Systematic pathway generation and sorting in martensitic transformations: Titanium α to ω

Martensitic phase transitions appear in a diverse range of natural and engineering material systems. Examination of the energetics and kinetics of the transformation requires an understanding of the atomic mechanism for the transformation. A systematic pathway generation and sorting algorithm is presented and applied to the problem of the titanium to transformation under pressure. The transformation pathways are separated into strain and shuffle components. All pathways are constructed within energetically motivated strain and shuffle constraints, and efficiently sorted by their energy barriers. The geometry and symmetry details of the seven lowest energy barrier pathways are given. The lack of a single simple geometric criterion for determining the lowest energy pathway shows the necessity of atomistic studies for pathway determination. The general algorithm can determine the pathway for any martensitic transformation.