Matching Crystal Structures Atom-to-Atom: Applications to Phase Transitions and Interface Structures*

Finding an optimal match between two different crystal structures underpins many important materials science problems including describing solid-solid phase transitions, developing models for interface and grain boundary structures, finding suitable substrates and their orientation, etc. We designed and implemented an algorithm that tackles this problem by finding the atom-to-atom map and alignment that minimizes a chosen distance function. We demonstrate its capacity to describe transformation pathways of several solid-solid transformations. In particular we show its ability to seamlessly predict important experimentally observed characteristics of the martensitic transformation of steel. Next, we study several interfaces and show our method's relevance in predicting interfacial planes and their orientation relationships. Finally, from our findings, we define a rigorous metric for measuring distances between crystal structures and use it as a tool to screen the Inorganic Crystal Structure Database.