Lattice dynamics approach towards Kelvin's nucleation criticality in martensitic transformations

The energetics of nucleation of martensite by soft mode mechanism is studied. First the soft modes of a 2D model material are identified by means of classical lattice dynamics. This soft mode is mimicked by inducing static displacement modulations in the austenitic lattice and calculating the potential energy of the whole material for various wave packages. It is found that modulations with small spatial extent cause an increase of the potential energy and are expected to yield oscillatory motion of the atoms. As the spatial extent of the modulation increases–the potential energy of unstable modes descends into local minima with increasing amplitude of the modulation. The spatial extent which thus allows the transformation is a critical modulation.