Study of Martensitic Phase Transformation in Silicon and Zirconium Using Scale-Free Phase-Field Model

Silicon undergoes martensitic phase transformation from cubic Si I to tetragonal Si II with large and very anisotropic transformation strain whereas zirconium transforms from hcp α – phase to simple hexagonal ω – phase under high pressure. Scale-free phase-field model for phase transformations at large strains is advanced and used to study the multivariant high-pressure phase transformations in Si and Zr under various nonhydrostatic loadings. The phase field model is implemented using finite element algorithms in deal.II. The model is calibrated using available experimental and atomistic data. It is applied to study forward and reverse phase transformations in single and polycrystal Si and Zr crystals under different non-hydrostatic conditions and varying strain rates. The mesh size is also varied to study the microstructure evolution in detail. The single crystal results were used to validate the model and the parameters with analytical results. The validated model was then used to study texture free polycrystal samples generated using DREAM.3D. Also, fields of all components of the stress and transformation strain tensors, volume fractions of martensitic variants and high-pressure phase, and macroscopic strain-strain and volume fractions strain plot are presented. The developed methodology can be used for studying similar PTs with large transformation strains and for further development by including plastic strain and strain-induced phase transformations.