Alladi Ramakrishnan Hall

Dynamical scaling after a quench: Coarsening exponents from a coarseniing-length kinetics

Subodh R Shenoy

TCIS, TIFR Hyderabad

After a temperature quench to below transition, the order-parameter correlation function C(R,t) describes the coarsening with time, of wandering patterns of domain walls separating competing low-temperature order-parameter variants. Dynamical scaling is found in experiment and simulations, with the separations R at evolution times t, entering only in scaled form C(R,t) = G(R/L(t)). The coarsening length L(t) or typical separation between domain walls, increases over broad time intervals as L(t) ~ t^\alpha, where the (various, sequential) exponents {\alpha} depend on the order parameter and its dynamics, independent of material parameters.

The exponents have been estimated by heuristic surface-bulk energy arguments (egSiggia); or by local/global dissipation matchings (eg Bray); or by self-consistent truncations of the correlation hierarchy (eg Langer), but it would be useful to have a theoretical approach in terms of the evolving coarsening length, alone.

We start with the correlation function dynamics, and insert the scaling function form G(R/L(t))
as an ansatz solution. With a hierarchy-closure truncation, and a coefficient evaluation at a plausible coarsening-front R / L(t) = constant, we directly derive an evolution kinetics of the curvature or inverse coarsening length, g(t) = 1/ L(t). Sequential balancings of curvature time-derivatives, with the curvature-powers from Ginzburg or Landau terms, directly yield the sequential exponents.

We apply this curvature-kinetics approach to the well-known Cahn-Hilliard (number-conserving) dynamics for the density, successfully bench-marking against well-known exponent values.
We further apply it to the Bales-Gooding type (momentum-conserving) dynamics for the strain evolution. Numerical simulations show dynamical scaling; and coarsening exponents, that match predictions. The curvature kinetics approach could be applied to predict exponents in other systems.

1. T Lookman, S R Shenoy, K O Rasmussen, A Saxena and A R Bishop,
Phys. Rev. B 67, 024114 (2003).
2. N Shankaraiah, A K Dubey, S Puri and S R Shenoy, submitted (2016).