B. Nestler, A multiphase-field model: sharp interface asymptotics and numerical simulations of moving phase boundaries and multijunctions, J CRYST GR, 204(1-2), 1999, pp. 224-228
In this paper we bring together, compare and extend two recent developments
in a special formulation of an anisotropic multiphase-field model; namely
the results of sharp interface asymptotic analysis by Nestler and Wheeler [
B. Nestler, A.A. Wheeler, Phys. Rev. E 57 (3) (1998) 2602.] and numerical s
imulations of moving phase boundaries and multijunctions by Garcke et al. [
H. Garcke, B. Nestler, B, Stoth, Physica D 115 (1998) 87; SIAM J, Appl, Mat
h., in press]. First, we present the formulation of the multiphase-held mod
el, which includes surface energy anisotropy. Then we state, how the leadin
g order conditions at both interfaces and junctions can succinctly be deriv
ed in the sharp interface limit by introducing a generalized Cahn-Hoffman z
eta-vector formalism and by using the motion of a stress tenser. These anal
ytical results contain that the force balance at multijunctions is recovere
d, which comprises Young's law and, in the anisotropic case, additional she
ar forces. Next, we present numerical simulations of evolving phase boundar
ies and junctions, concentrating on the case of isotropic phases. We find t
hat our numerical solutions of the multiphase-field model compare favorably
with the exact solutions of the sharp interface analytical results. We obs
erve that the classical angle conditions at trijunctions are obtained numer
ically. Finally, we perform simulations of grain growth evolution and numer
ically verify the validity of the qualitative features of the von Neumann l
aw. (C) 1999 Elsevier science B.V. All rights reserved.