x Ð rays & crystalsees2.geo.rpi.edu/earth_mat/slides/15_lecturex.pdf · wave behavior vs....
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X – Rays & Crystals
Characterizing Mineral Chemistry &Structure
J.D. Price
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Wave behavior vs. particle behavior
If atoms are on the 10-10 m scale, we need to use sufficientlysmall wavelengths to explore this realm if we want to learnsomething about atoms and lattices.
Light - electromagnetic spectrum
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Dif
fra
cti
on
E.B. Watson
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E.B. Watson
wave property
Diffraction of light
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Where intersections of the diffracted
wave fronts occur, there is
constructive interference
E.B. Watson
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The difference is only of scale. We can use optical
wavelengths for the grid on the left, because they are
appropriately spaced for those wavelengths. With
small wavelengths, lattices diffract.
Scale – grating and !
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Crystalline structurediffracts x-rays(XRD)
Bragg equation: ! = 2d sin "
Crystal with unknownd spacing
X-ray source withknown !
Crystal diffractometry
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Modern diffractometer
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Diffraction lines are generated byany plane within the crystalgeometry. That of course meansthe root planes to the unit cell, but italso includes all of the possiblediagonals.
Miller indices are used to label tothe lines resulting from the planes(you know all about indexing).
In a powdered sample, grainstypically orient in a myriad ofdirections*, such that manydiffraction lines are simultaneouslygenerated
*exception – sheet silicates
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The resulting information is structural!
(100) 4.1341!
(011) =3.259!
(110) 2.3868!
This is the diffraction patter for quartz(mindat.org). Peaks correspond to specific latticeplanes. Their relative intensity is diagnostic.
Powder diffraction plot
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This is great forpolymorphs.Calcite (top)and aragonite(bottom) havethe samecomposition,but differentstructures asevidenced fromtheir diffractionpatterns.
Polymorphs
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Most minerals are sizedbetween 0.1 – 100’s of mm.
The rather ordinary rock slab onthe left is composed of small (1-5mm) grains of quartz andfeldspar.
The feldspar below is large (15mm) but is concentrically zoned.
Chemical analysis
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Feldspars are solid-solutions and exhibit arange of compositions.
How might we determinethe composition of theminerals in our rocks?
What is unique about eachelement?
MM
TT
TT
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Ephoton = EH – EL = h f = h c / !
1. To obtain composition, we need a measurablecharacteristic for each element.
Electron structure is element specific. In other words,Ephoton is the result of a specific jump in a specific element.
Fluorescence: electromagneticradiation results from movingelectrons closer to the nucleus
Photoelectric characteristic
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Photo by Elizabeth Frank
Fluorescence Visible light is produced byenergies in U.V. light.
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Examples of transitionlevels in Barium
K 37.44 keV
LI 5.99 keV
LII 5.63 keV
LIII 5.25 keV
So LII to K (K #1) is…
31.81 keV
Heavier atoms have many energy levels
Energy levels
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So LIIto K is 31.81 keV or 31,810 eV
The wavelength of the photon produced by this jump is
! = h c / E
h = 6.626 ! 10-34 m2 kg/s
c = 3 ! 108 m/s
E = 31,810 eV ! 1.602 ! 10-19 J/ eV = 5.096 ! 10-15 J
So ! = 3.900 ! 10-11 m
Calculating the wavelength
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2. To get analysis at micron scale, we need highenergies (keV) focused on small area
Electrons are chargedparticles that can be focusedand redirected using amagnets
Lower energy example: theCRT
Raymond Castaingformulated the techniquefor microanalysis andbuilt the first working unitby 1951.
Focus!
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3. Fluoresced x-rays need to be collected and counted.
Recall that crystalline structurediffracts x-rays (XRD)
Bragg equation: ! = 2d sin "
Crystal with unknownd spacing
X-ray source withknown !
Count
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Castaing’s machine: focused electron beam that produces x-raysin an unknown, that may be counted at known diffraction angles.
Wavelength dispersive spectrometry (WDS)
Bragg equation: ! = 2d sin "
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The intensity of x-rays ismuch smaller relative tothose generated from atube (as in XRD)
The EMP wavelength spectrometer uses crystals with curvedlattices and ground curvature to reduce lost x-rays
The Rowland Circle
Crystal
Detector
InboundX-rays
Maximizing counts
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Example of amodern EM probe
Locate the following:Cathode and
anodeBeamMagnetsSampleCrystalDetector
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The Cameca SX100• Five spectrometers• Each with 2–4 crystals
The new RPI facility
Cameca SX 100 EMPRontec EDS detectionGatan mono CL
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Electron forces jump
Char. photon produced
Glancing background phn
Produced photon adsorbed – may produce Auger e-
Electron bounces off atom(high E): backscattered
Electron knocks out another e-
(low E): secondary
Electron-sample interactions
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EMPA does not analyze surfaces (thin film), but penetrates asmall volume of the sample.
The collectable products of electron collision origin originatefrom specific volumes under the surface.
Analysis volume
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Secondary electrons emittedfrom the first 50 nm
Images surface topography
Backscattered electron intensityare a function of atomic density
Images relative composition
Useful interactions
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Ti
Characteristic x-ray emission
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The x-ray volumechanges as a function of anumber variables.
A sample with higheraverage atomic densitywill have a shallower butwider volume than onewith a lower density.
A beam with higherenergy (keV) will producea larger volume than onewith a lower E0.
Nonunique nature of emission volume
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From the excitation volume behavior, it is clear atomicdensity (Z) makes a difference in the emitted intensities.
Some of the x-rays are absorbed into atoms within andadjacent to the excitation volume.
Some of the x-rays promote electron jumps in atomswithin and adjacent to the excitation volume.
Z
A
F
Raw data are corrected for ZAF influences. Thetotal correction produces a rather long equationthat may be satisfied only through iteration.
The microprobe advanced as a tool because of
the microprocessor
Sample effects
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The number of x-rays counted at the appropriate diffractionangle is proportional to the concentration of the fluorescingelement. But the excitation volume is not unique.
Quantification requires comparison to a well-characterizedstandard.
Standard analyzed by
other meansYour sample with
unknown composition
Standardization
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Castaing’s micro WDS machine was a breakthrough. By1960, advances in semiconduction permitted theconstruction of a new detector that could collect all of theemitted x-ray energies (pulses and background) within afew seconds.
Energy Dispersive Spectrometry (EDS)
•Measures charges in semiconductor [Si(Li)]
•Makes histogram of measured charges
•Extremely fast
•Very inexpensive
•Lower accuracy relative to WDS
EDS
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EDS spectrum for a 15kV beam on a gemmy crystal from theAdirondacks (M. Lupulescu, NYSM).
Al K# & $
Si K# & $
K K#
K K$
Energy spectrum
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EMPA traverses of spinel using WDS
Formula for the spinel
Nom: Mg Al2O4
Act: Mg1-3x Al2+2x O4
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EMPA is a powerful tool for compositional analysis atthe micrometer scale
High voltage electron beam can be focused on onemicrometer area
Composition is determined by characteristic x-raysfrom excited atoms
WDS
•Characteristic x-rays are focused throughdiffraction
•Permits better resolution
EDS
•All x-rays are counted simultaneously
•Permits faster analysis / identification
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Limitations
•Good standards are essential
•Quantification is dependant on accuratecorrection for ZAF effects
•User needs to be aware of excitation volume
Results
•Accurate assessment of mineral stoichiometry
•WDS provides trace element compositions
•May assess inhomogeneity at small scales