A characteristic feature of quantum materials is the presence of lattice degrees of freedom manifesting themselves as local structural distortions leading to competing ground state phases and exotic behavior. More often than not, the distortions are not well expressed and/or perfectly periodic, making it difficult to identify and quantify them using traditional crystallographic techniques. We will demonstrate the advantages of total x-ray scattering and large-scale structure modeling in studying the temperature and composition evolution of lattice instabilities related to the emergence of charge density wave (CDW) and superconducting (SC) orders in archetypal Ta(Se/Te)₂ quantum materials. In particular, we will show that the low-temperature CDW phase of hexagonal 2H-TaSe₂ emerges via a gradual buildup of locally correlated clusters of Ta atoms, and not via a sudden onset of a Ta superstructure at the transition temperature [1]. We will also show the presence of a hierarchical relationship among the crystal lattice, CDW and SC orders in ternary Ta-Te-Se solid solutions, where different degrees of crystal lattice order appear to promote and maintain the competing CDW and SC orders to a different extent. The relationship may well explain the observed irregular evolution of the SC transition temperature with the relative Te to Se ratio in the solid solutions [2].

1. V. Petkov et al. Phys. Rev. B 101, 121114(R) (2020).
2. V. Petkov et al. Phys. Rev. B 103, 094101 (2021).

Modern materials science is increasingly concerned with the engineering of the periodic and aperiodic features of crystalline materials, thus making structural information on both aspects a key analytical target. In this regard, diffuse scattering from single-crystal diffraction data contains a wealth of structural information, which has been already used to unravel the local 3D structures of several inorganic and organic materials.^[1] Yet, the use of this analysis remains a long-lasting challenge in the field of one of the most researched and ubiquitous materials, metal–organic frameworks (MOFs).

In our work, we elucidated the defect structure of the renowned MOF ZIF-90^[2] by Monte Carlo based single-crystal diffuse scattering simulations (Figure 1). Our analysis showed how correlated disorder of framework components induces lattice distortions affecting the framework local symmetry and porosity. Moreover, we observed that these characteristics are influenced by the synthetic conditions and are always present in ZIF-90 crystals. While allowing a new understanding of the structure-property relationship of this MOF, our study provides a blueprint for future total-scattering studies of MOF single crystals featuring entangled substitutional and displacive disorder.

[1] T. R. Welberry, T. Weber, Crystallography Reviews 2016, 22, 2–78.

[2] W. Morris, C. J. Doonan, H. Furukawa, R. Banerjee, O. M. Yaghi, Journal of the American Chemical Society 2008, 130, 12626–12627.

There is no question that atomic pair distribution function analysis has had a profound impact on the analysis of crystalline and amorphous materials[1]. As a complement to the use of synchrotron sources for collecting PDF data, we have explored the use of home laboratory-based single crystal diffractometers to analyze both crystalline and amorphous materials. In order to generate the most useful reduced radial distribution functions, G(r), we have found it necessary to modify existing code in CrysAlis^Pro[2] and develop new code to generate G(r) data for refinement in PDFgui[3]. In this presentation we will explore the collection and analysis of total scattering data on both crystalline and amorphous materials with wavelengths readily available to home laboratory systems.

[1] Underneath the Bragg Peaks: Structural Analysis of Complex Materials, T. Egami and S. J. L. Billinge, Elsevier, Amsterdam, 2012, ISBN: 978-0-08-097133-9.

[2] Rigaku Oxford Diffraction, (2021), CrysAlisPro Software system, version 1.171.41.64, Rigaku Corporation, Wrocław, Poland.

[3] C. L. Farrow, P. Juhás, J. W. Liu, D. Bryndin, E. S. Božin, J. Bloch, Th. Proffen and S. J. L. Billinge, PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals, J. Phys.: Condens. Matter, 19, 335219 (2007)

Reverse Monte Carlo (RMC) model is a powerful tool based on supercell approach, targeting at the structure model that explains comprehensive experimental datasets. Typically, the RMCProfile package can incorporate neutron/X-ray total scattering, Bragg and extended X-ray absorption fine structure (EXAFS) data. For practical implementation, apart from theoretical pattern calculation and structure model adjustment based on metropolis algorithm, there are various effects under certain circumstances that one needs to take into account to avoid artificial effects. Here we are going to introduce several different types of correction that we recently developed and implemented, in the framework of RMCProfile, namely, 1) the correction for nano-size effect concerning total scattering modelling for nano-systems from 0D nanoparticles to 2D nanosheets [1]. 2) the implementation of arbitrary Bragg peak profile in a tabulated manner, through interacting with Topas software [2]. 3) the correction for finite instrument resolution effect going beyond the conventionally used analytical approach based on Gaussian assumption for peak shape [2]. Through such development and implementation, we hope to extend the scope of application of RMCProfile package for solving structural problems from local perspective. Typically, the implementation of resolution correction enables the modelling to an otherwise-unreachable super-large length scale, e.g., 100 Å, following the supercell approach.

Thin film structures that exhibit exotic phases and topologies have attracted the attention of diverse condensed matter communities. X-ray characterization-based investigations on such systems have been so far restricted to the study of microstructural analysis such as epitaxial match between substrate and film and of the polarization domain sizes and arrangements. Detailed investigations of the local atomic structure and the complex interplay between polarization states within the domains and the domain walls have remained elusive with X-ray diffraction. Here, we present an approach for atomic-scale structural characterization of ferroelectric single crystalline thin films based on comprehensive three-dimensional diffuse scattering data sets. The diffuse scattering will be evaluated with the three-dimensional pair distribution function (3D-ΔPDF) method¹. Specifically, we investigate superlattices of alternating ferroelectric lead titanate and dielectric strontium titanate layers with complex electrical polarization structures^2,3. This work does not only gain insights on structure-property correlations of epitaxially grown single crystalline thin films, but also lay groundwork for developing experimental and modelling tools for analyzing the local structures of thin films.

¹ Weber & Simonov 2012

² Yadav A. et al. 2016

³ A. R. Damodaran et al. 2017

in the attached file