Pressure effects for crystal growth in a closed system

We analyze the growth of a crystal from its supercooled liquid in a closed domain (constrained growth), taking into account the effects due to the different densities ρs and ρl of the solid and liquid phases. We assume ρl>ρs, i.e., the liquid expands upon solidification. Then, the growth is contrasted by an increasing pressure, which results in a continuous decrease of the coexistence temperature and the effective supercooling. These phenomena have been simulated in two dimensions through a modified version of the classic phase-field model. We observe that for spherical growth the interface temperature reflects almost instantaneously the change of the coexistence temperature. For dendritic growth, we observed a relaxation time for the dendrite tip velocity and the tip radius which is comparable to the characteristic time of the process; however, after the first fast transient, the growth dynamics seems to follow the changing pressure with no appreciable lag. The onset of the morphological instability is slightly anticipated in respect to free growth.