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 geometrybased and a symmetryadapted 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 symmetryadapted 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 firstprinciples datasets used to parameterize onlattice Hamiltonians.
more » « less NSFPAR ID:
 10305132
 Publisher / Repository:
 Nature Publishing Group
 Date Published:
 Journal Name:
 npj Computational Materials
 Volume:
 7
 Issue:
 1
 ISSN:
 20573960
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

Symmetryadapted distortion modes provide a natural way of describing distorted structures derived from highersymmetry parent phases. Structural refinements using symmetrymode 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 realspace pair distribution function (PDF) data. Here, the value of performing symmetrymode fits to PDF data is further demonstrated through the successful application of this method to two topical materials: TiSe 2 , where a subtle but longrange structural distortion driven by the formation of a chargedensity wave is detected, and MnTe, where a large but highly localized structural distortion is characterized in terms of symmetrylowering displacements of the Te atoms. The analysis is performed using fully opensource 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 symmetryadapted PDF analysis by enabling highthroughput analysis and removing the need for any commercial software.more » « less

We consider a social choice setting in which agents and alternatives are represented by points in a metric space, and the cost of an agent for an alternative is the distance between the corresponding points in the space. The goal is to choose a single alternative to (approximately) minimize the social cost (cost of all agents) or the maximum cost of any agent, when only limited information about the preferences of the agents is given. Previous work has shown that the best possible distortion one can hope to achieve is 3 when access to the ordinal preferences of the agents is given, even when the distances between alternatives in the metric space are known. We improve upon this bound of 3 by designing deterministic mechanisms that exploit a bit of cardinal information. We show that it is possible to achieve distortion 1+sqrt(2) by using the ordinal preferences of the agents, the distances between alternatives, and a threshold approval set per agent that contains all alternatives for whom her cost is within an appropriately chosen factor of her cost for her mostpreferred alternative. We show that this bound is the best possible for any deterministic mechanism in general metric spaces, and also provide improved bounds for the fundamental case of a line metric.more » « less

New additions to quasiracemic materials have been developed by cocrystallizing a ternary component – hydrogen oxalate – with pairs of amino acid quasienantiomers where at least one of the sidechain R groups contains a sulfur atom. Of the eight quasiracemates investigated, six exhibit crystal packing that drastically deviates from the expected centrosymmetric alignment present in the racemic counterparts and the extant database of quasiracemic materials. These structures were quantitatively assessed for conformational similarity (CCDCMercury structure overlay) and the degree of inversion symmetry (Avnir's Continuous Symmetry Measures) for each quasienantiomeric pair. Despite the variance in quasienantiomeric components, these structures exhibit a high degree of isostructurality where the principal components assemble by a complex blend of common N + –H⋯O and O–H⋯O − interactions. These chargeassisted hydrogenbonded networks form thermodynamically favored crystal packing that promotes cocrystallization of a structurally diverse set of quasienantiomeric components.more » « less

null (Ed.)The 2Wasserstein distance (or RMS distance) is a useful measure of similarity between probability distributions with exciting applications in machine learning. For discrete distributions, the problem of computing this distance can be expressed in terms of finding a minimumcost perfect matching on a complete bipartite graph given by two multisets of points A, B ⊂ ℝ2, with A = B = n, where the ground distance between any two points is the squared Euclidean distance between them. Although there is a nearlinear time relative ∊approximation algorithm for the case where the ground distance is Euclidean (Sharathkumar and Agarwal, JACM 2020), all existing relative ∊approximation algorithms for the RMS distance take Ω(n3/2) time. This is primarily because, unlike Euclidean distance, squared Euclidean distance is not a metric. In this paper, for the RMS distance, we present a new ∊approximation algorithm that runs in O(n^5/4 poly{log n, 1/∊}) time. Our algorithm is inspired by a recent approach for finding a minimumcost perfect matching in bipartite planar graphs (Asathulla et al, TALG 2020). Their algorithm depends heavily on the existence of sublinear sized vertex separators as well as shortest path data structures that require planarity. Surprisingly, we are able to design a similar algorithm for a complete geometric graph that is far from planar and does not have any vertex separators. Central components of our algorithm include a quadtreebased distance that approximates the squared Euclidean distance and a data structure that supports both Hungarian search and augmentation in sublinear time.more » « less

Balcite (Ba x Ca 1− x CO 3 ) is a synthetic analog of rhombohedral carbonate minerals like calcite and dolomite that is disordered on both the cation and anion sublattices. Here, we show that multiple exotic superlattice structures, including a dolomite analog that we call balcomite, can form from balcite at elevated temperatures. The secondorder balcitetobalcomite conversion at temperatures between 150–600 °C is driven by the preference of barium and calcium for different oxygen coordination numbers and facilitated by local carbonate reorientation. At elevated pressure, further superlattice order arises from cation segregation in all three dimensions, producing a supercell with the same R 3̄ m symmetry as balcite but 6× larger. This highly ordered structure relaxes back to the balcomite structure upon returning to ambient conditions. None of the three naturally occurring polymorphs of Ba 0.5 Ca 0.5 CO 3 (alstonite, paralstonite, barytocalcite) formed from balcite despite being putatively energetically favored. Instead, alstonite transformed to a balcomitelike structure via a firstorder process after transiently converting to a paralstonitelike structure via a secondorder process. Together, these results show that high temperature transformation pathways between structures in the barium calcium carbonate system can be driven by coarsening and are facilitated by similarity in shortrange order, conceptually analogous to previously described lowtemperature transformations. Many of the exotic high temperature carbonate structures are unstable, but may participate in transformation pathways between naturally observed metastable mineral phases, suggesting important roles for ephemeral phases in shaping past and current mineral distributions.more » « less