Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW...
Transcript of Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW...
![Page 1: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/1.jpg)
Computational X-Ray SpectroscopySummer 2015 UW INT Physics REU
Jonathan Curtis
University of Rochester
August 19th, 2015
1 / 35
![Page 2: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/2.jpg)
Table of Contents
1 BackgroundX-Ray SpectroscopyX-Ray Theory
2 ProjectSexithiopheneC60 FullereneTransition Metals
3 Future Efforts
2 / 35
![Page 3: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/3.jpg)
Section 1
Background
3 / 35
![Page 4: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/4.jpg)
What Is X-Ray Spectroscopy?
Use X-Rays to investigate molecular physics
Probes electronic structure
Chemical properties
Study collective excitations
Important applications in nano-science, materials science,chemical physics, and condensed matter physics
4 / 35
![Page 5: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/5.jpg)
What is X-Ray Photoelectron Spectroscopy
Photoelectric effect
Intensity of ejected electrons vs. kinetic energy
Study quasi-particle excitations
Experiments conducted in high-vacuum
Often use high-energy synchrotron x-rays
Goal
To calculate a spectrum from first principles and have it agree withexperiment.
5 / 35
![Page 6: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/6.jpg)
Molecular Physics
Typically ∼ 10 atoms
Typically ∼ 10 electron per atom
Many body problem
Often ignore core electrons
Often ignore nuclear motion
6 / 35
![Page 7: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/7.jpg)
Electrons and Photons
Fermi Rule
The XPS photocurrent is given by Jk(ω)1
Jk(ω) =∑f
|〈f ,N − 1; ~k |Hdipole|0,N〉|2δ(ω − ωs) (1)
Looks simple to calculate! But it isn’t...
Need eigenstates
Must sum over many states
Photoelectron not seperable
Core-hole also interacts
1J.J. Kas, F.D. Vila, J.J. Rehr, S.A. Chambers, Physical Review B 91, 12112(R) (2015): d.o.i. 10.1103/PhysRevb.91.121112
7 / 35
![Page 8: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/8.jpg)
Electrons and Photons
Figure 1: A diagram demonstrating the XPS interaction
Image from https://wiki.utep.edu/pages/viewpage.action?pageId=51217584
8 / 35
![Page 9: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/9.jpg)
Excitations
Appear as secondary “satellite” peaks
Due to inelastic losses
Collective excitations absorb energy
Mostly plasmons
Plasmon
Quanta of valence electron oscillation. Analogous to phonons andlattice vibrations. Couples to both photoelectron and core-hole.
9 / 35
![Page 10: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/10.jpg)
Spectral Function A(ω)
Roughly proportional to Jk(ω)
Represents distribution of energies
Are normalized to one
Calculated using density fluctuations
A(ω)
A(ω) = − 1
πIm
∫dωe iωtGc(t) (2)
where Gc(t) is the Green’s function for the core-hole 2
2Ibid
10 / 35
![Page 11: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/11.jpg)
Project Background
Used RT-SIESTA
DFT/TD-DFT calculation of electron density
Pseudo-potentials
Basis set of LCAO
Relax to ground state
Add core-level Coulomb potential
Calculate density fluctuations in real time
Effective to ∼ 300 atoms
11 / 35
![Page 12: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/12.jpg)
Section 2
Project
12 / 35
![Page 13: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/13.jpg)
Subsection 1
Sexithiophene
13 / 35
![Page 14: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/14.jpg)
Sexithiophene
Figure 2: Sexithiophene
14 / 35
![Page 15: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/15.jpg)
What is sexithiophene?
Planar molecule
Rotationally symmetric 180◦ about midpoint
Formula is C24S6H10 ⇒ 250e−
Possible uses as organic semiconductor
Label Sulphur from outermost (S1) to innermost (S3)
15 / 35
![Page 16: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/16.jpg)
Experimental Data
Figure 3: The “On Res” curve is the XPS for sexithiophene on theSulphur resonant energy.
16 / 35
![Page 17: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/17.jpg)
Computed Results
Figure 4: The XPS for each individual sulphur atom and their sum17 / 35
![Page 18: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/18.jpg)
Subsection 2
C60 Fullerene
18 / 35
![Page 19: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/19.jpg)
C60 Fullerene
Figure 5: C60 Fullerene “Bucky-ball”
Image from https://upload.wikimedia.org/wikipedia/commons/4/41/C60a.png
19 / 35
![Page 20: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/20.jpg)
C60 Fullerene Crystal
Figure 6: C60 fcc crystal
Image from https://en.wikipedia.org/wiki/Buckminsterfullerene#/media/File:Fullerite structure.jpg20 / 35
![Page 21: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/21.jpg)
What is Fullerene?
Most common of the fullerenes
Molecule has diameter ∼ 1 nm
Forms face-centered cubic (fcc) crystals in solid phase
Natural semi-conductor
Can be doped to become super-conducting
Nano-engineering
21 / 35
![Page 22: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/22.jpg)
Measured XPS3
Figure 7: Measured C60 XPS
3J.A. Leiro, M.H. Heinonen, T. Laiho, I.G. Batirev, Journal of Electron Spectroscopy and Related Phenomena 128 (2003) 22 / 35
![Page 23: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/23.jpg)
Comparison
0
500
1000
1500
2000
−40 −35 −30 −25 −20 −15 −10 −5 0 5
Inte
nsity
(arb
.uni
ts)
Energy (eV)
C60 XPS Data vs. Experiment
C60 XPS ExperimentalC60 XPS Calculate
Figure 8: Comparison of calculated and measured. Centered and rescaledto same sizes
23 / 35
![Page 24: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/24.jpg)
Subsection 3
Transition Metals
24 / 35
![Page 25: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/25.jpg)
Transition Metals
Metals like Ni , Co, and Fe
Many-body effects are very important
Possible applications to highly-correlated systems
“High Tc” super conductors
Crystalline structure requires band-theory in addition tomolecular theory
25 / 35
![Page 26: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/26.jpg)
Cobalt XPS
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
−80 −70 −60 −50 −40 −30 −20 −10 0
Inte
nsity
(arb
.uni
ts)
Energy (eV)
Cobalt XPS
Cobalt XPS
Figure 9: Calculated Cobalt XPS
26 / 35
![Page 27: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/27.jpg)
Section 3
Future Efforts
27 / 35
![Page 28: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/28.jpg)
Sexithiophene
Include ghost atoms
Examine different core charges
Density fluctuations at frequency
Ongoing invstigation
28 / 35
![Page 29: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/29.jpg)
C60
Examine crystal effects
Compute XAS with many body effects
Include extrinsic interactions
Compare with graphene
29 / 35
![Page 30: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/30.jpg)
Transition Metals
Check for supercell convergence
Analyze other metals
Compare to experiment
Check accuracy of quasi-peak weights
Apply to correlated materials
30 / 35
![Page 31: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/31.jpg)
Acknowledgements
I would like to acknowledge the Condensed Matter Theory groupfor all the help they have given me over the summer. In particular,I would like to thank John Rehr, Joshua Kas, and Fernando Vilafor all of their help and guidance. I’d also like to thank DeepGupta, Alejandro Garcia, Gray Rybka, Shih-Chieh Hsu, LindaVilett, Farha Habib, and the INT program for organizing this REU.Finally, I would like to acknowledge Ron Musgrave for his guidancethrough the machine shop program.
31 / 35
![Page 32: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/32.jpg)
Section 4
Backup Slides
32 / 35
![Page 33: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/33.jpg)
Calculation
Energy Spectrum4
SIESTA outputs potential energy of density fluctuations ∆(t).First compute the energy spectrum β(ω)
β(ω)/ω = Re
∫dte−iωt∆(t) (3)
and then the cumulant C (t)
C (t) =
∫β(ω)
(e iωt − iωt − 1
ω2
)dω (4)
Finally, the spectral function
A(ω) = − 1
πRe
∫e iωteC(t)dt (5)
4J.J. Kas, F.D. Vila, J.J. Rehr, S.A. Chambers, Physical Review B 91, 12112(R) (2015): d.o.i. 10.1103/PhysRevb.91.121112 33 / 35
![Page 34: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/34.jpg)
Calculated XPS
Figure 10: Calculated XPS of C60. Quasi-peak weight of Z = 58.4%34 / 35
![Page 35: Computational X-Ray Spectroscopy · 2015-09-09 · Computational X-Ray Spectroscopy Summer 2015 UW INT Physics REU Jonathan Curtis University of Rochester August 19th ... chemical](https://reader033.fdocuments.in/reader033/viewer/2022060412/5f10d0227e708231d44af070/html5/thumbnails/35.jpg)
Peak Weights
Material Z 1− Z
S1 .768 .232S2 .666 .334S3 .667 .333
C60 .584 .416
Fe .316 .684Co .283 .717Ni .147 .853
Table 1: Quasi-particle peak weights, in increasing order of satelliteweight. Z for metals may be inaccurate.
S1, S2, S3 refer to the various Sulphurs in sexithiophene
35 / 35