Thermal grooving by surface diffusion: Mullins revisited and extended to multiple grooves

We extend the original Mullins theory of surface grooving due to a single interface to multiple interacting grooves formed due to closely spaced flat interfaces. First, we show that Mullins' analysis for one groove can be simplified by using Fourier cosine transforms instead of Laplace transforms. Second, we solve the corresponding problem for an infinite periodic row of grooves. For both of these problems, symmetry considerations ensure that the interface conditions reduce to boundary conditions. Third, we solve the problem for two interacting grooves. Continuity requirements at the groove roots require sliding at the interfaces or tilting of the groove roots. We adopt the latter model. We find that the groove roots tilt until the surface curvature of the semi-infinite profiles is eliminated.