Neural network approach to EXAFS analysis

The knowledge of the local atomic structure of functional materials is a key point for understanding and optimizing their properties. This task can be addressed by X-ray absorption spectroscopy, however in many practical cases the problem becomes challenging and requires the use of unconventional approaches. High-temperature phase transitions are an example of such complicated case both from experimental and theoretical sides. 

An international team of researchers from the Stony Brook University, the Institute of Solid State Physics, University of Latvia and the Brookhaven National Laboratory has used an artificial neural network (ANN) approach to extract the information on the local structure of bulk iron and its in situ temperature dependence directly from the Fe K-edge extended X-ray absorption fine structure (EXAFS) spectra, measured at the XAFS beamline of Elettra. The capability of the method has been demonstrated by extracting the radial distribution functions (RDFs) of iron atoms in ferritic (body-centered cubic) and austenitic (face-centered cubic) phases across the temperature-induced transition, occurring at about 1190 K. 
The approach is illustrated in Figure 1 and requires a pre-trained ANN to convert experimentally measured EXAFS data (we have used the wavelet transform (WT) representing EXAFS spectrum in k and R spaces simultaneously) to the radial distribution function (RDF) G(R). The crucial part of the analysis is the ANN training process. Here the classical molecular dynamics (MD) simulations have been used first to generate several thousands of training examples, corresponding to different iron phases with different degrees of disorder. Next, the atomic configurations have been used to calculate the corresponding RDFs and the time- and ensemble-averaged EXAFS spectra. The main part of thus obtained sets of theoretically produced data have been employed in the ANN training, whereas some sets have been used for the ANN validation.  

Figure 1.  Scheme of the EXAFS spectrum analysis using the artificial neural network on the example of the Fe K-edge for bcc iron at 300 K.

Finally, the pre-trained ANN has been used to interpret the temperature-induced transitionfrom the body-centered cubic (bcc) phase to the face-centered cubic (fcc) phase in iron. The obtained RDFs at selected temperatures are compared in Figure 2 to those found by reverse Monte Carlo (RMC) method. The use of ANN has allowed us to trace the bcc-to-fcc phase transition from the analysis of EXAFS spectra without any preliminary information. The important advantage of the ANN-based approach is very small computing time required to extract the RDF from EXAFS: when pre-trained ANN is available, it takes just few seconds compared to several weeks using the RMC method. 
 

Figure 2.  Comparison of the radial distribution functions (RDFs) G(R) for iron in bcc (300 and 900 K) and fcc (1273 K) phases obtained by reverse Monte Carlo (RMC) and artificial neural network (ANN) methods.

The ANN approach has a wide range of possible applications for rapid analysis and real-time control of in situ and in operando experiments. The pre-trained ANNs can be easily shared, therefore an openly available library of ANNs can be developed in the future, allowing the researchers in the field to analyse their own data without the need to do the tedious ANN training process themselves.

This research was conducted by the following research team:

Janis Timoshenko,¹ Andris Anspoks,² Arturs Cintins,² Alexei Kuzmin,² Juris Purans,² and Anatoly I. Frenkel^1,3

¹ Department of Materials Science and Chemical Engineering, Stony Brook University, Stony Brook, New York, USA
² Institute of Solid State Physics, University of Latvia, Riga, Latvia
³ Division of Chemistry, Brookhaven National Laboratory, Upton, New York, USA

Contact persons:

Janis Timoshenko, e-mail:
Anatoly I. Frenkel, e-mail:
Juris Purans, e-mail: