Structure determination using Reverse Monte Carlo (RMC) relies on atomistic moves where, after each move, the target property is computed and compared to experiment. The move is accepted if improving the agreement and accepted only with a probability if not. Since of the order a few hundred million moves need to be performed, this requires very rapid evaluation of the property in question. Typical applications include X-ray and neutron scattering and EXAFS in single-scattering mode. Different experimental probes are sensitive to different structural aspects, however, and it can thus be advantageous to combine with, e.g., spectroscopic data to narrow down the range of solutions.

To this end we have developed SpecSwap-RMC [1-3] which performs RMC on a large library of potential structures with precomputed scattering and spectroscopic signals associated with each structure. A subset of structures is selected and all properties built from the selected structures and compared to the experimental data. The RMC is then performed by exchanging structures instead of moving atoms. A set of weights is then generated based on how often each structure is found in the sample set when probed. These SpecSwap-RMC weights can then be used to reweigh the library, to extract an average structure that is consistent simultaneously with all the supplied data.

I will give examples of applications to liquid water, where we combine X-ray diffraction (XRD) and multiple-scattering EXAFS [2], to ice where we use SpecSwap-RMC to analyse what structures have actually been measured in XAS on various samples [4], and discuss XRD, NMR, XAS and XES [5] data on liquid water.

[1] M. Leetmaa, K.T. Wikfeldt, L.G.M. Pettersson, J. Phys.: Cond. Mat. 22 (2010) 135001

[2] K.T. Wikfeldt et al., J. Chem. Phys. 132 (2010) 104513

[3] https://github.com/leetmaa/SpecSwap-RMC.

[4] I. Zhovtobriukh, P. Norman, L.G.M. Pettersson, J. Chem. Phys. 150 (2019) 034501

[5] I. Zhovtobriukh et al., Science China 62 (2019) 107010

Materials containing microporous networks are an important topic of study for the development of improved technologies for a wide variety of applications including catalysis and gas storage. Widespread interest in metal– and more recently covalent–organic frameworks (MOFs/COFs) endures due to wide-ranging topologies and functionalities imbued by apparently limitless combinations of structural building units. However, while the focus remains primarily on crystalline products, semantics of how to interpret said crystallinity can vary widely in different communities, sometimes leading to oversight of important aspects of the structure that have essential implications on the material properties, or help to understand formation and functionalization processes [1].

The characterization of layered COFs in particular is difficult due to the presence of only a few, low-angle peaks in their diffraction patterns. This has led to a longstanding, dichotomous relationship between expectations based on energetic calculations and the structures observed by diffraction. We have recently demonstrated an experimental resolution, by considering the total rather than just Bragg scattering, and pair distribution function (PDF) analysis, to show how high apparent symmetries can emerge from random, local offsets of the layers [2].

Equipped with a fresh tool-set to characterize these structures, this talk will discuss our on-going efforts in this area — leveraging different length-scale sensitivities of real- and reciprocal-space vantage points for building and fitting models to obtain a more precise depiction of the structural states contained within.

[1] Grunenberg, L., Savasci, G., Terban, M. W., Duppel, V., Moudrakovski, I., Etter, M., Dinnebier, R. E., Ochsenfeld, C. & Lotsch, B. V. (2021). J. Am. Chem. Soc. 143, 3430.
[2] Pϋtz, A. M., Terban, M. W., Bette, S., Haase, F., Dinnebier, R. E. & Lotsch, B. V. (2020). Chem. Sci. 11, 12647.

Development of novel electrode materials for intercalation type batteries have in the past focused on highly crystalline materials with the capability to retain long-range order during cycling. However, recent years have seen an increased interest for disordered materials, e.g. with the discovery of multiple high capacity electrodes based on disordered rock-salt structures or even completely amorphous materials exhibiting higher capacities than their crystalline counterparts [1,2]. Furthermore, it was recently showed by Ceder and co-workers, that long-range order is not a prerequisite for maintaining percolating intercalation pathways [3]. Still very little is known about the structural mechanisms behind order-disorder transitions induced by ion-intercalation or about ion-storage mechanisms in disordered mate-rials. This is in spite that fact that understanding these processes may also provide enhanced insights about how disorder influences the properties of traditional ordered electrodes.

Using operando synchrotron X-ray total scattering with pair distribution function analysis, we have studied a series of battery electrode materials, which undergo severe disordering during charge or discharge, i.e. during ion-extraction or -intercalation [4]. This allows us to map out the structural evolution during battery charge and discharge at the atomic-scale, and begin to understand the ion-storage mechanisms in such materials. The studied materials cover both Li-, Na and Mg-ion electrode materials composed of transition metal (Tm) oxides and phosphates with both layered and 3D-framework structures, e.g. Na_xTmO₂, Na_xFePO₄, Li_xTiO₂, Li_xV₂O₅ etc.[4] Our findings reveal that the order-disorder transition can occur both reversibly and irreversibly, via topotactic or completely reconstructive transitions and entail several disordering phenomena such as cation disorder, nano-crystallization, amorphization etc. This talk will illustrate the large variety in order-disorder phenomena within battery electrodes and highlight our methodology for the operando total scattering studies and pair distribution function analysis.

[1] Lee,, J., Kitchaev, D. A., Kwon, D.-H. Lee, J. K,. Papp, C.-W., Liu, Y.-S., Lun, Z., Clément, R. J., Shi, T., McCloskey, B. D., Guo, J., Balasubramanian, M., Ceder, G. (2018) Nature 556, 185-190.

[2] Uchaker, E., Zheng, Y. Z., Li, S., Candelaria, S. L., Hu, S., Cao, G. Z. (2014) J. Mater. Chem. A 2, 18208-18214.

[3] Lee, J., Urban, A., Li, X., Su, D., Mautier, G., Ceder, G. (2014) Science 343, 519-522.

[4] Christensen, C. K., Ravnsbæk, D. B. (2021) J Phys Energy DOI: 10.1088/2515-7655/abf0f1

To close the carbon cycle, the direct hydrogenation of CO₂ to methanol (CH₃OH) plays a key role allowing to convert a major greenhouse gas into a valuable energy carrier and platform chemical.^[1] Supported bimetallic catalysts are gaining increasing attention for CO₂ hydrogenation reaction due to the possibility of tuning their catalytic properties by judicious choice of the ratio of the alloying elements. The development of highly active and selective catalysts for CO₂ hydrogenation relies hence on obtaining a fundamental understanding of the relationship between a catalyst’s structure and its activity. However, heterogeneous catalysts are complex systems, typically composed of various phases and sites that exhibit different functionalities which requires the use of multiple and complementary techniques for their characterization. ^[2] X-ray absorption spectroscopy and atomic pair distribution function analysis (PDF) of X-ray total scattering data can provide detailed information on the structure of bimetallic supported nanoparticles. XAS, being element selective, allows to study the electronic state and geometry of each metal via XANES analysis (X-ray absorption near edge structure analysis) and their local atomic structure between ~1-5 Å by EXAFS (extended X-ray absorption fine structure) analysis. Probing the longer-range order (i.e. above ca. 5 Å) via EXAFS analysis is however challenging. PDF can interrogate the local to nanoscale structure of supported bimetallic nanoparticles, extending substantially the atomic length scale that can be studied, from ~1 Å up to several nanometers. In this presentation, we will show how XAS (Ni and Ga K-edges) and PDF analyses provide structural information of a series of Ni_xGa_y nanoparticles supported on SiO₂ (total metal loading of ca. 5 w.%). The PDF analysis was performed via a so-called differential PDF approach, i.e. subtracting the signal of the SiO₂ support and, thus, allowing us to characterize the nanocrystalline phases (disordered or intermetallic alloys) of the supported nanoparticles. Ga K-edge XANES and EXAFS reveal the presence of GaO_x species while Ni XANES and EXAFS confirm the presence of Ni⁰. Thus, combining the information obtained via XAS and PDF techniques is highly important to obtain a full atomic to nanoscale description of heterogeneous catalysts.

Crystalline phases are usually characterised by their periodic structures and space group symmetry. However, some crystalline materials have periodic structures only on average and deviate on a local scale. Several different locally ordered structures can exist with identical average periodic structure and space group symmetry, making them difficult to distinguish using regular crystallographic techniques.

Using high-quality single-crystal x-ray diffuse scattering the local order in thermoelectric half-Heusler Nb_1-xCoSb is investigated, for which different local orderings are observed. Half-Heusler materials have been intensely studied for their thermoelectric properties, but a general issue is their high thermal conductivity due to their simple structure. The defective half-Heuslers such as Nb_1-xCoSb have high vacancy concentrations (x=1/6), giving them much lower thermal conductivities than other half-Heusler compounds. From measurements on different samples of Nb_1-xCoSb, it is shown that crystals with identical stoichiometry and average crystal structure, but with different locally ordered structures, can be made by changing the synthesis method. The local structures in these samples are analysed using the three-dimensional difference pair distribution function (3D-ΔPDF).

A new method is shown which allows isolation of the substitutional correlations in the 3D-ΔPDF, showing that the vacancy distributions follow a vacancy repulsion model. Furthermore, the local structural relaxations around vacancies are quantised from analysis of Bragg peaks and 3D-ΔPDF. From the found short-range correlations, a physical model of the system is simulated using Monte-Carlo methods, and it is shown that the different samples correspond to the ground state and simulated quenched states of the model.

Advanced x-ray scattering techniques can unravel hidden local structures and for Nb_1-xCoSb these local structures can be controlled by the synthesis conditions. If the local structure of crystalline materials can be more generally related to the properties, then a new frontier in materials research will be available.

Aluminosilicate-based oxide-glasses are natural materials forming volcanic magmas [1] and frequently the main constituent of manufactured products like ceramic glazes, fiber optic materials and, more recently, biocompounds [2]. To characterise the atomic structure of these materials requires techniques sensitive to the very local structural environment, like spectroscopies (i.e. Nuclear Magnetic Resonance - NMR, Extended X-ray Absorption Fine Structure – EXAFS) and scattering methods (i.e. Total Scattering), due to their lack in periodic order that prevents the application of conventional crystallography. The oxide-glass structure is shaped by silicon centered corner-sharing tetrahedra, which can be combined, depending on composition, with aluminium centered motifs, while large cations like sodium, potassium and calcium tend to depolymerize the network, affecting, in this way, some of the glass properties, such as thermal expansion and glass transition temperature, as demonstrated in a previous study [3]. The glass structural complexity increases when their composition involves some intermediate element, like zinc and beryllium, whose role in the network can vary as a function of the bulk composition, see [4] for some examples. This is the case of the present study that is based on a structural modeling of 2 series of different aluminosilicate-based oxide-glasses with different zinc amounts (3 samples each series). These samples have been prepared by melt-quenching route at 1350°C and then measured by combining EXAFS spectroscopy (BM23 beamline, ESRF, France) with both neutron (SANDALS instrument, ISIS, UK) and synchrotron (ID11 beamline, ESRF, France) Total Scattering data. Zn K-edge EXAFS has been applied at the beginning, in order to evaluate some of the bond distances and the Zn geometrical environment, and this information is used later as constraints for total scattering data modelling, performed by the Empirical Potential Structure Refinement (EPSR) method [5]. The refinements show good residuals, as displayed in Figure 1 (on the left-hand side) and the results indicate that zinc is mostly 4-fold coordinated, but with some 3-fold, 5-fold and 6-fold species. In such complex glasses, therefore, the parameters describing the polymerization degree, like NBO (Non-Bonding-Oxygens), BO (Bonding Oxygens) and triclusters are not predictable by theoretical models, based on prior assumptions of the structural role of zinc. Figure 1 (on the right-hand side) shows the variations of NBO with ZnO mole fraction, comparing the results of this work and of theoretical calculations. Furthermore, the data modelling gave access to a wide number of structural parameters like bond angles, cluster size and cation charge compensating characteristics, that are valuable for further structure-properties studies.