Model study of local enhancement of chemical potential gradient after facet formation on growing spherical Cu2−δSe crystals

The growth of spherical copper selenide single crystals (fed by Cu atoms at constant rate) is driven by the gradient of the chemical potential, which is in the absence of facets isotropic and proportional to inverse square of crystal radius. We investigate the influence of the facets on the local chemical potential gradient on the facet site by a model based on diffusion of Cu atoms with appropriate boundary conditions. The average chemical potential gradient decreases as crystal grows, acquiring values that are, except for the initial growing period, below the threshold value for activation of 2D nucleation. We show that in spite of this fact the local chemical potential gradient, due to the facet presence, may acquire large values, sufficient to activate 2D nucleation and to justify the occurrence of the growing mode consisting of alternation of time intervals of facet vertical growth with those in which facet does not advance, as has been preliminary detected in our experiments.