Minimization of Atomic Displacements as a Guiding Principle of the Martensitic Phase Transformation.

We present a unifying description for the martensitic transformation of steel that accounts for important experimentally observable features of the transformation, namely, the Neumann bands, the interfacial (habit) plane between the transformed and untransformed phases and their orientation relationship. It is obtained through a simple geometric minimization of the total distance traveled by all the atoms from the austenite (fcc or γ) phase to the martensite (bcc or α) phase, without the need for any explicit energy minimization. Our description unites previously proposed mechanisms but it does not rely on assumptions and experimental knowledge regarding the shear planes and directions, or external adjustable parameters. We show how the Kurdjumov-Sach orientation relationship between the two phases and the {225}_{γ} habit plane, which have both been extensively reported in experiments, naturally emerge from the distance minimization. We also propose an explanation for the occurrence of a different orientation relationship (Pitsch) in thin films.

Matching crystal structures atom-to-atom.

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.