Parent grain reconstruction from partially or fully transformed microstructures in MTEX

A versatile generic framework for parent grain reconstruction from fully or partially transformed child microstructures has been integrated into the open-source crystallographic toolbox MTEX. The framework extends traditional parent grain reconstruction, phase transformation and variant analysis to all parent–child crystal symmetry combinations. The inherent versatility of the universally applicable parent grain reconstruction methods and the ability to conduct in-depth variant analysis are showcased via example workflows that can be programmatically modified by users to suit their specific applications. This is highlighted by three applications, namely α′-to-γ reconstruction in a lath martensitic steel, α-to-β reconstruction in a Ti alloy, and a two-step reconstruction from α′ to ɛ to γ in a twinning and transformation-induced plasticity steel. Advanced orientation relationship discovery and analysis options, including variant analysis, are demonstrated via the add-on function library ORTools.

Comparing crystal structures with symmetry and geometry

Measuring the similarity between two arbitrary crystal structures is a common challenge in crystallography and materials science. Although there are an infinite number of ways to mathematically relate two crystal structures, only a few are physically meaningful. Here we introduce both a geometry-based and a symmetry-adapted similarity metric to compare crystal structures. Using crystal symmetry and combinatorial optimization we describe an algorithm to arrive at the structural relationship that minimizes these similarity metrics across all possible maps between any pair of crystal structures. The approach makes it possible to (i) identify pairs of crystal structures that are identical, (ii) quantitatively measure the similarity between crystal structures, and (iii) find and rank structural transformation pathways between any pair of crystal structures. We discuss the advantages of using the symmetry-adapted cost metric over the geometric cost. Finally, we show that all known structural transformation pathways between common crystal structures are recovered with the mapping algorithm. The methodology presented in this study will be of value to efforts that seek to catalogue crystal structures, identify structural transformation pathways or prune large first-principles datasets used to parameterize on-lattice Hamiltonians.