A Kinetic Phase-Field Model of Diffusion Bonding: A Nonlocal Approach to Interface Coalescence

Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain thermodynamic conditions. We develop a kinetic phase-field model to address this problem, using an evolution equation based on a geometric conservation law for interfaces, rather than the gradient descent evolution that is typical in phase-field modeling. This formulation enables us to specify complex kinetic laws, and we use this to incorporate a physically-motivated geometric criterion to control interface merging. This criterion, based on nonlocal higher-derivative curvature invariants of the phase field, can be temperature-dependent, allows for a range of behaviors from complete coalescence to the preservation of distinct boundaries. Simulations show controlled bonding kinetics, demonstrating capabilities that are not available with existing methods for modeling interfaces that must remain distinct under given thermodynamic conditions.