Lecture 2. Surface Diffraction

Transcripción

1 Lecture 2 Surface Diffraction

2 1. LEED 2. Surface X-ray Diffraction

3 Electron diffraction

4 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. E o E o

5 Rear view LEED G1,G4: grounded (field-free region between sample and screen) G2, G3: retarding grids (filter out inelastic electrons)

6 LEED: Front-view Apparatus Grid 2: retarding voltage (selects only elastic electrons) Fluorescent Screen Sample

7 LEED optics Si{111}-(7x7) Pt{110}-(1x2)

8 Low Current LEED Cu(100) E p = 160 ev!

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10 Substrate + Overlayer LEED patterns adsorbate overlayer typically larger lattice spacing than substrate adsorbate spots typically smaller lattice spacing than substrate spots

11 k-space: Ewald Sphere for LEED LEED spots Diffracted e-beams fk Ewald Sphere Incoming e-beam eleci2pkπλ== ik Diffraction order 2aπ Reciprocal Lattice Rods Direction of scattered LEED beam sample

12 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. X-ray Diffraction Electron Diffraction k i α Angle φ k f k i k f D xray2sinndλθ= d d θ nλ=2dsinθ ()()2sincossin2nDnDλααλα== elecsinndλφ= nλ = D sinφ

13 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

14 Real Space: Si surface atoms 7x bulk spacing LEED: Si(111)7x7 Longer periodicities in real space give closer spots in k-space. Higher energy LEED images show spots closer together. K-Space 35 ev 65 ev

15 Methodology I Thy Expt Ep

16 Methodology II

17 Rutile TiO 2 Unit Cell

18 (110) Rutile TiO 2 Unit Cell

19 TiO 2 (110)1x1 Structure! Unit Cell: x Å

20 Tasker s Rules

21 Previous Work! [001]" STM"

22 Previous Work! Atom" Shift (Å)" Ti(1)" 0.12 ± 0.05" Ti(2)" ± 0.05" Ti(3)" ± 0.04" Ti(4)" 0.07 ± 0.04" O(1)" ± 0.08" O(2)vert" 0.05 ± 0.05" O(2)horz" ± 0.08" O(3)" 0.05 ± 0.08" O(4)" 0.00 ± 0.08" O(5)vert" 0.02 ± 0.06" O(5)horz" ± 0.08" O(6)" ± 0.08" O(7)" ± 0.07" SXRD" Charlton et al"

23 Structure Determination: New Phaseshifts

24 Optimised Structure Displacement (Å)" Atom" Atom" LEED-IV" LEED-IV" DFT(LDA)" SXRD" HF" ± 0.15! ± 0.15! -0.05! ± 0.08! -0.06! 0.06 ± 0.10! 0.06 ± 0.10! 0.03! 0.05 ± 0.08! 0.02!

25 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.

26 ESRF, Grenoble

27 Diamond, Oxfordshire--2008

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29 What do we mean by synchrotron? A machine; A collection of laboratories; An enabling technology; A scientific infrastructure.

30 Experimental Stations Optics hutch Synchrotron light Sample Control cabin Bending magnet Focussing magnets

31 Magnets for the storage ring dipoles quadrupoles sextupoles

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33

34 Difracción de rayos X Haces difractados: Distribución espacial Intensidad

35 Difracción de rayos X Difracción por un cristal Periodicidad tridimensional Espacio recíproco: puntos de Bragg

36 Difracción de rayos X Difracción por una monocapa Periodicidad bidimensional Espacio recíproco: husos ó varillas

37 Difracción de rayos X Difracción por una superficie Periodicidad tridimensional se pierde en la superficie Espacio recíproco: puntos de Bragg y husos de truncación

38 Difracción de rayos X Crystal Truncation Rods Diffuse intensity between Bragg peaks gives information about the surface structure

39 N.B. Systematic absences and different Struc factors Difracción de rayos X Relajación de la capa externa

40 Difracción de rayos X Relajación de la capa externa

41 Difracción de rayos X Relajación y reconstrucción de la capa externa Espacio recíproco de una superficie reconstruida (2x1)

42 Experimental Keep photon energy fixed--typically 10 kev

43 Fig. 2.4 Ewald Sphere construction. The origin of the sphere is at the tip of Ewald Sphere a* = 2π/a k -1 ' k 0 ' 2π/λ k -2 ' θ 0 k 0 k 1 ' Ewald Sphere construction. The origin of the sphere is at the tip of the incident wavevector, and has radius 2π/λ. k 0 is the incident wavevector of incident angle θ 0, and k x ' 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.! Diffraction Order, n

44 Difracción de rayos X Cómo se realizan las medidas

45 Difracción de rayos X Intensidades integradas y factores de estructura Factores de corrección Errores experimentales Intensidad integrada Factores de estructura Conjunto de datos final

46 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 calculado Factor de estructura experimental χ = 2 1 N p hk 2 calc F hk F σ hk exp hk 2 2 Número de factores de estructura Número de parámetros libres Error experimental

47 Difracción de rayos X Difractómetro de ID3 (ESRF)

48 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

49 6 CIRCLE DIFFRACTOMETER!

50 Surface x-ray diffraction (200 nm) 2 area Measurement on ID32 / SCL at the ESRF"

51 2006 Surface x-ray diffraction results TiO 2 (110) with STM characterisation

52 2006 Surface x-ray diffraction results Displacement (Å) Atom SXRD SXRD LEED-IV MEIS [3] Current work [4] [5] Ti(1) 0.12 ± ± ± ± 0.07 Ti(2) ± ± ± ± 0.09 Ti(3) ± ± ± ± 0.09 Ti(4) 0.07 ± ± ± ± 0.06 O(1) ± ± ± ± 0.16 O(2) [110] 0.05 ± ± ± * O(2) [1 10] ± ± ± * O(3) 0.05 ± ± ± ± 0.13 O(4) 0.00 ± ± ± O(5) [110] 0.02 ± ± ± O(5) [1 10] ± ± ± O(6) ± ± ± O(7) ± ± ± O(8) [110] ± O(8) [1 10] ± Ti(5) ± ± 0.07 Ti(6) ± ± 0.08 O(9) ± O(10) ±