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Lecture 2
Surface Diffraction
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1. LEED
2. Surface X-ray Diffraction
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Electron diffraction
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• The elastic mean free path of slow electrons in solids is only a few atomic layers, so elastic electrons remain near the surface.
Eo Eo
mean free path
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Rear view LEED
G1,G4: grounded (field-free region between sample and screen)
G2, G3: retarding grids (filter out inelastic electrons)
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LEED: Front-view Apparatus
Sample
Grid 2: retarding voltage (selects only elastic electrons)
Fluorescent Screen
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LEED optics
Si{111}-(7x7)
Pt{110}-(1x2)
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Low Current LEED
Cu(100) Ep = 160 eV!
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Substrate + Overlayer LEED patterns
adsorbate overlayer typically larger lattice spacing than substrate adsorbate spots typically smaller lattice spacing than substrate spots
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k-Space: Ewald Sphere for LEED
sample
LEED spots Diffracted e-beams
Ewald Sphere
Reciprocal Lattice Rods
eleci2pkπλ==Incoming e-beam
ik
fk
2aπDiffraction order
Direction of scattered LEED beam
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k-Space: Bragg Scattering and LEED Equation
X-ray Diffraction
Derive LEED equation using Bragg’s Law for X-ray diffraction, where appropriate angles are substituted and λ is for the electron wavelength.
elecsinnDλφ=()()2sincossin2nDnDλααλα==
ki kf D
Angle φ ki
kf
xray2sinndλθ=
α
θ d d
Electron Diffraction
nλ=2dsinθ
nλ = D sinφ
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LEED: History
• LEED = Low Energy Electron Diffraction
• 1924: Discovered accidentally by Davisson and Kunsman during study of secondary electron emission from Ni crystal
• 1927: Davisson and Germer found maxima occurred for: – nλ = D sinφ – D = spacing atomic row spacing, λ = electron wavelength (h/p)
• 1931: Davisson and Thomson shared Nobel Prize for discovery of matter waves
• 1934: Ehrenburg developed fluorescent screen for data imaging
• 1960: Ultrahigh vacuum technology enabled clean surfaces to be studied with LEED
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LEED: Si(111)7x7
35 eV 65 eV
Real Space: Si surface atoms
7x bulk spacing K-Space
• Longer periodicities in real space give closer spots in k-space.
• Higher energy LEED images show spots closer together.
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Methodology I
Thy Expt
Ep
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Methodology II
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Rutile TiO2 Unit Cell
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Rutile TiO2 Unit Cell
(110)
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TiO2(110)1x1 Structure!
Unit Cell: 6.495 x 2.958 Å
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Tasker’s Rules
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Previous Work!
STM"
[001]"
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Previous Work!
SXRD"Charlton et al"
Atom" Shift (Å)"
Ti(1)" 0.12 ± 0.05"
Ti(2)" -0.16 ± 0.05"
Ti(3)" -0.09 ± 0.04"
Ti(4)" 0.07 ± 0.04"
O(1)" -0.27 ± 0.08"
O(2)vert" 0.05 ± 0.05"
O(2)horz" -0.16 ± 0.08"
O(3)" 0.05 ± 0.08"
O(4)" 0.00 ± 0.08"
O(5)vert" 0.02 ± 0.06"
O(5)horz" -0.07 ± 0.08"
O(6)" -0.09 ± 0.08"
O(7)" -0.12 ± 0.07"
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Structure Determination:New Phaseshifts
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Optimised Structure
Displacement (Å)"
Atom" LEED-IV" SXRD"
-0.17 ± 0.15! -0.16 ± 0.08!
0.06 ± 0.10! 0.05 ± 0.08!
Displacement (Å)"
Atom" LEED-IV" DFT(LDA)" HF"
-0.17 ± 0.15! -0.05! -0.06!
0.06 ± 0.10! 0.03! 0.02!
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SXRD �
• R. Feidenhans’l, Surf. Sci. Rep. 10 (1989) 105
• I.K. Robinson, D.J.Tweet, Rep. Prog. Phys. 55 (1992) 599
• nλ=2dsinθ
• X-rays interact weakly with matter (scattered by core electrons).
• Positive side this means single scattering approximation is adequate.
This is very quick and cheap computationally. A another major advantage over other diffraction techniques is that work at high pressures is possible, as is magnetic scattering.
• Negative side it means that we need a very bright source of X-rays to study surfaces, because they don’t contain many atoms, ie synchrotron radiation. Work at grazing incidence to maximise surface sensitivity.
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ESRF, Grenoble
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Diamond, Oxfordshire--2008
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What do we mean by synchrotron?
• A machine;
• A collection of laboratories;
• An enabling technology;
• A scientific infrastructure.
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Focussing magnets
Synchrotron light
Experimental Stations
Bending magnet
Control cabin Sample
Optics hutch
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Magnets for the storage ring
dipoles
quadrupoles
sextupoles
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Difracción de rayos X
Haces difractados: • Distribución espacial
• Intensidad
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Difracción de rayos X Difracción por un cristal
Periodicidad tridimensional
Espacio recíproco: puntos de Bragg
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Difracción de rayos X Difracción por una monocapa
Periodicidad bidimensional
Espacio recíproco: husos ó varillas
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Difracción de rayos X Difracción por una superficie
Periodicidad tridimensional se pierde en la superficie
Espacio recíproco: puntos de Bragg y
husos de truncación
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Difracción de rayos X Crystal Truncation Rods
Diffuse intensity between Bragg peaks gives information about the surface structure
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Difracción de rayos X Relajación de la capa externa
N.B. Systematic absences and different Struc factors
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Difracción de rayos X Relajación de la capa externa
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Difracción de rayos X Relajación y reconstrucción de la capa externa
Espacio recíproco de una superficie reconstruida (2x1)
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Experimental
Keep photon energy fixed--typically 10 keV
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Ewald Sphere
a* = 2π/a
k1'
k0'k-1'
k-2'
θ0 k0
DiffractionOrder, n
0-1-2-3 1 2
Fig. 2.4 Ewald Sphere construction. The origin of the sphere is at the tip ofthe incident wavevector, and has radius 2 π/λ. K0 is the incident wavevector ofincident angle θ0, and kx' the scattered wavevectors, where x is the diffractionorder. Diffraction occurs when the tip of a dif fracted wavevector and a latticeline intersect.
2π/λ
Ewald Sphere construction. The origin of the sphere is at the tip of the incident wavevector, and has radius 2π/λ. k0 is the incident wavevector of incident angle θ0, and kx' the scattered wavevectors, where x is the diffraction order. Diffraction occurs when the tip of a diffracted wavevector and a lattice line intersect. To observe the diffraction the detector must be looking along the scattered wavevector.!
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Difracción de rayos X Cómo se realizan las medidas
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Difracción de rayos X Intensidades integradas y factores de estructura
Factores de corrección
Factores de estructura
Conjunto de datos final
Intensidad integrada
Errores experimentales
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Difracción de rayos X Análisis de datos y determinación del modelo atómico
∑⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛ −
−=
hk hk
hkcalc
hk FFpN
22exp2
2 1σ
χ
La calidad de un modelo estructural se evalúa comparando los factores de estructura experimentales y calculados mediante un
factor de acuerdo:
Número de factores de estructura Número de
parámetros libres Error experimental
Factor de estructura calculado
Factor de estructura experimental
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Difracción de rayos X Difractómetro de ID3 (ESRF)
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Experimental
• Station 9.4 SRS Daresbury
• 5 sample and detector positioning circles needed.
• 6th “out of plane” circle maximises out of plane resolution.
• Scattered intensity measured by “rocking” across diffraction condition.
• Scans then integrated and corrected
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6 CIRCLE DIFFRACTOMETER!
![Page 50: Lecture 2 Surface Diffraction · 2012. 9. 12. · EwaldSphere a* = 2π/a k 1 '-1 'k 0 k-2 ' θ 0 k 0 Diffraction Order, n-3 -2 -1 0 1 2 Fig. 2.4 EwaldSphere construction. The origin](https://reader036.vdocuments.net/reader036/viewer/2022071603/613e80e569193359046d299b/html5/thumbnails/50.jpg)
Surface x-ray diffraction
Measurement on ID32 / SCL at the ESRF"
(200 nm)2 area
![Page 51: Lecture 2 Surface Diffraction · 2012. 9. 12. · EwaldSphere a* = 2π/a k 1 '-1 'k 0 k-2 ' θ 0 k 0 Diffraction Order, n-3 -2 -1 0 1 2 Fig. 2.4 EwaldSphere construction. The origin](https://reader036.vdocuments.net/reader036/viewer/2022071603/613e80e569193359046d299b/html5/thumbnails/51.jpg)
2006 Surface x-ray diffraction results
• TiO2(110) with STM characterisation
![Page 52: Lecture 2 Surface Diffraction · 2012. 9. 12. · EwaldSphere a* = 2π/a k 1 '-1 'k 0 k-2 ' θ 0 k 0 Diffraction Order, n-3 -2 -1 0 1 2 Fig. 2.4 EwaldSphere construction. The origin](https://reader036.vdocuments.net/reader036/viewer/2022071603/613e80e569193359046d299b/html5/thumbnails/52.jpg)
2006 Surface x-ray diffraction results
Displacement (Å)
Atom SXRD[3]
SXRDCurrent work
LEED-IV[4]
MEIS[5]
Ti(1) 0.12 ± 0.05 0.25 ± 0.01 0.25 ± 0.03 0.19 ± 0.07Ti(2) -0.16 ± 0.05 -0.11 ± 0.01 -0.19 ± 0.03 -0.09 ± 0.09Ti(3) -0.09 ± 0.04 -0.08 ± 0.01 -0.09 ± 0.07 -0.09 ± 0.09Ti(4) 0.07 ± 0.04 0.19 ± 0.01 0.14 ± 0.05 -0.06 ± 0.06O(1) -0.27 ± 0.08 0.10 ± 0.04 0.10 ± 0.05 0.13 ± 0.16O(2) [110] 0.05 ± 0.05 0.17 ± 0.03 0.27 ± 0.08 0.05*O(2) [110] -0.16 ± 0.08 0.01 ± 0.05 -0.17 ± 0.15 0.00*O(3) 0.05 ± 0.08 0.07 ± 0.04 0.06 ± 0.10 0.10 ± 0.13O(4) 0.00 ± 0.08 0.00 ± 0.03 0.00 ± 0.08 -O(5) [110] 0.02 ± 0.06 0.04 ± 0.03 0.06 ± 0.12 -O(5) [110] -0.07 ± 0.06 0.05 ± 0.05 -0.07 ± 0.18 -O(6) -0.09 ± 0.08 0.01 ± 0.04 0.00 ± 0.17 -O(7) -0.12 ± 0.07 0.01 ± 0.04 0.01 ± 0.13 -O(8) [110] - 0.01 ± 0.03 - -O(8) [110] - -0.03 ± 0.05 - -Ti(5) - 0.08 ± 0.01 - 0.00 ± 0.07Ti(6) - -0.04 ± 0.01 - -0.02 ± 0.08O(9) - 0.02 ± 0.04 - -O(10) - -0.02 ± 0.04 - -