Type n boundaries in n-component diffusion couples

When multicomponent alloys are in contact at elevated temperatures, complex interdiffusion microstructures with distinctive multiphase regions may form around the contact interface. The boundaries between these regions can be classified according to the number of phases that change on crossing the boundary. Accordingly, a type n boundary is a boundary in an n-component system across which n phases change. Such boundaries are shown to require that diffusion paths must pass through special features on a phase diagram. Special features are those that cannot be intersected by a random line, such as the corners of tie-triangles or the edges of tie-tetrahedra. Therefore such boundaries are expected to be seen infrequently and only when there is a kinetic benefit for a diffusion path to intersect the feature. Also it is shown that the number of ways that a type n boundary can form is given by the floor function ⌊n/2⌋. Examples are given using phase-field simulations of a model system for n = 3 and 4. Simulated diffusion paths with type 3 boundaries are shown to be comparable to those reported for Ni-Cr-Al diffusion couples. In addition, it is shown that the eigenvector direction of the diffusivity and the composition of the initial alloys relative to the phase diagram can dictate whether or not a type n boundary will form in an n-component system.