Morphological instability of stressed spherical particles growing by diffusion in a matrix

摘要

The morphological stability of a growing spherical particle epitaxially stressed in a supersaturated matrix has been investigated with respect to shape deviation of the particle from sphericity expanded on a basis of spherical harmonics Y_l~0 (θ). A dispersion law has been determined for the growth rate of each harmonic, and a critical radius of the particle above which the sphere is unstable has been determined as a function of the different parameters of the problem such as the lattice mismatch between the matrix and the particle or the ratio of shear modulus. The influence of stress on the instability threshold already studied [Mullins and Sekerka, J. Appl. Phys. 34, 323 (1963)] in the case of a stress-free particle has been finally investigated.