The structural dynamics of chemical systems can be investigated by in situ or operando X-ray experiments. Advanced and fast computational methods are needed to cope with the huge amount of data collected, and to extract precious information hidden in data through a model-free analysis. Data analysis approaches based on multivariate analysis are particularly suited to this aim, as they are able to efficiently process in a probe-independent way multiple measurements, by considering them as a whole data matrix [1].

We have developed a fully automatic and big-data set of computing procedures based on principal component analysis, which is able to process with the same algorithms in situ/operando X-ray diffraction and XAFS data to extract qualitative and quantitative information. The multivariate approach has been adapted to treat crystallographic data, by optimizing the directions of the principal components [2], or by including kinetic models in the extraction of the reaction coordinate [3]. The procedure includes several pre-processing strategies that can be applied on crystallographic and XAFS data; among them a peak-shift correction to disentangling lattice variations from changes of the atomic parameters [4]. The procedures have been implemented in the computer program RootProf [5], available from www.ic.cnr.it/ic4/en/software/. It can be also used for fast on-site analysis while running in situ experiments (Fig.1).

Here we show how in situ experiments coupled with new data analysis methods can disclose the structural mechanism underlying: i) the thermal adsorption of gas in zeolites [4]; ii) the non-isothermal solid-state synthesis of materials based on poly-aromatic molecular complexes [6]; iii) the temperature-induced transitions of metal halide perovskites [7].

Figure 1. The RootProf program processes data from in situ experiments to locate atoms responding to an external stimulus.

[1] Guccione, P., Lopresti, M., Milanesio, M., Caliandro R. Crystals 11, 12.

[2] Caliandro, R., Guccione, P., Nico, G., Tutuncu, G., Hanson, J.C. (2015). J. Appl. Cryst. 48, 1679.

[3] Guccione, P., Palin, L., Belviso, B. D., Milanesio, M., Caliandro R. (2018). Phys. Chem. Chem. Phys. 20, 19560.

[4] Guccione, P. Palin, L., Milanesio, M., Belviso B.D., Caliandro, R. (2018). Phys. Chem. Chem. Phys. 20, 2175.

[5] Caliandro, R., Belviso, B. D., (2014). J. Appl. Cryst. 47, 1087.

[6] Palin, L., Conterosito, E., Caliandro, R., Boccaleri, E., Croce, G., Kumar, S., van Beek, W., Milanesio M. (2016). CrystEngComm 18, 5930.

[7] Caliandro, R., Altamura, D., Belviso, B. D., Rizzo, A., Masi, S., Giannini. C. (2019). J. Appl. Cryst. 52, 1104.

In the last years a growing number of studies have been devoted, both experimentally and theoretically, to understanding the structural properties of disorder systems and chemical processes occurring in solution and more clear pictures are emerging. This was possible by the improvements of the experimental techniques and the development of more sophisticated and reliable theoretical models. As we will detail in this presentation, experimentally in the last years X-ray absorption spectroscopy (XAS) played a major role in unravelling many structural aspects of disordered systems and it was exploited to gain unprecedent information on chemical reactions occurring in solution. This was possible by coupling experiments with theoretical simulations and multivariate analysis, and by better exploiting the X-ray absorption near edge spectroscopy (XANES) that is very sensitive to three-dimensional structures. Here, we will show specific applications to several liquid systems and chemical reaction occurring in the ms time scale. Aqueous solutions containing lanthanoid and actinoid ions are analysed with the aim of providing a unified description of the hydration properties of these series. We will show how the combined approach using XAS and molecular dynamics simulations can be applied to the study of complex systems such as ionic liquids and deep eutectic solvents, that represent an innovative research field. Lastly, we will show how it is possible to shed light into mechanistic properties of bimolecular reactions in solution by combining XANES, UV-Vis with multivariate data analysis.

Tektites and impactites are mainly amorphous silicate glass bodies of impact genesis. The conditions, such as pressure (P), temperature (T), oxygen fugacity (fO₂), that existed during glass formation process influence the cation coordination. One of the common elements in impact glasses is iron, so it a useful probe of atmospheric parameters and collision conditions in geological history of Earth. X-ray absorption spectroscopy (XAS) is a direct probe of the local atomic structure around specific element applicable to liquids, single molecules or amorphous solids. Recent developments in theoretical interpretation of the X-ray absorption fine structure along with machine learning (ML) methods opened a new perspective for quantitative structural analysis of complex systems [1,2]. In this work we extend ML-driven fitting procedure to the amorphous structures of tektites, where several inequivalent sites with different coordination numbers can coexist. The analysis was performed in PyFitIt software [3]. For each possible coordination number N = 2…6 we constructed a fragment of silica where Fe ion was coordinated by several (SiO₄) tetrahedral units. Structural parameters of Fe(SiO4)_N cluster were varied to simulate possible bond length variation in amorphous silica both for Fe²⁺ and Fe³⁺ ions, e.g. all Fe-O distances were varied in the range [1.8…2.3 Å].

Figure 1 shows geometry parameters for the three-coordinated Fe ions: distance to the nearest oxygen, distance to the rest two oxygens, bending angle (distortions are marked with overlay of two structures for each of three deformations). In the space of structural parameters we selected a set of 700 points where XANES spectra were calculated by means of finite difference approach implemented within FDMNES software. These spectra were used as training set for machine learning method which established the relation between spectrum and structural parameters. The best quality of approximation was achieved for Radial Basis Functions method. After algorithm was trained the PyFitIt software allows user to predict structural parameters for a given spectrum in the input (so called direct method) or predict spectrum for a given set of structural parameters (so called indirect method, the analogue of multidimensional interpolation). Figure 2 shows the analysis of the Muong-Nong tektite spectrum. The two best fits are shown as red and blue lines and use a combination of 6-coordinated iron ions either with 4-coordinated or 3-coordinated species. The resulting parameters of two fits provided average coordination number <CN>=5.4±0.2 and average Fe-O distance <R>=1.96±0.04 Å which are in a good agreement with classical EXAFS analysis.

Copper molybdate (CuMoO₄) is a thermochromic and piezochromic material, which exhibits structural phase transitions under the influence of pressure and/or temperature that make this material perspective in chromic-related applications starting from the user-friendly temperature and pressure indicators to "smart" inorganic pigments.

Since the functional properties of CuMoO₄ are directly connected with its local structure, X-ray absorption spectroscopy (XAS) is an obvious choice to probe structural changes during temperature variation including the phase transition. However, the interpretation of extended X-ray absorption fine structure (EXAFS) and X-ray absorption near-edge structure (XANES) spectra is not straightforward and often requires the use of advanced simulation tools. Treatment of thermal fluctuations and static disorder in XAS is a complex task, which can be successfully addressed by reverse Monte-Carlo (RMC) method [1, 2].

In this study, we used XAS at the Cu and Mo K-edges to probe the temperature-induced evolution of the local structure of CuMoO₄ in the range from 10 to 973 K (Fig. 1). At low temperatures, the thermochromic phase transition between α-CuMoO₄ and γ-CuMoO₄ with a hysteretic behaviour was observed [3] while at temperatures above 400 K, the thermochromic properties of α-CuMoO₄ were related to temperature-induced changes in the O²⁻ → Cu²⁺ charge transfer processes [4].

The structural information encoded in the EXAFS spectra was extracted by RMC simulations based on an evolutionary algorithm (EA) implemented in the EvAX code [1]. This method allows one to obtain a structural model of such complex material as copper molybdate accounting for multiple-scattering effects as well as structural and thermal disorder contributions in the experimental EXAFS data. The structural models obtained by RMC were used to simulate the Cu K-edge XANES spectra at a high-temperature range, in which the temperature effect is the most pronounced. The simulated XANES spectra are in good agreement with the experiment and reproduce the main temperature-dependent XANES features.

[1] J. Timoshenko, A. Kuzmin, and J Purans, (2014) J. Phys.: Condens. Matter 26, 055401.

[2] I. Jonane, A. Anspoks, and A. Kuzmin, (2018) Model. Simul. Mater. Sci. Eng. 26, 025004.

[3] I. Jonane, A. Cintins, A. Kalinko, R. Chernikov, and A. Kuzmin, (2020) Rad. Phys. Chem. 175, 108411.

[4] I. Jonane, A. Anspoks, G. Aquilanti, and A. Kuzmin, (2019) Acta Mater. 179, 1901132.

Developments over the last two decades have achieved accuracies in attenuation coefficient and X-ray absorption fine structure of below 0.2%. This generally requires careful sample characterisation, monochromator and detector characterisation and additional experimental components to measure and correct for a range of systematics. More recently similar levels of accuracy have been obtained in fluorescence measurement. These techniques, XERT developed by Chantler, Barnea, Tran and group; and Hybrid, developed by Chantler, Tran, Best et al. offer accuracies and insight for disordered systems up to 100x more than previous work. To bring them to standard routine implementations for all users would strengthen hypothesis discrimination and testing for molecular and disordered structure and dynamics including for ideal crystals. In this they are complementary to XRD and ND investigations.

Over the past two years parts of this system have been implemented at the Australian Synchrotron with excellent precision and control of a range of systematics using XERT and Hybrid techniques in both transmission and fluorescence geometries.

Insight includes high accuracy of derived dynamical bond length, thermal parameters, consistency and inconsistency of energy offsets revealed from the data, and structural determination of nearby shells approaching an ab initio manner with XAS. It has allowed exploration of atomic form factors [1], XAFS dynamical bonding [2], electron inelastic mean free paths [3] and nanoroughness [4] appropriate for circuit quality control for microcomputers, with technological offshoots into detector and synchrotron diagnostics. As a consequence, the accurate characterization of fluorescence spectroscopy is developing [5], together with the accurate investigation of organometallic complexes. Further it has allowed investigation of several types of dynamic behaviour including the investigation of the reaction coordinate [6], thermal isotropy, and potentially Debye behaviour. The reaction coordinate investigations permit study of catalytic paths in Amyloid beta, and other electrochemical studies of ifficult or fragile organometallic systems in solid or solution form, at room temperature or in a cryostat.

Perhaps intriguingly, it has permitted the first X-ray measurements of electron inelastic mean free path [7]. This paper will explore the requirements for and applicability of higher accuracy in XAFS, the advantage of theory simultaneously fitting XANES and XAFS [8], and the opportunities for advanced dynamics and Debye studies, in addition to the potential for resolving challenges in catalytic and active centres.

The quality of XAFS data and the intrinsic information content can be outstanding, and its ability to determine bonding and dynamical modes can be unsurpassed. The talk will also look towards future opportunities not yet realised in advanced analysis and disorder measurement.

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[2] Glover, JL et al. Measurement of the X-ray mass-attenuation coefficients of gold, derived quantities between 14 keV and 21 keV and determination of the bond lengths of gold, J. Phys. B 43 085001 (2010)

[3] Chantler, CT, Bourke, JD, X-ray Spectroscopic Measurement of the Photoelectron Inelastic Mean Free Paths in Molybdenum, Journal of Physical Chemistry Letters 1 2422 (2010); Bourke, JD, Chantler, CT, Phys. Rev. Lett. 104, 206601 (2010)

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[5] Chantler, CT, et al., Stereochemical analysis of Ferrocene and the uncertainty of fluorescence XAFS data, J Synch. Rad.19 145 (2012)

[6] Best, SP et al., Reinterpretation of Dynamic Vibrational Spectroscopy to Determine the Molecular Structure and Dynamics of Ferrocene, Chemistry - A European Journal, 22 18019-18026 (2016)

[7] Chantler, CT, Bourke, JD, Electron Inelastic Mean Free Path Theory and Density Functional Theory resolving low-Energy discrepancies for low-energy electrons in copper, Journal of Physical Chemistry A118 909-914 (2014)

[8] Bourke, JD et al., FDMX: Extended X-ray Absorption Fine Structure Calculations Using the Finite Difference Method, J Synchrotron Radiation 23 551-559 (2016)

Palladium nanocatalysts play significant role in wide range of reactions such as selective hydrogenation of alkynes. The information extracted during operando experiments on working catalysts allows us to consider various processes from a new point of view. In particular, X-ray absorption near edge structure (XANES) spectroscopy is a powerful tool widely applied for determining atomic and electronic properties of working catalysts [1]. In many cases, analysis of XANES data requires construction of theoretical models with a huge number of variable parameters. In this case, application of machine learning (ML) to in situ and operando XANES offers new horizons for structural characterization [2].

In this work, we discuss the construction of the theoretical models of palladium nanoparticles covering a big number of structural parameters. We investigate how the particle size, concentration of carbon impurities, which can be formed during hydrogenation of alkynes, and their distribution in the bulk and at the surface of palladium particles affect the Pd K-edge XANES features. We demonstrate step-by-step increasing similarity between the experimental difference spectra and theoretical model by increasing the complexity of the theoretical model, e.g. taking into account only interatomic distances (Fig. 1 dashed red), interatomic distances and carbon concentration (Fig. 1 dashed blue) and interatomic distances, carbon concentrations and particle size effects (Fig. 1 green line). Finally, we suggest a set of formal descriptors relevant to possible structural diversity and construct a library of theoretical spectra for ML-based analysis realized in PyFitit software [3].

Figure 1. Experimental difference Pd K-edge XANES for 2.8 nm Pd NPs in acetylene (solid black) and best fit results using theoretical spectra with interatomic distances only (dashed red), interatomic distances and carbon impurities in the bulk (dashed blue), and interatomic distances, carbon impurities in the bulk and surface (solid green) contribution as variable parameters. The best fit made by ML algorithm is represented by purple line [4].

[1] Bordiga, S., Groppo, E., Agostini, G., Bokhoven, J.A. & Carlo Lamberti, C. (2013). Chem. Rev. 113, 1736.

[2] Guda, A.A., Guda, S.A., Lomachenko, K.A., Soldatov, M.A., Pankin, I.A., Soldatov, A.V., Braglia, L., Bugaev A.L., Martini, A., Signorile, M., Groppo, E., Piovano, A., Borfecchia, E. & Lamberti, C. (2019). Catal. Today. 336, 3.

[3] Martini, A., Guda, S.A., Guda, A.A., Smolentsev, G., Algasov, A., Usoltsev, O., Soldatov, M.A., Bugaev, A., Rusalev, Yu., Lamberti, C. & Soldatov, A.V. (2019). Comput. Phys. Commun, 23, 107064.

[4] Usoltsev, O.A., Bugaev, A.L., Guda, A.A., Guda, S.A. & Soldatov, A.V. (2020) Top. Catal., in press.