Finding transition states for crystalline solid-solid phase transformations.

We present a method to identify transition states and minimum energy paths for martensitic solid-solid phase transformations, thereby allowing quantification of the activation energies of such transformations. Our approach is a generalization of a previous method for identifying transition states for chemical reactions, namely the climbing image-nudged elastic band algorithm, where here the global deformation of the crystalline lattice (volume and shape fluctuations) becomes the reaction coordinate instead of atomic motion. We also introduce an analogue to the Born-Oppenheimer approximation that allows a decoupling of nuclear motion and lattice deformation, where the nuclear positions along the path are determined variationally according to current deformation state. We then apply this technique to characterize the energetics of elemental lithium phase transformations as a function of applied pressure, where we see a validation of the Born-Oppenheimer-like approximation, small energy barriers (expected for martensitic transformations), and a pronounced pressure dependence of various properties characterizing the phase transitions.