Dynamical structural phase transition model of the electrical behavior of NiTi

A general phenomenological model of the kinetics of thermally induced structural phase transitions in multi-phase alloys is introduced for arbitrary numbers of lattice phases and transitions. The model is based on a system of ODEs yielding the temporal evolution of lattice phase fractions caused by temperature variation described by a heat balance equation. The kinetics of each transition are modeled by temperature rates of phase fractions rather than sigmoids, where an extra multiplicative parameter describing the shape of the transition rate curves is introduced. The model is applied to the electrical behavior of thin NiTi filaments by relating its resistivity to the relative proportions of three main structural phases, namely Martensite, Austenite and an intermediate phase, known as R-phase. The model yields resistivity time-series for successive heating/cooling cycles. Computer simulations are compared to previously published resistivity measurements on filaments self-heated by time-varying currents of various frequencies and passively heated samples.