On Lattice Transformations

What is it about?

A group of objects, arranged in a regular and periodic configuration, is forced to rearrange itself into a different periodic structure by following a common and ordered movement. Out of the arbitrarily many ways of doing so, which is the one requiring least movement? This question is particularly relevant in displacive phase transitions in crystalline solids, where the objects could be atoms forced to rearrange themselves due to changes in temperature. Our paper addresses these questions within a general framework and applies the developed techniques to prove a conjecture by E.C. Bain from 1924 concerning phase transformations in steels.

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Why is it important?

The design of better and stronger materials is a central topic in modern research. Many processing methods of materials such as steels rely on phase transformations.