科研之友
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摘要
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 N-OP = 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) similar to t(alpha). We find at intermediate and long times that the coarsening exponent sequentially takes on respective values close to alpha = 2/3 and 1/2. For deep quenches, the coarsening can be arrested at long times, with alpha similar or equal to 0. These exponents are also found in 3D. To understand such behavior, 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) equivalent to 1/L(t). The curvature solutions have time windows of power-law decays g similar to 1/t(alpha), with exponent values a 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 N-OP = 1 order parameter yields exponents alpha = 1/4 and 1/3 for intermediate and long times. For vector order parameters with N-OP >= 2, the exponents are alpha = 1/4 only, consistent with previous work. The curvature kinetics method could be useful in extracting coarsening exponents for other phase-ordering dynamics.
- 出版日期2016-12-2
