Shape evolution by surface and interface diffusion with rigid body rotations

We consider the simultaneous shape evolution (controlled by diffusion along the particle surface) and rigid body rotation (controlled by diffusion along the particle–substrate interface) of particles deposited on inert rigid substrate. We demonstrate that the particle shape, the surface energy anisotropy of the particle, and the misorientational anisotropy of the particle–substrate interface all contribute to the driving force for particle rotation. We introduce a new interface parameter, the weighted mean torque, which convolutes all driving forces for particle rotation into the local distribution of the chemical potential of atoms diffusing along the interface. The weighted mean torque is defined as an increase in the total surface and interface energy of the particle and substrate as a result of an infinitesimally small rotation of the particle, normalized by the rotation angle and interface area. This generalized torque may not vanish even in the case of a fully isotropic particle–substrate interface. We used several simple two-dimensional examples to illustrate how the asymmetry of initial particle shape and the anisotropy of the particle surface energy lead to particle rotation with respect to substrate. An exact analytic expression for the rotation rate of an anisotropic triangular particle is obtained.