Theory and Parameter Free Calculations of EELS and X-ray Spectra

Transcription

1 M&M Conference Columbus, OH June, 2016 Theory and Parameter Free Calculations of EELS and X-ray Spectra J.J. Rehr 1, J. J. Kas 1, K. Jorissen 2, and F. Vila 1 1 Department of Physics, University of Washington, 2 Amazon Web Services Seattle, WA

2 Theory and Parameter Free Calculations of EELS and X-ray Spectra GOAL: Ab initio theory & interpretation of core level EELS & XAS IR VIS UV X-ray TALK: Advanced Codes & Workflow tools Theory: FEFF/Green s function + OCEAN/BSE

3 If I can t calculate it, I don t understand it. (Often attributed to R. P. Feynman)

4 Challenge: Full spectrum electron- and X-ray spectra Cu loss function

5 Challenge: Improve on Hydrogenic model of EELS* L. Konrad et al., MCM2015 *L. Pauling, Proc. Roy Soc. A London 114, 181 (1927)

6 ~ 35 years later: Ab initio optical constants* Cu loss function *

7 Optical constants Dielectric function Energy Loss (EELS) Absorption coefficient Refractive index Reflectivity X-ray scattering factors Hamaker constants ε = ε 1 + iε 2 Im ε 1 μ n + i k R f = f 0 + f 1 + i f 2 ε iω

8 Broad Spectrum Calculations: Theory vs. Expt. fcc Al UV Deep core Photon energy or Energy Loss (ev)

9 EELS Theory a lá Fermi s golden rule 2 σ E Ω E, Q = ξ k F k I I k I V k F F 2 δ E I E F I,F V = 1 r r Coulomb interaction S q, ω Dynamic Structure Factor ~ Loss function Computational bottleneck: S q, ω ~ Im ε 1 q, ω Too many states! All state k F, k I (probe) and F, I (sample) contribute

10 Paradigm shift: Real-space Green s Function Approach Golden rule via wavefunctions μ E ~ i ε r f 2 f δ E E f Golden rule via Green s functions: G = 1 E h Σ μ E ~ 1 π Im i ε r G r, r, E ε r i Efficient: No sums over final states! Ψ

11 XAS & EELS Real-space Green s function theory J. J. Rehr & R.C. Albers, Rev. Mod. Phys. 72, 621 (2000)

12 FEFF8 Core-hole SCF potentials Self-energy DW factors Efficient Core level spectra: EELS, XAS, XES 89 atom BN cluster

13 Parallel (MPI) FEFF μ E ~ 1 π Im i ε r G r, r, E ε r i MPI: Natural parallelization Each proc. does a few energies Needed for state-of-the-art XANES simulations

14 EELS in FEFF9: Impurity Green s function EELS in periodic systems w/o supercell* +++ Real space Recip. space w/o supercell Expt N K-edge ELNES of GaN* *K. Jorissen & J. J. Rehr Phys. Rev. B 81, (2010)

15 Relativistic corrections to EELS* Relativistic Coulomb interaction where 2 σ E Ω E, Q k = ξ k 1 Q 2 E ħc 2 I r Q F 2 δ E I E F E I,F 2 σ E Ω E, Q = f Q Q i Q j σ ij E Q = Q Q z β 2 e z 3 i,j=1 and the abs. tensor is σ ij E = ξ E F r i I I r j F δ E I E F E I,F *P. Schattschneider et al., Phys. Rev. B 2005

16 Relativistic EELS Incorrect Correct 2.4 mrad 0.6 mrad Non-relat. Relat. Relativistic Magic Angle in FEFF9 agrees with expt.

17 FEFF9: Advanced methods Cu K-edge FEFF 8.4 FEFF 9

18 FEFF9: Advanced methods Ab initio: Mean free paths Self-energies Debye-Waller factors RPA core-hole screening Multi-electron excitations x-ray Inelastic Losses Self-energy Σ + Real-Space Green s Function Screened core-hole

19 Loss Function Many-Pole Self-Energy (MPSE) Extension of Hedin-Lundqvist (HL) plasmon-pole (pp) GW SE model Σ approximated as sum of PP models matched to loss function Cu Many-pole (full) much better than HL (dashed) vs better theory (dot-dashed) J. J. Kas et al., PRB 76, (2007)

20 MPSE corrections in BSE and DFT* LiF (BSE+MPSE) MgAl 2 O 4 (ΔSCF-DFT+MPSE) MPSE MPSE Energy (ev) *J. J. Kas et al., J. Phys. Conf. Series 190, (2009)

21 Question: Can we improve the theory? V. Mauchamp, M. Jaouen, JJR, and J. J. Kas, U. Poiters, Preprint (2010)

22 Answer: GW/BSE Ab initio optical & low-loss spectra Si AI2NBSE: Abinit+NIST BSE+UW MPSE Plane-wave, pseudo-potential GW/BSE code UW + NIST collaboration

23 Ab initio GW/BSE core-spectra: ELNES & XANES LiF: F K edge OCEAN: Obtaining Core Excitations from Abinit and NBSE UW + NIST Collaboration SrTiO 3 : Ti L 2,3 edge

24 Are we there yet? Optical constants: THz to X-ray UV-VIS X-ray Challenge: Efficient phonon spectra Can we compute vibrational properties ab initio?

25 Ab initio Debye Waller Factors: e 2σ R 2 k 2 Projected Vibrational DOS: Use efficient pole model ρ R ω = 2ω π Im 0 1 ω 2 D + iε 0 w vδ ω ω v N v=1 Ψ EXAFS MSRDs: σ R 2 T = ħ 1 2μ R ω coth 0 βħω 2 ρ R ω dω Helmholtz Free Energy: N coor F T = E + k B T ln 2 sinh βħω 2 i 0 ρ i ω dω Vila et al, Phys. Rev. B 76, (2007)

26 Vibrational Density of States Cu

27 Typical Results

28 ZrW 2 O 8 : Complex unit cell

29 ZrW 2 O 8 : MSRDs

30 Phonon-contributions to final-state broadening in Cu Satellites visible only at low T

31 User-friendly Java GUI: JFEFF

32 VESPA - Virtual EELS Software Package Goal: Integrated EELS software for STEM using CORVUS Workflow Manager

33 Prototype: Virtual STEM in the Cloud State-of-the-art EELS modeling FEFF9+JFEFF AI2NBSE and OCEAN TELNES Precompiled & Optimized on the Amazon EC2 K. Jorissen et al.

34 CONCLUSIONS Goals: Mostly achieved or in sight Complementary theoretical techniques: Real-space Supercell/reciprocal space Next generation theory & codes including: Many-body effects Relativistic effects Broad spectrum response: IR VIS UV X-ray

35 Acknowledgments: Thanks to DOE BES for $$ Rehr Group + L. Reining, M. Guzzo, E. Shirley, K. Gilmore, et al. From left to right: Ken Nagle Yoshi Takimoto Kevin Jorissen Towfiq Ahmed Hadley Lawler Aleksi Soininen Fernando Vila Adam Sorini Alex Ankudinov Micah Prange John Vinson (Shauna Story) John Rehr Josh Kas (Egor Clevac)

36 Theory and Parameter Free Calculations of EELS and X-ray Spectra J.J. Rehr 1, J. J. Kas 1, K. Jorissen 2, and F. Vila 1 1 Department of Physics, University of Washington, 2 Amazon Web Services Seattle, WA Thank you!

37 Thank you!