Theory, Interpretation and Applications of X-ray Spectra*

Transcription

1 REU Seminar University of Washington 27 July, 2015 Theory, Interpretation and Applications of X-ray Spectra* J. J. Rehr et al.

2 A theoretical horror story Starring Fernando Vila & Anatoly Frenkel with J. Kas, S. Bare & S. Kelly Directed by J. J. Rehr a Sequel

3 Part I: Application Operando theory of nanocatalysts: Structure, thermal properties, catalytic activity Pt Clusters on γ-al 2 O 3

4 Theoretical Challenge: Anomalous properties* of Pt 10 /γal 2 O 3 Pt-Pt nn Negative Thermal Expansion & Bond expansion in H 2 Anomalous Pt-Pt disorder NOT bulk-like! *J.H. Kang, L. D. Menard, R. G. Nuzzo, and A. I. Frenkel. JACS 2006, 128, 12068

5 More Anomalous properties* Pt 10 /γal 2 O 3 Increased edge intensity X-ray spectra Pt L III Redshift of XANES with increasing T Standard analysis fails! *J.H. Kang, L. D. Menard, R. G. Nuzzo, and A. I. Frenkel. JACS 2006, 128, 12068

6 Challenge: multiple length and time-scales ν BSE True Molecular Crystals Crystals IR V/UV X-Rays RSGF Molecules Clusters Liquids k r DFT/MD s ns ps fs as RT-TDDFT t

7 What s going on? Blob 573 K The BLOB Cluster center of mass

8 Fuzzy structure DFT/MD nn distance

9 Negative Thermal Expansion Explained R Å Å Å ( Å)

10 High Pt-Pt Disorder Explained σ² Ų ( Ų) Ų ( Ų)

11 Increased intensity and redshift explained XAS FEFF9 on ensemble of finite T DFT/MD structures

12 Dynamic structural disorder +δ ( Oxidized ) -δ ( Metallic ) Pt 10 on γ-al 2 O 165 K Need Operando AIMD dynamics* to reproduce experiment *F. Vila, J. J. Rehr, J. Kas,R. G. Nuzzo, and A. I. Frenkel, Phys. Rev. B 78, (R), 2008

13 Conclusion Must consider dynamic structure to understand the nano-scale

14 Part II: Theory and Interpretation of X-ray Spectra GOALS: ab initio theory Accuracy ~ experiment TALK: I. Introduction History II. Real-space Green s function theory FEFF codes III. Improvements XAS, Optical spectra, etc,

15 GOAL Theoretical X-rayBeamline

16 Questions we want to answer: What are the structure and dynamics? and other physical properties? of complex systems? Cu(NH 3 ) 4 SO 4 H 2 O Pt/γ-Al 2 O 3 Zirconium Tungstate

17 Experiment: X-ray Spectroscopy Theory vs expt X-ray absorption spectra UV fcc Al Photon energy (ev) X-ray EXAFS? What s in a spectrum?

18 Historical interpretation of EXAFS* *Stern Sayers Lytle, UW 1971 Short range order theory EXAFS EXAFS Fourier Transform Cu Shifted Radial Distribution shift X-ray Microscope! R nn BUT need to calibrate experiment with Standard

19 Can you write an equation for the theory? P.A.M. Dirac (to R. Feynman)

20 Answer: Exact EXAFS Equation* Effective Scattering Amplitude f eff S 0 2 Many body amplitude factor Mean free path λ k σ 2 EXAFS measures local structure & disorder Distance R Coordination N Disorder σ 2 Mean square vib amplitude *JJR, RC Albers, CR Natoli, EA Stern, Phys Rev B34, 4350 (1986)

21 BUT: need many parameters! Question: Can the EXAFS parameters k f eff Φ k σ 2 λ k S 0 2 be calculated theoretically?

22 Answer 1 I always thought it was easier to measure x-ray absorption than to calculate it. Hans Bethe ca 1980

23 Gotcha: Standard theory fails! Ground state = no damping LARGE ERRORS! Ground-state DFT theory vs Excited State vs Expt

24 Why? Fermi Golden Rule for XAS μ(ω) Too many quasi-particle final states ψ f Final state rule V coul = V coul + V core hole Non- hermitian self-energy Σ(E) (replaces DFT Vxc)

25 Answer 2 (JJR)* Now** it is often easier to calculate x-ray absorption than to measure it (**if structure is known) ** 10 years later - JACS 113, 5136 (1991)

26 How? (10 more years) Quantitative XAS theory FEFF J. J. Rehr & R.C. Albers Rev. Mod. Phys. 72, 621 (2000)

27 Theoretical Tricks: Green s functions Σ + Real-space Green s function Theory Mean free path, Self-energy Σ Screened core-hole

28 Real-space Green s Function Theory Golden rule via Wave Functions Paradigm shift Ψ Golden rule via Green s Functions G = 1/( E h Σ ) No sums over final states!

29 What s a Green s function? Wave function in QM H Ψ = E Ψ Ψ(r) = Amplitude to find particle at r Green s function (H E) G = - δ(r-r ) G(r,r,E) = aka Propagator = Amplitude to go from r to r

30 Multiple-scattering theory of G Path Full MS Ingredients: G 0 free propagators t-matrix = e i δ l sin δ l δ RR δ ll

31 Implementation: FMS FEFF code 89 atom cluster Core-hole, SCF potentials Essential! BN

32 Example: Pt EXAFS MS path expansion Phase Corrected EXAFS Fourier Transform * Rnn= fcc Pt χ(r) Path Expansion 15 paths No peak shift! *Theoretical phases R (Å) accurate distances to < 0.01 Å

33 Example: Pt XANES full multiple-scattering Pt L 3 -edge 1.4 Pt L 2 -edge (S. Bare, UOP) Normalized Absorption FEFF calculation Experiment' Normalized Absorption FEFF calculation Experiment PtL3_xmu '98feb002_xmu' PtL2_xmu '98feb004_xm 0.0 PtL3edge Photon Energy, ev PtL2edge Photon Energy, ev Good agreement: Relativistic FEFF8 code reproduces all spectral features, including absence of white line at L 2 -edge. Self-consistency essential: position of Fermi level strongly affects white line intensity

34 Green s Functions and Parallel Computation Energy E is just a parameter! 1/N CPU Natural parallelization Each CPU does one energy

35 Interpretation of XANES : Excited State Electronic Structure Cu pdos vs XAS and XES XAS XES pdos Fermi energy E F Final state energy E

36 Application EXAFS analyis of Re-catalysts Simon R. Bare, et al., J. Phys. Chem. 115, 5740 (2011)

37 Application: Pt catalysts Pt 10 /γ-al 2 O 3 Finite Temp, Real-time DFT/MD calculations of supported Pt nano-catalysts* Pt L 3 XAS fs time-steps Mean nn distance *F. Vila et al. Phys Rev B78, (R) (2008)

38 What s Next: Even better theory A. Other spectra: NIXS, RIXS, Optical, Compton B. Ab initio mean free paths λ k C. Ab initio Debye Waller factors σ 2 D. Multi-electron excitations S 2 0

39 (10 more years) Quantitative XAS FEFF9 JJR et al., Comptes Rendus Physique 10, 548 (2009) in Theoretical Spectroscopy L. Reining (Ed) (2009)

40 Application: Optical Spectra Europhysics News 43, 1 (2012)

41 2014

42 Debye-Waller factors σ 2 in Zr tungstate Mean square vibration amplitudes

43 + Easy to use GUI for everyone JFEFF Proceedings of XAFS 15 in press 2012

44 Rehr Group J. Kas (UW) F. Vila (UW) J. Vinson (UW) K. Jorissen (UW) T. Ahmed (UW) S. Williams E. Clevac Acknowledgments Key collaborators E. Shirley (NIST) A. Soininen (U. Helsinki) A.L. Ankudinov (STM) R.C. Albers (Los Alamos)) Supported by DOE-BES

45 That s all folks!