Pathways for martensitic high-pressure phase transitions in bismuth

Atomistic pathways for strain-induced subsolidus martensitic transitions between Bi-I, Bi-II', Bi-II, and Bi-V were found by computing the set of the smallest atomic displacements required to transform the initial structures into the final structures. Minimal transformation cells with maximum of 12 Bi atoms are sufficient to describe the diffusionless martensitic transitions. We identified families of invariant shear planes during the martensitic transitions and calculated the reaction barriers using density functional theory. The barrier for the Bi-I/II reaction is about $73\phantom{\rule{0.16em}{0ex}}\mathrm{m}\mathrm{e}\mathrm{V}$/atom at ambient conditions and decreases with increasing pressures to $\ensuremath{\approx}20\phantom{\rule{0.16em}{0ex}}\mathrm{m}\mathrm{e}\mathrm{V}$/atom at $5\phantom{\rule{0.16em}{0ex}}\mathrm{G}\mathrm{Pa}$. A similar decrease in the reaction barriers for reactions towards high-pressure phases was observed for the other transitions. The barriers for the reverse reactions increase with increasing pressures. The model calculations show quantitatively that the transitions will occur well below the equilibrium transition pressure when samples are strained.