Constrained evolution of nanocrystallites

Abstract

Deviations from the universal predictions of shape-preserving structure evolution have been investigated in the context of realistic physical boundary conditions for supported nanoscale crystallites. Structural evolution was simulated using the continuum step model with volume conservation, variable interface free energy, and incorporating analytical solutions for equilibrium and metastable crystallite shapes. Early stages of evolution following a simulated temperature drop are consistent with the kinetics of shape-preserving evolution, e.g., not limited by the constant volume constraint. Later stages of decay show a distinct slow down, with an empirically-determined exponential form. The time constant of the slow final evolution increases linearly with the length scale of the crystallite, and also increases monotonically with interface adhesion strength. Under normal evolution, where the interface area between the crystallite and substrate is constant or increasing, the evolution progresses through the metastable states accessible to the volume. If a decreasing interface area can be induced, an alternative progression ending much closer to equilibrium is possible. The late-stage slow down provides additional kinetic information that allows the nonuniqueness of early-stage modeling to be resolved. The slow down observed in the late stages of relaxation of Pb crystallites has been fit, with a unique determination of the relative values of the terrace diffusion constant and step attachment constant.