Determination of the stretch tensor for structural transformations

TL;DR

This paper presents an algorithm to determine the transformation stretch tensor from x-ray data, aiding in phase compatibility analysis, with surprising results on various phase transformations.

Contribution

The paper introduces a novel algorithm for calculating the transformation stretch tensor from experimental x-ray measurements.

Findings

Algorithm yields unexpected results on traditional phase transformations.

Method provides a new way to evaluate phase compatibility.

Potential for improved understanding of structural transformations.

Abstract

The transformation stretch tensor plays an essential role in the evaluation of conditions of compatibility between phases and the use of the Cauchy-Born rule. This tensor is difficult to measure directly from experiment. We give an algorithm for the determination of the transformation stretch tensor from x-ray measurements of structure and lattice parameters. When evaluated on some traditional and emerging phase transformations the algorithm gives unexpected results.