We investigate the stability of a nonlinear atomistic model for austenite and martensite lattices in 2D. In the harmonic limit, where the atomitic interaction forces are linearized so as to decouple the atomic Equations of Motion, the model incorporates four independent branches of the dispersion relation due to longitudinal and transversial waves in both optical and accoustic vibration modes. Most part of their frequency spectra have real values, but the transverse acoustic wave mode also includes imaginary frequencies. These indicate unstable shear waves, known as soft modes, which lead to the formation of martensitic microtwins. Switching to the quantum mechanical picture, the harmonic spectra are interpreted as a Bose gas, known as phonons. We consider this gas as a mixture of two species: stable phonons associated with real frequencies and soft mode phonons associated with imaginary frequencies. Calorical equations of state for these species can be defined for (local) thermal equilibria according to the Bose-Einstein distribution. These allow us to evaluate the phase equilibrium temperature $$T_E$$ between austenite and martensite by comparing the respective free energy densities of these lattice types, as is customary. We then provide a preliminary argument for the stability of the soft mode phonon gas in an austenitic lattice. We show that the density of states functions for the austenitic phonons species result in free energy densities that may coincide at the temperature $$M_s