Comparing crystal structures with symmetry and geometry

Thomas, John C.; Natarajan, Anirudh Raju; Van der Ven, Anton

doi:10.1038/s41524-021-00627-0

Comparing crystal structures with symmetry and geometry

Journal Article · Thu Oct 07 00:00:00 UTC 2021 · npj Computational Materials

DOI:https://doi.org/10.1038/s41524-021-00627-0· OSTI ID:1824706

Thomas, John C.; ;

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.

View Journal Article

Research Organization:: University of California, Oakland, CA (United States); University of California, Santa Barbara, CA (United States); University of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)

Grant/Contract Number:: AC02-05CH11231; SC0008637

OSTI ID:: 1824706

Alternate ID(s):: OSTI ID: 1978592

Journal Information:: npj Computational Materials, Journal Name: npj Computational Materials Journal Issue: 1 Vol. 7; ISSN 2057-3960

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (58)

Factoring polynomials with rational coefficients Lenstra, A. K.; Lenstra, H. W.; Lov�sz, L. Mathematische Annalen, Vol. 261, Issue 4 https://doi.org/10.1007/BF01457454	journal	December 1982
Simple models for the omega phase transformation Fontaine, D. Metallurgical Transactions A, Vol. 19, Issue 2 https://doi.org/10.1007/BF02652523	journal	February 1988
An X-ray examination of the to phase in TiV, TiMo and TiCr alloys Silcock, J. M. Acta Metallurgica, Vol. 6, Issue 7 https://doi.org/10.1016/0001-6160(58)90111-1	journal	July 1958
The ω-phase in zirconium base alloys Hatt, B. A.; Roberts, J. A. Acta Metallurgica, Vol. 8, Issue 8 https://doi.org/10.1016/0001-6160(60)90112-7	journal	August 1960
Mechanical instabilities in the b.c.c. lattice and the beta to omega phase transformation De Fontaine, D. Acta Metallurgica, Vol. 18, Issue 2 https://doi.org/10.1016/0001-6160(70)90035-0	journal	February 1970
Generalized cluster description of multicomponent systems Sanchez, J. M.; Ducastelle, F.; Gratias, D. Physica A: Statistical Mechanics and its Applications, Vol. 128, Issue 1-2 https://doi.org/10.1016/0378-4371(84)90096-7	journal	November 1984
On the process of transition of the cubic-body-centered modification into the hexagonal-close-packed modification of zirconium Burgers, W. G. Physica, Vol. 1, Issue 7-12 https://doi.org/10.1016/S0031-8914(34)80244-3	journal	May 1934
Cluster Approach to Order-Disorder Transformations in Alloys Fontaine, D. De Solid State Physics, p. 33-176 https://doi.org/10.1016/S0081-1947(08)60639-6	book	January 1994
Perspectives on Titanium Science and Technology Banerjee, Dipankar; Williams, J. C. Acta Materialia, Vol. 61, Issue 3 https://doi.org/10.1016/j.actamat.2012.10.043	journal	February 2013
Recursive alloy Hamiltonian construction and its application to the Ni-Al-Cr system Goiri, Jon Gabriel; Van der Ven, Anton Acta Materialia, Vol. 159 https://doi.org/10.1016/j.actamat.2018.06.048	journal	October 2018
Crystallography, thermodynamics and phase transitions in refractory binary alloys Natarajan, Anirudh Raju; Dolin, Pavel; Van der Ven, Anton Acta Materialia, Vol. 200 https://doi.org/10.1016/j.actamat.2020.08.034	journal	November 2020
AFLOWLIB.ORG: A distributed materials properties repository from high-throughput ab initio calculations Curtarolo, Stefano; Setyawan, Wahyu; Wang, Shidong Computational Materials Science, Vol. 58 https://doi.org/10.1016/j.commatsci.2012.02.002	journal	June 2012
Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis Ong, Shyue Ping; Richards, William Davidson; Jain, Anubhav Computational Materials Science, Vol. 68 https://doi.org/10.1016/j.commatsci.2012.10.028	journal	February 2013
MultiShifter: Software to generate structural models of extended two-dimensional defects in 3D and 2D crystals Goiri, Jon Gabriel; Van der Ven, Anton Computational Materials Science, Vol. 191 https://doi.org/10.1016/j.commatsci.2021.110310	journal	April 2021
Identifying duplicate crystal structures: XtalComp, an open-source solution Lonie, David C.; Zurek, Eva Computer Physics Communications, Vol. 183, Issue 3 https://doi.org/10.1016/j.cpc.2011.11.007	journal	March 2012
Bayesian uncertainty quantification in the evaluation of alloy properties with the cluster expansion method Kristensen, Jesper; Zabaras, Nicholas J. Computer Physics Communications, Vol. 185, Issue 11 https://doi.org/10.1016/j.cpc.2014.07.013	journal	November 2014
Quantifying uncertainties in first-principles alloy thermodynamics using cluster expansions Aldegunde, Manuel; Zabaras, Nicholas; Kristensen, Jesper Journal of Computational Physics, Vol. 323 https://doi.org/10.1016/j.jcp.2016.07.016	journal	October 2016
The exploration of nonlinear elasticity and its efficient parameterization for crystalline materials Thomas, John C.; Van der Ven, Anton Journal of the Mechanics and Physics of Solids, Vol. 107 https://doi.org/10.1016/j.jmps.2017.06.009	journal	October 2017
Crystallographic features of phase transformations in solids Zhang, Ming-Xing; Kelly, Patrick M. Progress in Materials Science, Vol. 54, Issue 8 https://doi.org/10.1016/j.pmatsci.2009.06.001	journal	November 2009
Toward an Understanding of Deformation Mechanisms in Metallic Lithium and Sodium from First-Principles Raju Natarajan, Anirudh; Van der Ven, Anton Chemistry of Materials, Vol. 31, Issue 19 https://doi.org/10.1021/acs.chemmater.9b03422	journal	September 2019
Evolutionary approach for determining first-principles hamiltonians Hart, Gus L. W.; Blum, Volker; Walorski, Michael J. Nature Materials, Vol. 4, Issue 5 https://doi.org/10.1038/nmat1374	journal	April 2005
The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies Kirklin, Scott; Saal, James E.; Meredig, Bryce npj Computational Materials, Vol. 1, Issue 1 https://doi.org/10.1038/npjcompumats.2015.10	journal	December 2015
Machine-learning the configurational energy of multicomponent crystalline solids Natarajan, Anirudh Raju; Van der Ven, Anton npj Computational Materials, Vol. 4, Issue 1 https://doi.org/10.1038/s41524-018-0110-y	journal	November 2018
AFLOW-XtalFinder: a reliable choice to identify crystalline prototypes Hicks, David; Toher, Cormac; Ford, Denise C. npj Computational Materials, Vol. 7, Issue 1 https://doi.org/10.1038/s41524-020-00483-4	journal	February 2021
Linking electronic structure calculations to generalized stacking fault energies in multicomponent alloys Natarajan, Anirudh Raju; Van der Ven, Anton npj Computational Materials, Vol. 6, Issue 1 https://doi.org/10.1038/s41524-020-0348-z	journal	June 2020
Materials Cloud, a platform for open computational science Talirz, Leopold; Kumbhar, Snehal; Passaro, Elsa Scientific Data, Vol. 7, Issue 1 https://doi.org/10.1038/s41597-020-00637-5	journal	September 2020
Commentary: The Materials Project: A materials genome approach to accelerating materials innovation Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy APL Materials, Vol. 1, Issue 1 https://doi.org/10.1063/1.4812323	journal	July 2013
Structural phase transitions I. Landau theory Cowley, R. A. Advances in Physics, Vol. 29, Issue 1 https://doi.org/10.1080/00018738000101346	journal	February 1980
Construction of crystal structure prototype database: methods and applications Su, Chuanxun; Lv, Jian; Li, Quan Journal of Physics: Condensed Matter, Vol. 29, Issue 16 https://doi.org/10.1088/1361-648X/aa63cd	journal	March 2017
The NOMAD laboratory: from data sharing to artificial intelligence Draxl, Claudia; Scheffler, Matthias Journal of Physics: Materials, Vol. 2, Issue 3 https://doi.org/10.1088/2515-7639/ab13bb	journal	May 2019
Systematic pathway generation and sorting in martensitic transformations: Titanium α to ω Trinkle, D. R.; Hatch, D. M.; Stokes, H. T. Physical Review B, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRevB.72.014105	journal	July 2005
Algorithm for generating derivative structures Hart, Gus L. W.; Forcade, Rodney W. Physical Review B, Vol. 77, Issue 22 https://doi.org/10.1103/PhysRevB.77.224115	journal	June 2008
Bayesian approach to cluster expansions Mueller, Tim; Ceder, Gerbrand Physical Review B, Vol. 80, Issue 2 https://doi.org/10.1103/PhysRevB.80.024103	journal	July 2009
Compressive sensing as a paradigm for building physics models Nelson, Lance J.; Hart, Gus L. W.; Zhou, Fei Physical Review B, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevB.87.035125	journal	January 2013
Thermodynamics of the Zr-O system from first-principles calculations Puchala, B.; Van der Ven, A. Physical Review B, Vol. 88, Issue 9 https://doi.org/10.1103/PhysRevB.88.094108	journal	September 2013
Cluster expansion made easy with Bayesian compressive sensing Nelson, Lance J.; Ozoliņš, Vidvuds; Reese, C. Shane Physical Review B, Vol. 88, Issue 15 https://doi.org/10.1103/PhysRevB.88.155105	journal	October 2013
Finite-temperature properties of strongly anharmonic and mechanically unstable crystal phases from first principles Thomas, John C.; Ven, Anton Van der Physical Review B, Vol. 88, Issue 21 https://doi.org/10.1103/PhysRevB.88.214111	journal	December 2013
Elastic properties and stress-temperature phase diagrams of high-temperature phases with low-temperature lattice instabilities Thomas, John C.; Van der Ven, Anton Physical Review B, Vol. 90, Issue 22 https://doi.org/10.1103/PhysRevB.90.224105	journal	December 2014
Phase and structural stability in Ni-Al systems from first principles Goiri, Jon Gabriel; Van der Ven, Anton Physical Review B, Vol. 94, Issue 9 https://doi.org/10.1103/PhysRevB.94.094111	journal	September 2016
First-principles investigation of phase stability in the Mg-Sc binary alloy Natarajan, Anirudh Raju; Van der Ven, Anton Physical Review B, Vol. 95, Issue 21 https://doi.org/10.1103/PhysRevB.95.214107	journal	June 2017
Connecting the Simpler Structures to Topologically Close-Packed Phases Natarajan, Anirudh Raju; Van der Ven, Anton Physical Review Letters, Vol. 121, Issue 25 https://doi.org/10.1103/PhysRevLett.121.255701	journal	December 2018
New Mechanism for the α to ω Martensitic Transformation in Pure Titanium Trinkle, D. R.; Hennig, R. G.; Srinivasan, S. G. Physical Review Letters, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevLett.91.025701	journal	July 2003
Resolving phase stability in the Ti-O binary with first-principles statistical mechanics methods Gunda, N. S. Harsha; Puchala, Brian; Van der Ven, Anton Physical Review Materials, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevMaterials.2.033604	journal	March 2018
First-principles insights on phase stability of titanium interstitial alloys Gunda, N. S. Harsha; Van der Ven, Anton Physical Review Materials, Vol. 2, Issue 8 https://doi.org/10.1103/PhysRevMaterials.2.083602	journal	August 2018
Finite-temperature simulation of anharmonicity and octahedral tilting transitions in halide perovskites Bechtel, Jonathon S.; Thomas, John C.; Van der Ven, Anton Physical Review Materials, Vol. 3, Issue 11 https://doi.org/10.1103/PhysRevMaterials.3.113605	journal	November 2019
Order-disorder versus displacive transitions in Jahn-Teller active layered materials Radin, Maxwell D.; Thomas, John C.; Van der Ven, Anton Physical Review Materials, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevMaterials.4.043601	journal	April 2020
Discovering hierarchies among intermetallic crystal structures Kolli, Sanjeev Krishna; Natarajan, Anirudh Raju; Thomas, John C. Physical Review Materials, Vol. 4, Issue 11 https://doi.org/10.1103/PhysRevMaterials.4.113604	journal	November 2020
CMPZ – an algorithm for the efficient comparison of periodic structures Hundt, R.; Schön, J. C.; Jansen, M. Journal of Applied Crystallography, Vol. 39, Issue 1 https://doi.org/10.1107/S0021889805032450	journal	January 2006
STRUCTURE TIDY – a computer program to standardize crystal structure data Gelato, L. M.; Parthé, E. Journal of Applied Crystallography, Vol. 20, Issue 2 https://doi.org/10.1107/S0021889887086965	journal	April 1987
A Procedure for the Clasification of Non-Organic Crystal Structures. I. Theoretical Background Burzlaff, H.; Malinovsky, Y. Acta Crystallographica Section A Foundations of Crystallography, Vol. 53, Issue 2 https://doi.org/10.1107/S0108767396013852	journal	March 1997
Method for the computational comparison of crystal structures Willighagen, E. L.; Wehrens, R.; Verwer, P. Acta Crystallographica Section B Structural Science, Vol. 61, Issue 1 https://doi.org/10.1107/S0108768104028344	journal	January 2005
Method of crystal-structure similarity searching Dzyabchenko, A. V. Acta Crystallographica Section B Structural Science, Vol. 50, Issue 4 https://doi.org/10.1107/S0108768193013552	journal	August 1994
Comparison of structures applying the tools available at the Bilbao Crystallographic Server de la Flor, Gemma; Orobengoa, Danel; Tasci, Emre Journal of Applied Crystallography, Vol. 49, Issue 2 https://doi.org/10.1107/S1600576716002569	journal	March 2016
Recent developments in the Inorganic Crystal Structure Database: theoretical crystal structure data and related features Zagorac, D.; Müller, H.; Ruehl, S. Journal of Applied Crystallography, Vol. 52, Issue 5 https://doi.org/10.1107/S160057671900997X	journal	September 2019
Algorithms for the Assignment and Transportation Problems Munkres, James Journal of the Society for Industrial and Applied Mathematics, Vol. 5, Issue 1 https://doi.org/10.1137/0105003	journal	March 1957
First-Principles Statistical Mechanics of Multicomponent Crystals Van der Ven, A.; Thomas, J. C.; Puchala, B. Annual Review of Materials Research, Vol. 48, Issue 1 https://doi.org/10.1146/annurev-matsci-070317-124443	journal	July 2018
Letter to the Editor—An Algorithm for Ranking all the Assignments in Order of Increasing Cost Murty, Katta G. Operations Research, Vol. 16, Issue 3 https://doi.org/10.1287/opre.16.3.682	journal	June 1968
Automating first-principles phase diagram calculations Walle, A.; Ceder, G. Journal of Phase Equilibria, Vol. 23, Issue 4 https://doi.org/10.1361/105497102770331596	journal	August 2002

Similar Records

A structural interpretation of the Southwestern Venezuelan Andes

Conference · Mon Feb 01 04:00:00 UTC 1993 · AAPG Bulletin (American Association of Petroleum Geologists); (United States) · OSTI ID:6102180

Fundamental cosmology from ANDES precision spectroscopy

Journal Article · Fri May 05 00:00:00 UTC 2023 · Monthly Notices of the Royal Astronomical Society · OSTI ID:1974254

Related Subjects

36 MATERIALS SCIENCE
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Comparing crystal structures with symmetry and geometry

Citation Formats

References (58)

Similar Records

Related Subjects