Lecture 2 Surface Diffraction

Lecture 2
Surface Diffraction
1. LEED
2. Surface X-ray Diffraction
Electron diffraction
mean free path
•  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
Rear view LEED
G1,G4: grounded
(field-free region between
sample and screen)
G2, G3: retarding grids
(filter out inelastic electrons)
LEED: Front-view Apparatus
Grid 2: retarding voltage
(selects only elastic electrons)
Fluorescent Screen
Sample
LEED optics
Si{111}-(7x7)
Pt{110}-(1x2)
Low Current LEED
Cu(100) Ep = 160 eV!
Substrate + Overlayer LEED patterns
adsorbate overlayer typically larger lattice spacing than substrate
adsorbate spots
typically smaller lattice spacing than substrate spots
k-Space: Ewald Sphere for LEED
Diffractedfk
e-beams
LEED spots
Ewald
Sphere
Reciprocal
Lattice Rods
ik
Incoming e-beam
eleci2pkπλ==
Direction of scattered
LEED beam
2aπ
Diffraction order
sample
k-Space: Bragg Scattering and LEED Equation
Derive LEED equation using Bragg’s Law for X-ray diffraction, where
appropriate angles are substituted and λ is for the electron wavelength.
Electron
Diffraction
X-ray Diffraction
ki
Angle φ
kf
α
ki
D
kf
d
xray2sinndλθ=
d
θ
nλ=2dsinθ
()()2sincossin2nDnDλααλα==
elecsinnDλφ=
nλ = D sinφ
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
LEED: Si(111)7x7
Real Space:
•  Longer periodicities in real space
give closer spots in k-space.
Si surface atoms
•  Higher energy LEED images
show spots closer together.
7x bulk spacing
K-Space
35 eV
65 eV
Methodology I
Thy
Expt
Ep
Methodology II
Rutile TiO2 Unit Cell
Rutile TiO2 Unit Cell
(110)
TiO2(110)1x1 Structure!
Unit Cell: 6.495 x 2.958 Å
Tasker’s Rules
Previous Work!
[001]"
STM"
Previous Work!
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"
SXRD"
Charlton et al"
Structure Determination:
New Phaseshifts
Optimised Structure
Displacement (Å)"
Atom"
Atom" LEED-IV" LEED-IV" DFT(LDA)" SXRD"
HF"
-0.17 ± 0.15!
-0.17 ± 0.15! -0.05! -0.16 ± 0.08! -0.06!
0.06 ± 0.10!
0.06 ± 0.10!
0.03! 0.05 ± 0.08!
0.02!
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.
ESRF, Grenoble
Diamond, Oxfordshire--2008
What do we mean by synchrotron?
• 
A machine;
• 
A collection of laboratories;
• 
An enabling technology;
• 
A scientific infrastructure.
Experimental Stations
Control cabin
Sample
Optics hutch
Synchrotron light
Focussing magnets
Bending magnet
Magnets for the storage ring
dipoles
quadrupoles
sextupoles
Difracción de rayos X
Haces difractados:
• Distribución espacial
• Intensidad
Difracción de rayos X
Difracción por un cristal
Periodicidad
tridimensional
Espacio recíproco:
puntos de Bragg
Difracción de rayos X
Difracción por una monocapa
Periodicidad
bidimensional
Espacio recíproco:
husos ó varillas
Difracción de rayos X
Difracción por una superficie
Periodicidad tridimensional
se pierde en la superficie
Espacio recíproco:
puntos de Bragg y
husos de truncación
Difracción de rayos X
Crystal Truncation Rods
Diffuse intensity between
Bragg peaks gives
information about the
surface structure
Difracción de rayos X
Relajación de la capa externa
N.B. Systematic absences
and different Struc factors
Difracción de rayos X
Relajación de la capa externa
Difracción de rayos X
Relajación y reconstrucción de la capa externa
Espacio recíproco de una
superficie reconstruida (2x1)
Experimental
Keep photon energy fixed--typically 10 keV
Ewald Sphere
a* = 2π/a
k-1'
k 0'
k-2'
k 1'
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.!
2π/λ
θ0
Diffraction -3
Order, n
Fig. 2.4
-2
-1
k0
0
1
2
Ewald Sphere construction. The origin of the sphere is at the tip of
Difracción de rayos X
Cómo se realizan las medidas
Difracción de rayos X
Intensidades integradas y factores de estructura
Factores
de corrección
Intensidad
integrada
Errores
experimentales
Factores
de estructura
Conjunto de datos
final
Difracción de rayos X
Análisis de datos y determinación del modelo atómico
La calidad de un modelo estructural se evalúa comparando los
factores de estructura experimentales y calculados mediante un
factor de acuerdo:
Factor de estructura
experimental
Factor de estructura
calculado
calc 2
hk
⎛ F
1
⎜
2
χ =
∑
N − p hk ⎜⎜
⎝
Número de factores
de estructura
−F
σ hk
Número de
parámetros libres
exp 2
hk
⎞
⎟
⎟⎟
⎠
2
Error experimental
Difracción de rayos X
Difractómetro de ID3 (ESRF)
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
6 CIRCLE DIFFRACTOMETER!
Surface x-ray diffraction
(200 nm)2 area
Measurement on ID32 / SCL at the ESRF"
2006 Surface x-ray diffraction results
• 
TiO2(110) with STM
characterisation
2006 Surface x-ray diffraction results
Displacement (Å)
Atom
Ti(1)
Ti(2)
Ti(3)
Ti(4)
O(1)
O(2) [110]
O(2) [1
10]
O(3)
O(4)
O(5) [110]
O(5) [1
10]
O(6)
O(7)
O(8) [110]
O(8) [1
10]
Ti(5)
Ti(6)
O(9)
O(10)
SXRD
SXRD
LEED-IV
MEIS
[3]
Current work
[4]
[5]
0.12 ± 0.05
-0.16 ± 0.05
-0.09 ± 0.04
0.07 ± 0.04
-0.27 ± 0.08
0.05 ± 0.05
-0.16 ± 0.08
0.05 ± 0.08
0.00 ± 0.08
0.02 ± 0.06
-0.07 ± 0.06
-0.09 ± 0.08
-0.12 ± 0.07
-
0.25 ± 0.01
-0.11 ± 0.01
-0.08 ± 0.01
0.19 ± 0.01
0.10 ± 0.04
0.17 ± 0.03
0.01 ± 0.05
0.07 ± 0.04
0.00 ± 0.03
0.04 ± 0.03
0.05 ± 0.05
0.01 ± 0.04
0.01 ± 0.04
0.01 ± 0.03
-0.03 ± 0.05
0.08 ± 0.01
-0.04 ± 0.01
0.02 ± 0.04
-0.02 ± 0.04
0.25 ± 0.03
-0.19 ± 0.03
-0.09 ± 0.07
0.14 ± 0.05
0.10 ± 0.05
0.27 ± 0.08
-0.17 ± 0.15
0.06 ± 0.10
0.00 ± 0.08
0.06 ± 0.12
-0.07 ± 0.18
0.00 ± 0.17
0.01 ± 0.13
-
0.19 ± 0.07
-0.09 ± 0.09
-0.09 ± 0.09
-0.06 ± 0.06
0.13 ± 0.16
0.05*
0.00*
0.10 ± 0.13
0.00 ± 0.07
-0.02 ± 0.08
-