Dynamical scaling for underdamped strain order parameters quenched below first-order phase transitions

Abstract

In the conceptual framework of phase ordering after temperature quenches below transition, we consider the underdamped Bales-Gooding-type 'momentum conserving' dynamics of a 2D martensitic structural transition from a square-to-rectangle unit cell. The one-component or NOP = 1 order parameter is one of the physical strains, and the Landau free energy has a triple well, describing a first-order transition. We numerically study the evolution of the strain-strain correlation, and find that it exhibits dynamical scaling, with a coarsening length L(t) ∼ t α . We find at intermediate and long times that the coarsening exponent sequentially takes on respective values close to α = 2/3 and α = 1/2. For deep quenches, the coarsening can be arrested at long times, with α 0. These exponents are also found in 3D. To understand such behaviour, we insert a dynamical-scaling ansatz into the correlation function dynamics to give, at a dominant scaled separation, a nonlinear kinetics of the curvature g(t) ≡ 1/L(t). The curvature solutions have time windows of power-law decays g ∼ 1/t α , with exponent values α matching simulations, and manifestly independent of spatial dimension. Applying this curvature-kinetics method to mass-conserving Cahn-Hilliard dynamics for a double-well Landau potential in a scalar NOP = 1 order parameter yields exponents α = 1/4 and 1/3 for intermediate and long times. For vector order parameters with NOP ≥ 2, the exponents are α = 1/4 only, consistent with previous work. The curvature kinetics method could be useful in extracting coarsening exponents for other phase-ordering dynamics.