X-ray diffraction from powders and single crystals has for decades been the key analytical tool in materials science. Bragg intensities provide information about the average crystals structure, but often it is disorder and specific local structure that control key material properties. For 1D data there has been an immense growth in combined analysis of Bragg and diffuse scattering using the Pair Distribution Function (PDF), and in our group we frequently use 1D PDF analysis to study nanocrystal nucleation in solvothermal processes [1] or thin films [2], or to analyse materials under operating conditions [3]. For single crystals, diffuse scattering studies have a long history with elaborate analysis in reciprocal space, but direct space analysis of the 3D-PDF is still in its infancy. We have used 3D-PDF analysis to study the crystal structures of high performance thermoelectric materials Cu₂Se (Fig 1) [4], PbTe [5], and 19-e half-heusler Nb_1-xCoSb [6], where the true local structure is essential for understanding the unique properties. For frustrated magnetic materials direct space analysis of diffuse magnetic scattering provides a new route to magnetic structures [7].

[1] N. L. N. Broge et al., Auto-catalytic formation of high entropy alloy nanoparticles, Angew. Chem. Intl. Ed., 59, 21920-21924 (2020)

[2] M. Roelsgaard et al., Time-Resolved Surface Pair Distribution Functions during Deposition by RF Magnetron Sputtering, IUCrJ, 6, 299–304 (2019)

[3] L. R. Jørgensen et al., Operando X-ray scattering study of thermoelectric β-Zn₄Sb₃, IUCr-J, 7, 100-104 (2020)

[4] N. Roth et al., Solving the disordered structure of β-Cu_2-xSe using the three-dimensional difference pair distribution function, Acta Crystallogr. Sect. A, 75, 465–473 (2019)

[5] K. A. U. Holm et al., Temperature Dependence of Dynamic Dipole Formation in PbTe, Phys. Rev. B, 102, 024112 (2020)

[6] N. Roth et al., A simple model for vacancy order and disorder in defective half-Heusler systems, IUCrJ, 7, 673-680 (2020)

[7] N. Roth et al., Model-free reconstruction of magnetic correlations in frustrated magnets, IUCr-J, 5, 410–416 (2018)

Many advanced functional properties of crystalline materials derive from complex disorder and short-range correlations that emerge from a subtle balance among competing interactions involving spin, charge, orbital, and strain degrees of freedom. Materials that harbor such disorder generally exhibit strongly enhanced responses, with electronic, magnetic, optical, and thermal properties that are extremely sensitive to perturbations such as magnetic or electric fields and are of considerable importance for future applications. Obtaining a detailed understanding of such complex disorder is required to control and exploit these unusual patterns that persist within short-range ordered states in order to access functional responses inaccessible to conventional, long-range ordered materials. Diffuse scattering is a powerful probe of such complex disorder and when measured from single crystals over large 3D volumes of reciprocal space provides detailed information regarding the existence and morphology of local distortions, as well as defect–defect correlations, i.e., the tendency for defects to cluster into nanoscale ordered structures [1,2].

Recent developments in instrumental advances now efficient measurements of single crystal diffraction data over large volumes of reciprocal space using synchrotron x-rays or neutrons. For the latter, dedicated instrumentation, in particular the Corelli instrument at the Spallation Neutron Source, has been constructed that enables measurements of such volumes with elastic discrimination [3]. The value of combining the complementarity of neutrons and x-rays of such measurements over large space of temperature and compositions will be demonstrated on recent investigation of relaxor ferroelectrics that provide new insight on the relation of local order to material properties relaxors [4]. While analyzing diffuse scattering data and obtaining detailed models of the underlying remains challenging, the availability of comprehensive measurements of the scattering over large 3D volumes enables new ways of analyzing the data, by utilizing the 3D-ΔPDF method [5]. This method allows to derive for example, direct, model free reconstructions of ionic correlations [6], which are essential in many energy materials, as well as magnetic correlations in frustrated magnets [7]. Recent advances in Machine Learning methods further provide invaluable and new, rapid insight into the information contained in these large data sets, in particular when measured over varying experimental parameters such as temperature or external fields [8].

[1] Welberry,T.R. Weber, T. (2016) Crystallography Reviews 22, 2-78[2] see contributions in Issue Diffuse Scattering (2005). Z. Kristallogr. Cryst. Mater. 220, Issue 12[3] Ye, F., et al. (2018). J. Appl. Cryst.. 51, 315 - 322.[4] Krogstad, M.J., et al. (2018). Nat. Mater. 17, 718 - 724.[5] Weber, T., Simonov, A. (2012). Z. Kristallogr. 225, 238.[6] Krogstad, M.J, et al. (2020). Nat. Mater. 19, 63 - 68.[7] Roth, N., May, A.F., Ye, F., Chakoumakos, B.C., Iversen, B.B. (2018). IUrJ. 5, 410.[8] Venderley, J., et al. (2020). Cond-Mat. Archiv arXiv:2008.03275.

Keywords: IUCr2020; abstracts; total scattering; single crystal diffuse scattering, complex disorder, short range correlations

Work supported by U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division

Many important functional materials are complex mixtures that derive their properties from the interplay of various individual component phases. In each case, the interfaces between phases are a crucial component in their own right, since they are the point at which much of the key chemistry (and/or physics) takes place [1, 2]. By their very nature, interfaces are notoriously more difficult to characterise than the bulk phases they connect; and the process of translating experimental measurements into a picture of atomic-scale structure remains a significant general challenge [3]. Here we explore the possibility that pair distribution function (PDF) measurements offer sensitivity to interface structure in a way that is strongly complementary to existing experimental and computational approaches.

Using a non-negative matrix factorisation (NMF) approach [4, 5], we show how the PDF of complex mixtures can be deconvolved into the contributions from the individual phase components and also the interface between phases. Our focus is on the model system Fe||Fe₃O₄. First, we establish proof-of-concept using idealised PDF data generated from established theory-driven models of the Fe|| Fe₃O₄ interface. Using X-ray PDF measurements for corroded Fe samples, and employing our newly-developed NMF analysis, we extract the experimental interface PDF (‘iPDF’) for this same system. We find excellent agreement between theory and experiment.

[1] Baraff, G. A., Appelbaum J. A. & Hamann, D. R. (1977) Phys. Rev. Lett. 38, 237.

[2] Harrison, W. A., Kraut, E. A., Waldrop J. R. & Grant R. W. (1978) Phys. Rev. B 18, 4402.

[3] Goodwin, A. L. (2019) Nat. Commun. 10, 4461.

[4] Lee, D. D. & Seung, H. S. (1999) Nature 401, 788.

[5] Geddes, H. S., Blade, H., McCabe, J. F., Hughes, L. P. & Goodwin, A. L. (2019) Chem. Commun. 55, 13317.

Complementary to x-ray diffraction patterns that represent the crystal lattice in Q space, the atomic pair distribution function (PDF) describes the structure of a material as a histogram of interatomic distances r in real space. The total scattering (TS) approach that enables PDF analysis requires that scattering data is collected over a wide Q range of the order of 20 Å^-1 and subsequent Fourier transformation of the entire scattering pattern into direct space. While TS at high-energy beamlines has become a standard routine for bulk-type samples, the unfavorable thickness ratio of a thin film (nanometer regime) to its substrate (micrometer regime) limits the detectability of the film signal in simple transmission geometry as described e.g. in Ref. [1]. Therefore, we applied the high-energy surface diffraction technique established for single-crystal surfaces [2] to less ordered films and thus pushed the capabilities for PDF analysis of thin films to unprecedented limits in terms of minimum thickness and time resolution. [3,4] Besides polycrystalline and textured metal and oxide layers, we studied amorphous and naocrystalline thin films. By careful data treatment, we successfully derived PDFs of comparable data quality from different HfO₂ films with thicknesses down to 15 nm independent on their degree of ordering with domain sizes between ~5 and >30 Å. All films were deposited on fused silica which provides an easily scalable background to subtract from the sample data to isolate the film signal. Real thin film devices e.g. for electronic applications, however, typically consist of multiple layers, and the film growth is largely affected by the nature of the underlying layer. Therefore, we further developed grazing incidence total scattering towards a depth-resolving method by scanning the incidence angle. In this way, the technique provided insight into the structure of different types of bilayer samples studied for their use e.g. in next-generation computer memory applications. PDFs were successfully extracted from the individual layers of different combinations and stackings of amorphous and crystalline materials exhibiting high and low (electron) density and, hence, x-ray scattering power from TiO₂ to Pt [5]. As thermal treatment is an essential part of thin film device manufacturing, we are developing a laser-interferometer based system that, beyond data collection during isothermal heat-treatment as applied in [4], enables following structural changes during variable-temperature processes up to several hundred degrees. Fig. 1 shows data from the proof-of-concept experiment on a 30 nm HfO₂ thin film deposited by chemical vapor deposition in an amorphous state, crystallized in situ while continuously acquiring TS data.

The antiferromagnetic semiconductor MnTe has recently attracted significant attention as both a high-performance thermoelectric and a candidate material for spintronics. The magnetic properties of MnTe play a crucial role in both of these technological applications. MnTe has a hexagonal layered structure in which magnetic Mn2+ spins order ferromagnetically within the plane and antiferromagnetically between the planes below TN = 307 K. Above TN, robust short-range magnetic correlations survive to high temperature. It has been shown that these short-range correlations are a significant contributor to the high thermoelectric figure of merit zT in MnTe through a mechanism known as paramagnon drag. Here, we present comprehensive atomic and magnetic pair distribution function (PDF) analysis of neutron total scattering data collected from pure and doped MnTe powders, together with three-dimensional magnetic PDF data obtained from a single crystal of MnTe. These complementary data sets allow us to track in detail the evolution of the magnetic correlations from the long-range ordered state at low temperature to the short-range ordered state at high temperature. We present real-space magnetic models that reproduce the observed mPDF patterns with quantitative accuracy and discuss the significance of these results in the context of existing work on MnTe.

The local structure of NaTiSi₂O₆ is examined across its Ti-dimerization orbital-assisted Peierls transition at 210 K. An atomic pair distribution function approach evidences local symmetry breaking pre-existing far above the transition. The analysis shows the dimers evolve on heating into a short-range orbital degeneracy lifted (ODL)[1] state of dual orbital character, present up to at least 490 K. The ODL state is correlated over the length scale spanning ~6 sites of the Ti zigzag chains. Our results imply that the ODL phenomenology extends to strongly correlated electron systems.