Lecture 2

Surface Diffraction

1. LEED

2. Surface X-ray Diffraction

Electron diffraction

•  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

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

Sample

Grid 2: retarding voltage (selects only elastic electrons)

Fluorescent Screen

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

sample

LEED spots Diffracted e-beams

Ewald Sphere

Reciprocal Lattice Rods

eleci2pkπλ==Incoming e-beam

ik

fk

2aπDiffraction order

Direction of scattered LEED beam

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

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

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.

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!

STM"

[001]"

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"

Structure Determination:New Phaseshifts

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!

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.

Focussing magnets

Synchrotron light

Experimental Stations

Bending magnet

Control cabin Sample

Optics hutch

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

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.!

Difracción de rayos X Cómo se realizan las medidas

Difracción de rayos X Intensidades integradas y factores de estructura

Factores de corrección

Factores de estructura

Conjunto de datos final

Intensidad integrada

Errores experimentales

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

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

Measurement on ID32 / SCL at the ESRF"

(200 nm)2 area

2006 Surface x-ray diffraction results

•  TiO2(110) with STM characterisation

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 - -