Extracting rates and activation free energies of martensitic transitions using nanomechanical force statistics: theory, models, and analysis

Nanomechanical responses (force-time profiles) of crystal lattices under deformation exhibit random critical jumps, reflecting the underlying structural transition processes. Despite extensive data collection, interpreting dynamic critical responses and their underlying mechanisms remains a significant challenge. This study explores a microscopic theoretical approach to analyse critical force fluctuations in martensitic transitions. Extensive sampling of the critical forces was performed using nonequilibrium molecular dynamics simulations of an atomic model of single-crystalline titanium nickel. We demonstrate that a framework of nonequilibrium statistical mechanics offers a principled explanation of the relationship between strain rate and the critical force distribution as well as its mean. The martensitic transition is represented on a free energy landscape, taking into account the thermally activated evolution of atomic arrangements over a barrier during its time-dependent deformation. The framework enables consistent inference of the relevant fundamental properties (e.g., intrinsic rate, activation free energy) that define the rate process of structural transition. The study demonstrates how the statistical characterisation of nanomechanical response-stimulus patterns can offer microscopic insights into the deformation behaviours of crystalline materials.