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 elast ic fields. These conditions are used to test the stability of a homogeneous alloy against composition fluctuations and to write dynamical equations fo r 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 eff ect 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 s phere radius. and the composition dependence of the lattice parameter, and demonstrate the existence of two different equilibrium states for a given a lloy composition and temperature. (C) 2001 Acta Materialia Inc. Published b y Elsevier Science Ltd. All rights reserved.