Near-square islands form during sub-monolayer homoepitaxial growth on metal (100) surfaces. Diffusion of these islands after deposition leads to collision of island pairs, typically corner-to-corner creating dumbbell-shaped clusters. Subsequent coalescence (or sintering) recovers a near-square equilibrium shape. This process is mediated by periphery diffusion (PD) and its study can provide detailed insight into the underlying dynamic processes and energetics. Atomistic modeling reveals that the size scaling of the characteristic relaxation time, τ, depends on the detailed energy barriers of various hopping processes that contribute to PD. Simulations without an extra kink or corner rounding barrier for PD reveals τ ∼ L4, while behavior approaching τ ∼ L3 is observed with a significant extra kink rounding barrier for PD. The latter is consistent with experimental observations for Ag/Ag(100) at 300 K.