Spinodal decomposition in a small radially stressed sphere

The conditions for thermodynamic equilibrium are derived for a binary alloy configured as a small sphere with radially symmetric composition and elastic fields. These conditions are used to test the stability of a homogeneous alloy against composition fluctuations and to write dynamical equations for microstructural evolution. The surface stress ((T) over cap) and external traction interact with the second compositional derivative of the lattice parameter (e(cc).). and can either enhance or diminish the stability of the alloy depending on the sign of (T) over cape(cc). The magnitude of the effect is inversely proportional to the sphere radius. Numerical calculations of the non-linear dynamical equations for decomposition are given that show the dependence of the precipitate composition on the surface stress, the sphere radius. and the composition dependence of the lattice parameter, and demonstrate the existence of two different equilibrium states for a given alloy composition and temperature. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.