Barriers to shape evolution of supported nano-crystallites

Abstract

Continuum solutions for supported crystallite shapes are combined with the continuum step model to yield a quantitative description of the physically-allowed metastable states, including the dependence on interfacial adhesion energy. Using a model of layer-by-layer shape evolution, the activation barriers for transitions between metastable states are calculated. The results collapse to a universal scaled form and for which the barrier height decreases (increases) for metastable states taller (shorter) than the equilibrium structure. Following Rohrer and Mullins [W.W. Mullins, G.S. Rohrer, Journal of the American Ceramic Society 83 (2000) 214; G.S. Rohrer, C.L. Rohrer, W.W. Mullins, Journal of the American Ceramic Society 84 (2001) 2099], we evaluate the smallest crystal volume where the energy barrier is less than 10 k B T as a function of the metastable state and interfacial energy. The results yield a family of curves showing the lowest energy accessible structure as a function of the dimensionless volume for different adhesions energies. Increasing adhesion energy correlates with increasing activation barriers at the same volume. Using realistic parameters for Pb, the equilibrium structure can only be reached by peeling for volumes ⩽50 nm 3, and crystals of volume ⩾10 6 nm 3 will be trapped in the least favorable metastable state.