Precipitation of Cu in Ge. II. Supersaturation Effects

Studies have been made on the precipitation kinetics of Cu from supersaturated solid solution in Ge crystals with dislocation densities <100/${\mathrm{cm}}^2$. We found that the precipitation rates are very strongly dependent upon the degree of supersation. We believe this is evidence for the nucleation of the precipitate particles upon a single type of nucleation site, whose identity has not been established. An attempt is made to fit the experimental data to the simple theory of nucleation in which $\sigma$, the surface tension in the phase boundary between precipitate and host lattice, and $E_p$, the structure-sensitive increase in strain energy in the crystal upon formation of the precipitate, are parameters. We find that the data can be fit by $\sigma \approx 500\pm 50$ ergs/${\mathrm{cm}}^2$, and $E_p\approx (1\mathrm{}\pm 1)\times {10}^{-13\mathrm{}}$ erg/atom, assuming spherical precipitates. No other information about these quantities is available for comparison. An appendix gives a simplified treatment of Ham's derivation of the kinetic law for diffusion-limited precipitation upon spherical precipitate particles, which relates the observed precipitation rate to the number of precipitate particles. Theory and experiment are in reasonable agreement.