Matching crystal structures atom-to-atom

Abstract

Finding an optimal match between two crystal structures underpins many important materials science problems including describing solid-solid phase transitions, developing models for interface and grain boundary structures, etc. 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.

A method to computationally screen for tunable properties of crystalline alloys

“… 26 Such pairs are not included in this database; however, advances in methodologies for determining whether displacive phase transformations are possible between a given pair of materials could allow the database to be expanded in future. 41 , 42 In some cases, incommensurate structures, where symmetries are distinct from one another but can be connected through a reconstructive transformation, can also form heterostructural alloys, which are of increased interest for materials design (e.g., rocksalt MnO and wurtzite ZnO can alloy to form Mn x Zn 1− x O). 26 Similarly, a material might be tuned by varying vacancy concentration topotactically (e.g., NiO x ).…”

Pathway for a martensitic quartz–coesite transition

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Figure 2 Distribution of the distances which atoms have to move during a martensitic transformation. The distances for silicon and oxygen in the martensitic transition from quartz to coesite are compared to the FCC to BCC martensitic transition in iron, reproduced from Therrien et al 45 . The transformation cell of Fe was rescaled to match the number of atoms in the quartz–coesite transformation cell.

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“…We interpolated the intermediate structures by a geometric approach and perform the geometry optimization by DFT of only a few intermediate structures as a second step (for details see Methods). Here, the intermediate structures of the martensitic transformation pathway from quartz to coesite were generated using the p2ptrans package 45 and then employed in density functional theory (DFT-GGA-PBE), and density functional theory tight binding (DFTB) model calculations.…”

Tunable properties and composition of ZnO films supported on metal surfaces

“…Similarly to previous studies, the atomic structures of ZnO lm on metal surfaces were designed through lattice matching minimizing the strain generated on the interface. 9,11,45,[80][81][82][83] In this study, the strain was applied to the oxide lm whose lattice parameters were adjusted to match the lattice parameters of the unstrained metal support. To nd the combination that minimizes the deformation of the lm, we wrote a python code that scanned all surface lattice transformation matrices with elements in the range of [−9, 9].…”