Stability of an axisymmetric two-grain system with a hole

The stability of holes in solid thin films is crucial, as an absence of holes is necessary in some applications and holes are needed in others. We develop an axisymmetric two grain model with a central hole, with surface diffusion governing the exterior surfaces and mean curvature motion governing the grain boundary. The model can exhibit grooving, wetting, dewetting, as well as void, hole, and hillock formation. Here, we extend an earlier work [Zigelman and Novick-Cohen, J. Appl. Phys. 130, 175301 (2021)], where it was shown for an axisymmetric single grain system with a hole at the center that there exists a critical effective radius, which is independent of the contact angle. The stability of the steady states, which consist of coupled nodoidal and catenoidal surfaces, is analyzed numerically by imposing the steady state configurations as initial conditions. This approach yields stability criteria in terms of (i) the effective energy, (ii) the ratio between the maximal thickness of the inner and outer grains, (iii) a generalized effective radius, and (iv) the ratio between the mean curvature of the exterior surfaces and the total volume of the system. Some of these criteria partially reflect the Rayleigh stability criterion. Hillock formation tends to be stabilizing. Modes of instability include growth of one grain at the expense of the other, breakup induced by grooving, and hole closure.