The document discusses using theory, computation, and machine learning to interpret experimental X-ray absorption spectroscopy data and determine local atomic structures. It presents examples of using density functional theory calculations of X-ray absorption near edge structure (XANES) spectra to benchmark predictions against experiments and develop machine learning models for structure classification. The models are able to classify local structures like tetrahedral, square pyramidal, and octahedral coordination with over 85% accuracy across different materials systems. This approach provides a way to solve the inverse problem of determining structures from spectroscopy measurements in real time.

1. Predicting local atomic structures from X-ray absorption
spectroscopy using theory and machine learning
Deyu Lu
Center for Functional Nanomaterials, Brookhaven National Laboratory
AIMS Workshop at NIST
August 1, 2019

2. Experiments supplemented by theory and data analytics
Exp
measurement
Evolution of local
structures and
electronic states,
mechanisms
Structure models
properties
Prior knowledge
Simulations
energy
validation
Constructive
theory
interpretation
in situ exp
database ML workflow
Nat. Comm., 6, 7583 (2015)
• Time consuming
• Human labor
intensive

3. Smart experiments enabled by theory and data analytics
Exp
measurement
Evolution of local
structures and
electronic states,
mechanisms
Property
descriptors
Theory &
Computation
energy data analytics
validation
Real-time
characterization
interpretation
interactive high
throughput in
situ exp database ML workflow
feedback
optimization
automation
Nat. Comm., 6, 7583 (2015)

4. Motivation: Solve the inverse problem
Quantum
Mechanical Laws
Atomistic
Structure
Electronic
Structure
the forward problem
y = f (x)x y
Structure
Descriptors
Electronic
Structure
the inverse problem, often ill-conditioned
x' ⊂ x
x' = !f −1
(y')
y' ⊂ y

5. X-ray absorption spectrum
Fermi’s golden rule:
Dipole app. :
Single particle app. :
Phil. Trans. R. Soc. A 371.1995 (2013)
Core hole final state effect:
Ø valence electron SCF
relaxation (XSpectra)
Ø linear response of
valence electrons
(OCEAN, exciting)
− + −
−
− −
−

6. X-ray absorption spectra
§ Great time/energy resolution
§ Sensitive to electronic structure
§ Sensitive to local symmetry,
coordination number and charge state
Extended X-ray absorption fine structure
X-ray absorption
near edge structure
(XANES)
http://www.ati.ac.at/typo3temp/pics/617d72ef66.png

7. Decipher the spectra-structure relationship
Exp core-level
spectra
Weights of the ref.
spectra
Linear combination
fitting with exp refs.
Ti4+ with 4,5 and 6 CNs
energy
Phys. Rev. B, 56 1809, 1997
Nat. Comm., 6, 7583 (2015)

8. Empirical fingerprints
Phys. Rev. B, 56 1809, 1997
Ti K-edge
XANES
Fe K-edge
XANES
Geochim. Cosmochim. Acta 69, 4315, 2005
Spectral descriptor generation
• Requires prior knowledge
• Subject to human bias
• Strong emphasis on pre-edge
• Difficult to capture more subtle
features
Transferability
• Structure-spectral relationship
is system dependent

9. • We don’t have experimental references.
– Predictive, computational spectroscopy
Emerging Challenges
energy

10. Photoelectrochemical water splitting
photoelectrochemical water
splitting cell
band alignment
Topics in Catalysis 61.9-11 (2018): 1043-1076.

11. Water splitting over ZnO nanowires
• Wide band gap (3.2 eV), high carrier
mobility
• Seed-mediated growth from aqueous
solution
• Supports water splitting
• Photocorrosion
J. Phys. Chem. C 2013, 117, 13396−13402

12. Ultrathin titania coating layer
• Can sustain photocorrosion
• Higher photo current and energy conversion efficiency
• Reduced the overall surface recombination rate by 40%
ZnO-agT
ZnO-APT
as grown ZnO nanowires
Mingzhao Liu

13. Structure characterization
An unknown structure
• XRD doesn’t show
identifiable peaks,
suggesting amorphous
structure
• Ti L-edge XANES suggests
that crystal domain size is
~ a few nanometers
• Ti K-edge shows very
different features from
rutile or anatase
• Can we learn anything
about its local structure of
amorphous TiO2?

14. Benchmark of theory
Rutile
Anatase

15. Ti K-edge XANES basis sets
4970 4980 4990 5000
(nergy (e9)
Normalizedχµ(()
4c
4970 4980 4990 5000
(nergy (e9)
5c
4970 4980 4990 5000
(nergy (e9)
6c
• 334 site-specific Ti K-edge spectra calculated from structures in the
Materials Project using XSpectra
• Spectra clustered according to the local coordination number (4c: four
coordinated; 5c: five coordinated and 6c: six coordinated); each
cluster is represented by an average spectrum.
• A large number of Ti6c spectra are distinct essentially only in the pre-edge
region and cannot be separated in the clustering step; we choose
representative spectra for Ti6c sites by hand, considering experimentally
available structures.
• Total 11 Ti4+ K-edge XANES basis sets

16. Local structure distribution
amorphous model: 50% Ti5c,
47% Ti6c, and 3% Ti7c
Basis set (best fit): 21.8% Ti4c,
15.8% Ti5c and 62.4% Ti6c atoms

17. Conclusion
• The quality of ALD titania coatings over ZnO nanowires is strongly
correlated to the post-processing procedures performed on the NWs,
including thermal annealing and plasma sputtering.
• Ti L-edge XANES studies suggest that the titania shell is highly amorphous
with crystalline domains limited to a size of 1 nm or smaller.
• Ti K-edge XANES studies at high spectral resolution indicate that the
titania shell over ZnO has a significantly different structure from those of
crystalline TiO2.
• Two different first-principle computational approaches to analyze the Ti
K-edge data arrive at the same conclusion that the experimental
spectrum can be satisfactorily fitted only by introducing a large fraction
(40~50%) of undercoordinated Ti atoms.
• Trends in the intensity ratio between the white line doublet in the Ti K-
edge spectra measured for different post-processing procedures point to a
lower oxidation state in the titania shell due to the plasma sputtering of
the ZnO cores.
D. Yan, M. Topsakal, S. Selcuk, J. L. Lyons, W. Zhang, Q. Wu, I. Waluyo, E. Stavitski, K. Attenkofer, S.
Yoo, M. S. Hybertsen, DL, D. J. Stacchiola and M. Liu,, Nano Lett. 19:6, 3457-3463 (2019)

18. energy
• We don’t have experimental references.
– Predictive, computational spectroscopy
• Vast chemical and configurational space.
– Database and machine learning
– Avoid human bias
Emerging Challenges
energy

19. 3D metal nanoparticle structure
determination from XANES
Anatoly Frenkel Janis Timoshenko
§ Challenge: None of the traditional methods
can determine MNP structures on-the-fly.
§ Can we find good structure descriptors?
Frenkel, J. Synch. Radiat. 6, 293 (1999)
Frenkel, Hills, and Nuzzo, J. Phys. Chem. B,
105, 12689 (2001)
Nano particle size can be determined from
average coordination numbers.

20. Pt L3-edge XANES: not enough data
0.9 nm
2.9 nm
EXP
Theory

21. Training set using artificial NP structures
Physical cluster
(~20)
Artificial cluster
from mixed sites
(~C60
3=34,200)
Training Set
Nonequiv. Pt sites
(~60)

22. Determine average coordination
number from machine learning
Feature
site specific Pt
L3-edge XANES
Target
average (C1~C4)
artificial neural network Prediction
NP size/shape

23. Test on physical cluster

24. Prediction of Pt NP structure
Sample !!
a
!!
a
!!
a
!!
a dTEM
a,b
(nm) Model NPs CNsc
Model NPs sizec
(nm)
Foil 11.6(2) 5.8(2) 23(1) 11.1(8) - {12, 6, 24, 12} ∞
A3 9.1(3) 4.3(3) 11(2) 8(1) 3(1) {9.4, 4.0, 14.4, 7.1} 2.8
S4 8.9(3) 4.2(4) 10(2) 7(1) 1.2(2) {8.5, 3.2, 11.5, 5.0} 1.2
S2 8.1(3) 3.7(4) 8(2) 4.5(8) 1.2(3) {7.8, 3.3, 9.6, 4.1} 1.1
S3 7.7(4) 3.8(4) 4(2) 3.9(9) 0.9(2) {7.7, 3.1, 9.2, 3.8} 1.1
S1 7.4(4) 2.0(3) 3(1) 6(1) 1.1(2) {7.4, 2.6, 8.0, 3.3} 1.2
A2 6.6(4) 2.3(4) 3(1) 5(1) 1.1(3) {6.6, 2.1, 6.0, 2.9} 1.4
A1 6.3(3) 1.5(3) 2(1) 5(1) 0.9(2) {6.2, 1.9, 5.1, 2.4} 1.1
J. Timoshenko, DL, Y. Lin and A. I. Frenkel,, J. Phys. Chem. Lett., 8, 5091, 2017
J. Timoshenko, A. Anspoks, A. Cintins, A. Kuzmin, J. Purans, and A. I. Frenkel, Phys. Rev. Lett.
120, 225502, 2018

25. Summary
Ø Real time interpretation of core-level spectra is an emerging
challenge in operando measurements that requires correlating
operando measured spectral features to key local structure motifs,
i.e. solving the inverse problem, since standard fingerprints do not
exist.
Ø Ab initio X-ray absorption near edge structure (XANES) modeling is
a good complement of extend X-ray absorption fine structure
(EXAFS), for structural refinement.
Ø Our method enables the inverse modeling, where the unknown
structural motifs are deciphered from the experimental spectra.
Ø We illustrate our approach by 3D structure determination of metal
nanoparticles using neural network.
Ø Combination of theory, database and data analytics tools can have
a huge impact on materials discovery.

26. Local structure classification
from XANES using ML
Phys. Rev. B, 56 1809, 1997
Ti K-edge
XANES
• Avoid human bias
• Go beyond pre-edge features
• Extract spectral features automatically
• Regulate the ill-condition of fitting
through the loss function
• Has better transferability over materials
classes
• Provide real time feedback
Matthew Carbone Mehmet Topsakal

27. Machine learning workflow
Tetrahedral
T4
Square
Pyramidal
S5
Octahedral
O6
Ti K-edge
FEFF database
Sci. Data 5, 180151 (2018); npj Comput. Mater. 4, 12 (2018); Inorg. Chem. 37, 5575 (1998).

28. Materials space

29. Raw spectra and PCA
analysis
Tetrahedral
T4
Square
Pyramidal
S5
Octahedral
O6

30. Accuracy
P: precision; R: recall
T4
S5
O6

31. Conclusion
• XANES encodes important information about the local chemical
environment of an absorbing atom (e.g. coordination number,
symmetry and oxidation state).
• Extract such information is akin to solving a challenging inverse
problem
• The robustness and fidelity of the machine learning method are
demonstrated by an average 86% accuracy across the wide
chemical space of oxides in eight 3d transition metal families using
FEFF spectra database
• Spectral features beyond the pre-edge region play an important
role in the local structure classification problem, especially for late
3d transition metal elements.
• This study is a precursor to a potentially very powerful tool for real
time structure refinement using experimental XANES.
Carbone, Yoo, Topsakal and D.L. Phys. Rev. Mater, 3, 033604 (2019). Editor’s Suggestion.

32. Acknowledgment
This research used resources of the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility,
at Brookhaven National Laboratory under Contract No. DE-SC0012704. MC is supported by Computational Sciences
Graduate Fellowship (DOE CSGF) under Grant No. DE-FG02-97ER25308.
Experiment
• Anatoly Frenkel (BNL / SBU)
• Mingzhao Liu (BNL)
• Dario Stacchiola (BNL)
• Klaus Attenkhofer (ALBA)
• Eli Stavitski (BNL)
Theory
• Matt Carbone (Columbia)
• Mehmet Topsakal (BNL)
• Sencer Selcuk (Google)
• Mark Hybertsen (BNL)
• Xiaohui Qu (BNL)
• John Vinson (NIST)
Machine Learning
• Shinjae Yoo (BNL)
• Yuewei Lin (BNL)