Particle size effects on the coherent phase equilibria of binary nanoparticles

The phase stability of isolated, radially symmetric nanoparticles of a binary system that exhibits a miscibility gap was analyzed by constructing coherent phase diagrams which account for both the surface stress (T _s) and the second-order compositional dependence of the lattice parameter (η)_cc). Although the elastic stress field in a two-phase coherent particle with a concentric core-shell structure is heterogeneous and nonhydrostatic at equilibrium, the appropriate free energy extremized for equilibrium could be expressed as a function solely of the temperature (θ), composition (c), and effective pressure (P), which are homogeneous in each phase at equilibrium. The construction of coherent phase diagrams in the three-dimensional θ-c-P space showed that the miscibility gap can be either extended or reduced by decreasing the particle radius, depending on the sign of T_sη_cc and that the tie-lines lie in the c-P plane.