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Symmetry-adapted distortion modes provide a natural way of describing distorted structures derived from higher-symmetry parent phases. Structural refinements using symmetry-mode amplitudes as fit variables have been used for at least ten years in Rietveld refinements of the average crystal structure from diffraction data; more recently, this approach has also been used for investigations of the local structure using real-space pair distribution function (PDF) data. Here, the value of performing symmetry-mode fits to PDF data is further demonstrated through the successful application of this method to two topical materials: TiSe 2 , where a subtle but long-range structural distortion driven by the formation of a charge-density wave is detected, and MnTe, where a large but highly localized structural distortion is characterized in terms of symmetry-lowering displacements of the Te atoms. The analysis is performed using fully open-source code within the DiffPy framework via two packages developed for this work: isopydistort , which provides a scriptable interface to the ISODISTORT web application for group theoretical calculations, and isopytools , which converts the ISODISTORT output into a DiffPy -compatible format for subsequent fitting and analysis. These developments expand the potential impact of symmetry-adapted PDF analysis by enabling high-throughput analysis and removing the need for any commercial software.
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Comparing crystal structures with symmetry and geometry
Abstract Measuring the similarity between two arbitrary crystal structures is a common challenge in crystallography and materials science. Although there are an infinite number of ways to mathematically relate two crystal structures, only a few are physically meaningful. Here we introduce both a geometry-based and a symmetry-adapted similarity metric to compare crystal structures. Using crystal symmetry and combinatorial optimization we describe an algorithm to arrive at the structural relationship that minimizes these similarity metrics across all possible maps between any pair of crystal structures. The approach makes it possible to (i) identify pairs of crystal structures that are identical, (ii) quantitatively measure the similarity between crystal structures, and (iii) find and rank structural transformation pathways between any pair of crystal structures. We discuss the advantages of using the symmetry-adapted cost metric over the geometric cost. Finally, we show that all known structural transformation pathways between common crystal structures are recovered with the mapping algorithm. The methodology presented in this study will be of value to efforts that seek to catalogue crystal structures, identify structural transformation pathways or prune large first-principles datasets used to parameterize on-lattice Hamiltonians.
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- PAR ID:
- 10305132
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Computational Materials
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2057-3960
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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