2016/12/02 by N. Shankaraiah, Awadhesh K. Dubey, Awadhesh Kumar Dubey +2
Earth and Planetary Sciences · Materials Science · Mathematics · Physics and Astronomy · #Ansatz #Block Copolymer Self-Assembly #Condensed matter physics #Critical exponent #Curvature #Exponent #Geometry #Mathematical physics #Mathematics #Order (exchange) #Phase transition #Physics #Scaling #Theoretical and Computational Physics #cond-mat.mtrl-sci #cond-mat.stat-mech #nanoparticles nucleation surface interactions
paper · pdf · doi:10.1103/physrevb.94.224101
18 pages, 16 figures
openalex publication_date 2016/12/02 · arxiv created 2016/12/06 · arxiv updated 2016/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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)\ensuremath∼t^\ensuremathα. We find at intermediate and long times that the coarsening exponent sequentially takes on respective values close to \ensuremathα=2/3 and 1/2. For deep quenches, the coarsening can be arrested at long times, with \ensuremathα\ensuremath≃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)\ensuremath≡1/L(t). The curvature solutions have time windows of power-law decays g\ensuremath∼1/t^\ensuremathα, with exponent values \ensuremathα 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 \ensuremathα=1/4 and 1/3 for intermediate and long times. For vector order parameters with NOP\ensuremath≥2, the exponents are \ensuremathα=1/4 only, consistent with previous work. The curvature kinetics method could be useful in extracting coarsening exponents for other phase-ordering dynamics.