Phase Field Study of Lattice Instability and Nanostructure Evolution in Silicon During Phase Transformation Under Complex Loading

An advanced phase-field approach (PFA) to study martensitic phase transformations is developed for finite strains, particularly taking into account crystal lattice instability conditions under complex triaxial compression-tension loading obtained using molecular dynamics (MD) simulations. Calibration of novel phase-field instability criteria with those from MD simulations for Si I \( \leftrightarrow \) Si II phase transformations leads to unexpected interpolation functions for transformation strain and elastic constants. A finite element algorithm and a numerical procedure are developed and implemented using code deal.II. The effect of stress state on lattice instability and nanostructure evolution is studied. Within a specific stress range for which direct and reverse transformation instability stresses coincide, a unique homogeneous, hysteresis-free, and dissipation-free transformation is observed. For such a transformation, a continuum of intermediate phases exists along the transformation path, all in indifferent thermodynamic equilibrium. The absence of interfaces results in the absence of internal stresses and minimizes damage. All these properties are optimal for various PT-related applications.