over 100 μm in length.
Figure 19 : Study of cracks in a stainless steel after stress-corrosion cracking. (a) Nano-SIMS
composite map of the distribution of 56
Fe16
O- (red),
52Cr
16O
- (blue), and
11B
16O2
- (green) showing
oxidized deformation shear bands (arrowed). (b) Bright-field TEM image showing two orientations of
shear bands (arrowed) either side of an advancing crack. APT maps of (c) Cr and (d) CrO species from
a volume taken from the vicinity of a crack tip, showing O diffusion along a serrated, Cr-segregated
shear band [Cerezo2007].
In Figure 19 a), a region containing the tip of a crack has been mapped, clearly showing
different oxides within the crack, oxidation of shear bands, and boron segregation at a grain
boundary. However, nano-SIMS has a limited lateral resolution (≈ 50 nm in the present case),
and. TEM can add complementary information on the microstructure. Figure 19 b) shows the
different orientations of the shear bands in the grains on either side of an intergranular crack,
but no unambiguous chemical data can be deduced from the TEM work, since the authors
have estimated here the chemical analysis accuracy to about 0.1 wt.% in concentrations. APT
can offer three-dimensional mapping with atomic resolution and much more efficiency in
order to detect any minor impurities. In this particular geometry, FIB techniques were used to
56
cut out a volume of material at a crack tip in order to prepare a sharp specimen adapted to
APT. Figure 19 c) and d) show the analysis of a region containing an oxidized shear band that
has been in contact with the grain boundary plane followed by the crack (above the analyzed
region). The presence of the shear band is shown by the pattern of Cr segregation (Figure 19
c), which indicates a serrated band. Oxygen is seen to have diffused along the shear band
plane, with a very obvious gradient in concentration with distance from the grain boundary
(Figure 19 d). Clearly, the deformation shear bands can act as easy diffusion paths for oxygen
and Fe, locally accelerating the oxidation rate. Atom-probe analysis allows measurement of
diffused oxygen down to <100 ppm levels, at ultrahigh spatial resolution. This type of data
will contribute to clarifying the operating mechanisms in SCC of cold-worked materials, as
well as providing information on the diffusion coefficients of oxygen down grain boundaries
or shear bands at low temperatures [Cerezo2007].
1.3. 3D analysis different from tomography
1.3.1. Difference between 3D analysis and tomography
Ideally, the tomography approach allows reconstruction of the truly three-dimensional
visualized object, whatever the complexity of its shape. A strong advantage of tomography is
that it does not depend on averaging or on the assumption and exploitation of symmetry of
samples, as it is the case for methods like angular reconstitution (electron microscopy),
stereoscopy, nuclear magnetic resonance spectroscopy (NMR), and X-ray crystallography.
Once the volume has been reconstructed, any measurement of extraction of information from
tomogram is generally easier and more accurate than with other 3D techniques. When
electron tomography experience is impossible for different reasons such as bad contrast or
beam damage, alternative 3D approaches can be undertaken to extract some 3D
measurements, but generally not to reconstruct the 3D shape.
It must be reminded here than tomography is, in itself, not the actual goal to achieve when
studying the 3D microstructure of any material. Indeed what is to reach is the pertinent
information regarding a given 3D problem. In this sense, stereoscopy can be sufficient as it
will be detailed in the next sub-section. However, it can even be sufficient to obtain
projections of the microstructure under 2 or 3 different viewing directions in order to obtain a
relevant key feature. Figure 20 illustrates this basic approach in the case of a Si-based
mesoporous material, the empty structural channels are expected to be filled by some
additional non-crystalline phase. A simple observation of the object under two perpendicular
57
directions enables the question of the actual filling of the pores to be answered
unambiguously.
Figure 20: SBA15 mesoporous material observed a) along the structural channels after a tilt of -28°
(sample provided by V. Dufaux, ENS-Lyon), b) perpendicularly to the previous projection (tilt +62°).
The first micrograph shows some filled channels edge-on (arrows; the filling material is a non-
crystalline (W,P)-based oxide). On the second micrograph, the length of the „filaments‟ filling the
channels is directly evidenced (MET 2010F; tilting at 90° in this microscope has been made possible
by using a dedicated home-made modified holder tip, see §.2.1).
1.3.2. Introduction to the stereoscopy
Stereoscopy consists in combination of two images acquired at different angles. It intends to
extract three dimensional information (topography of surface, real distance, 3D position,
shape, distributions, volume or surface density…). It can be applied to different techniques
imaging (SEM6 [Podsiadlo1997, Venkatesh2008, Podsiadlo1999], satellite [Tanaka1996,
Perlant2000], light imaging [Ruff1995, Guesalaga2003, Pappa2000], X-ray imaging
[Darambara2001], telescope [Lemoine-Goumard2006]). Depending upon the system, either
the sample is fixed and the detector (or camera) is tilted or the sample turns around a fixed
detector [Midgley2003, Guckenberger1982]. The principle of the measurement is simply to
deduce a 3D information from 2 tilted views or projections. However, the use of more than 2
images can improve the accuracy of the method as it will be seen in §.3.2.
After alignment of images by cross correlation, the tilt axis is calculated by following the
trajectory of some details, and images are rotated to make the tilt axis parallel to the vertical
(Oy) axis (details about the necessity of alignment procedures, and how they can be achieved,
6 SEM : Scanning Electron Microscopy
a) b)
58
will be given in §.1.10. Principle of alignment of images). For simplicity, particles are
considered here to be spherical with R radius, and the objective of stereoscopy approach is to
calculate the position of their barycentre M(X, Y, Z). For any given tilt , the M centre of
each particle is positioned at M (X , Y , Z ), its elevation being defined by the angle ( 0
+ ) where 0 is particle elevation at zero tilt. According to the convention that Oy is the tilt
axis, the projected coordinate Y is constant for all tilts. Then the projected position X is
given by X = cos( 0 + ), where is the radius of the circular trajectory of the particle
around tilt axis. The coordinate Z is given by Z = sin( 0 + ) (Figure 21).
Figure 21 :conventions used to describe the motion of a given particle during a tilt experiment, (a) M
particle at M0(X0, Y0, Z0) position at zero tilt. The angle 0 characterizes the elevation of M, is the
radius of the circular trajectory described by M around the tilt axis Oy, (b) M particle moved from M0
to M (X , Y , Z ).
1.4. Results obtained by electron tomography on material science during
the last decade
To illustrate which kind of information can be extracted by electron tomography approaches
(TEM-HAADF-EFTEM), some literature examples of characterization of 3D structures of
nanomaterials are described below:
The first example concerns a heterogeneous catalyst [Midgley2003] composed of Pd6Ru6
particles (with a diameter of about 1 nm) within a mesoporous silica support (MCM-41)
whose mesopores are hexagonal in cross-section with a diameter of about 3 nm (Figure 22).
The nanoparticles stand out very well against the light SiO2 background and some appear to
lie within the mesopores. However, to ensure that this is the case it is necessary to determine a
3D reconstruction of these regions (Figure 23 and Figure 24).
a) b)
M=M0 M=M0
M=M
59
Figure 22: a typical STEM HAADF image of Pd6Ru6 nanoparticles and an MCM-41 mesoporous
silica support [Midgley2003].
The second example concerns the determination of 3D morphology of magnetite (Fe3O4)
crystals contained in a magneto-tactic bacteria (Figure 25) [Midgley2003]. STEM-HAADF
tomography is illustrated in Figure 26, by surface rendering of tomogram of a single biogenic
magnetite nanocrystal viewed along different directions, and shows six {1 1 0} facets along
the length of the crystal and two {1 1 1} facets at its ends, as well as some smaller {1 1 1}
corner ones.
60
Figure 23 : (a) a montage in which each image is a voxel projection of the 3D reconstruction of an
MCM41-Pd6Ru6 catalyst viewed at angles shown in the figure. The 3D structure of the mesopores is
well resolved. The nanoparticles are coloured red to improve clarity [Midgley2003].
Figure 24: an illustration of how an individual nanoparticle can be isolated in the reconstructed data
set to show that it is anchored to a wall of a mesopore of the MCM-41. The mesoporous channels are
about 3 nm in diameter and the single nanoparticle of Pd6Ru6 is about 1 nm in diameter. The scale bar
corresponds to image (c) [Midgley2003].
61
Figure 25: (a) BF image of a magneto tactic bacterium showing the backbone of magnetite crystals
surrounded by the organism‟s organic „drapery‟. (b) A high magnification STEM HAADF image of a
similar bacterium to that shown in (a), which shows the excellent Z-contrast and spatial resolution of
this technique [Midgley2003].
Figure 26: tomographic reconstruction of a magnetite nanocrystal from a magnetotactic bacterium.
The reconstruction was made from a tilt series of STEM HAADF images. The montage shows the
three-dimensional morphology of the crystal viewed from a range of directions [Midgley2003].
These magnetotactic bacteria crystals can also be visualized by EFTEM tomography, in order
to investigate any possible compositional variation in the iron or oxygen signal related to the
growth mechanism of the crystals (Figure 27). The oxygen and iron reconstructions can be
visualised as a combined RGB image (Figure 28), iron is set to red and oxygen to green and
where both iron and oxygen coincide in the crystals, shades of orange appear.
62
Figure 27: a comparison between (a) an original zero tilt oxygen jump-ratio image taken from a
magnetite chain in a magnetotactic bacterium and (b) the zero tilt projection of the tomographic
reconstruction. Note the dramatic improvement in the signal-to-noise ratio in the reconstruction
[Midgley2003].
Figure 28: two colour sections through the EFTEM reconstructions of the magnetite crystal chain. The
pixel intensity of the oxygen (green) has been rescaled to better compare with the iron (red). The main
image is a section (perpendicular to z) taken approximately midway though the centre crystal. Sections
have also been taken perpendicular to the chain axis from five of the crystals and are displayed in A–E
[Midgley2003].
The next example concerns another EFTEM tomography application to the characterization of
a grain boundary in a stainless steel [Midgley2003]. The area shown in Figure 29 is rich in
chromium and reveals, although not clearly, the presence of carbide precipitates. The shape of
the carbides are analysed from a tomographic reconstruction of a tilt series of chromium
jump-ratio images. Voxel projections of tomogram (Figure 30) clearly show that chromium
carbides have complex 3D shapes and orientations.
63
Figure 29: zero-loss BF image of a stainless steel grain boundary used for EFTEM tomography, the
general direction of which is shown by the arrow. Diffraction contrast obscures most of the carbide
structure, which is complex and irregular both along the length of, and across, the boundary
[Midgley2003].
Figure 30: voxel projections of a tomographic reconstruction using Cr jump-ratio images of the grain
boundary carbide structure seen in Figure 29. The carbides are viewed (a) at 45° from all major axes,
and parallel to (b) the z-axis, (c), the x-axis and (d) the y-axis, respectively. The box edge is 1.5 mm in
length [Midgley2003].
The further example illustrates the interest of tomography in the localisation of small objects
in heterogeneous „nano-systems‟, such as nanoparticles embedded in a mesoporous system
[Ziese2004]. The density of an Au/SBA-15 model catalyst particle is reconstructed by TEM
tomography, which allows the 3D shape, volume, connectivity and location of internal pores
to be determined. In addition, the location of internal gold nano-particles can be statistically
64
studied (Figure 31). This kind of information could not be gained from single transmission
electron micrographs, owing to the overlap of structures in projection.
Figure 31: the center panel of the top three images shows the surface rendered visualization of the
reconstructed density of an Au/SBA-15 model catalyst particle (~256 nm × 256 nm × 166 nm). The
size and location of Au particles inside the material can be seen unambiguously (left: virtual cross-
section - thickness 0.64 nm - through the reconstruction, right: surface rendering of gold particles -
size 8 nm -) and subjected to statistical evaluation. The slices at the bottom display three of the 151
electron microscopy projection images (−55◦, 0◦ and +55◦ tilt angle) that were used to calculate the
volume. The two-sided arrows indicate the reversible process of projection and back-projection
[Ziese2004].
A final example is presented, which also concerns nano-systems linked to computer industrial
applications and especially hard disk storage capacity. A potentially interesting solution to
increase the density of magnetic storage consists in a complex nano-system where nickel
nanocrystals decorate the top of silica beads arranged in a compact ordered two-dimensional
(2D) array [Ersen2007]. A 5-nm thick nickel layer deposited by molecular beam epitaxy onto
65
the 2D array, leads through a thermal treatment, to a dewetting process and then to the
formation of metallic nanocrystals on top of the beads (Figure 32 a).
Figure 32: silica bead topped with a nickel nanocrystal. (a) scanning electron microscopic view of a
2D array of packed silica beads topped with nickel nanocrystals. (b) projection image of a single silica
bead topped with a nickel nanocrystal showing the supporting membrane and the gold nanoparticles
used as spatial reference. (c) a cross-section in the voxel matrix of a silica bead decorated with nickel
nanocrystals. The bead diameter is 300 nm and the volume of the topping metal nanocrystal is 0.7.106
nm3. The dark structures are related to Ni particles while the contribution of the silica shows up as a
large grey disk. (d) 3D modelling of the silica bead (white) and Ni nano-object (blue). The gold
particles that were used for geometric corrections are shown in red [Ersen2007].
3D-TEM technique has been applied to provide topological data on this kind of nanostructure.
After recording the projections (Figure 32 b) and applying the reconstruction procedure,
segmentation extraction process yields 3D models for the surfaces that resolve various
elements. Figure 32 c) shows a cross-section of the object that was numerically extracted
from the voxel matrix. The dark parts correspond to nickel nanocrystals while the large
circular disk is the silica bead. This cross-section clearly reveals that the metallic nanocrystals
are embedded inside the silica beads, indicating a surface fusion of the silica beads during the
thermal treatment. This penetration of the metal inside the silica cannot be observed on
66
classical single projection images (Figure 32 b) that integrate the contributions of all atoms
superimposed along the electron path. Figure 32 d) shows a reconstruction with surface
modelling. By producing stunning 3D models through a reconstructed voxel matrix as shown
in the example of Figure 32 d), 3D-TEM can yield an in-depth understanding of the
morphology of a nano-object and thus provide quantitative data that are useful hints to
understand the growing process and to explain the material‟s behaviour under working
conditions.
1.5. Algorithms of reconstruction
1.5.1. Back Projection (BP)
BP is a method of reconstruction of tomograms from acquired projections; the principle is to
position slices of projections in Fourier space of the object, then to produce a tomogram by an
inverse Fourier transform. Indeed, according to the theorem of the central section [Kak1985],
the Fourier transform of each projection is a hyperplane in Fourier space of the object; this
hyperplane is oriented accordingly to its angular orientation during acquisition (Figure 34).
1.5.2. Weighted Back Projection
Using a given set of acquired projections, the basic reconstruction by back projection induces
artefacts, because all points of Fourier space are not equally distant. Near the centre of Fourier
space, low frequencies are well-sampled compared to edges of Fourier space (details at high
frequencies) [Kak1988] (Figure 33). To compensate this sampling non-uniformity, each point
of Fourier space can be weighted according to its distance from the centre; this method is
called the weighted back-projection (WBP) [Frank1992].
Figure 33 : illustration of the non-uniform sampling of tomogram brought about by the acquisition of a
tilt series in the Fourier space: the centre is much well-sampled compared to edges .This implies a
greater error in the calculation of the high frequency components in the tomogram than in the low
frequency ones, which results in image degradation [Kak1988].
frequency domain
ν
μ
67
1.5.3. Algebraic Reconstruction Technique (ART)
A tomogram is composed by voxels, each of them being a sum of pixel values corresponding
to the corresponding voxel in each projection. The ART [Herman1973] consists in evaluating
weighting values that are added iteratively to each pixel, in order to obtain a theoretical
volume. Initial projections from this „seed‟ volume can then be compared to the experimental
images in order to modify the volume in an iterative way: the difference between the
theoretical and experimental projections is retro-projected in the theoretical volume. In the
initial method [Herman1973], this volume modification is carried out after each comparison
between projections. Input of this algorithm, requires a value of coefficient of relaxation,
which controls speed of convergence to an optimal volume, for ART, this coefficient must to
be less than the inverse of the number of iterations in order to avoid an increased error
between calculated projections and experimental reconstructions.
Figure 34: relationship between a projection P acquired at tilt and Fourier transform of sample f as
described by central slice theorem, a) geometry of acquisition of projection of sample at tilt, t axis is
image of x axis by rotation, b) frequency domain of the sample, which can be fulfilled by all
projections , then a tomogram is obtained by an inverse Fourier transform, Fourier transform of P is a
section oriented by θ with u axis on Fourier space of sample.
1.5.4. Simultaneous Iterative Reconstruction Technique (SIRT)
The SIRT method [Gilbert1972] is similar to the ART method, but the modification of the
reconstructed volume is here done after having performed all comparisons between
experimental and theoretical projections. The convergence towards the optimal solution is
much slower than in the ART because the updated volume is updated less frequently. This
method is however less sensitive to noise in the experimental data because it averages all
modifications of each voxel. Input of this algorithm, requires a value of coefficient of
68
relaxation, which controls speed of convergence to an optimal volume, for SIRT, the
coefficient of relaxation is close to the inverse of the number of acquired projections.
1.6. Practical aspects of tilting tomography
1.6.1. Geometry of acquisition
Whatever the source used to produce the required projections, algorithms of reconstruction
must be adapted to the geometry of acquisition, that is mainly a simple tilt axis, double tilt
axis or conical geometry.
1.6.1.1. Simple tilt axis
Simple tilt axis geometry consists on tilting the specimen around one single axis. To get a
whole information about the sample, the tilt range should be 180°. However, in electron
microscopy, and especially TEM, a tilt range of 180° is generally not possible simply because
of the sample geometry (see §.2). From a practical point of view, the tilting range is generally
limited to ±70°. In the case of a reduced angular tilting range the tomogram reconstruction is
carried out with a lack of information (Figure 35 a), which obviously decreases the quality of
the tomography approach. This missing of information leads to artefacts in the
reconstruction, such as an elongation of the reconstruction in the direction of the optical axis.
This will be further discussed when the question of resolution of the reconstruction will be
developed (1.6.3.3 Resolution through optical axis direction). To resolve the problem, double
tilt or conical geometry of acquisition could be preferably used.
1.6.1.2. Double tilt axis
A method to reduce the problem of the missing information explained in the previous sub-
section is dual tilt, for which two tilt series are recorded with mutually perpendicular tilt axes,
which reduces the missing information to a pyramid form (Figure 35 b) [Penczek1995]. In
this way the tomogram fidelity is improved without increasing the tilt range. This is
particularly advantageous for thick samples, because images at high tilt suffer from a great
loss of signal-to-noise ratio. All algorithms of reconstruction (evoked in the §.1.5. Algorithms
of reconstruction) have to be adapted to dual axis geometry [Tong2006]. At least, both two tilt
series are used for independent reconstructions which are finally combined into a single
tomogram [Koster1997]. Obviously this dual axis approach increases the total time of the
procedure including both acquisition and reconstruction steps. Regarding the algorithmic
69
incidence of that, any possibility to speed up the computer processes, such as using the GPU
programming language [Schoenmakers2005] is worth being applied.
1.6.1.3. Conical tomography
Conical electron tomography is a powerful acquisition method to reduce artefacts met in
simple or dual tilt axis (Figure 35 c). The principle consists in acquiring several complete tilt
series around different tilt axis. This approach improves the resolution of tomograms, which
become isotropic, since anisotropy due to the missing regions are eliminated [Turner1992].
These different approaches (simple-tilt, double-tilt or conical tomography) can then be
visually compared from the point of view of the missing regions in Fourier space of
tomogram (Figure 35). Regarding the efficiency in reducing the anisotropy of resolution and
artefacts of elongation, it appears that the adaptation of the sample holder and possibly sample
geometry in order to approach a tilt range of 180° is a better strategy than using a double tilt
axis system. Moreover, it should be reminded that double or conical tilt methods increase time
of acquisition, which may be inconvenient not only from the point of view of the duration of
the experiment, but also from the point of view of the required stability of the specimen
during the experimental process.
Figure 35: Comparison of the single-tilt, double-tilt, and conical tilt geometries used to image
specimens in electron tomography [Lanzavecchia2005]. In Fourier space, each image is represented by
a central plane oriented orthogonal to the viewing direction. The empty regions represent the „„missing
volume‟‟ resulting from limitations in tilt. (A) The stack of central planes obtained in single-tilt with
the missing volume shaped as a double wedge. (B) The stack of planes obtained in double-tilt
geometry with the missing volume shaped as a double pyramid. (C) The layout obtained in conical tilt
geometry. The missing volume is shaped as a double cone, which greatly reduces the anisotropy in the
resolution along the XY plane. The tilt angle was 55° in all three examples.
1.6.2. Principle of alignment of images
70
Tomographic approaches need to acquire an image series over a large angular range (usually
±70° at least) with small increments (usually 1° − 5°). The quality of the reconstruction
depends strongly on the precision of images alignment [Frank1992], and slight misalignments
induce artefacts in tomogram [Russ2000]. We will then describe the various parameters that
are of importance in the alignment procedure.
1.6.2.1. Tilt axis
The geometrical tilt axis must be positioned precisely within the whole image series. Its
position can be calculated by tracking some details (ideally small particles) throughout the
series. Superimposing all images together after a good alignment underline clearly that
trajectories of particles, which must be all parallel one to each other.
Their movement is then perpendicular to the tilt axis, which determines its angular position
(Figure 36). An optional approach at this stage is to perform a Fourier transform of this
montage: a diffuse intensity should extend perpendicularly to the direction of the projected
trajectories, that is parallely to the tilt direction (Figure 37).
Although this approach may give satisfactory results, it will be seen that a more accurate
determination of the tilt axis is possible when an detailed analytical analysis of the trajectories
of numerous particles is performed (see §.3.2.4. Results. Figure 15).
Figure 36: positioning the tilt axis from a tilt series obtained on a group of Pd nano-particles deposited
on a carbon substrate (see §.3.3). (a) single STEM HAADF image acquired at zero tilt. (b)
Superimposition of all images (about 100 images) from the whole series. The montage is displayed
with artificial colours to highlight the trajectories: their elongation underline the direction
perpendicular to the tilt axis as indicated. Note further that the particles located at the top of the
images exhibit less trajectory „streaking‟, which indicate that they are closer to the exact position of
the tilt axis.
particles trajectory
tilt axis direction
50 nm
a) b)
71
Figure 37 : Fourier transform of the summation of the entire (aligned) tilt series in order to
determine the tilt axis [Midgley2003]. (a) A single STEM HAADF image acquired at zero tilt from a
catalyst structure (palladium particles embedded within a carbon matrix). (b) Summation of the entire
(aligned) tilt series showing a distinct movement in one direction at an angle to the horizontal. (c)
The power spectrum allows the positioning of the tilt axis direction.
For convenience regarding the reconstruction step, all images of the series are generally
rotated to make the tilt axis parallel to the vertical y direction.
1.6.2.2. Alignment with cross-correlation
Once the tilt axis has been positioned, the images of the series must be aligned in a unique
referential, that is to say possible drifts of the object during the acquisition of successive
images must be corrected. The most commonly used method for that alignment procedure is
to use a bi-dimensional cross-correlation. Assuming two numerical images described by
matrix of pixels M(r) and M‟(r) (where r represents the positional vector of the pixel at the
column „k‟ and the line „l‟within the image), the cross-correlation function C(M,M‟) can be
written as:
C(M,M‟) = TF[M(r)] x TF[M‟(r)*] (2)
Where TF represents the Fourier transform (which is classically made by a Fast-Fourier
Transform algorithm to reduce the computational time).
For properly aligned images, the cross-correlation results in a maximum located at the centre
of the power spectrum of C(M,M‟). This is obviously what happens in the trivial case where
both images are identical (auto-correlation). If the compared images are not aligned, this peak
is off centre, and the maximum‟s shift from the centre can be regarded as the displacement
vector of the first image with respect to the second one. Thus applying this shift to the second
image aligns it back to the first one. This procedure is illustrated by Figure 38, and has to be
applied to the whole image series.
72
It may be useful to apply filters to the image series in order to reduce noise and to enhance
features which increases the accuracy of the cross-correlation (i.e. sharpness of the maximum
such as in Figure 38 c).
1.6.2.3. Alignment using fiducial markers
Depending on the signal-to-noise ratio, or contrast of the imaged features, the cross-
correlation may fail to lead to a satisfactory alignment. One alternative technique consists in
depositing fiducial markers (such as nanogold particles) before the observation (after or
during the specimen preparation) in order to get easily identifiable high-contrast details
[Lawrence1992]. The „marked‟ images can then further be aligned either by tracking the
trajectories of those particles, or simply by cross-correlation. It must be emphasized that
nano-particles (generally, gold) can be considered as spheres, which presents the great
advantage that they always appear as circles independently of the tilt value, which helps the
cross-correlation alignment. In principle, the accuracy of the alignment is equal to the size of
the particle (i.e. 1 nm particles allow a 1 nanometer accuracy).
This approach is very efficient for biological samples, which exhibit generally a poor contrast
not suitable for a direct cross-correlation alignment. Several examples can be found in the
literature of the application of fiducial markers in the domain of biological materials
[Ress1999, Zheng2004, Tchelidze2006,].
Figure 38 : illustration of the cross-correlation procedure for image alignment. The two first
micrographs (a) and b) are HAADF images of carbide particles observed on a carbon
extraction replica at tilt respectively equal to 27 and 32°; c) shows the cross-correlation: the
vector linking the centre of the image to the peak of maximum intensity (arrow) represents the
displacement of the first image (a) relatively to the second one (b).
1.6.2.4. Improving alignment by image stretching
a) b) c)
73
The applicability of the cross-correlation alignment is based on the similarity between the
images, since in principle the cross-correlation measures the relative spatial displacement
between 2 identical objects. From a practical point of view, two successive images of a tilt
series can be considered as sufficiently similar objects to allow a correct alignment with a
cross-correlation approach. However, the more the angular difference between successive
projections is large, the more the cross correlation becomes inaccurate, since corresponding
details will not exhibit the same projected shape within the images. To correct this problem,
each image can be stretched in the direction perpendicular to the tilt axis by a factor equal to
1/cos(θ), where θ is the tilt angle. Doing so, the difference in shape induced by the projection
effects at different tilts is minimized [Guckenberger1982].
1.6.3. Resolution of tomogram
The electron tomography resolution depends on several parameters, such as the imaging mode
(EFTEM, STEM-HAADF, TEM), the acquisition conditions (focus correction, tilt range,
number of acquired images, holder and goniometer geometry, pixel size, SNR), and the
sample geometry (thickness, structure, symmetry and complexity). Whatever the imaging
mode, tilting tomography suffers a limitation in resolution: an anisotropy in the tomogram
results form the missing of information, which produces an elongation in the projection
direction [Midgley2003, Hart1968]. In practice, the more images and the larger the angular
range, the higher the resolution will be within a 3D reconstruction. A rule-of-thumb for the
achievable „tomographic resolution‟ is that it equals three times the thickness of the sample
divided by the number of images. Obviously, this criterion has sense when the resulting value
remains greater than that physically imposed by the imaging system. It should be noted that
when this is the case, the practical achievable resolution seems to be rather better than worse
than the calculated value [Ziese2004]. The various parameters affecting this „tomographic
resolution‟ will be briefly discussed below.
1.6.3.1. Influence of acquisition parameters and sample geometry
As already mentioned, a limited tilt range (that is to say inferior to 180°), introduces an
elongation effect parallel the optical axis of the imaging system (e.g. microscope). According
to the previous resolution criterion, a small thickness and a high number of acquired images
improves the resolution of tomogram.
However, it is not possible to deduce universal criteria from this basic strategy, since the
„mass-thickness‟ nature of the sample greatly affects the intrinsic resolution. The common
74
shape of the TEM samples corresponds to the thin foil aspect, that is a parallelepiped
geometry. In this case, the thickness of the crossed specimen is increased by a factor of )cos(
1
at a tilt angle . It is instructive to keep in mind orders of magnitude: for example, the
specimen will be respectively 2.9 and 5.7 times thicker at 70° and 80° tilt with respect to its
„zero-tilt‟ thickness.
In the case of electrons and because of the complex nature of the interaction between
electrons and matter (scattering and dynamical effects, inelastic events - i.e. absorption -),
high thicknesses should result in a reduction of the achievable resolution in projections
acquired at high tilts. Starting from a 100 nm thin foil at zero tilt, the 570 nm thickness at 80°
as calculated above will represent a very high quantity of matter to be crossed by electrons for
usual inorganic materials.
Further experimental parameters difficult to quantify and to control generally affect the
resolution. Contamination effects, leading to image blurring, and beam damage, are typical
examples of what can drastically reduce the resolution in any tomography approach.
Another limiting factor to the resolution is the possible shadowing effects which will reduce
the maximal tilting angle. The shadowing may result from the geometry of the sample itself,
but more frequently comes from specimen holder, or the use of a supporting TEM grid. In the
latter case, the tilting limit max is linked to the width of the grid hole (w) and to the grid
thickness (h) (Figure 39):
)
h
wtan(a
max
Figure 39: illustration of the tilt limitation when using a TEM grid.
grid type hole diameter w (µm) Thickness h (µm) maximal tilt (°)
200 lines/inch 127 15 76
100 lines/inch 254 15 83
αmax max
max
max
h
w/2
grid
z-axis (optical axis)
x-axis
(3)
75
1.6.3.2. Spatial dependence of resolution regarding various directions
In the case of a single tilt axis experiment, resolution values through the three directions of
space (respectively dx, dy and dz, assuming that Ox represent the direction perpendicular to the
tilt axis within the image, Oy the tilt axis, and Oz the optical axis ) are given by the Crowther
relations [Crowther1970, Koster1997]. With the assumption of a perfect alignment, the
resolution dy along the tilt direction should be that of a single image (limited by the physical
processes involved in the viewing system). The resolutions dx and dz are given by the
following relationships:
N
Dd
x
where D and N are respectively the diameter of the object and the number of projections
recorded at equally spaced angles.
dz = dx.exz (5)
with exz is a coefficient of elongation given by:
maxmaxmax
maxmaxmax
xz
cossin
cossine
where max is the maximal angle of tilt.
Thus, for a tilt range less than 180°, the effect of elongation is to decrease the resolution along
the direction of the optical axis (if max is equal to 90°, exz = 1 and both values of resolution dx
and dz are equal, that is to say no elongation effect).
Projections of a sphere are simulated; with (Oy) and (Oz) are respectively tilt and optical axis
to observe effect of elongation in the tomogram at different tilt ranges (Figure 40).
(4)
(6)
76
Figure 40 : different projections respectively on (Ox,Oy), (Ox,Oz) and (Oy,Oz) plans, of a tomogram
of a sphere (radius = 50 pixel) reconstructed with WBP method, from different tilt ranges with step
angle of 1°, to illustrate elongation effect: a) tilt range of 180°: no effect of elongation is observed on
projections, b) tilt range varies from -45° to 45°: projections seems to be stretched on Oz direction
because of elongation effect, c) tilt range varies from 0 to 90°: direction of elongation effect, is not
parallel to optical axis, but it‟s oriented by the half of the tilt range from Oz axis.
References of chapter 1 [Angert2000] Angert I, Majorovits E, Schröder R R. Zero-loss image formation and modified contrast
transfer theory in EFTEM. Ultramicroscopy (2000) 81: pp. 203-222.
[Bals2004] Bals S, Kabius B, Haider M, Radmilovic V, Kisielowski C. Annular dark field imaging in
a TEM. Solid State Communications (2004) 130: pp. 675-680.
[Badel2008] Badel P, Vidal-Sallé E, Maire E, Boisse P. Simulation and tomography analysis of textile
composite reinforcement deformation at the mesoscopic scale. Composites Science and Technology
(2008) 68: pp. 2433-2440.
[Baruchel2000] Baruchel J, Buffiere JY, Maire E, Merle P, Peix G. X-ray tomography in material
science. Ed. Paris: Hermès, 2000.
c)
b)
a) (Ox,Oy) (Ox,Oz) (Oy,Oz)
45°
77
[Baumeister1999] Baumeister W, Grimm R, Walz J. Electron tomography of molecules and cells.
Trends in Cell Biology (1999) 9: pp. 81-85.
[Boudier2005] Boudier T, Lechaire J P, Frébourg G, Messaoudi C, Mory C, Colliex C, Gaill F, Marco
S. A public software for energy filtering transmission electron tomography (EFTET-J): application to
the study of granular inclusions in bacteria from Riftia pachyptila. Journal of Structural Biology
(2005) 151: pp. 151-159.
[Caballero2009] Caballero F G, Garcia-Mateo C, Santofimia M J, Millar M K, García de Andrés C.
New experimental evidence on the incomplete transformation phenomenon in steel. Acta Materialia
(2009) 57: pp. 8-17.
[Cerezo2007] Cerezo A, Clifton P H, Galtrey M J, Humphreys C J, Kelly T F, Larson D J, Lozano-
Perez S, Marquis E A, Oliver R A, Sha G, Thompson K, Zandbergen M, Alvis R L. Atom probe
tomography today (2007) 10: pp. 36-42.
[Chen1997] Chen C C, Herhold A B, Johnson C S, Alivisatos A P. Size dependence of structural
metastability in semiconductor nanocrystals. Science (1997) 276: pp. 398-401.
[Crowther1970] Crowther R A, DeRosier D J, Klug A. The reconstruction of a three-dimensional
structure from projections and its application to electron microscopy. Proc. Roy. Soc. Lond A (1970)
317: pp. 319-340.
[Darambara2001] Darambara D G, Speller R D, Horrocks J A, Godber S, Wilson R, Hanby A.
Preliminary evaluation of a prototype stereoscopic a-Si:H based X-ray imaging system for full-field
digital mammography. Nuclear Instruments and Methods in Physics Research (2001) 471: pp. 285-
289.
[Deconihout2008] Deconihout B, Vella A, Vurpillot F, Da Costa G, Bostel A. 3D atom probe assisted
by femtosecond laser pulses. Appl Phys A (2008) 93: pp. 995-1003.
[De Rosier1968] De Rosier D J, Klug A. Reconstruction of Three Dimensional Structures from
Electron Micrographs. Nature (1968) 217: pp. 130-134.
[Dierksen1992] Dierksen K, Typke D, Hegerl R, Koster A J, Baumeiester W. Towards automatic
electron tomography. Ultramicroscopy (1992) 40: pp. 71-87.
[Eckermann2008] Eckermann F, Suter T, Uggowitzer P J, Afseth A, Davenport A J, Connolly B J,
Larsen M H, F De Carlo, Schmutz P. In situ monitoring of corrosion processes within the bulk of
AlMgSi alloys using X-ray microtomography. Corrosion Science (2008) 50: pp. 3455-3466.
[Elmoutaouakkil2002] Elmoutaouakkil A, Salvo L, Maire E, Peix G. 2D and 3D Characterization of
Metal Foams Using X-ray Tomography. Advanced Engineering Materials (2002) 4: pp. 803-807.
[El-Sayed2001] El-Sayed M A. Some interesting properties of metals confined in time and nanometer
space of different shapes. Accounts of Chemical Research (2001) 34: pp. 257-264.
[El-Sayed2004] El-Sayed M A. Small is different: shape-, size-, and composition-dependent properties
of some colloidal semiconductor nanocrystals. Accounts of Chemical Research (2004) 37: pp. 326-
333.
[ESRF] ESRF. A light for science [on line]. Grenoble : ESRF, 2009. Available on http://www.esrf.eu
(date accessed 09/07/08)
[Frank1992] Frank J. Electron Tomography: Three-Dimensional Imaging with the Transmission
Electron Microscope. New York Plenum, 1992.
78
[Friedrich2005] Friedrich H, McCartney M R, Buseck P R. Comparison of intensity distributions in
tomograms from BF TEM, ADF STEM, HAADF STEM, and calculated tilt series. Ultramicroscopy
(2005) 106: pp. 18-27.
[Gatan2004] DigiScan User’s Guide. Part Number: 788.20003 (2004), Gatan, Inc.
[Grimm1998] Grimm R, Typke D, Baumeister W. Improving image quality by zero-loss energy
filtering: quantitative assessment by means of image cross-correlation. J. Micros (1998) 190: pp. 339-
349.
[Gilbert1972] Gilbert P. Iterative methods for the three-dimensional reconstruction of an object from
projections. J Theor Biol (1972) 36: pp. 105-117.
[Guckenberger1982] Guckenberger R. Determination of a common origin in the micrographs of tilt
series in three-dimensional electron microscopy. Ultramicroscopy (1982) 9: pp. 167-174.
[Guesalaga2003] Guesalaga A, Irarrazabal P, Guarini M, Alvarez R. Measurement of the
glaucomatous cup using sequentially acquired stereoscopic images. Measurement (2003) 34: pp. 207-
213.
[Hart1968] Hart RG. Electron Microscopy of Unstained Biological Material: The Polytropic Montage.
Science (1968) 159: pp. 1464-1467.
[Hawkes1992] Hawkes P W. The electron microscope as a structure projector. In [Frank1992]: pp.
17-38.
[Henry2005] Henry C R. Morphology of supported nanoparticles. Progress in Surface Science (2005)
80: pp. 92-116.
[Herman1973] Herman G T, Lent A, Rowland S W. ART : mathematics and applications. A report on
the mathematical foundations and on the applicability to real data of the algebraic reconstruction
techniques. J Theor Biol (1973) 42: pp. 1-32.
[James1999] James E M, Kyosuke K, Browning N D. Atomic resolution Z-contrast imaging of
interfaces and defects. JEOL News (1999) 34: pp. 16-19.
[Janssen2001(1)] Janssen A H, Koster A J, De Jong K P. Imaging the Mesopores in Zeolite Y with
Three-Dimensional Transmission Electron Microscopy Z. Stud. Surf. Sci. Catal (2001) 135: pp. 2144-
2151.
[Janssen2001(2)] Janssen A H, Koster A J, De Jong K P, Angew Y. Three-Dimensional Transmission
Electron Microscopic Observations of Mesopores in Dealuminated Zeolite. Chem (2001) 40: pp.
1102-1104.
[Jesson1995] Jesson D E, Pennycook S J. Incoherent imaging of crystals using thermally scattered
electrons. Proc. Roy. Soc. Lond. (1995) 449: pp. 273-293.
[Kak1985] Kak A C. Tomographic imaging with diffracting and non-diffracting sources. In Haykin S,
Array Signal Processing. Englewood Cliffs, N.J. : Ed. Prentice-Hall Englewood Cliffs (1985): pp.
351-428.
[Kak1988] Kak A C, Slaney M. Principles of Computerized Tomographic Imaging. New York : IEEE
Press, (1988).
[Kelly2003] Kelly K L, Coronado E, Zhao L L, Schatz G C. The optical properties of metal
nanoparticles: the influence of size, shape, and dielectric environment. Journal of Physical Chemistry
B (2003) 107: pp. 668-677.
79
[Klie2005] Klie R F, Zhu Y. Atomic resolution STEM analysis of defects and interfaces in ceramic
materials. Micron (2005) 36: pp. 219-231.
[Koster1992] Koster A J, Chen H, Sedat J W, Agard D A. Automated microscopy for electron
tomography. Ultramicroscopy (1992) 46: pp. 207-227.
[Koster1997] Koster J, Grimm R, Typke D, Hegerl R, Stoschek A, Walz J, Baumeister W.
Perspectives of molecular and cellular electron tomography. J. of Structural Biology(1997) 120: pp.
276-308.
[Koster2000(1)] Koster A J, Ziese U, Verkleij A Y, Janssen A H. Three-Dimensional Transmission
Electron Microscopy: A Novel Imaging and Characterization Technique with Nanometer Scale
Resolution for Materials Science. Journal of Physical Chemistry B (2000) 104: pp. 9368-9370.
[Koster2000(2)] Koster A J, Ziese U, Verkleij A J, Janssen A H, De Graaf J, Geus J W, De Jong K P.
Development and application of 3-dimensional transmission electron microscopy (3D-TEM) for the
characterization of metal-zeolite catalyst systems. Studies in Surface Science and Catalysis (2000)
130: pp. 329-334.
[Krivanek1995] Krivanek O L, Kundmann M K, Kimoto K. Spatial resolution in EFTEM elemental
maps. Journal of Microscopy(1995) 180: pp. 277-287.
[Kübel2005] Kubel C, Voigt A, Schoenmakers R, Otten M, Su D, Lee T C, Carlsson A, Engelmann H
J, Bradley J. Recent advances in electron tomography: TEM and HAADF-STEM tomography for
materials science and IC Applications. Microscopy and Microanalysis (2005) 11: pp. 378-400.
[Lanzavecchia2005] Lanzavecchia S, Cantele F, Bellon P L, Zampighi L, Kreman M, Wright E,
Zampighi G A. Conical tomography of freeze-fracture replicas: a method for the study of integral
membrane proteins inserted in phospholipid bilayers. Journal of Structural Biology (2005) 149: 87-98.
[Lawrence1992] Lawrence M. Least-squares method of alignment using markers. [Frank1992]: pp.
197-204.
[Lengeler2001] Lengeler B, Schroer C G, Benner B, Günzler T F, Kuhlmann M, Tümmler J,
Alexandre S. Simionovici, M Drakopoulos, A Snigirev, I Snigireva. Parabolic refractive X-ray lenses:
a breakthrough in X-ray optics. Nuclear Instruments and Methods in Physics Research A (2001) 467–
468: pp. 944-950.
[Lemoine-Goumard2006] Lemoine-Goumard M, Degrange B, Tluczykont M. Selection and 3D-
reconstruction of gamma-ray-induced air showers with a stereoscopic system of atmospheric
cherenkov telescopes. Astroparticle Physics (2006) 25: pp. 195-211.
[Madi2007] Madi K, Forest S, Boussuge M, Gailliègue S, Lataste E, Buffière J Y, Bernard D, Jeulin
D. Finite element simulations of the deformation of fused-cast refractories based on X-ray computed
tomography. Computational Materials Science (2007) 39: pp. 224-229.
[Marco2004] Marco S, Boudier T, Messaoudi C, Rigaud J L. Electron tomography of biological
samples. Biochemistry (2004) 69: pp. 1219-1226.
[McDonald2009] McDonald S A, Ravirala N, Withers P J, Alderson A. In situ three-dimensional X-
ray microtomography of an auxetic foam under tension. Scripta Materialia (2009) 60: pp. 232-235.
[Midgley2001] Midgley P A, Weyland M, Thomas J M, Johnson B F G. Z-Contrast tomography: a
technique in three-dimensional nanostructural analysis based on Rutherford scattering. Chem
Commun (2001) 10: pp. 907-908.
[Midgley2003] Midgley P A, Weyland M. 3D electron microscopy in the physical sciences: the
development of Z-contrast and EFTEM tomography. Ultramicroscopy (2003) 96: pp. 413-431.
80
[Miller1996] Miller M K, et al. Atom probe field-ion microscopy. Oxford University Press, Oxford,
(1996).
[Muller1941] Muller E W. Abreißen adsorbierter Ionen durch hohe elektrische Feldstärken. Die
Naturwissenschaften(1941) 29: pp. 533-534.
[Möbus2001] Möbus G, Inkson B J. Three-dimensional reconstruction of buried nanoparticles by
element-sensitive tomography based on inelastically scattered electrons. Applied Physics Letters
(2001) 79: pp. 1369-1371.
[Möbus2003] Möbus G, Doole R C, Inkson B J. Spectroscopic electron tomography. Ultramicroscopy
(2003) 96: pp. 433-451.
[Moriarty2001] Moriarty P. Nanostructured materials. Reports on Progress in Physics (2001) 64: pp.
297-383.
[Nellist1998(a)] Nellist P D, Pennycook S J. Subangstrom resolution by underfocussed incoherent
transmission electron microscopy. Phys. Rev. Lett (1998) 81: pp. 4156-4159.
[Nellist1998(b)] Nellist P D, Pennycook S J. Accurate structure determination from image
reconstruction in ADF STEM. J. Microsc (1998) 190: pp.159-170.
[Nellist1999] Nellist P D, Pennycook S J. Incoherent imaging using dynamically scattered coherent
electrons. Ultramicroscopy (1999) 78: pp. 111-124.
[Pappa2000] Pappa A, Tzamtzis N, Statheropoulos M, Fasseas C. The pyrolytic behavior of pinus
halepensis needles observed by transmission light microscopy and stereoscopy. Journal of Analytical
and Applied Pyrolysis (2000) 55: pp. 195-202.
[Parra Denis2008] Parra Denis E, Barat C, Jeulin D, Ducottet C. 3D complex shape characterization
by statistical analysis: Application to aluminium alloys. Materials Characterization (2008) 59 pp. 338-
343.
[Penczek1995] Penczek P, Marko M, Buttle K, Frank J. Double-tilt electron tomography.
Ultramicroscopy (1995) 60: pp. 393-410.
[Pennycook1990] Pennycook S J, Jesson D E. High resolution incoherent imaging of crystals. Phys.
Rev. Lett (1990) 64: pp. 938-941.
[PERLANT2000] Perlant F. Using stereo images for digital terrain modeling. Surveys in Geophysics
(2000) 21: pp. 201-207.
[PHOENIX] 3D computed tomography – Applications [online]. Germany : Phoenix X-ray. Available
on : http://www.phoenix-xray.com/en/applications/3d_computed_tomography (date accessed:
12/07/08)
[Podsiadlo1997] Podsiadlo P, Stachowiak G W. Characterization of surface topography of wear
particles by SEM stereoscopy. Wear (1997) 206: pp. 39-52.
[Podsiadlo1999] Podsiadlo P, Stachowiak G W. 3-D imaging of surface topography of wear particles
found in synovial joints. Wear (1999) 230: pp. 184-193.
[Radon1917] Radon J. Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser
Mannigfaltigkeiten. Berichte Verhandl. Königl. Sächs. Gessellsch. Wiss. Leipzig, Math-Phys. K1
(1917) 69: pp. 262-277.
81
[Reimer1995] Reimer L. Electron spectroscopic imaging, in energy-filtering transmission electron
microscopy. Berlin : Springer, 1995.
[Ress1999] Ress D, Harlow M L, Schwarz M, Marshall R M, McMahan Uel J. Automatic acquisition
of fiducial markers and alignment of images in tilt series for electron tomography. J. Electron Microsc
(1999) 48: 277-287.
[Ruff1995] Ruff B P, Marchant J A, Frost A R. Fish sizing and monitoring using a stereo image
analysis system applied to fish farming. Aquacultural Engineering (1995) 14: pp. 155-173.
[Russ2000] Russ J C. The image processing handbook. 3rd Edition, Piscataway : IEEE Press, 2000.
[Schoenmakers2005] Schoenmakers R H M, Perquin R A, Fliervoet T F, Voorhout W, Schirmacher H.
New software for high resolution, high throughput electron tomography. Microsc. Microanal (2005)
208: pp. 5-6.
[Tanaka1996] Tanaka S, Sugimura T, Takasaki K, Tsutsumi K. Digital terrain model from jers-l/ops
stereo-pairs and its verification using GSI numerical elevation map. Adv. Space Res (1996) 17:
pp.111-114.
[Tchelidze2006] Tchelidze P, Sauvage C, Bonnet N, Kilian L, Beorchia A, O‟Donohue M F, Ploton D,
Kaplan H. Electron tomography of amplified nanogold immunolabelling: Improvement of quality
based on alignment of projections with sinograms and use of post-reconstruction deconvolution.
Journal of Structural Biology (2006) 156: pp. 421-431.
[Thomas2001] Thomas P J, Midgley P A. Image-spectroscopy – I. The advantages of increased
spectral information for compositional EFTEM analysis. Ultramicroscopy (2001) 88: pp. 179-186.
[Tong2006] Tong J, Arslan I, Midgley P. A novel dual-axis iterative algorithm for electron
tomography. Journal of Structural Biology (2006) 153: pp. 55-63.
[Treacy1999] Treacy M M J. Pt agglomeration and entombment in single channel zeolites: Pt/LTL.
Microporous and Mesoporous Materials (1999) 28: pp. 271-292.
[Turner1992] Turner J N, Valdrè U. Tilting stage for biological applications. [Frank1992]: pp. 167-
196.
[Vanderesse2008] Vanderesse N, Maire E, Darrieulat M, Montheillet F, Moreaud M, Jeulin D. Three-
dimensional microtomographic study of widmanstätten microstructures in an alpha/beta titanium
alloy. Scripta Materialia (2008) 58: pp. 512-515.
[Venkatesh2008] Venkatesh B, Chen D L, Bhole S D. Three-dimensional fractal analysis of fracture
surfaces in a titanium alloy for biomedical applications. Scripta Materialia (2008) 59: pp. 391-394.
[Wang2000] Wang Z L. Transmission electron microscopy of shape-controlled nanocrystals and their
assemblies. Journal of Physical Chemistry B (2000) 104: pp. 1153-1175.
[Wang2003] Wang Z L. New developments in transmission electron microscopy for nanotechnology.
Advanced Materials (2003) 15: pp. 1497-1514.
[Weyland2001(1)] Weyland M, Midgley P A. Three dimensional energy filtered transmission electron
microscopy (3D-EFTEM). Proceedings of: Microscopy and Microanalysis (2001) 7: pp. 1162-1163.
[Weyland2001(2)] Weyland M, Midgley P A, Thomas J M. Electron tomography of nanoparticle
catalysts on porous supports: A new technique based on rutherford scattering. J Phys Chem (2001)
105: pp. 7882-7886.
82
[Weyland2001(3)] Weyland M, Thomas J M, Dunin-Borkowski R E, Midgley P A. High spatial
resolution tomographic reconstruction from STEM high angle annular darkfield (HAADF) images.
EMAG Proceedings Dundee (2001) 161: pp. 107-110.
[Weyland2004] Weyland M, Midgley P A. Electron tomography. Materials today (2004) 7: pp. 32-40.
[Weyland2005] Weyland M. On the limits of high angle annular dark field (HAADF) Tomography:
Electron Beam damage. Microsc Microanal (2005) 11: pp. 20-21.
[Withers2007] Withers P J. X-ray Nanotomography. Materials Today (2007) 10: pp. 26-34.
[Zheng2004] Zheng Q S, Braunfeld M B, Sedat J W, Agard D A. An improved strategy for automated
electron microscopic tomography. Journal of Structural Biology (2004) 147: pp. 91-101.
[Zeiss] ZEISS. Nano Technology Systems [on line]. Nanterre : ZEISS. Available on :
http://www.smt.zeiss.com/nts (date accessed 10/07/08)
[Ziese2002] Ziese U, Janssen AH, Murk JL, Geerts WJC, Van der Krift T, Verkleij AJ, Koster AJ.
Automated high-throughput electron tomography by pre-calibration of image shifts. J Microscopy
(2002) 205: pp. 187-00.
[Ziese2004] Ziese U, De Jong K P, Koster A J. Electron tomography: a tool for 3D structural probing
of heterogeneous catalysts at the nanometer scale. Applied Catalysis A: General (2004) 260: pp. 71-
74.
83
Experimental procedures
84
85
2.1. Adaptation of tip of holder
Any TEM tomography experience requires acquisition of hundreds of images over a tilt range
of about 130°, in order to get a correct reconstructed tomogram. Thus the first and major
experimental problem is to allow such a tilting capabilities within the gap of the pole pieces,
that is the objective lens of the microscope.
A first example of tip of holder is adapted to reach a tilt of ±90° [Kawase2007], to get
complete information, and to eliminate artefacts in the tomogram. The rode shaped specimen
was fabricated by FIB method, then attached at the tip of a modified specimen holder without
any supporting film, this arrangement enabled to freely rotate the rod-shaped specimen
(Figure 41).
A second example is an adaptation of a standard CM300 single tilt holder [Midgley2003],
shown in Figure 42(a), it allows a maximum tilt angle of 42° before contact with the objective
lens polepiece. The polepiece gap of the SuperTWIN objective lens in the CM300 FEG-
(S)TEM is 5.2 mm. In order to improve the tilt range, a Philips EM series single tilt holder
was modified by reducing the width of the holder by one-third to 4mm (Figure 42(b)).
Consequently the holder can be rotated fully 360° inside the polepiece gap with the tilt range
restricted to 60° by the shadowing of the specimen by the holder edge.
Figure 41 : (a) a rod-shaped specimen, after a tungsten deposition for the purpose of protection
against the gallium ion irradiation, the specimen was first fabricated in a plate form, a prism form next,
and finally a rod form by FIB. (b) A modified molybdenum specimen grid with the fixing position of
the rod-shaped specimen indicated by an arrow. (c) a modified JEM2200FS specimen holder allowing
±90° tilt. The original profile is marked by the dashed line [Kawase2007].
a) b) c)
W deposition
86
Figure 42: (a) A standard Philips CM single tilt holder, with a width at the specimen of 6mm. (b) A
modified Philips EM400 holder, original profile marked as dashed line, with a width at the specimen
of 4mm allowing complete rotation inside the 5.2mm gap of the SuperTWIN objective lens
[Midgley2003].
In the present work, we had to use a microscope equipped with a STEM device and HAADF
detector as justified previously (§.1.2.2.3). The microscope available at the CLYM (Centre
Lyonnais de Microscopie) is a JEOL 2010F, equipped with a high resolution pole pieces
(URP), allowing a restricted tilting amplitude of ± 20° (commercial specification; ± 25° in
practice when the specimen holder is kept very near the central setting (neutral position in
(X,Y)). To increase this tilt range, by far not enough for any tomography experiment, the
holder was modified in a simple way, owing to the existence of a removable and easily
exchangeable holder tip. Figure 43 illustrates this modification.
a) b)
87
Figure 43: a) simple tilt specimen holder provided by JEOL for the 2010F microscope; the original tip,
limiting the tilt capabilities to about 25°, has been removed and replaced by the home-made
commercial tip of holder which allows tilting up to 85°; b) typical sample deposited on a 3 mm
copper grid; c) reduction of the grid size to be mounted on the home-made holder tip.
The maximal tilt max permitted with this modified tilt is limited by the width of the holder (L
about 1.5 mm) and the gap between the upper and lower pole pieces, 2H = 2 mm for the ultra-
high resolution pole pieces of the JEOL 2010F instrument. According to the thickness of our
home made tip (e 0.5 mm), one finds easily than this geometry does not lead to any tilting
limitation (since max = arcsin[2H/(e+L)] = 90°). In fact connections between goniometer and
electronics component are too short (Figure 44) this makes impossible to achieve tilt range
more than ±80°, but it still be enough for a correct tomography experience. Figure 44
illustrates these tilting capabilities; it has indeed been possible to tilt up to 85°, in most cases
shadowing effects remain the limiting factor to go further (see Figure 45). It is worth noting
that the fragments of 3 mm grids which were used in this work were systematically cut in a
way that the grating is at 45° of the tilt axis to minimize the shadowing effect due to the bars
of the grid (i.e. the diagonal of the grid holes is perpendicular to the tilt axis).
aa))
3 mm
c)
sample
copper grid b)
1.5 mm
88
Figure 44: illustration of the tilt capabilities of the JEOL 2010F with the modified tip of the single tilt
specimen holder: a) -67°, b) 0°, c) +75°.
Several successive modifications of the holder tip were performed. The first model was made
on copper material, with a width of 1.5 mm (see Figure 46a), it allows achieving tilt angle of ±
80° only if the z position of sample is the eucentric of the polar pieces of the electron
microscope. The second model is less wide (0.7 mm) and was made on stainless material to
increase its strength (Figure 46b), it allows achieving ±80° for different z positions and
different observed areas of sample. The third model was made from stainless material with
cylindrical geometry of diameter of 1 mm, to be adapted to atom probe samples (Figure 46c)
as will be used in the §.3.4.
Figure 45: sample on carbon grid tilted at different angles: a) -67°, b) 0°, c) +75°.
a) b) c)
tilt axis
a) b) c) holder
goniometer electronics
connections
89
Figure 46: a) successive versions of the holder tip: a-b) rectangular geometry with (a) and without (b)
a notch; c) cylindrical geometry compatible with samples adapted to atom probe tomography. The first
holder in a) was made in copper, b) and c) are in non-magnetic steel.
2.2. Correction of drift
While tilting the specimen, it is practically almost impossible to avoid any drift of the area of
interest. Correction of such drifts can be carried out manually before each acquisition of
90
image by using the mechanical (X,Y) position controller. Also a fully automatic is thought to
be preferable, this manual adjustment is indeed fast and easy to perform without any
significant waste of time during the acquisition step. It is of course possible to correct the
sample drift electronically instead of mechanically: an image shift can be produced by
modifying the excitation of an adequate deflector lens. On the JEOL 2010F, the deflector N°
6 has two controls allowing an image shift to be produced along two perpendicular directions
Ox and Oy. Figure 47, Figure 48 and Figure 49 illustrate the effect of varying the excitation of
this deflector to produce controlled image shifts. Although this procedure appeared to be fully
reproducible and could be perfectly calibrated, we noticed that important variations of the
excitation of this lens N°6 produced a misalignment of the microscope in the STEM mode. It
was in practice not possible to use this method to centre the object while acquiring the tilting
series, and in most cased we have corrected the sample displacements manually.
In the TEM imaging mode however, the misalignment of microscope produced by the
excitation modification is weak, thus the electric correction can be realized. Lenses that are
used in TEM for shifting images, don‟t work in STEM mode, the only lenses that allowed
correction of drift of sample, is lens N°6, but it introduces important misalignment of the
microscope. The relationship between the variation of the excitation of deflector N°6 and the
image drift is linear and thus easy to calibrate according to:
dI = cM.Rβ.dD with Rβ = (7)
This equation expresses the relationship between the variation of the deflector excitation dI
(dI = (dix, diy), the two components along x and y axes) and the image drift dD = (dX, dY).
The rotation matrix R expresses the rotation between the X,Y directions of drift within the
image and the x,y directions associated to the deflector lens. The parameter cM is a calibration
constant which depends on the image magnification, and which can be simply measured in a
few minutes through a linear regression procedure. For an automatic correction of drift
automatically, in TEM mode, First, measure of drift is calculated by cross correlation,
between the last acquired image at previous tilt and the image test acquired at the present tilt,
then this drift is converted to variation of excitation of lenses of deflector, and introduced into
the electron microscope.
cos sin
-sin cos
91
Figure 47: STEM HAADF images of VNbC nano-precipitates (arrow), acquired at tilt of 0°, and
showing the image shift due to the modification of the "x" excitation of deflector N°6 (excitation value
equal to dix= 9477, 5381, and -507 mA from a) to c) respectively).
Figure 48: same as Figure 47 for the "y" excitation of deflector N°6: diy = 4324, -1052 and -5404 mA
from a) to c).
Figure 49 : montage showing the superimposition of series of micrographs from Figure 47 (a) and
Figure 48 (b), to show that the two directions of shift x and y are perpendicular, and related to the X,Y
directions of drift of the image by a rotation angle β (c).
2.3. Correction of focus
The major drawback of the STEM HAADF mode is its weak depth of focus, as explained by
Figure 50. For an inclined object (supposed to be flat as sketched in Figure 50), the image is in
a) b) c)
50 µm
a) b) c)
50 µm
a) b) c)
50 µm
90° x axis
y axis
X
Y
92
focus when the incident probe is properly converged at the entrance surface such as in Figure
50a); if no excitation change of the objective lens is operated during the scan, the probe
arrives out of focus at the bottom part of the object (Figure 50b), because of the inclination
angle θ. Ideally the probe should be refocused continuously during the scan as shown in
Figure 50c). Figure 51 illustrate this effect on a typical example. It clearly demonstrates that it
is practially not possible to acquire correct images without re-focussing the probe during the
scan within each single image. It has thus been necessary to write a dedicated routine in order
to allow such a "dynamic focus" procedure.
Figure 50: illustration of the poor depth of focus in the STEM image mode; a) the probe is focussed at
the upper part of an inclined flat object (tilt ); b) without any further settings, the probe is out of focus
at the bottom part of the object; c) ideal situation where the probe is re-focussed at each „height‟ of the
object.
Figure 51: VC precipitates on a carbon extraction replica used to illustrate the poor depth of focus in
the STEM-HAADF imaging mode. Whatever the excitation of the objective lens, only a small part of
the image is in focus (top, middle and bottom from a) to c) respectively; the tilt axis is as indicated).
2.3.1. Linearity of focus with angle of tilt
From simple geometry, the variation of focus f(h) between the optimal focus f(h) at line
defined by h and the optimal focus f(0) at the centre of image varies linearly with the tangent
of the tilt angle (Figure 52):
a) b) c)
tilt axis
a) b) c) θ
93
f(h) = f(h) - f(0) = d tan( ) (8)
where d is the distance of the scan line at height h from the tilt axis (supposed located
horizontally at the centre of the image, see Figure 52).
This obviously applies at the „edges‟ of the image at heights equal to +h and –h respectively:
Figure 53 shows that the corresponding focus variation focus, or equivalently the variation of
the excitation of the objective lens, varies linearly with tan( ).
In principle, equation (8) is enough to proceed with a fully automatic procedure as permitted
by the commercial software Xplore3D©
provided by the FEI company for its microscopes
[FEI]. Knowing the magnification, the focus difference f(h) from equation (8) is simply
converted into a variation of excitation of the objective lens after calibration, and the only
operation to be done by the user is to adjust the „neutral‟ focus f(0). Note further that this
value of f(0) should ideally not change during the tilt series if the „neutral‟ scan line is
perfectly adjusted on the tilt axis.
Figure 52: geometry of an inclined flat object (tilt angle ).
optical axis
bottom of image
top of image
θ
direction of acquisition
and correction of focus
d
tilt axis
h
h
sample tilted
at 0°
sample tilted
at θ
94
Figure 53: calibration of the focus variation (excitation of the objective lens) for an indicative tilt
series; a) for each tilt θ, the focus is manually adjusted to get respectively optimal focus on the bottom
and top of image; b) verification of the linear variation of the focus difference focus between top and
bottom of image with tan(θ).
From an experimental point of view we realize that the above strategy, although geometrically
correct as shown by Figure 52, is not practically applicable: a first reason is that is can be
tedious to adjust perfectly the position of the tilt axis at the median position of the image,
which breaks the symmetry with respect to the centre of image. A second reason is that a
manual focus is still required for the central „line‟ (f(0)), and it has been observed many times
that this value did not remain constant during the tilt series.
We thus preferred to adopt a more flexible approach consisting in two manual adjustments at
the „top‟ and „bottom‟ regions of each image, as detailed in the following sub-section.
2.3.2. Dynamic focus
From the above, the „dynamic focus‟ procedure requires that the scanning of the image is
performed parallely to the tilt axis in order to maintain the same focus conditions along each
„line‟. Furthermore, the acquisition has to be synchronized with the desired variation of focus.
On the JEOL 2010F electron microscope equipped with a RS232 connection, one main
problem is the low speed of the communication between an external computer and the
microscope processor. The RS 232 link is a standard series port of communication available
on PCs. In MS-DOS and Windows systems, the RS-232 ports are designated as COM1,
COM2, etc… Several tests were made, which led us to the conclusion that the microscope
cannot accept external commands at time interval less than about 50 ms: for more rapid
exchanges, the microscope misunderstands or simply ignores the commands. This low speed
represents a rather severe limitation of what can done. Let us consider for example an image
with size of 512x512 pixels image. With an elementary acquisition time of 10 µs/pixel,
acquiring a complete line requires about 5 ms; thus, the communication limit delay of 50 ms
implies that the focus variation cannot be performed more rapidly than roughly every ten
95
lines. This leads to about 50 updates of the focus throughout the whole image, which in
practice is fortunately enough to get an optimal focus in any place (see illustration in Figure
54). In these conditions, the image is completed after nearly 3 seconds.
From an algorithmic point of view, the procedure was written according to the following
steps:
(i) the focus is adjusted manually by the user for the upper part of the image
(designated as the „top‟ below), and the corresponding excitation Itop of the
objective lens is stored.
(ii) the same procedure is repeated for the lower or „bottom‟ part (Ibottom).
(iii) a linear excitation ramp is established between Itop and Ibottom, with 50 steps, and
the acquisition of the image is started in a synchronized way.
Figure 54: STEM HAADF image acquired with a dynamic focus correction every 10 lines; it is
required to have direction of tilt axis perpendicular to direction of scanning in order to keep
synchronisation between variation of focus and time of scanning of image.
2.3.3. Examples
direction of correction line by line of focus perpendicularly to tilt axis
1st focus change 2nd focus change
last focus change
ith focus change
10 lines 10 lines
10 lines
tilt axis 10 lines
96
The „dynamic focus‟ procedure has been incorporated in a computer routine developed under
the Digital Micrograph scripting language, as it will be detailed hereafter. Figure 55 shows its
application to 3 different examples treated in the course of this study. These micrographs
show that an acceptable correction can be obtained with this simple method.
Figure 55: examples of focus corrections applied to STEM-HAADF images of: a) Au@SiOx nano-
composites, b) VNbC nano-precipitates, c) Palladium nano-particles. In each case, the series of 3
images correspond respectively to the „focus top‟, „focus bottom‟ and „dynamic focus‟ conditions.
2.4. Software
2.4.1. aim of the software
In TEM tomography, the acquisition of the experimental tilting series is a critical step because
it may take a lot of time, during which the studied sample must remain unaltered (i.e. no
contamination, no irradiation, no shape or dimension modification). As a matter of fact, 5
a)
b)
c)
0.5 µm
1 µm
1µm
97
seconds of „true‟ acquisition per image (as roughly in the previous section), plus about 10
seconds for the manual adjustments of the „top‟ and „bottom‟ focus, plus about 15 seconds to
tilt from one image to the following (including shift correction) lead to an uncompressible
time of almost one hour for a tilting series of 100 images. In practice, it is not rare to send at
least twice this time to achieve the complete acquisition. It is then of the greatest importance
to optimise the acquisition in a computer-controlled way.
The microscope used in our study is equipped with the Digiscan hardware device
(Gatan©
)[GATAN_DigiScan], which allows the HAADF-STEM images to be recorded from
a dedicated Gatan©
plug-in installed within the Digital Micrograph (DM©
) software. For this
reason, it appeared judicious to develop routines with the scripting language available in DM.
This choice was all the more pertinent than (i) numerous scripts are freely available on the
internet (see for example [Mitchell2005, DM_SCRIPTS, GATAN]); (ii) internal DM
commands already exist to dialog with the microscope through the RS 232 link. Regarding
the latter point, the communication through the RS232 connexion with the external computer
has to be declared by typing the JEOL command „EXT 1‟ on the keyboard of the microscope.
Figure 56 shows the main introductive window of the „Tomo‟ script. Essentially, the program
intends to:
(i) define, through the „Tilt parameters‟ button, the experimental acquisition
conditions
(ii) establish the saving of the experimental data („Save Images‟ button)
(iii) drive the acquisition in a semi-automatic assisted way („Start Acquisition‟)
(iv) possibly manipulate the images (i.e. change the image format through the
„Managing Files‟ button)
These various steps, among which point (iii) is the most important, are described in the next
sub-section.
Figure 56: principal window interface is composed by five pushbuttons: „tilt parameters‟, „save
images‟, „start acquisition‟, „managing files‟, and close interface. All these pushbuttons open further
windows, except „Close interface‟ which closes the „EXT 1‟ communication between the microscope
and the computer.
98
2.4.2. The software ‘step by step’
The first step of the „Tomo‟ software concerns the definition of the „Tilt parameters‟ (Figure
57). It allows the tilt parameters to be initialised, i.e. the initial tilt, tilt step and the number of
images to acquire. For security reasons, minimal and maximal tilt angles are fixed, which
avoid an undesirable contact of the tip of holder with the pole pieces.
Figure 57: „Tilt parameters‟ interface allowing the initial tilt, tilt step and number of images to acquire
(or equivalently the final tilt to reach) to be defined. The minimal and maximal tilt angles are lower
and upper limits fixed to protect the pole pieces of microscope.
The „Save images‟ interface (Figure 58a) allows the directory where acquired images will be
saved to be defined; managing of these files can further be performed with the „Managing
Files‟ menu (Figure 58b), which allows the image format to be changed and the files to be re-
saved automatically after the acquisition.
Figure 58: „Save images‟ (left) and „Managing Files‟ (right) interfaces allowing elementary image
saving and manipulation.
The „Start acquisition‟ menu (Figure 59) allows the tilting series to be acquired. During this
procedure the magnification is verified continuously: it has to be constant during the
acquisition since some calibrations are magnification dependent (see eq. (1) for example).
99
At any stage of the procedure, the „tilt to be reached‟ value yields for the next image to be
acquired; when clicking the „Reach‟ button the goniometer is driven to the desired tilt
position. This operation, as most of the following ones, is performed by sending a JEOL
command to the microscope, as summarized in Appendix 1.
Figure 59: „Start acquisition‟ interface to control iteratively tilting of sample, correction of focus, and
saving images.
We have estimated the mechanical errors of the goniometer to less than 0.5°, and the tilt
command is repeated to reduce this error. It should however be mentioned that the tilt values
used in the phase of reconstruction are the actual ones.
The controls in the „Correct shift versus previous image‟ frame, also fully functional, have not
been used according to the previous remark that these adjustments may lead to a
misalignment of the STEM imaging mode. In fact the drift is corrected roughly and manually,
100
by keeping the area of interest centred within the field of view. The automatic drift correction
can however be used in the TEM imaging mode, where misalignment effect is negligible.
The next step is the „Dynamic focus‟ frame. Focus is manually adjusted „in live‟ respectively
on the „top‟ and „bottom‟ of the image, assuming the scanning is exactly performed parallely
to the tilt axis. These focus, or more precisely excitation values are stored and used for
synchronising a focus ramp with the acquisition. Once the pixel acquisition time has been
chosen by the user (8 s in the example shown in Figure 59), the total time for one image
(„Current time for a single loop‟) is updated. In our preliminary tests, we have allowed to
generate several full scanning runs, thus the „Time of the Loop(s)‟ value can be independently
chosen. In practice, the program drives directly the acquisition of the image through the
Digiscan hardware device (Gatan©
)[GATAN_DigiScan], and there is no need to run several
loops.
As already said, the corrections of focus and drift are time consuming, thus the total duration
of the tomography experiment takes generally 2 to 3 hours for acquiring about 130
1024x1024 images. It could be reminded that such a long exposure time to electrons can
generally not be used in the case of biological materials, whereas most of „material science‟
samples tackled in this study did not suffer from any significant and detectable beam
damages. There is however an exception with the Au@SiOx nano-composites, for which an
extended stereoscopic approach was employed to minimize the acquisition time (see §.3.2).
References of chapter 2 [GATAN_DigiScan] Gatan. DigiScan II [online]. Germany : Gatan. Available on :
http://www.gatan.com/products/sem_products/products/digiscan.php (date accessed: 12/07/08 )
[DM_SCRIPTS] Digital Micrograph(tm) Script Database [online]. Austria : Graz University of
Technology. Disponible sur : http://www.felmi-zfe.tugraz.at/dm_scripts (date accessed: 12/07/08)
[GATAN] Gatan [online]. Germany : Gatan. Available on : http://www.gatan.com (date accessed:
12/07/08)
[Kawase2007] Kawase N, Kato M, Nishioka H, Jinnai H. Transmission electron microtomography
without the “missing wedge” for quantitative structural analysis. Ultramicroscopy (2007) 107: pp. 8-
15.
[Midgley2003] Midgley P A, Weyland M. 3D electron microscopy in the physical sciences: the
development of Z-contrast and EFTEM tomography. Ultramicroscopy (2003) 96: pp. 413-431.
[Mitchell2005] Mitchell D R G, Schaffer B. Scripting-customised microscopy tools for digital
micrograph. Ultramicroscopy (2005) 103: pp. 319-332.
[FEI] FEI.Scanning electron microscope [online]. The Netherlands : FEI company. Available on
: http://www.fei.com (date accessed: 12/07/08)
101
Applications
102
103
3.1. VC nanoprecipitates
A high purity model alloy FeCV (0.5 ± 0.01 wt% of carbon and 0.2 ± 0.01 wt% of vanadium),
was investigated in the laboratory for the purpose of a thorough characterization of the
precipitation state after different dissolution treatments [Acevedo-Reyes2007]. The final goal
of this study concerns a detailed analysis of the microstructure of vanadium carbide
precipitates, in terms of volume fraction and size distribution, which plays a significant role in
final mechanical properties of the material.
These VC nanoprecipitates were used in the present tomography approach as a test sample for
two main reasons: (i) for developing and calibrating our home-written script dedicated to
semi-automatic acquisition (focus correction, sample tilting,…), (ii) for various test
procedures, including getting used to run the softwares of 3D reconstruction and visualisation.
3.1.1. Experimental background: sample preparation
The FeCV alloy was elaborated by the MHP group at the E.N.S.M, Saint Etienne, France; it
was a solution treated at 1000°C for 30 minutes and water quenched to room temperature. In
order to study the dissolution of carbides, a heat treatment was designed to precipitate almost
all the vanadium and obtain precipitates as large as possible. For that purpose, specimens
were heated at 700°C for 10 h (nucleation and growth in ferrite) in vacuum (quartz
encapsulation), then they were heated at 800°C for 10 days (coarsening in austenite), and
finally slowly cooled down to room temperature [Acevedo Reyes2005].
During the precipitation study, thin foils were prepared but most of TEM observations were
performed on extraction replicas, in order to avoid magnetic effects due to the Ferritic matrix.
To elaborate replica of carbon on a polished section (Figure 60), a metallographic cut is
chemically attacked to dissolve the iron matrix and make visible the precipitates. The degree
of attack is determined by the expected particle size; it must be high enough to reveal well the
particles, however the precipitates to observe should not react with the reagent of attack, and
should remain embedded in the matrix. A low concentration of nital (~0.4%) has been used as
classically employed for extraction of replicas for extraction of replicas of carbides, nitrides
and other oxides in ferritic matrix (or martensitic). Then carbon is sprayed on the treated
surface to fix precipitates. This operation is carried out by evaporating carbon from two
graphite electrodes in contact in the vacuum. Afterwards the matrix in contact with the film of
carbon, up to about 20 nm thick, is dissolved by immersing the sample in a bath of ethanol,
and each ~ 4 hours, drops of nitric acid are added close to the sample. After the unsticking of
104
replica, they are rinsed respectively in baths of: ethanol, methanol, and again ethanol. Finally
they are deposited on copper grids to be observed in TEM.
Figure 60 : steps of preparation of carbon replicas. Precipitates on the film of carbon are extracted
from the attacked matrix: (a) sample after mechanical polishing, (b) chemical attack by nital to reveal
precipitates, (c) deposition of a carbon film, (d) chemical attack of the underlying matrix, (e) replica of
extraction ready to be observed [Acevedo-Reyes2007].
3.1.2. Interest of electron tomography characterization
As expected, the vanadium carbides are essentially crystalline [Epicier2008], and we then
have to consider the problem of the validity of the projection requirement described in section
§.1.2.2.1. Even under conditions where Bragg diffraction does not change significantly the
contrast of the precipitates, it has been shown in §.1.2.2.2.Figure.5 that diffraction contrast in
BF images may appear while tilting (depending on orientation of crystalline structure of VC
nanoprecipitates), which prevents a true quantification. However, for HAADF images, no
diffraction contrast appears, because this imaging mode is insensitive to crystalline orientation
(§.1.2.2.2.Figure.7). The relationship between intensity and the projected atomic density is
thus preserved, as result, HAADF is well adapted for a quantitative electron tomography of
crystalline samples. The aim of this approach is to study the 3D morphology and determine
the real volume and the equivalent radius of these nanoprecipitates.
3.1.3. Results
STEM HAADF series of VC nanoprecipitates are acquired over a tilt range of about 130°,
with a step of 1.5°. Images were aligned by cross correlation, then the tilt axis is calculated by
following the trajectory of some details (i.e. particles themselves), and finally images are
rotated to align the tilt axis along Oy. The difference of atomic number between carbon grid
(Z=6) and V (Z=23) is the origin of the good chemical contrast on images (Figure 61).
Volume rendering of the reconstructed tomogram of VC nanoprecipitates is shown in Figure
a) b) c) d) e)
105
62, while projections of the tomogram on xy, xz, and yz planes are reported in Figure 63.
Note that the back projected views in Figure 63.b)-c) confirm that all particles lie roughly on
the same plane, as expected for precipitates supported on an extraction replica, and elongation
effect is observed along Oz direction. 3D statistical measurements are summarized in Figure
64. Also mean error between equivalent radius of VC nanoprecipitates, calculated
respectively from a tomogram and a 2D projection is estimated in this example to 17%
(Figure 65), and finally the morphology of the largest particle is highlighted in Figure 66.
Figure 61 : aligned series of projections of VC nanoprecipitates acquired at different tilt in the STEM
HAADF imaging mode: (a) -58°, (b) -41.5°, (c) -23.5°, (d) -7°, (e) 9.5°, (f) 27.5°, (g) 44°, (h) 60.5°, (i)
75.5°. Tilt axis is (Oy).
x
a) b) c) d)
200 nm
y
e) f) g) h)
i)
106
Figure 62 : volume rendering of a tomogram of VC nanoprecipitates (Figure 61) reconstructed by the
ART algorithm (number of iterations = 14 and relaxation coefficient t = 0.07) (see §.1.5.3), TOMOJ
[Messaoudi2007]) and visualized by AMIRA software [AMIRA].
Figure 63 : projection of the tomogram respectively along (a) xy, (b) yz, and (c) xz.
a) b) c)
200 nm
y
x
y
z
z
x
107
VC particles x(pixel) y(pixel) z(pixel) volume(voxel) equivalent radius(pixel) radius(nm)
1 225 260 97 42105 21,58 98
2 167 234 104 632 5,32 24
3 172 198 99 277 4,04 18
4 75 178 99 3773 9,66 44
5 60 168 105 897 5,98 27
6 200 153 94 2533 8,46 38
7 181 144 95 3930 9,79 44
8 215 140 99 4870 10,52 48
9 200 139 97 307 4,18 19
10 201 127 97 342 4,34 20
11 221 129 101 184 3,53 16
12 214 128 93 292 4,12 19
13 180 121 106 4669 10,37 47
14 197 119 98 168 3,42 16
15 197 105 98 4571 10,3 47
Figure 64 : (a) labelling of VC nanoprecipitates (STEM HAADF image acquired at tilt=0.5°); (b)
results of an automatic segmentation of tomogram in order to measure the real volume and equivalent
radius (sphere approximation) of VC particles.
Figure 65: a) measure of area of VC nanoprecipitates in a projection acquired at 6.5° tilt, in order to
obtain an approximation of equivalent radius of nanoprecipitates; b) superposition of yellow and pink
circles on the projection in a), their radius is calculated respectively from a) and from segmentation of
the tomogram (Figure 62).
1
2
3 4
5 6
7 8
9
10
11
12
13
14
15
a)
b)
200 nm
1
2
3 4
5
6
7
8
9
11
10
12 13
14 15
a) b)
200 nm
108
Figure 66 : different magnified views of surface rendering [AMIRA] of tomogram of a VC particle (on
the centre), to highlight its 3D morphology.
3.1.4. Conclusion
VC crystalline nanoprecipitates have been characterised by an adapted approach of electron
tomography in STEM-HAADF mode, to highlight accurately their 3D morphology and to
measure their 3D localisation, real volume, and equivalent radius. In the study of precipitation
of VC nanoparticles [Acevedo-Reyes2007], significant measures of size from 2D images are
carried out then correlated with thermal and thermodynamical state of precipitation.
Generally, accuracy of this correlation can be improved by measuring sizes directly from the
tomogram.
200 nm
109
3.2. Au@SiOx
The second example studied in this work concerns hybrid nanocomposites made of an
assembly of gold nanoparticles with larger silica-based particles. These materials are
synthesized in collaboration between the LPCML (Laboratory of Physico-Chemistry of
Luminescent Materials, UMR CNRS 5620) at the University of Lyon and the MATEIS
laboratory at INSA de Lyon [B. N. Diop, M. Martini, theses in progress].
Properties of nanoparticles are often different from those of bulk materials; they strongly
depend on size, shape and surface configuration [Cai12001, Hadjipanayis1994]. Inorganic
and metallic nanoparticles have several technical applications as catalyst, colloids, templates,
probes, and carriers [Ghica2007, Liu2006, Kim2006, Zhelev2006, Guari2003, Alonso2005].
Core shell nanocomposites facilitate bioseparation of organic molecules, incorporation of
fluorescent and organic dyes during synthesis, with dual functions of magnetic and
fluorescent properties. They are used in various fields such as cell labelling [Nagao2008,
Vuu2005], biosensing [Dubus2006], or drug delivery [Holzapfel2006, Guo2006].
Among the various systems that can be synthesized, Au@SiOx nanocomposites are of optical
interest. On the one hand, silica is an attractive support for metals because it is mildly acidic,
relatively inert, and has good mechanical properties [Zhu2005]. The synthesis and assemblies
of silica spheres [Bergna1994, Stoeber1968, De2000] are of significant importance for the
development of advanced nanotechnology. Several materials have been successfully
incorporated into silica spheres for different applications (medical [Donbrow1992,
Langner1990, Caruso1998], catalytic [Wang2002, De-Sousa2003], magnetic particles
[Lyubchanskii2003, Koerdt2003, Bizdoaca2002, Murray2001, Wiesendanger1997,
O‟Brien2002], metal ions [Lyubchanskii2003, Bizdoaca2002, O‟Brien2002, Haes2001,
Moroz2000, Jiang2003, Eradat2001]). On the other hand, gold nanoparticles in the range of
1–100 nm size have unique electronic, optic, and catalytic properties [Ionita2008, Daniel2004,
Tsunoyama2004, Pengo2003, Daniel2005, Ghosh2007], they are used in medicine as carriers
of drugs, bio-markers, or in the treatment of several diseases [Liu2006, Salata2004,
Huang2007].
3.2.1. Synthesis of Au@SiOx nanocomposites
The synthesis involves micro-emulsions. In fact, the native micellar structure (oil in water,
presence of surfactant and co-surfactant) defines the final silica morphology, and the
localization of gold particles with respect to the silica ones depends on the order of adding
nanoreactors (alcoxysilanes) as shown in Figure 67.
110
An optimised feedback on the synthesis conditions requires a detailed geometrical and
chemical analysis of the final product. It‟s particularly important to assess precisely the
position of the gold nanoparticles inside or at the surface of the silica, depending on the
synthesis conditions. According to the nanometre size of these objects, a 3D approach in
HAADF (High Angle Annular Dark Field) imaging mode in STEM (Scanning Transmission
Electron Microscopy) appears to be an elegant way for that purpose. A drop of an alcoholic
solution of the Au@SiOx nanocomposites have been deposited on a half carbon grid glued on
the „tomographic‟ holder tip. Figure 68 shows a comparison of TEM and HAADF images on
both systems illustrated by Figure 67, and which will be designated as “external Au@SiOx”
and “internal Au@SiOx” respectively. In the bright field TEM images (Figure 68. a-c), gold
particles appear much darker than the silica ones owing to the fact that the contrast is mainly
due to the strongest absorption of gold particles. In the HAADF images (Figure 68. b-d),
where the Rutherford-scattered signal is collected with an annular detector, the contrast is
reverse since heavier atoms scatter more efficiently the incident electrons, which leads to a
„Z-contrast‟. A quantitative analysis of the HAADF intensity will be presented in §.3.2.4.
Figure 67: two types of geometry of Au@SiOx nanocomposites. (a), (b) and (c) are steps to synthesize
respectively a silica core, then a silica shell and finally gold particles on the surface of the silica shell
(M. Martini, thesis in progress, INSA-Lyon). (d) and (e) are respectively steps to synthesise gold
nanoparticles before the silica ball: in this geometry, gold particles are expected to be inside the silica
sphere.
d) Au@DTDTPA colloidal solution e) Si(OEt)4 TEOS addition
a) Si(OEt)4 TEOS b) H2N(CH2)3 Si(OEt)3 APTES addition
c) Au@DTDTPA addition
111
Figure 68 : BF TEM and HAADF imaging of both “external” and “internal” Au@SiOx systems. (a)-
(b): same area of “external” Au@SiOx particles deposited on a holey grid of carbon and visualized at
low magnification, respectively imaged in TEM-BF and STEM-HAADF mode. (c)-(d): respectively,
BF and HAADF images of the “internal” Au@SiOx nanocomposites.
3.2.2. Interest of stereoscopy characterization
As previously mentioned, the aim of our 3D approach is to quantify the distribution of gold
nanoparticles with respect to the silica balls at a nanometre resolution. For that purpose, 2D
imaging measurements are not appropriate since they could easily lead to false or inaccurate
results (Figure 69). The most adapted solution is thus a tomography or a stereoscopy
approach.
Our first attempt was to reconstruct the 3D morphology by an electron tomography approach.
But during acquisition, an increasing contamination layer grew around the silica balls (Figure
70). A second problem concerned the stability of the particles during the observations: it was
100 nm
50 nm c) d)
a) b)
a) b) c)
112
not possible to ascertain that the arrangement of silica particles remained intact during a long-
term acquisition (2 to 3 hours), according to the fact that those particles are simply aggregated
through weak interaction forces. It‟s thus decided to proceed in a simpler and faster way as a
stereoscopy approach, which can be applied whatever the used imaging mode (BF-TEM or
STEM-HAADF).
Figure 69 : basic illustrations showing the interest of a 3D approach to measure accurately distances,
volume and surface density of nanogold particles with respect to the silica balls, (a) 3D representation
of gold nanoparticles and (b) corresponding 2D projection along the Z direction; (c) 3D representation
of silica and gold nanoparticles, and (d) corresponding Z‟ projection. These examples illustrate the
artefacts visible in both 2D projections. For example in d), the central gold particle could be though to
be inside the silica ball, and the bottom right one at its surface: both particles are in fact outer the silica
sphere as seen in c).
Figure 70 : evidence for rapid contamination during STEM observations: (a) HAADF image acquired
at tilt = –65°, (b) HAADF image recorded after 20‟ at tilt = 15°: the halo around the silica particles
arises from contamination, due to a prolonged exposure to the electron beam.
100 nm a) b)
c) d) Z
x
y
y
x
SiOx
a) b)
y
x Z
x
y
Au
113
The stereoscopy approach has been introduced in §.1.3.2. Although it requires in principle
only two images acquired at different tilt for the object of interest, about ten images have been
recorded in the present study, in order to increase the accuracy of the image alignment and the
calculation of the tilt axis position of (i) and (ii). Regarding the geometry of the
nanocomposites, several shadowing effects involving essentially gold nanoparticles but also
larger silica „balls‟ made some of the images inaccurate for positioning some of those
particles: the availability of several images within a large tilt range has thus enabled a better
quantitative analysis.
According to the different synthesis routes followed to elaborate the two kinds of
nanocomposites studied in the present work, we will labelled hereafter as:
(i) Au@„homogeneous‟SiOx for the materials developed by Diop (thesis in progress,
Figure 67d-e), where the silica particles are realized in one step and are thus
expected to be chemically homogeneous.
(ii) Au@„core-shell‟SiOx for the materials developed by Martini (thesis in progress,
Figure 67a-c), where the silica particles are realized in two steps and are thus
expected to present an internal „core-shell‟-type structure.
3.2.3. Discussion of the imaging mode
In this context of simply locating the gold nanoparticles relatively to the silica particles, the
fact that the TEM mode does not fulfill the projection requirement is not very important, since
diffraction effects will not strongly affect the accuracy of positioning the particles. It could
even be concluded that the TEM mode presents the advantage of a greater contrast for the
gold particles than in STEM-HAADF (see Figure 68c) compared to Figure 68d), where the
smallest gold particles exhibit a poor signal-to-noise ratio). The comparison of TEM and
STEM images in Figure 71 is a further evidence of that: as general rule, the gold
nanoparticles exhibit a better contrast in the TEM BF image. However, diffraction contrast is
clearly visible: some small gold particles (arrows „S‟) appear with a very dark intensity
(because they are strongly diffracting), while a larger particle „L‟ has a lighter intensity. This
is another evidence that the TEM BF mode does not fulfill the projection requirement unlike
STEM HAADF which is insensitive to crystalline orientations.
2 nm
114
Figure 71 : comparison of TEM and HAADF images of the Au@SiOx nanocomposite elaborated by
Diop (thesis in progress, Figure 67d-e). a) TEM bright field micrograph showing some gold
nanoparticles with a high contrast because of strong diffracting conditions (Au „S‟), compared to
others (e.g. „L‟). The inset shows a single gold particle imaged under high resolution conditions along
the [110]fcc direction. b) STEM-HAADF of another area, showing a direct relationship between
contrast and “mass-thickness”.
Despite the better contrast in BF-TEM imaging, most of the series of images were mainly
acquired in the STEM HAADF mode. It will indeed be seen that a quantification of the
HAADF intensity is possible (according to the incoherent scattering collected in this mode),
which presents the advantage of a chemical analysis, as will be detailed in §.3.2.6.
Although gold particles are much smaller than silica ones (1 to 5 nm for Au particles to be
compared with 25 to 100 nm for the silica ones), their HAADF intensity remains higher than
that of the silica ones. According to equation (1) in §.1.2.2.3, it is easy to relate the HAADF
intensity scattered by a given volume of matter V to the atomic density i of a given chemical
specie „i‟, that is the number of atoms ni in an elementary volume:
IHAADF V i iZix
(9)
For any quantitative evaluation of the HAADF intensity, it is clearly necessary to know the
value of the exponent x with accuracy. As already reported in §.1.2.2.3, this parameter varies
from about 1.6 to 2, depending on the collection conditions. Previous calibration experiments
in the laboratory have established that for the nominal settings of the HAADF imaging mode,
the equivalent camera length leads to an angular collection range of 70 – 186 mRad. Under
these conditions, the exponent value has been determined to be x = 1.85. This value will then
be used in the following. We can thus justify easily that the integrated intensity of gold
particles remains higher than that of the silica particles: assuming a typical gold particle with
a mean diameter Au of say 5 nm, and a silica particle with SiO2 equal to 100 nm, the volume
of matter intercepted by a probe of typically 1 nm in diameter (or Full-Width at Half
Maximum FWHM, assuming a gaussian intensity profile) when located at the centre of the
particle is of the order of (see Figure 72a):
SiO2
Au ‘S’ SiO2
Au
1100 nnmm
Au ‘L’
a) b)
115
VAu = 3.9 nm3
VSiO2 = 78.5 nm
3 (10)
In the case of gold, the atomic density Au is simply 4/(4.1)3 0.058 atoms/nm
3 (4 atoms in
the f.c.c. structure of gold, with aAu = 0.41 nm). In the case of non-crystalline silica, several
literature data indicate that the partial atomic densities ρSi and ρO for the silicon and oxygen
species are respectively about 0.021 and 0.042 atoms/nm3 [Bell1972,Gladden1990]. From
these values, the maximal intensities at the center of each type of particles can be
calculated from relation (9):
IHAADF(Au) = VAu [ρAuZAu1.85
]
IHAADF(SiO2) = VSiO2 [ρSiZSi1.85
+ ρOZO1.85
] (11)
That is, according to ZAu = 79, ZSi = 14 and ZO = 8 :
IHAADF(Au) 738
IHAADF(SiO2) = 372 (12)
This indicative calculation confirms that the gold nanoparticles will appear significantly
brighter than the silica „balls‟, which insures that they will be detected in any geometrical
configuration, as illustrated by the graphical display in Figure 72b). Note that this image is
qualitatively very comparable to experimental micrographs, such as reported in Figure 70 and
Figure 71 for example.
Figure 72 : HAADF imaging of Au@SiO2 nanocomposites: a) simplified geometry showing the
volume of interaction of a probe crossing a spherical particle (note that the electron beam is supposed
to be parallel and that no beam spreading throughout the particle is considered). b) display of the
expected contrasts resulting from intensity calculations according to a) for various situations: (1) and
(2): an external 5 nm gold particles at the surface of a 100 nm SiO2 „ball‟, (3) gold nanoparticle inside
the SiO2 sphere.
FWHM
particle (Au or SiO2)
electron probe
1
2
3
50 nm
a) b)
116
3.2.4. Internal localisation of gold particles in the Au@‘homogeneous’SiOx nanocom-
posites
We will focus first on the Au@„homogeneous‟SiOx nanocomposites in which gold
nanoparticles are expected to lie inside the silica spheres. A first series, consisting of 9
experimental images acquired with a step tilt equal to 7.5° between 73.5° and 13.5°, shows
18 silica and 64 gold particles (see Figure 74). After having aligned all images and
determined the position of the tilt axis, the coordinates of few particles are extracted from all
projections in order to illustrate the quality of alignment (Figure 75).
The projected positions (X,Y), as well as the projected radius R of silica and gold particles
that have been used for the 3D analysis, were extracted according to home developed
software on Digital Micrograph (© Gatan) language (Figure 73). It should be reminded that
we intend here to describe all particles as perfect spheres, the position of which in each image
will be characterized by the set of data (X ,Y ,R ), where X ,Y are the coordinates of the
particle at tilt , and R its radius (expected to be constant whatever ). Hence, the final 3D
position (X,Y,Z,R) is deduced (see §.1.3.2.Figure 21).
As already said, the fact that we have several images for the extended stereoscopic approach
offers the possibility to select the best images for analysing a given particle, according to the
fact that superimposition problems make its positioning delicate in several images (this is
especially true for the smallest gold particles). Nevertheless, some particles, although clearly
visible on one or two images of the series, could not be accurately analysed due to these
„shadowing‟ effects. Consequently, for most silica and gold particles, the positions were
extracted from 3 experimental projections among all available images (in this example about
33 % of the experimental series).
Figure 73: a) a DM GUI is developed to load images, then to extract radius and 2D position of
nanoparticles semi-automatically (b); and finally projections can be recalculated at the same
experimental tilt (c).
a) b) c)
117
Figure 74 : acquired series of Au@„homogeneous‟SiOx on STEM HAADF imaging mode at different
tilt, images are aligned, then tilt axis is calculated, and images are rotated to make tilt axis parallel to
(Oy) axis: (a) -73.5°, (b) -66°, (c) -58.5°, (d) -51°, (e) -43.5°, (f) -36°, (g) -28.5°,(h) -21°, (i) -13.5°, (j)
For sake of clarity, the first image is enlarged -73.5°.
10 nm
x
y
a) b) c)
d) e) f)
j)
g) h) i)
50 nm
118
Figure 75 : (a) (x,y) positions of some nanoparticles extracted from aligned projections, tilt axis is
calculated by following trajectory of some nanoparticles, and images are rotated to make tilt axis
parallele to (Oy) axis, (b) in aligned images, x(pixel) coordinate of nano particles, is linear with cos( -
tilt), is the elevation of the particle at tilt of 0°.
When the 3D analysis has been completed, all particles were then re-projected (Figure 76),
and to estimate error of accuracy of position of nanogold particles, calculated projections are
superimposed on the experimental ones (Figure 77), from such results, the positioning
accuracy could be evaluated, by plotting the evolution of the error representing the distance
between the calculated centre and the experimental one, as a function of the tilt for the „best‟
and the „worst‟ Au particle (Figure 78). The maximal error found is 4 nm, it can be
considered as the „resolution‟ of our stereoscopy analysis; this represents also the upper limit
of the accuracy of positioning the gold nanoparticles.
0
100
200
300
400
500
600
-1 -0,5 0 0,5 1 1,5
0
100
200
300
400
500
600
0 20 40 60 80
x(tilt)=f(cos( -tilt))
y(tilt) a)
b)
y(tilt)=g(tilt)
tilt(°) cos( -tilt)
119
Figure 76 : projections of Au@SiOx nanocomposites calculated at the same tilt like experimental
projections in Figure 74: (a) -73.5°, (b) -66°, (c) -58.5°, (d) -51°, (e) -43.5°, (f) -36°, (g) -28.5°,(h) -
21°, (i) -13.5°, (j) -73.5°.
10 nm x
y
j)
a) b) c)
d) e) f)
g) h) i)
50 nm
120
Figure 77 : superposition of calculated and experimental projections, to show the high precision of the
calculated projections: (a) -73.5°, (b) -66°, (c) -58.5°, (d) -51°, (e) -43.5°, (f) -36°, (g) -28.5°,(h) -21°,
(i) -13.5°, (j) -73.5°.
10 nm
a) b) c)
j)
x
y
d) e) f)
g) h) i)
50 nm
121
Figure 78 : accuracy of x position of two nanogold particles, that have respectively maximal and
minimal error, it‟ is measured from images in Figure 74 by comparing experimental with calculated
projections at different tilt. Triangular and square marks illustrate error of x(nm) position of nanogold
particle that have respectively maximal and minimal error.
In this example, with an accuracy of 4 nm, one can use different colours in order to sort the
position of gold particles: either inside the silica balls, on their surface or „outside‟ (Figure
79). It can be observed that, as expected from the synthesis route of the
Au@„homogeneous‟SiOx nanocomposites, the very large majority of gold nanoparticles lie
inside the silica particles. Only one appears to be consistent with a location at a surface, and
15 (over 64) are classified as being „outside‟. If nanoparticles are strongly aggregates, it
becomes difficult to select all particles, because some of themes are hidden by others.
Visualisation of a reconstructed volume from Figure 74 is carried out by Amira software
(Figure 80). The meaning of „outside‟ must be precised here: obviously, no particle can lie in
the vacuum without any support. Some gold nanoparticles will however appear „outside‟ in
the sense than the silica particle to which they are necessarily attached could not be located
because of the shadowing effects already mentioned.
error of x(nm)
tilt(°) 0
0,5
1
1,5
2
2,5
3
3,5
4
-80 -60 -40 -20 0
122
Figure 79 : colored particles on projection series (from Figure 74): blue for gold particles inside the
silica balls, green for gold particles on their surface and red for gold particles „outside‟.
d) e) f)
g) h) i)
j)
50 nm
a) b) c)
x
y
123
Figure 80 : visualization of 3D position of Au@SiOx nanocomposites assuming its spherical geometry.
Some of gold particles are hung in the vacuum, this does not have any physical significance, but in
fact only because silica particles to which they are associated, are not selected.
From this analysis, one can draw out several interesting statistics regarding the relative
positon of the gold and silica particles, the mean distance between internal gold particles, the
average number of particles per silica one, ect… From a statistical point of view, all these
data can serve to characterize the microstructure quantitatively, and they can be correlated to
the synthesis conditions. The next figures illustrate different kinds of 3D measurements.
Figure 81 reports the histogram of gold inter-particles distance inside the same silica particle,
while Figure 82 shows a relatively narrow distribution of the volume fraction of gold inside
the silica particles. In order to increase the statistical meaning of our measurements, several
other areas of the for the Au@„homogeneous‟SiOx nanocomposite have been analysed in 3D,
as summarized in Figure 83. Thus, from all these experimental data, Table 1 summarized the
dimensional measurements that have been performed on more than 200 gold particles related
to 42 silica spheres.
Figure 81: histogram of distance between gold nanoparticles inside the silica balls for the
Au@„homogeneous‟SiOx nanocomposite.
50nm
0
1
2
3
4
5
6
7
8
9
3635333129272524222016151311974
distance (nm)
number of particles
124
0
1
2
3
4
5
0 0,0002 0,0004 0,0006 0,0008 0,001 0,0012 0,0014
Figure 82 : histogram of volume fraction of gold nanoparticles for the Au@„homogeneous‟SiOx
nanocomposite.
Figure 83 : different areas from the same sample of Au@„homogeneous‟SiOx nanocomposite are
characterized by a stereoscopy approach, results are added in order to obtain 3D statistics, (a)
experimental projection acquired on STEM-HAADF at tilt 0°, (b) superposition of experimental and
calculated projection, (c) classification of gold nanoparticles, (d) experimental projection acquired on
STEM-HAADF at tilt 0°, (e) superposition of experimental and calculated projection, (f) classification
of gold nanoparticles.
On the surface Outside Inside
a) b) c)
d) e) f)
50 nm
volume fraction
Distribution of volume fraction
125
Series 1 2 33 4
Number of gold particles 64 60 53 30
Number of silica particles 18 7 12 5
Average distance between gold particles inside silica particles (nm)
22.54 20.91 16.2 20.62
Average of volume fraction 7.73.10-4 1.54.10-3
7.63.10-4 2.10-3
Average number of gold particles inside silica particles
2.88 6.28 4.9 6.75
Average number of gold particles on the surface of silica particles
0.06 0.43 0.27 0
Average diameter of silica particles (nm)
57 54 51 54
Number of Gold particles 207
Number of Silica particles 42
Average distance between Gold particles (nm) 20.06
Average of volume fraction 0.00078
Average number of Gold particles inside Silica particles 4.74
Average number of Gold particles on the surface of Silica particles
0.19
Average diameter of Silica particles (nm) 54
Table 1 : 3D statistics established from 4 series or areas from the same Au@„homogeneous‟SiOx
nanocomposite: a) per series, b) mean results.
3.2.5. External localisation of gold particles in the Au@‘core-shell’SiOx
nanocomposites
The second type of Au@SiOx nanocomposites studied in this work is expected to exhibit gold
nanoparticles attached at the surface of silica spheres (see synthesis route summarized in
Figure 67a-c). We will focus here on the particles shown in the montage of Figure 84 and
Figure 85.
The positions and radii of the gold nanoparticles and the (unique) silica particle have been
determined according to the Digital Micrograph © routine introduced in the previous sub-
section (§.3.2.4.). The sets of data (X ,Y ,R ) obtained for each particle at different tilts
allows the 3D position (X,Y,Z,R) to be determined.
b)
a)
126
Although it can be suspected that the silica particle of interest presents some elliptic
deformation on most of the projections in Figure 84 or Figure 85, we first consider that it can
be described as a perfect sphere, with a mean radius of 64 ±6 nm.
Figure 84 : series of projections of Au@„core-shell‟SiOx nanocomposite acquired at different angles
of tilt on STEM HAADF imaging mode, and aligned with tilt axis is parallel to Oy.
50 nm x
y
-24.5° -19.5° -14.5°
9.5° -4.5° 0°
5.5° 10.5° 15.5°
20.5° 25.5°
127
Figure 85 : series of projections of Au@„core-shell‟SiOx nanocomposite acquired at different angles
of tilt on TEM imaging mode, and aligned with tilt axis is parallel to Oy.
The first treatment of the series, assuming the spherical shape, leads to the conclusion that
some gold nanoparticles lie significantly inside the silica one, as shown in Figure 86. Since
analysing the exact 3D shape of the silica particle is impossible without a complete
tomographic approach, we can simply re-consider the relative positions of the gold particles
with respect to the silica surface by considering a “thickness” of its surface of about 12 nm
(that is, the silica sphere is considered as having a radius ranging from 58 to 70 nm). The
second treatment is summarized in Figure 87: we clearly see that all gold nanoparticles are
confidently identified as being located at the surface of the silica particle, as expected from
the synthesis route, this is highlighted in Figure 88.
50 nm x
y
-24.5° -19.5° -14.5°
9.5° -4.5° 0°
5.5° 10.5° 15.5°
20.5° 25.5°
128
Figure 86: a) localisation of gold nanoparticles: blue, green, and red colours correspond to gold
nanoparticles localized respectively inside, on the surface, and outside of the silica sphere; b) distance
between gold nanoparticles and the silica centre.
Figure 87: a) localisation of gold nanoparticles; the green colour corresponds to gold nanoparticles on
the surface of the silica particle; b) distance between gold nanoparticles and the centre of the silica
particle assuming contact with each gold nanoparticle.
Figure 88: different views to show that all nanogold particles analysed in Figure 87, are localized
between two spherical silica particles which have respectively minimal and maximal radius, measured
from projection series in Figure 85.
radius (nm)
2.5
2.3
3.2
3.6
2.7
4.5
63.6 6
61.6 5
69.4 4
71.5 3
75.1 2
64.3 1
distance to SiOx centre (nm) Au particles
1
2
3 4 5
6 inside
on the surface outside
50nm
b)
1 1
2
3 4 5
6
inside
on the surface outside
61.1 6
59.3 5
66.2 4
67.9 3
2
59.8
SiOx radius assuming contact (nm) Au particles
50nm
72.4
a)
b)
a)
5500 nnmm
1
2
6
3 4
5
129
3.2.6. Chemical quantification of the core-shell structures of silica particles in the
Au@‘core-shell’SiO2 nanocomposites
The silica particle analysed in the previous subsection (§.3.2.5) clearly exhibits a radial
intensity variration which can be qualified as a „core-shell‟ structure. According to the
synthesis route employed to elaborate the Au@„core-shell‟SiOx nanocomposites Figure 67(a-
c), an internal structure is expected within the silica particles: the central region consists in a
TEOS-based „dense‟ silica, while the periphery is made of a less-dense APTES-based
compound, in which one oxygen bond in the tetraedric configuration of the SiO4 molecule is
replaced by a more complex branch.
Figure 89 show STEM and TEM images of this silica particle, and associated diametral
intensity profiles (without intersecting any gold nanoparticle) are also reported. Although the
visual inspection of the STEM micrograph in Figure 89a) supports the idea that the core of the
particle is slightly denser than its periphery, this variation is less obvious in the TEM intensity
profile (Figure 89d) than in the HAADF profile (Figure 89b): this shows that STEM-HAADF
is more sensitive to chemical variations comparing to TEM.
We intend here to analyse quantitatively this contrast variation, with the aim of providing a
local measurement of the density of the shell region of the silica particle ( shell).
As previously said, the central region of the particle is expected to be relatively pure silica,
with a density core 2 g.cm-3
[Graf2003, Gladden1990]. In order to measure the absolute
value of the external density ( shell), we must provide an absolute calibration of the intensities
in the HAADF image. The presence of gold nanoparticles with different sizes but a well
defined chemical composition (thus density gold) will serve to establish this calibration.
We will re-examine the basic equation (relation (9) in §.3.2.3) relating the HAADF intensity
to the atomic number of the scattering atoms. For that purpose, we will use the formalism
introduced by Treacy and Rice [Treacy1989], who have shown that the integrated HAADF
intensity Iint of spherical homogeneous particles can be related to their projected surface S
according to:
(Iint)1/3
= C S1/2
(13)
130
where C is a constant depending on the experimental conditions (illumination parameters,
collection range, acquisition time, dynamic of the image essentially).
We can easily understand this equation with the following argument: the HAADF intensity
integrated over the whole particle is evidently proportional to its volume (in the case of the
incoherent scattering), thus (Iint)1/3
is simply proportional to its mean size (e.g. diameter for a
spherical object), as it is the case for the square root of the surface S.
To establish this relation, it is obviously necessary to correct the integrated intensity from any
background (in the case of supported particles), and this will be required to analyse the
intensity of the gold particles which are superimposed on the silica particle.
This „Treacy and Rice‟ analysis has thus been applied to 7 gold particles visible in the
HAADF image of Figure 89a). Figure 90 shows that the evolution of Iint1/3
vs. S1/2
is relatively
well fitted by a linear relation, which confirms that the nanoparticles can be considered as
perfect spheres in a good approximation. From this treatment, the constant C in equation (13)
is directly deduced. Thus, for any gold particle of known volume and atomic density ( Au =
0.058 atoms/nm3as calculated in section §.3.2.3), we can deduce the other multiplicative
constant k expressing the proportionality of the elementary HAADF intensity for a single
atom Iatom from any atomic specie Zi:
Iatom = k Zi
1.85 (14)
Under the experimental conditions used in this study, we found k = 0.0093.
Therefore, all ingredients can be brought together in order to simulate the expected HAADF
intensity profile across a silica sphere of radius R, consisting of a core with outer radius Rcore
made of pure silica (with partial atomic densities ρSi and ρO for the silicon and oxygen species
are respectively about 0.021 and 0.042 atoms/nm3
as previously reminded), and a shell with
an unknown density ρshell. A simple trial-and-error procedure has allowed to estimate the
„best‟ density value allowing to fit as close as possible the experimental profile, as shown in
Figure 91.
We obtain shell = 0.75 core for this best fit, with an error of 3% (according to the Euclidian
distance between both profile).
131
This work clearly confirms that the shell is less dense (reticulation less efficient in the APTES
SiOx compared to the TEOIS-based silica), and gives a numerical value for its density at a
nanometric scale.
Figure 89: detail of a silica particle in the Au@„core-shell‟ SiO2 nanocomposite. a) STEM HAADF
image, and b) corresponding intensity profile through a diameter line; c) TEM micrograph and d)
corresponding profile as in b).
Figure 90 : linear regression between (Iint)1/3
and S0.5
, with Iint is the integrated HAADF intensity of all
pixels within the projected gold particle (crystalline) after a background subtraction, and S is the
projected area of the gold particle (assumed to be spherical).
c) d)
a) b)
50 nm
50 nm
(atm(1/3))
(pixel unit)
132
Figure 91 : superposition of the experimental and simulated profile of STEM HAADF intensity IHAADF
through a diameter of the projected sphere of SiO2 core-shell.
3.2.7. Conclusion
We have studied in TEM a relatively simple case of nanocomposites, consisting in a mixture
of gold and silica (nano-)particles with a spherical shape, which are sensitive to beam damage
and/or contamination effects. It was shown that a stereoscopy approach in STEM-HAADF
imaging mode can replace advantageously a complete tomographic analysis for the
characterisation of the relative 3D distribution of both populations of particles.
A positioning accuracy of about 4 nm has been obtained for gold nanoparticles with a
diameter of 1 to 5 nm.
The 3D analysis has allowed statistics of sizes and relative distribution of the gold and the
silica particles to be established in 3D, which allows a feedback on the synthesis conditions
and provides quantitative parameters for their characterization. On some of the areas studied
in this work, it was checked that traditional 2D-measurements gave false inter-particles
distances of gold (variation up to 25%), and over-estimate the number of internal gold
particles by a factor up to 4, since unique projections do not allow to discern internal and
external gold nanoparticles.
Also, it has been demonstrated that the STEM HAADF mode can be well adapted to chemical
quantification approaches. In the presence of gold nanoparticles used as internal calibration
tools, a quantitative simulation of the intensity profile of a silica „sphere‟ with a core-shell
structure has been possible, enabling to estimate the density of the material at a local
nanometric scale.
core= 2 g.cm-3
‘pure’ dense TEOS-silica core
shell
Less-dense APTES silica shell
Experimental profile
Simulated profile
distance (pixel)
IHAADF(a.u.)
133
3.3. Pd (bi-pyramidal, nano-rod)
3.3.1. Justification of the study
In the first part of this chapter (§.3.1) we have seen that nano-particles deposited on a
supporting film (i.e. VC carbides on a carbon extraction replica) could easily be characterized
by TEM tomography. We will extend this approach to a more dedicated case, in order to
explore the possibilities of the technique in terms of “measuring” the geometry of the
particles. “Measuring” has here a quantitative meaning: for example, determining angles
between crystallographic facets, indexing those facets, estimating their surfaces,…
The case of palladium nano-particles used for specific catalysis applications
[Berhault2007(1)] has been chosen for that purpose.
Generally speaking, the morphological control of metallic nano-particles (Ag, Au, Pd, Pt)
with a complex geometry (cubes, rods, icosahedrons, tetrahedrons, bi-pyramids [Wiley2006])
opens the way to new applications in photonics [Maier2003], electronic devices [Huang2001],
biological or chemical detectors [Sudeep2005], and catalysis [Fukuoka2001, Berhault2007(2),
Ziese2004]. Obviously, reasonable estimations of the shape of nanoparticles remains possible
using conventional 2D imaging, assuming simultaneous crystallographic analysis of their
structure and symmetries [Wang2000, Wang2003]. But this approach becomes difficult for
objects with complex shapes and structures, and requires anyway to explore several
orientations. Hence, electron tomography appears to be the most elegant and efficient way to
achieve accurate measurements and avoid errors and inaccuracy that are difficult to overcome
in classical 2D imaging. The experiments were conducted in the STEM-HAADF mode, since
it remains preferable owing to the crystallographic nature of Pd particles (fcc phase with a =
0.39 nm) which will induce diffraction contrast effects.
3.3.2. Synthesis of Palladium nanoparticles
We summarize here the conditions under which the palladium particles were synthesized prior
to this work [Berhault2007(1)]. Palladium tetrachloropalladate (Na2PdCl4) (98%),
cetyltrimethylammonium bromide (CTAB), sodium borohydride (NaBH4) (98%), and sodium
ascorbate ( 98%) were purchased from Sigma Aldrich. All aqueous solutions of palladium
tetrachloropalladate, CTAB, NaBH4, ascorbic acid, and sodium ascorbate were freshly
prepared before use.
134
In order to control nucleation and growth steps, the preparation of Pd nanocrystals was
divided into two steps: 1) preparation of Pd isotropic particles used as seeds, 2) injection of
Pd seeds into a growth solution to produce Pd nanocrystals. Then, in the first step, Pd seeds
were prepared following a method developed previously [Nikoobakht2003]. 50 mL of an
aqueous 0.5 mM Na2PdCl4 solution was mixed with 25 mL of an aqueous 0.3 M CTAB
solution prepared at 30°C. Next, 6 mL of an ice-cold aqueous 0.01 M NaBH4 solution was
added quickly under vigorous stirring. The solution turned dark immediately after the
borohydride addition, indicating metallic palladium nanoparticle formation. The palladium
suspension was stirred for 15 min. The seed solution was used 2 h after its preparation.
In the second step, the growth solution was obtained by mixing 50 mL of an aqueous 1.0 mM
Na2PdCl4 solution with 50 mL of an aqueous 0.08 M CTAB solution under gently stirring at
30°C. After 5 min of mixing, 0.7 mL of an aqueous 0.08 M sodium ascorbate solution was
added. Finally, 60 µL of the seed solution was injected. The initial orange red solution
changed progressively in 30 min into a dark solution indicating the reduction of the metallic
precursor.
3.3.3. Results
3.3.3.1.Pentagonal rods
Several tilt series have been acquired, which have allowed numerous particles to be
reconstructed. A large number of them appear to be pentagonal rods, as was previously found
in the literature [Berhault2007(2)] and illustrated in (Figure 92). Such a particular shape
occurs owing to multiple twinning in the fcc structure of Pd, leading to pseudo-five fold
symmetries along an elongated axis parallel to [110] [Berhault2007(2)]. In (Figure 92.c), a
perfect pentagon is superimposed to the edge-on projection of the rod. Note that deviations
from the ideal pentagonal shape are minor and remain within less than 2 nanometers, which
should roughly correspond to the spatial resolution of the 3D reconstruction. According to the
relations (4 to 6) given in §.1.6.3), one can easily estimate the resolution dx and dz in the x and
y directions on the one hand, and z direction on the other hand. With a particle equivalent
diameter of about 50 nm, 130 images acquired up to a maximal tilt angle 65°, one finds
dx = 1.2 nm. Calculating the elongation factor exz from relation (6) gives the z-resolution dz =
2 nm.
135
Figure 92 : reconstruction of a pentagonal rod; (a): selection of images recorded every 15° from a
HAADF tilted series acquired on a Pd nano-particle between -65 and 65° by step of 1° (tilt axis
parallel to y-axis); (b): volume rendering of the reconstructed particle; (c): nearly edge-on projection:
the dotted line shows a perfect pentagon superimposed for comparison.
3.3.3.2. Bipyramids
The most interesting feature regarding these Pd particles is indeed the evidence of particles
exhibiting triangular 2D projections. According to a previous study [Wiley2006] by
conventional TEM imaging, these particles could be bi-pyramids rather that platelets with a
triangular section. More than 10 such particles were reconstructed, and they all appear to
-65° -50° -35°
25° 40° 55°
a)
x
y
10 nm
10 nm 10 nm
-50° -40° -30°
-20° -5° 10°
b) c)
136
present a complex bi-pyramidal shape as in the representative case shown in (Figure 93 and
Figure 94). Figure 92a) shows the surface rendering and various slices of the reconstructed
volume which clearly evidence the two elementary pyramids with a common triangular basis
(Figure 94. b). Based on this 3D approach, it is expected that quantitative information, such as
angle measurements and facets indexing should be possible from the tomogram. This is
indeed the case: the complete crystallographic analysis of this particle shows that it consists in
a 'top' pyramid made of {100} facets intersecting along <100> edges, and a 'bottom' one made
of {111} facets intersecting along <101> edges (Figure 94. c). The common triangular basis
of both pyramids is a (111) plane, its edges belonging to both pyramids being along the [110],
[-101] and [0-11] directions. Further illustrations are shown in Figure 94. d-e), where the
particle is tilted to low-index axes in order to allow angle measurements. Note that both
pyramid summits are truncated roughly parallelly to the basal (111) plane. This analysis
shows that not only the projected angles measured from the tomogram are in good agreement
with the values expected from crystallography for the corresponding directions in the fcc
structure, but also the tilting angles themselves are those expected in order to view the particle
along the indicated low-index axes.
137
Figure 93: Pd nano-particle exhibiting triangular projections (bottom line): selection of images
recorded every 10° from a typical HAADF tilted series acquired between -50 and 71° by step of 1°
(tilt axis parallel to y-axis).
25 nm
138
Figure 94: 3D analysis of the Pd particle shown in Figure 93. a): surface rendering of the tomogram.
b): stretched superposition of slices extracted every 6 nm from the tomogram. c): geometrical model
used to describe the particle; the summits of the top and bottom pyramids are labeled A and B
respectively. d): tomogram seen along the [111] axis (horizontal direction = [1-10]); note that the A
summit appears to be flat, i.e. truncated. e): tomogram rotated 54.5° around the [1-10] axis to be seen
along the [001] direction (theoretical tilt angle = 54.44°), showing that both summits are truncated;
two angles of 90° can be measured as expected from crystallography. f): tomogram after a 180°
rotation from position d), thus showing the B summit.
3.3.4. Conclusion
The present work has illustrated the interest of a tomographic approach for the 3D analysis of
the shape of Palladium nano-particles using the STEM-HAADF imaging technique in a TEM.
Objects with sizes ranging from 10 to 50 nm were deposited on a carbon supporting film and
observed along hundreds of projecting directions in an angular range up to 130° in a single-tilt
configuration. A 3D-resolution of about 2 nanometers was obtained; this result could be
slighlty improved with the use of a double-tilt specimen holder [Mastronarde1997,
Penczek1995, Tong2006]. It has been shown that the 3D shape of those particles is readily
reconstructed; volumes have been identified, such as pentagonal rods and bipyramids. Such a
3D morphological study at a nanometer level may be of great interest, for example to follow
the morphological evolution of nano-particles at different stages of a catalysis reaction.
139
3.4. AlZnMg
3.4.1. Context of the study
Up to now, most tomography experiments that have been performed in this work were
essentially used to describe or measure geometric factors, such as the shape of particles, and
the relative positions of different types of relatively well-separated objects. It was thus judged
interesting to tackle a problem where TEM-tomography can really serve to reconstruct the
„inside‟ of a material, and not only its extrenal form. We have chosen a problem related to
precipitation in an Al-alloy for that purpose. As will be seen herebelow, this system has been
extensively studied previously by a combination of techniques, including Conventional TEM,
Small-Angle X-Ray Scattering (SAXS) and Atom Probe Tomography, which gives us good
„reference‟ data for an objective discussion of our own results.
3.4.2. Literature survey on the characterzation of the precipitation state in the Al-Zn-
Mg alloy used in this study
Commercial Al–Zn–Mg alloys, such as the 7108.50 reference with a nominal composition
Al–2.35 at.%Zn–0.92 at.%Mg–0.05 at.%Zr, are extensively used for automotive applications
where weldability is a concern. The investigated tempered state is named T7: it consists in a
water quenching after a solution treatment of 30 min at 480°C, followed by 2 h at room
temperature and 6 h at 100°C, then ageing for 6 h at 170°C. It contains precipitates with a
composition close to that of the equilibrium -MgZn2 phase, that is less than 10% Al. Two
populations are indeed encountered: metastable platelets labelled '-MgZn2, and mainly
relatively equiaxed stable -MgZn2, spherical-shaped precipitates. Both kinds of precipitates
have an average radius of 4 nm and a volume fraction of 2.5% [Dumont2005]. Effect of
welding on the 3D distribution and chemical composition of Zn-Mg precipitates in aluminium
alloys, was studied in the thesis of Myriam Nicolas, by using TEM, APT, and SAXS
techniques [Nicolas2002]. In fact the thermally affected zone contains a gradient of
temperature, which leads to precipitates with different sizes (the higher the temperature, the
bigger the precipitates (Figure 95).
140
Figure 95: microstructure of an Al-Zn-Mg alloy after welding: (a) schema showing the temperature
gradient, (b) TEM images acquired at different areas, show that size of nano precipitates is slightly
increasing with the temperature, (c) distribution of size of nanoprecipitates measured from TEM
images (adapted from [Nicolas2002]).
The chemical composition of precipitates in an Al–Zn–Mg alloy is studied by (3D) atom
probe analyses, developed in the University of Rouen [Deconihout1995]. Data analyses were
conducted using dedicated softwares (Table 2), and 3D rebuilt volumes for the T7 state is
presented in Figure 96. To measure precipitate volume fraction, precipitates have been
gathered into a single population (Table 3), the measured value is 2.44% ± 0.28.
Table 2: Overall composition of the material obtained by APT measurements in the T7 materials
[Dumont2005].
a)
b)
c)
Rmean= 4.03 nm Rmean= 4.4 nm Rmean= 4 nm
141
Figure 96: typical 3D reconstructed volumes of the T7 state obtained by the atom probe tomography
[Dumont2005].
Table 3: Precipitate composition and volume fraction obtained by APT for the T7 state of ageing
[Dumont2005].
Transmission electron microscopy was used to measure distribution of size and volume
fraction of nanoprecipitates. For that purpose, the foil thickness had to be estimated
simultaneously to the image analysis of the precipitates [Williams1996, Donnadieu1999]. The
convergent beam diffraction method was used to measure the sample thickness [Kelly1975,
Allen1981], however due to limitations in convergence of the microscope used, reliable
thickness measurements could not be obtained in areas thinner than 50 nm. In this case, the
sample thickness in the thinnest regions was extrapolated assuming a linear variation of the
thickness near the edge of the thin foils. The chosen characteristic size is the average between
the long and short axis of the measured precipitates. For the T7 state, the resulting volume
fraction is 2.54 ± 0.3%. This „TEM‟ value appears to be very close to that determined from
the APT technique, we can consequently consider a value of 2.5 ± 0.3% as a valid reference
to which we will compare our TEM-tomography evaluation.
142
3.4.3. Preparation of AlZnMg specimen for tomography
Contrarily to all previous specimens used for TEM tomography in his work, it is required here
to prepare the material under the form of a thin foil. Although thin foils can actually be used
for tilting tomography (e.g. [Barnard2006, Inoke2006, Kaneko2008]), the geometry of a
traditional thin foil obviously limits the maximal tilt due to the significant increase of
thickness above nominally 70° (see Figure 97).
Figure 97: illustration of the drastic thickness increase at large tilt when using a thin for tilting
tomography in the TEM.
Thus, one can find in the literature several attempts to prepare thin samples with a cylindrical
shape in order to keep the thickness constant while tilting: indeed, a Focused Ion Beam (FIB)
device has most frequently used for that purpose (for example: [Bender2007, Katoa2008,
Kawase2007, Koguchi2001, Ozasaa2004]).
Since previous Atom Probe experiments were already performed on the Al-Zn-Mg alloy
[Nicolas2002], it appeared logical to work on samples prepared for this technique. The
preparation route consists in cutting blanks from ingots, and thinning them into needles by
standard electro-polishing at 15 V at room temperature. Usually, APT needles are mounted on
nickel-based capillary tube (F. Danoix, personal communication). We then had to adapt our
home-made specimen holder to receive these needles, and fix strongly their nickel support to
avoid motion due to magnetic effects in the microscope. Figure 37 shows how the TEM
holder has been modified.
electrons electrons
70°
143
Figure 98: tip of the TEM specimen holder adapted for APT „needles‟
Several APT tips are thus been prepared in the T7 state. The first step was then to check
whether they could be efficiently used for a tomography experiment. Figure 99 shows that
different problems were encountered, which can be summarized as follows:
(i) it was observed that the extreme „tip‟ of the samples got oxidized very rapidly,
which decreased strongly the signal-to-noise ratio of the (Mg,Zn)-based
precipitates, as illustrated by Figure 99.a-b). This point will be re-discussed (see
§.3.4.5)
(ii) some of the tips appeared to be strongly bent (see Figure 99.c-d). In one case the
sample could not serve for the experiment, but in the case presented in Figure
99.c), a good quality tilting series (i.e. Figure 99.d) could surprisingly be
acquired
(iii) endly, Figure 99.e) shows the last problem encountered: a rather clean and thin
tip was observed, but exempt of any precipitate!
As can be seen from these illustrations, it has been possible to find adequate samples from
which successful tilting series could be recorded. Since the whole sample has a crystalline
nature, it is further interesting to comment briefly about the interest of the HAADF imaging
mode.
Figure 100 is a comparison of two images acquired with a tilt difference of 3.5° in BF-TEM
(a-b) and STEM-HAADF (c-d) respectively. It clearly appears that diffraction effects limit
seriously the contrast of the precipitates in the conventional BF imaging mode: first Bragg
ssaammppllee
11 ccmm
ssaammppllee ((AAPPTT nneeeeddllee))
nniicckkeell
ccaappiillllaarr
ffiixxiinngg ssccrreeww
144
fringes (bent coutours) decreases their visibility, and it can even been noticed that some
particles almost vanish.
Figure 99: problems encountered with AlZnMg specimens for the TEM tomography; (a-b) stringly
oxidized tip; (c-d) bent tip; e): nice tip but without any precipitate.
20 nm
a) b)
c) d)
e)
100 nm 50 nm
50 µm 20 nm
20 nm
145
Figure 100 : BF and STEM-HAADF projections of the same area of a top showing MgZn2
precipitates in the aluminium matrix (T7 state). (a) and (b) are respectively TEM images acquired at -
29° and -32.5°, which correspond to HAADF micrographs in (c) and (d) respectively. A clear
inspection reveals the presence of a grain-boundary, as indicated by arrows in b) and (d). Note that the
diffraction effects near the grain-boundary and in the matrix (especially in the top-right grain) degrade
significantly the visibility of the precipitates in the BF images.
In the HAADF mode, the relative contrast between the precipitates and the matrix is not
significantly dependent on the sample orientation. The precipitates appear brighter than the
matrix because of a slightly stronger scattering efficiency of the MgZn2 phase compared to
that of the aluminium matrix. This can easily be understood from the atomic arrangement of
both crystalline structures: as it was already done in the case of the Au@SiO2 nanocomposites
(§.3.2.3), one can evaluate the elementary HAADF intensity IHAADF(MgZn2) and IHAADF(Al)
for a volume V equal to unity according to the relation (9) recalled here for clarity:
IHAADF V i iZi1.85
(15)
the MgZn2 phase has an hexagonal structure P63/mmc with a = 0.522, c = 0.857 nm
[Komura1980], with 4 Mg atoms (ZMg = 12) and 8 Zn atoms (ZZn = 30) in a cell volume of
0.202 nm3: the atomic partial density of the Mg and Zn species are then respectively ρMg =
19.8 nm-3 and ρZn = 39.6 nm-3
, thus:
a) b)
c) d)
diffraction
contrast (matrix)
110000 nnmm
a) c)
b) d)
146
IHAADF(MgZn2) = 23345 nm-3 = IHAADF(Mg) + IHAADF(Zn) (16)
In a similar way, the Al (ZAl = 13) atomic density in f.c.c. aluminium (4 atoms in a cube of
volume (0.405 nm)3) is ρAl = 60.2 nm-3
, which leads to:
IHAADF(Al) = 6926 nm-3 (17)
These two relations show that the - and closely related ‟-precipitates will be imaged with a
higher intensity than the surrounding matrix, as was observed consitenly in all HAADF
micrographs from Figure 99 and Figure 100.
3.4.4. TEM Results
Four different series have been acquired on 2 APT tips; among them two have been
performed on the extreme end of the needle. Original micrographs were generally recorded at
a direct magnification of 400 K, thus about 100-140 images were obtained in each case over
an angular interval ranging between 110 and 140°.
The first series acquired at the end of the tip is illustrated by Figure 101. It can be seen that
rather few precipitates, less than 30, are present in the area of interest. Obviously one has to
search for a compromise between the thickness of the sample and the number of precipitates.
The tomogram has been calculated using 14 iterations of the ART algorithm [Herman1973]
(Figure 102.a). Once reconstructed the volume can be back-projected and compared to any of
the experimental projections (Figure 102.b): this montage allows to appreciate the gain in
contrast permitted by the 3D approach, which will improve the accuracy in measuring the size
and distribution of the precipitates.
Figure 103 is another part of the same sample that has been successfully reconstructed. In the
micrograph of Figure 103.a), crystallographic alignments of precipitates are indicated by
arrows: they do correspond to the '-MgZn2 precipitates with a platelet-like shape, as
described in the §.3.4.2. These observations will be further discussed in chapter 4. Moreover,
another series (the second one obtained from the end of a tip) will be described in the next
section (§.3.4.5).
From this tomography approach, more than 200 precipitates have been analysed in 3D. The
distribution of size and volume fraction of these (Zn-Mg) particles was measured from
segmentation of tomograms, and the obtained results are shown in Figure 104. We found a
value of the mean radius of precipitates equal to 4 nm, and the volume fraction can be
estimated to 2.35%. Referring to the previous TEM and SAXS work by Dumont et al.
147
[Dumont2005] (Figure 104.b), it can be concluded that a very good agreement has been
obtained.
Figure 101 : series of projections of Al-Zn-Mg alloy acquired at different angles of tilt on STEM
HAADF imaging mode, and aligned with tilt axis is parallel to oy. (a) -67°, (b) -56°, (c) -45°, (d) -33°
, (e) -11°, (f) 11°, (g) 33°, (h) 55°, (i) 75°.
a) b) c)
d) e) f)
g) h) i)
20 nm
x
y
148
Figure 102: analysis of the HAADF series from Figure 101; (a) volume rendering of the reconstructed
tomogram, using the Amira software [AMIRA], (b) corresponding experimental projection obtained at
a tilt of -1°for comparison: note that the particles are highlighted in the tomogram (a).
Figure 103 : illustration of an other area analysed in 3D; (a) typical HAADF STEM image from the tilt
series. Arrows indicate alignments of platelets-like precipitates (see text for details). (b): (xOy), (xOz)
and (yOz) projections of the reconstructed tomogram illustrating the 3D shape of the tip.
20 nm
20 nm
a) b)
a) b) 10 nm
149
Figure 104: histogram of size distribution of Zn-Mg nanoprecipitates as measured by STEM electron
tomography (a) and by (b) TEM [Dumont2005].
3.4.5. Towards a comparison between TEM and APT tomography
As explained in the §.3.4.3, we have been using samples with a geometry totally adapted to
possible APT. It was thus tempted to try a complementary approach in TEM and Atom Probe
Tomography.
Such a combined approach was recently applied to an Al-Ag system [Arslan2008]. In
principle, this strategy allows a true complementary analysis in the way that the APT may
complete efficiently the information at a higher spatial resolution than achieved in TEM.
Reciprocally, TEM can help in the calibration of dimensional measurements as performed in
the APT.
The only way to conduct both experiments was then to perform the TEM tomography first,
then bring back the specimen in the GPM laboratory in Rouen for the APT work. A major
difficulty came from the oxidation of the very near end of tip, as already mentioned and
further illustrated in Figure 105. Figure 105.a) is an HAADF-STEM image showing the oxide
layer around the aluminium matrix. This has not been a major problem for the TEM
tomography since it clearly appears that some intensity thresholding can easily „erase‟ the
external oxide form all images. However, this AlOx oxide layer has necessarily to be removed
for the APT experiment since, as a non-conductive material, it makes it impossible to
evaporate conveniently the atoms for the tomographic analysis. The specimen was thus
a) b)
Rmean = 4.0 nm fV = 2.35 %
Rmean = 3.6 nm
= 1.0 nm fV = 2.54 ± 0.3 %
50
25
0
60 40
20
0
Radius (nm) Radius (nm)
Number Number
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
150
cleaned by FIB prior to the APT study (Figure 105.c). During this operation, no precaution
was taken to estimate precisely the quantity of matter that had to be removed.
The resulting reconstructions are illustrated by Figure 106.a) and b) for the TEM and APT
experiments respectively. In both cases, nice information could be deduced for the restored
volumes. Unfortunately, it was not possible to establish an unambiguous one-to-one
correspondence between both tomograms because they definitely appeared to come from
slightly different locations within the sample, owing to the matter removal during the FIB
cleaning. Nevertheless, it seems that both volumes as they are displayed in the montage of
Figure 107 do match since some particles clearly appear to correspond in both tomograms.
Necessarily the TEM reconstructed volume does contain more precipitates that the APT one
since the latter was recorded after a volume reduction during the FIB procedure.
Figure 105: effect of oxidation observed on the head of TIP, and removed by a FIB cleaning: (a)
STEM image acquired at MATEIS-Lyon, (b) EDX nano-analysis of the tip of sample before FIB
cleaning, (c) image of tip of sample after FIB cleaning performed at GPM-Rouen.
oxide
OO
AAll
ZZnn
EDX nano-analysis
b)
residual oxide
100 nm 100 nm a) c)
151
Figure 106: result of a AlZnMg tip reconstruction: experimental HAADF image acquired at zero tilt
(left) and corresponding tomogram viewed in the corresponding projection (right).
Figure 107: comparison of TEM (a) and APT (b) reconstructed volumes of the same AlZnMg tip.
Note that corresponding details (arrows) can be found in both volumes displayed at the same scale.
head of tip is removed by FIB cleaning of oxidation before APT acquisition
100 nm
a) a) c)
head of tip is removed by FIB cleaning of oxidation before APT acquisition
100 nm
a)
a) b) 30 nm
152
3.4.6. Conclusion
To understand the effect of welding on the microstructure in an industrial AL-Zn-Mg alloy, a
quantitative analysis of the precipitation state has to be performed. A previous work was
devoted to this study by a combination of conventional TEM, SAXS and APT. We have
shown here that the distribution of size and volume fraction of MgZn2 nanoprecipitates in the
aluminium matrix can successfully be carried out by STEM-HAADF tomography. This
approach offers the advantage to get quantitative 3D information on the number and size of
precipitates but also simultaneously on their morphology: in particular, we will further discuss
the correlation that can be made between the shape and the crystallographic orientation with
respect to the aluminium matrix in the case of the '-MgZn2 platelets. An other interesting
correlation is that between electron and atom probe tomography. A first attempt was made in
this work, but difficulties due to the oxidation and practical aspects (i.e. travel time between
the TEM and APT equipments located in two different laboratories) have limited the success
of this complementary approach. In principle, both techniques should yield to a complete and
accurate chemical and morphological 3D characterization.
References of chapter 3
[Acevedo Reyes2005] Acevedo Reyes D, Perez M, Pecoraro S, Vincent A, Epicier T, P Dierickx.
Vanadium Carbide Dissolution During Austenitisation of A Model Microalloyed FeCV Steel.
Materials Science Forum (2005) 500-501: pp. 695-702.
[Acevedo Reyes2007] Acevedo-Reyes D. Evolution de l'état de précipitation au cours de
l'austénitisation d'aciers microalliés au vanadium et au niobium. Thèse. Villeurbanne : INSA de Lyon
2007.
[Allen1981] Allen S M. Foil thickness measurements from convergent-beam diffraction patterns.
Philos Mag (1981) 43: pp. 325-335.
[Alonso2005] Alonso B, Clinard C, Durand D, Veron E, Massiot D. New routes to mesoporous silica-
based spheres with functionalised surfaces. Chem Commun 13: pp. 1746-1748.
[AMIRA] AMIRA Visualize – Analyse – Present [online]. Germany : Visage Imaging. Available on
: http://www.amiravis.com (date accessed 01/02/2007)
[Arslan2008] Arslan I, Marquis E A, HOMER M, Hekmaty M A, Bartelt N C. Towards better 3-D
reconstructions by combining electron tomography and atom-probe tomography. Ultramicroscopy
(2008) 108: pp. 1579-1585.
[Barnard2006] Barnard J S, Sharp J, Tong J R, Midgley P A. High-resolution three-dimensional
imaging of dislocations. Science (2006) 313: pp. 319.
153
[Bell1972]Bell R J, Dean P. The structure of vitreous silica: validity of the random network
theory. Phil Mag (1972) 25: p.1381-1398.
[Bender2007] Bender H, Richard O, Kalio A, Sourty E. 3D-analysis of semiconductor structures by
electron tomography. Microelectronic Engineering (2007) 84: pp. 2707-2713.
[Bergna1994] Bergna H E. The Colloid Chemistry of Silica. Washington : American Chemical
Society, 1994. (Advances in chemistry series ; 234)
[Berhault2007(1)] Berhault G, Bisson L, Thomazeau C, Verdon C, Uzio D. Preparation of
nanostructured Pd particles using a seeding synthesis approach - application to the selective
hydrogenation of buta-1,3-diene. Applied Catalysis A: General (2007) 327: pp. 32-43.
[Berhault2007(2)] Berhault G, Bausach M, Bisson L, Becerra L, Thomazeau C, Uzio D. Seed-
Mediated Synthesis of Pd Nanocrystals: Factors Influencing a Kinetic- or Thermodynamic-Controlled
Growth Regime. Journal of Physical Chemistry C (2007) 111: pp. 5915-5925.
[Bizdoaca2002] Bizdoaca E L, Spasova M, Farle M, Hilgendorff, Caruso F. Magnetically directed
self-assembly of submicron spheres with a Fe3O4 nanoparticle shell. J. Magn. Magn. Mater (2002)
240: pp. 44-46.
[Cai12001] Cai1 W, Hofmeister H, Rainer T, Chen W. Optical properties of Ag and Au nanoparticles
dispersed within the pores of monolithic mesoporous silica. Journal of Nanoparticle Research (2001)
3: pp. 443-453.
[Caruso1998] Caruso F, Caruso R A, Mohwald H. Nanoengineering of inorganic and hybrid hollow
spheres by colloidal templating. Science (1998) 282: pp. 1111-1114.
[Daniel2004] Daniel M C, Astruc D. Gold nanoparticles: assembly, supramolecular chemistry,
quantum-size-related properties, and applications toward biology, catalysis, and nanotechnology.
Chem. Rev (2004) 104: pp. 293-346.
[Daniel2005] Daniel M C, Aranzaes J R, Nlate S, Astruc D. Gold-nanoparticle-cored polyferrocenyl
dendrimers: modes of synthesis and functions as exoreceptors of biologically important anions and
reusable redox sensors. J. Inorg. Organomet. Polym (2005) 15: pp. 107-119.
[De2000] De G, Karmakar B, Ganguli D. Hydrolysis–condensation reactions of TEOS in the presence
of acetic acid leading to the generation of glass-like silica microspheres in solution at room
temperature. J. Mater. Chem (2000) 10: pp. 2289-2293.
[Deconihout1995] Deconihout B, Bostel A, Bouet M, Sarrau J M, Bas P, Blavette D. Performance of
the multiple events position sensitive detector used in the tomographic atom probe. Applied Surface
Science (1995) 87-88: pp. 428-437.
[De-Sousa2003] De Sousa E M B, De Sousa A P G, Mohallem N D S, Lago R M. Copper-silica sol-
gel catalysts: structural changes of Cu species upon thermal treatment. J. Sol-Gel Sci. Technol (2003)
26: pp. 873-877.
[Donbrow1992] Donbrow M. Microcapsules and Nanoparticles in Medicine and Pharmacy. Boca
Raton, FL : CRC Press, 1992.
[Donnadieu1999] Donnadieu P, Roux-Michollet M, Chastagnier V. A quantitative study by
transmission electron microscopy of nanoscale precipitates in Al-Mg-Si alloys. Philos Mag A (1999)
79: pp.1347-1366.
154
[Dubus2006] Dubus S, Gravel J-F, Drogoff BL, Nobert P, Veres T, Boudreau D. PCR-free DNA
detection using a magnetic bead-supported polymeric transducer and microelectromagnetic traps.
Anal Chem (2006) 78: pp. 4457-4464.
[Dumont2005] Dumont M, Lefebvre W, Doisneau-Cottignies B, Deschamps A. Characterisation of
the composition and volume fraction of and ’ precipitates in an Al–Zn–Mg alloy by a combination
of atom probe, small-angle X-ray scattering and transmission electron microscopy, Acta Materialia
(2005) 53: pp. 2881-2892.
[Epicier2008] Epicier T, Acevedo D, Perez M. Crystallographic structure of vanadium carbide
precipitates in a model Fe-C-V steel. Philosophical Magazine (2008) 88: pp. 31-45.
[Eradat2001] Eradat N, Huang J D, Vardeny Z V, Zakhidov A A, Khayrullin I, Udod I, Baughman R
H. Optical studies of metal-infiltrated opal photonic crystals. Synth. Met (2001) 116: pp. 501-504.
[Frank1992] Frank J. Electron Tomography: Three-dimensional imaging with the transmission
electron microscope. New York : Plenum, 1992.
[Fukuoka2001] Fukuoka A, Higashimoto N, Sakamoto Y, Inagaki S, Fukushima Y, Ichikawa M.
Preparation and catalysis of Pt and Rh nanowires and particles in FSM-16. Microporous and
Mesoporous Materials (2001) 48: pp.171-179.
[Ghica2007] Ghica C, Ionita P. Paramagnetic silica-coated gold nanoparticles, J Mater Sci (2007) 42:
pp. 10058-10064.
[Ghosh2007] Ghosh S K, Pal T. Interparticle coupling effect on the surface plasmon resonance of
gold nanoparticles: from theory to applications. Chem. Rev (2007) 107: pp. 4797-4862.
[Gladden1990] Gladden L F. Medium Range Order in v-SiO2. J. Non-Cryst. Solids (1990) 119: p. 318-
330.
[Graf2003] Graf C, Vossen D L J, Imhof A, Van blaaderen A. A general method to coat colloidal
particles with silica. Langmuir (2003) 19: pp. 6693-6700.
[Guari2003] Guari Y, Thieuleux C, Mehdi A, Reye C, Corriu RJP, Gallardo SG, Plilippot K,
Chaudret. In Situ formation of gold nanoparticles within thiol functionalized HMS-C16 and SBA-15
type materials via an organometallic two-step approach. B Chem Mat (2003) 15: pp. 2017-2024.
[Guo2006] Guo J, Yang W, Wang C, He J, Chen J. Poly(N-isopropylacrylamide)-coated
luminescent/magnetic silica microspheres: preparation, characterization, and biomedical
applications. Chem Mater (2006) 18: pp. 5554-5562.
[Hadjipanayis1994] Hadjipanayis G C, Siegel R W. Nanophase materials: synthesis-properties-
applications. Dordrecht : Kluwer, 1994.
[Haes2001] Haes A J, Haynes C L, Van Duyne R P. Nanosphere lithography: self-assembled photonic
and magnetic materials. Mater. Res. Soc. Symp (2001) 636: pp. D4.8/1-D4.8/6.
[Herman1973] Herman G T, Lent A, Rowland S W. ART : mathematics and applications. A report on
the mathematical foundations and on the applicability to real data of the algebraic reconstruction
techniques. J Theor Biol (1973) 42: pp. 1-32.
[Holzapfel2006] Holzapfel V, Lorenz M, Weiss C K, Schrezenmeier H, Landfester K, Mailänder V.
Synthesis and biomedical applications of functionalized fluorescent and magnetic dual reporter
nanoparticles as obtained in the miniemulsion process. J Phys Condens Matter (2006) 18: pp. 2581-
2594.
155
[Huang2001] Huang Y, Duan X, Lieber C M. Directed assembly of one-dimensional nanostructures
into functional networks. Science (2001) 291: pp. 630-633.
[Huang2007] Huang X, Jain P K, El-Sayed I H, El-Sayed M A. Gold nanoparticles: interesting
optical properties and recent applications in cancer diagnostics and therapy. Nanomedicine (2007) 2:
pp. 681-693.
[Inoke2006] Inoke K, Kaneko K, Weyland M, Midgley P A, Higashida A K, Horita Z. Severe local
strain and the plastic deformation of Guinier-Preston zones in the Al-Ag system revealed by 3D
electron tomography. Acta Materialia (2006) 54: pp. 2957-2963.
[Ionita2008] Ionita P, Ghica C, Caproiu M T, Ionita G. Hybrid metal (gold)-inorganic (silica)
nanoparticles: synthesis, characterization, and spin-labeling. J Inorg Organomet Polym (2008) 18: pp.
414-419.
[Jiang2003] Jiang Y, Whitehouse C, Li J, Tam W Y, Chan C T, Sheng P. Optical properties of
metallo-dielectric microspheres in opal structures. J. Phys. Condens. Matter (2003) 15: pp. 5871-
5879.
[Kaneko2008] Kaneko K, Inoke K, Sato K, Kitawaki K, Higashida H, Arslan I, Midgley P A. TEM
characterization of Ge precipitates in an Al-1.6 at.% Ge alloy. Ultramicroscopy (2008) 108: pp. 210-
220.
[Katoa2008] Katoa M, Kawase N, Kaneko T, Toh S, Matsumura S, Jinnai H. Maximum diameter of
the rod-shaped specimen for transmission electron microtomography without the "missing wedge".
Ultramicroscopy (2008) 108: pp. 221-229.
[Kawase2007] Kawase N, Kato M, Nishioka H, Jinnai H. Transmission electron microtomography
without the “missing wedge” for quantitative structural analysis. Ultramicroscopy(2007) 107: pp. 8-
15.
[Kelly1975] Kelly PM, Jostsons A, Blake RG, Napier JG. The determination of foil thickness by
scanning transmission electron microscopy. Phys Stat Solidi (1975) 31: pp. 771-780.
[Kim2006] Kim J, Lee J E, Jang Y, Kim S W, An K, Yu J H, Hyeon T. Generalized Fabrication of
Multifunctional Nanoparticle Assemblies on Silica Spheres. Angew Chem Int Ed (2006) 45: pp. 4789-
4793.
[Koerdt2003] Koerdt C, Rikken G L J A, Petrov E P. Faraday effect of photonic crystals. Appl. Phys.
Lett (2003) 82: pp.1538-1541.
[Koguchi2001] Koguchi M, Kakibayashi H, Tsuneta R, Yamaoka M, Niino T, Tanaka N, Kase K,
Iwaki M. Three-dimensional STEM for observing nanostructures. J. of Electron Microscopy (2001),
50: pp. 235-241.
[Komura1980] Komura Y, Tokunaga K. Structural studies of stacking variants in Mg-base Friauf-
Laves phases. Acta cryst (1980) B36: pp. 1548-1554.
[Langner1990] Langner R. New methods of drug delivery. Science (1990) 249: pp. 1527-1533.
[Liu2005] Liu S, Han M. Synthesis, functionalization, and bioconjugation of monodisperse, silica-
coated gold nanoparticles: Robust bioprobes. Adv Funct Mater (2005) 15: pp. 961-967.
[Liu2006] Liu Z D, Huang C Z, Li Y F, Long Y F. Enhanced plasmon resonance light scattering
signals of colloidal gold resulted from its interactions with organic small molecules using captopril as
an example. Analytica Chim. Acta (2006) 577: pp. 244-249.
156
[Lyubchanskii2003] Lyubchanskii I L, Dadoenkova N N, Lyubchanskii M I, Shapovalov E A, Rasing
Th. Magnetic photonic crystals. J. Phys. D: Appl. Phys (2003) 36: pp. 277-287.
[Maier2003] Maier S A, Kik P G, Atwater H A, Meltzer S, Harel E, Koel B E, Requichia A A. Local
detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle
plasmon waveguides. Nature Materials (2003) 2: pp. 229-232.
[Mastronarde1997] Mastronarde D N. Dual-axis tomography: an approach with alignment methods
that preserve resolution. Journal of Structural Biology (1997) 120: pp. 343-352.
[Messaoudi2007] Messaoudi C, Boudier T, Sorzano C O S, Marco S. TomoJ: tomography software for
three-dimensional reconstruction in transmission electron microscopy. BMC Bioinformatics (2007) 8:
pp. 288-296.
[Moroz2000] Moroz A. Photonic crystals of coated metallic spheres. Europhys. Lett (2000) 50: pp.
466-472.
[Murray2001] Murray C B, Shouheng S, Gaschler W, Doyle H, Betley T A, Kagan C R. Colloidal
synthesis of nanocrystals and nanocrystal superlattices. IBM J. Res. Dev (2001) 45: pp. 47-56.
[Nagao2008] Nagao D, Yokoyama M, Saeki S, Kobayashi Y, Konno M. Preparation of composite
particles with magnetic silica core and fluorescent polymer shell. Colloid Polym Sci (2008) 286: pp.
959-964.
[Nicolas2002] Nicolas M. Precipitation evolution in an Al-Zn-Mg alloy during non-isothermal heat
treatments and in the heat-affected zone of welded joints. Thèse. Grenoble : INPG, 2002.
[Nikoobakht2003] Nikoobakht B, El-Sayed M A. Preparation and growth mechanism of gold
nanorods (NRs) using seed-mediated growth method. Chemistry of Materials (2003) 15: pp. 1957-
1962.
[O‟Brien2002] O‟Brien S, Pendry J B. Magnetic activity at infrared frequencies in structured metallic
photonic crystals. J. Phys. Condens. Matter (2002) 14: pp. 6383-6394.
[Ozasaa2004] Ozasaa K, Aoyagi Y, Iwaki M, Hara M, Maeda M. Nanofabrication of cylindrical
STEM specimen of InGaAs/GaAs quantum dots for 3D-STEM observation. Ultramicroscopy (2004)
101: pp. 55-61.
[Pengo2003] Pengo P, Polizzi S, Battagliarin M, Pasquato L, Scrimin P. Synthesis, characterization
and properties of water-soluble gold nanoparticles with tunable core size. J. Mat. Chem (2003) 13:
pp. 2471-2478.
[Penczek1995] Penczek P, Marko M, Buttle K, Frank J. Double-tilt electron tomography.
Ultramicroscopy (1995) 60: pp. 393-410.
[Salata2004] Salata O V. Applications of nanoparticles in biology and medicine. J. Nanobiotech
(2004) 2: pp.1-6.
[Stoeber1968] Stoeber W, Fink A, Bohn E. Controlled growth of monodisperse silica spheres in the
micron size range. J. Colloid Interface Sci (1968) 26: pp. 62-69.
[Sudeep2005] Sudeep P K, Shibu J S T, George T K. Selective Detection of Cysteine and Glutathione
Using Gold Nanorods. Journal of the American Chemical Society (2005) 127: pp. 6516-6517.
[Tong2006] Tong J, Arslan I, Midgley P. A novel dual-axis iterative algorithm for electron
tomography. Journal of Structural Biology (2006) 153: pp. 55-63.
157
[Tsunoyama2004] Tsunoyama H, Sakurai H, Ichikuni N, Negishi Y, Tsukuda T. Colloidal gold
nanoparticles as catalyst for carbon-carbon bond formation: application to aerobic homocoupling of
phenylboronic acid in water. Langmuir (2004) 20: pp. 11293-11296.
[Treacy1989] Treacy M M J, Rice S B. Catalyst particle sizes from rutherford scattered intensities. J.
Microsc (1989) 156: pp. 211-234.
[Vuu2005] Vuu K, Xie J, McDonald M A, Bernardo M, Hunter F, Zhang Y, Li K, Bednarski M,
Guccione S. Gadolinium-rhodamine nanoparticles for cell labeling and tracking via magnetic
resonance and optical imaging. Bioconjug Chem (2005) 16: pp. 995-999.
[Wang2000] Wang Z L. Transmission electron microscopy of shape-controlled nanocrystals and their
assemblies. Journal of Physical Chemistry B (2000) 104: pp. 1153-1175.
[Wang2002] Wang L, Velu S, Tomura S, Ohashi F, Suzuki K. Synthesis and characterization of CuO
containing mesoporous silica spheres. J. Mater. Sci (2002) 37: pp. 801-806.
[Wang2003] Wang Z L. New developments in transmission electron microscopy for nanotechnology.
Advanced Materials (2003) 15: pp. 1497-1514.
[Wiesendanger1997] Wiesendanger R, Bode M, Kleiber M, Lohndorf M, Pascal R, Wadas A, Weiss
D. Magnetic nanostructures studied by scanning probe microscopy and spectroscopy. J. Vac. Sci.
Technol. B (1997) 15: pp. 1330-1334.
[Wiley2006] Wiley B J, Xiong Y, Li Z-Y., Yin Y, Xia Y. Right Bipyramids of Silver: A New Shape
Derived from Single Twinned Seeds. Nano Letters (2006) 6: pp. 765-768.
[Williams1996] Williams DB, Carter CB. Transmission electron microscopy. Volume 2. Diffraction,
New York: Plenum Press, 1996.
[Zhelev2006] Zhelev Z, Ohba H, Bakalova R. Single quantum dot-micelles coated with silica shell as
potentially non-cytotoxic fluorescent cell tracers. J Am Chem Soc (2006) 128: pp. 6324-6325.
[Zhu2005] Zhu K, Hu J, Richards R. Aerobic oxidation of cyclohexane by gold nanoparticles
immobilized upon mesoporous silica. Catalysis Letters (2005) 100: pp. 195-199.
[Ziese2004] Ziese U, De Jong K P, Koster A J. Electron tomography: a tool for 3D structural probing
of heterogeneous catalysts at the nanometer scale. Applied Catalysis A: General (2004) 260: pp. 71-
74.
158
Perspectives
&
general conclusion
159
160
In this last short chapter, we intend to highlight the possible perspectives of this work,
according to what has been done in TEM tomography on the different systems detailed in
chapter 3.
Three main directions will be briefly explored:
(i) as it has been shown in this work, the STEM HAADF imaging mode may, in some
adequate cases, provide a mean for a quantitative chemical analysis of the probed
matter. We may then wonder how far it is possible to go in a 3D approach as
permitted by tilting tomography in the STEM mode.
(ii) As was noticed in the case of the precipitation in the AlZnMg alloy (§.3.4), the 3D
analysis provides in its principle accurate information about the shape of the „sub-
structure‟ or objects (particles, precipitates) present in the specimen. It is thus
interesting to relate these morphological information to crystallography.
(iii) A good strategy for the characterisation of materials is to cross-check results
obtained from different techniques. The present work was essentially focused on
the application of TEM tomography, it is worth discussing about the
complementarities of this approach with others in the microscope, such as EDX or
EELS of EFTEM analysis.
These three points will be discussed in the following sub-sections.
4.1. Chemical quantification in STEM tomography
As STEM HAADF imaging mode provides a chemical contrast, due to relationship between
intensity with mass-thickness (through the atomic number and density of chemical species
present in the probed volume), it is then possible to get some quantitative information about
the chemistry of the specimen from acquired projections. This is particularly true in the case
of nanoparticles.
Simulations were carried out to estimate the effect of various parameters on the intensity
distribution within tomograms [Friedrich2005]: indeed the variations of the intensity depend
on the imaging technique, experimental conditions, and algorithm of reconstruction.
To illustrate the problematic and thus estimate the possibility of chemical quantification
through the reconstructed tomograms, we will conduct simple calculations on ideal objects,
that is spherical particles of different but homogeneous chemical composition: STEM
HAADF images of 3 particles have then been simulated and used for a perfect tomography
reconstruction, in order to finally quantify the tomograms in terms of intensity.
161
We first clarify the simplifications adopted in these simulations. As already stated in
§.1.2.2.3, the STEM HAADF intensity is linear with Z , with 1.6 < < 2 according to the
experimental conditions. In the following simulations we fix the value = 2. The geometry of
the simulated particles corresponds to perfect spheres in order to avoid any non desirable
effect of thickness variation. Also an ideal range of tilt is 180° was considered in order to
avoid artefacts due to a lack of information, and finally the quality of the reconstruction is not
degraded by effects of misalignment of the projection series, electron beam broadening
effects and/or experimental noise.
Regarding the particles themselves: we consider 3 different spherical particles made of
aluminium, palladium and gold with the same atomic density (for simplicity) deduced from
the crystal structure of the corresponding fcc Al phase, according to the data summarized in
Figure 108.a). The STEM HAADF projections are then calculated and displayed with the
same grey scale in Figure 108.b). On this montage the projection of Al particle (underlined
with a white dotted circle) is almost invisible owing to the normalisation of the 8bits
brightness to the maximal intensity obtained for the Au particle, but its intensity profile
through the diameter appears clearly on (Figure 108.c). Images were not filtered and/or
treated before or after reconstruction, because any modification of their intensities will
introduce errors on the chemical extracted information.
According to these simulated projections (which obviously remain identical when a tilting
numerical experiment is performed), tomograms corresponding to the Al, Pd and Au particles
have been reconstructed and visualized (Figure 109.a). The distribution of intensity with the
tomograms is described by the histograms reported in Figure 109.b). Note that some minor
errors due to the algorithm of reconstruction are evidenced since although the particles have
the same size, the width and height of peaks associated to each particle are not exactly the
same. Nevertheless, the linearity of the HAADF optimal intensity with the square of atomic
number of nanoparticles is illustrated in Figure 109.c).
According to this simple analysis, it has been demonstrated that on the basis of the preserved
linearity between the intensity and the atomic number (at a constant atomic density) within
the tomograms reconstructed from tilting HAADF series, it is possible to think of a chemical
quantification through STEM-HAADF electron tomography.
162
In the most general case of heterogeneities which change the local atomic density, the
previously mentioned linearity should remain valid considering the product iZi instead of
simply Zi .
A more general approach should also be possible, to include correction of height and width of
peaks of distribution of intensity of tomograms. Numerical tests should also be done in order
to estimate the influence of errors due to misalignment, and artefacts due to lack of
information in the case of the missing wedge.
symbol name atomic number (Z) density (at. nm-3) radius (nm)
Al aluminium 13 60 75
Pd palladium 46 60 75Au gold 79 60 75
Figure 108 : a) data describing the particles used for STEM HAADF simulations (note that it was
chosen to use the same atomic density and size); b) calculated STEM HAADF projections of
homogeneous Au, Pd, and Al spheres perfectly centred on a virtual tilt axis, (in this ideal geometry all
projections remain the same whatever the tilt angle); c) intensity profile through the particle diameter
in order to highlight the darkest Al sphere.
b)
Tilt axis
a)
c)
b)
Au Pd Al
tilt axis
Au Pd Al
163
Figure 109 : a) volume rendering of Al, Pd and Au tomograms reconstructed by the ART algorithm
(number of iterations=14 and relaxation coefficient=0.07, TOMOJ [Messaoudi2007]) and visualized
with the AMIRA software [AMIRA], b) histogram of intensity within the tomogram, c) check of the
linear relationship between intensity and the square of the atomic number.
4.2. STEM tomography and crystallography
Performing a tilting series for TEM tomography offers the possibility of acquiring diffraction
patterns at certain tilt angles, which allows the crystal, for example the matrix in the case of a
precipitation problem, to be crystallographically oriented. Then, an a posteriori correlation
between the shapes of heterogeneities (e.g. precipitates) and the crystal structure can be
0
200000
400000
600000
0 50 100 150 200 250
a)
b)
Al Pd Au
Au Pd Al
number of voxels
c)
Z2
0
100
200
300
0 3000 6000 9000
intensity
intensity
164
performed on the reconstructed tomogram. This analysis can be applied to the case of the ‟-
MgZn2 platelets observed in the AlZnMg alloy, as detailed in §3.4.
Let us remind briefly the situation: in the T7 state, two kinds of precipitates co-exist within
the Al matrix: mainly stable -MgZn2 particles almost equi-axed, and metastable ‟-platelets.
Conventional TEM analysis show that the ‟-platelets nucleate in the {111} planes of Al (
[Dumont2005] and references within). This has been confirmed in the present work:
observing the Al matrix along a <110> viewing direction allows to reveal two ‟-variants
edge-on, that is lying in the two {111}Al in zone with the considered azimuth (Figure 110).
According to diffraction recorded during the tilting series as preconised above, the orientation
of the Al grain subjected to the tomography experiment depicted in Figure 105 to Figure 107
of §3.4 could be determined, as shown in Figure 111.a). Then, from a consistent
crystallographic indexing of the Al cubic phase, any desired viewing direction can be selected
in the stereogram, and the tomogram can then be projected along that specific azimuth (Figure
111.b). Choosing for example a <110> direction should allow two variants of ‟-platelets,
lying in {111}Al planes, to be seen edge-on (as was shown in the conventional TEM analysis
of Figure 110). Figure 111c) demonstrates the interest of this approach: the expected variants
show up in the predicted orientation when the tomogram is seen along the „good‟ direction. It
should be noted that similar correlation with crystallography is in principle possible in APT
when lattice resolution is achieved along at least two directions. This is partly illustrated by
Figure 112.
A similar crystallographic analysis was previously done in the Al-Ge system [Kaneko2008].
As a result, it is concluded that STEM HAADF tomography, can be used easily and quickly to
determine the 3D crystalline orientation of the object when associated to some diffraction
patterns adequately acquired during the tilting experiment.
165
Figure 110: precipitation microstructure as seen along the [1-10]Al zone-axis (a). Most precipitates
have a spherical shape (circles) but two variants of ‟-platelets lying in {111}Al planes are seen edge-
on (b).
a)
b)
20 nm
[110]
(002)
(111)
(111) _
_
166
Figure 111: orientation of an Al matrix grain in the AlZnMg alloy: (a) two diffraction patterns
recorded while acquiring the tilt series and consistently indexed using basic operations with the
stereographic projection [Johari1969]; (b) extension of the indexing in order to select a desired zone
axis to be reached, i.e. the [01-1]Al direction; (c) first step of the rotation to be achieved in order to
project the tomogram along the chosen [01-1]Al. (d) tomogram once viewed along the [01-1]Al : two
variants of edge-on ‟-platelets (arrows) appear in the (111) Al and (-111)Al planes (as expected).
b)
a)
167
Figure 112: (a) visualisation of a round-shape precipitate from a TAP experiment in the AlZnMg
alloy tempered in the T7 state. The (001)Al planes of the matrix are seen edge-on; (b) a Fourier
transform of the image further evidences the (113)Al reflections in addition to the (001)Al one
[Dumont2005].
4.3. Correlation of STEM tomography with crystallography
4.3.1. Case of EDX
As it was shown in §.3 and recalled in §.4.1, the STEM-HAADF provides a possible and
elegant way to collect quantitative information about the chemistry of the sample. It is
obvious that accompanying EDX (or EELS) analysis can help the method to be calibrated.
For example, one can imagine a collection of particles, the chemistry of which varies
continuously (case of a AxB1-x phase for example with a total miscibility), which can be
chemically analysed through its HAADF contrast. In such a case, preliminary EDX may be
required in order to ascertain the proportionality factor relating the HAADF intensity to the
square of the atomic number, with the help of objects of known composition. An illustration
of this approach is given in Figure 113 in the case of usual „2D‟ HAADF images. It has been
a) Al Zn Mg
b) 6*6*14 nm3
168
extensively applied in the case of a quantification of transition mixed carbides VxNb1-xC in a
recent precipitation study in the laboratory [Acevedo Reyes2007]. One can think of extending
this approach to a 3D analysis. An other possible and more straightforward use of EDX in
tomography would be to acquire EDX elementary maps during the titling series. This
approach would certainly be severely limited in resolution, and EFTEM imaging should be
preferred in TEM (see next section).
Figure 113 : chemical analysis of Fe-Pt nanoparticles in STEM. Particles encircled on the left HAADF
image were numerically analysed, and their intensity correlated to the Fe/Pt ratio according to EDX
analysis of a few particles. Then, the composition PtxFe1-x of each particle (right) was deduced from
the EDX calibration procedure ((courtesy T. Epicier, unpublished work; sample provided by M.
Delalande, CEA Grenoble, (2005)).
4.3.2. Case of EFTEM
The principle of tomography in EFTEM was briefly introduced in §.1.2.2.4. It is based on the
acquisition of 2D chemical maps at different tilts [Möbus2003, Boudier2005]. Since
laboratories in Lyon interested in TEM characterization of materials have access to different
microscopes, it should be interesting to adapt the EFTEM tomography on the Leo 912
microscope (EFTEM with a in-column filter) in the CLYM (Centre Lyonnais de
Microscopie). The actual commercial holder reaches a tilt range of 120°, it would then require
a slight modification in order to increase the tilt range to the more comfortable amplitude of
140 or 160° for tomography. As was done in the case of the 2010F microscope in this work,
or similarly to previous works [Schaffer2004, Boudier2005], a script for an automated
acquisition (correction of drift, tilt of sample, control of camera and microscope) has to be
developed. Then, for the reconstruction of 3D maps, it should be of the greatest interest to use
the adapted algorithms developed at the Institut Curie in Paris (i.e. a friendly Java-based
program: EFTET-J, implemented as a set of plug-in for ImageJ [Boudier2005]. EFTET-J
20nm
169
includes background subtraction for 3D-chemical mapping, as well as reconstruction
algorithms based on IMOD [Kremer1996]).
4.4. General conclusion
The aim of this thesis is to study the 3D structure and distribution of different nanoparticles
with a nanometer resolution, by STEM HAADF electron tomography or a stereoscopy
approach. The experimental work has consisted in adaptation of the used electron microscope
(Jeol 2010F), to a tomography experience, which has requied:
i. modification of a tip of holder in order to reach a tilt range of about 160°.
ii. development a software to control semi-automatically the microscope and the
detector, and especially to correct the focus in images during the phase of
acquisition.
Study of different samples were carried out as described below:
i. VC nanoprecipitates have been characterised by STEM-HAADF electron
tomography to highlight accurately their 3D morphology and to measure their
3D localisation, real volume, and equivalent radius.
ii. Au@SiOx nanocomposites with a spherical shape are sensitive to
contamination effects in STEM-HAADF mode. In this case a stereoscopy
approach is well adapted, it‟ is used to obtain 3D statistics of sizes and relative
distribution of the gold and the silica particles, with an accuracy of about 4 nm
for gold nanoparticles with a diameter of 1 to 5 nm. These measures allows a
feedback on the synthesis conditions.
iii. 3D analysis of the shape of palladium nanoparticles using the STEM-HAADF
tomography is carried out with a resolution of about 2nm; volumes that have
been reconstructed are pentagonal rods and bipyramids.
iv. 3D measures of distribution and size of MgZn2 nanoprecipitates in the
aluminium matrix (T7), have been performed by STEM-HAADF electron
tomography.
References of chapter 4
[Acevedo Reyes2007] Acevedo-Reyes D. Evolution de l'état de précipitation au cours de
l'austénitisation d'aciers microalliés au vanadium et au niobium. Thèse. Villeurbanne : INSA de Lyon
2007.
[AMIRA] AMIRA Visualize – Analyse – Present [online]. Germany : Visage Imaging. Available on :
http://www.amiravis.com (date accessed 05/02/2007).
170
[Boudier2005] Boudier T, Lechaire J P, Frébourg G, Messaoudi C, Mory C, Colliex C, Gaill F, Marco
S. A public software for energy filtering transmission electron tomography (EFTET-J): application to
the study of granular inclusions in bacteria from Riftia pachyptila. Journal of Structural Biology
(2005) 151: pp. 151-159.
[Dumont2005] Dumont M, Lefebvre W, Doisneau-Cottignies B, Deschamps A. Characterisation of
the composition and volume fraction of η′ and η precipitates in an Al–Zn–Mg alloy by a combination
of atom probe, small-angle X-ray scattering and transmission electron microscopy. Acta Materialia
(2005) 53: pp. 2881-2892.
[Friedrich2005] Friedrich H, McCartney M R, Buseck P R. Comparison of intensity distributions in
tomograms from BF TEM, ADF STEM, HAADF STEM, and calculated tilt series. Ultramicroscopy
(2005) 106: pp. 18-27.
[Johari1969] Johari O, Thomas G. The stereographic projection and its applications. In Bunshah R.F.
Techniques of metals research, volume II A.. New York : Wiley Interscience,1969.
[Kaneko2008] Kaneko K, Inoke K, Sato K, Kitawaki K, Higashida H, Arslan I, Midgley P A. TEM
characterization of Ge precipitates in an Al–1.6 at% Ge alloy. Ultramicroscopy (2008) 108: pp. 210-
220.
[KREMER1996] Kremer J R, Mastronarde D N, Mcintosh J R. Computer visualization of three-
dimensional image data using IMOD. Journal of structural biology (1996) 116: pp. 71-76.
[Messaoudi2007] Messaoudi C, Boudier T, Sorzano C O S, Marco S. TomoJ: tomography software for
three-dimensional reconstruction in transmission electron microscopy. BMC Bioinformatics (2007) 8:
pp. 288-296.
[Möbus2003] Möbus G, Doole R C, Inkson B J. Spectroscopic electron tomography. Ultramicroscopy
(2003) 96: pp. 433-451.
[Schaffer2004] Schaffer B, Grogger W, Kothleitner G. Automated spatial drift correction for EFTEM
image series. Ultramicroscopy (2004) 102: pp. 27-36.
171
172
Appendix 1
The most used JEOL commands to control semi-automatically the microscope JEOL
2010 F:
to send any command to the microscope through RS232 series by DM script:
number pass
JEOLcommand("COMMAND",pass)
to read magnification of microscope: MAGCOD
to read excitation of lens N° n: LCURDA n
to read excitation of a group of lenses of objective N° 5 and 6: LFCSET 1
to change respectively the excitation of the lenses of objective N°5 and N°6 to i5 and
i6: LFCSET 1,&Hi5,&Hi6
to read excitation of a lens of deflector N° n : DCURDA n
to change excitation of a lens of deflector N° n to (ix ,iy): DFCABS n, ix, iy
to read angle of tilt of the goniometer: GTILT
to change angle of tilt of the goniometer to (tiltx,tilty): GTILT tiltx, tilty
to open communication between DigitalMicrograph software and the microscope
through RS232 connection: EXT 1
to close communication between DigitalMicrograph software and the microscope
through RS232 connection: EXT 0
example of DM script : function to read excitation of the objective-lens (5 and 6)
string readobjective()
{
string reply, lens5, lens6
number pass
reply = JEOLcommand("LFCSET 1",pass)
// the last 8 characters of reply contain values of lens N° 5 and 6.
// the first 4 characters are hexadecimal value of excitation of objective-lens N° 5
//the second 4 characters are hexadecimal value of excitation of objective-lens N° 6
lens5=MID(reply,11,4) //extract hexadecimal value of excitation of objective-lens N° 5
lens6=MID(reply,16,4) //extract hexadecimal value of excitation of objective-lens N°6
return (lens5+lens6) // return the read value of lens N°5 and 6
}
173
174
FOLIO ADMINISTRATIF
THESE SOUTENUE DEVANT L'INSTITUT NATIONAL DES SCIENCES APPLIQUEES DE
LYON
NOM : BENLEKBIR DATE de SOUTENANCE : 30/03/2009
Prénoms : Samir
TITRE : Nanotomographie en Mode STEM-HAADF: Application aux Nanomatériaux
NATURE : Doctorat Numéro d'ordre : 2009-ISAL-0025
Ecole doctorale : Matériaux de Lyon
Spécialité : Matériaux
Cote B.I.U. - Lyon : T 50/210/19 / et bis CLASSE :
RESUME:
La tomographie électronique est une technique utilisée pour caractériser en 3D la structure et la
chimie des matériaux, avec une résolution nanométrique dans le cas d‟un microscope électronique
par transmission. Le mode d‟imagerie choisi est le champ sombre annulaire à grand angle, car il
est adapté à la tomographie quantitative à la fois pour les échantillons cristallins et non-cristallins.
De plus, le contraste en champ sombre annulaire dépend de la nature chimique des éléments
observés, et la simulation des images permet d‟extraire des informations chimiques, comme la
densité volumique ou le numéro atomique des espèces chimiques présentes. L‟objectif de cette
thèse est triple: (i) dans un premier temps, adapter le microscope électronique par transmission
(MET) à émission de champ du CLYM (Centre Lyonnais de Microscopie) à la tomographie par
rotation, (ii) ensuite, appliquer cette approche à l‟étude de nanostructures hétérogènes ainsi que de
nanomatériaux, (iii) finalement, explorer des méthodes 3D alternatives, comme la stéréoscopie,
qui nécessite l‟acquisition d‟un nombre plus faible d‟images qu‟en tomographie électronique. Le
travail expérimental a consisté à adapter l‟embout du porte objet du MET, afin d‟atteindre une
plage de tilt au delà de 160° : une expérience de tomographie nécessite l‟acquisition d‟une
centaine d‟images sur différentes inclinaisons. Un logiciel a été développé pour contrôler semi-
automatiquement le microscope et les conditions d‟utilisation du détecteur, notamment la
correction du focus dans les images durant la phase d‟acquisition. Différents matériaux ont été
étudiés: des nanoprécipités de carbure de vanadium (VC), des nanoparticules de catalyseurs (Pd),
des nanocomposites de type «Au@SiOx» et un alliage présentant une nano-précipitation
(AlZnMg).
MOTS-CLES: microscopie électronique - tomographie - champ sombre annulaire -
stéréoscopie - nanoprécipités - nanocomposites - catalyseurs - alliages.
Laboratoire (s) de recherche: Matériaux, Ingénierie et Science (MATEIS), UMR CNRS 5510
Directeur de thèse: Thierry EPICIER
Président de jury :
Composition du jury : C. GEANTET, F. DANOIX, P. DONNADIEU, J. WERCKMANN, T. EPICIER, S. MARCOS