A Cahn-Hilliard equation is derived and used to explore the effect of compositional strain on the sequence of phase formation in a binary alloy capable of sustaining five distinct, but isostructural, phases in its stress-free state. The system is configured as a thin plate capable of bending and initially has a layered composition profile. The system evolves to reduce the sum of its chemical and elastic energies when strains arise from the nonlinear dependence of the lattice parameter on composition. The compositional strain can stabilize the growth of phases that are nonequilibrium in the absence of stress, give different phase trajectories to various equilibrium states depending on the initial configuration of the system, and can induce a sequence of phase formation in which only one or two intermediate phases grow at any time. These sequences are especially pronounced when deviations from Vegard's law are realized.
|Original language||English (US)|
|Number of pages||11|
|Journal||Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science|
|State||Published - 2002|
Bibliographical noteFunding Information:
We gratefully acknowledge the financial support of the Division of Materials Science, Department of Energy, through Grant Nos. DE-FG02-99ER45770 (PHL) and DE-FG02-99ER45771 (WCJ). We also thank J.S. Lowengrub for suggesting the dual grid method and the Minnesota Supercomputer Institute for computational resources.