  Structural phase transitions are governed by the underlying atomic
transformation mechanism; martensitic transformations can be separated into
strain and shuffle components. A systematic pathway generation and sorting
algorithm is presented and applied to the problem of the titanium alpha to
omega transformation under pressure. In this algorithm, all pathways are
constructed within a few geometric limits, 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.
