Domain growth morphology in curvature-driven two-dimensional coarsening

Abstract

We study the distribution of domain areas, areas enclosed by domain boundaries ("hulls"), and perimeters for curvature-driven two-dimensional coarsening, employing a combination of exact analysis and numerical studies, for various initial conditions. We show that the number of hulls per unit area, n_{h}(A,t)dA , with enclosed area in the interval (A,A+dA) , is described, for a disordered initial condition, by the scaling function n_{h}(A,t)=2c_{h}(A+lambda_{h}t);{2} , where c_{h}=18pi sqrt[3] approximately 0.023 is a universal constant and lambda_{h} is a material parameter. For a critical initial condition, the same form is obtained, with the same lambda_{h} but with c_{h} replaced by c_{h}2 . For the distribution of domain areas, we argue that the corresponding scaling function has, for random initial conditions, the form n_{d}(A,t)=2c_{d}(lambda_{d}t);{tau'-2}(A+lambda_{d}t);{tau'} , where c_{d} and lambda_{d} are numerically very close to c_{h} and lambda_{h} , respectively, and tau'=18791 approximately 2.055 . For critical initial conditions, one replaces c_{d} by c_{d}2 and the exponent is tau=379187 approximately 2.027 . These results are extended to describe the number density of the length of hulls and domain walls surrounding connected clusters of aligned spins. These predictions are supported by extensive numerical simulations. We also study numerically the geometric properties of the boundaries and areas.