Matching Crystal Structures Atom-to-Atom

Félix Therrien, Peter Graf, Vladan Stevanović

Research output: Contribution to journalArticlepeer-review

16 Scopus Citations


Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions and developing models for interface and grain boundary structures. In this work, we formulate the matching of crystals as an optimization problem where the goal is to find the alignment and the atom-to-atom map that minimize a given cost function such as the Euclidean distance between the atoms. We construct an algorithm that directly solves this problem for large finite portions of the crystals and retrieves the periodicity of the match subsequently. We demonstrate its capacity to describe transformation pathways between known polymorphs and to reproduce experimentally realized structures of semi-coherent interfaces. Additionally, from our findings, we define a rigorous metric for measuring distances between crystal structures that can be used to properly quantify their geometric (Euclidean) closeness.

Original languageAmerican English
Article number074106
Number of pages15
JournalThe Journal of Chemical Physics
Issue number7
StatePublished - 21 Feb 2020

Bibliographical note

Publisher Copyright:
© 2020 Author(s).

NREL Publication Number

  • NREL/JA-5K00-76277


  • crystal lattices
  • crystal structure
  • functions and mappings
  • metric geometry
  • optimization problems
  • phase transitions
  • polymorphism


Dive into the research topics of 'Matching Crystal Structures Atom-to-Atom'. Together they form a unique fingerprint.

Cite this