Modelling spinodal decomposition at the atomic scale: beyond the Cahn - Hilliard model

In this paper three models are used to describe spinodal decomposition in Fe - Cr alloys. The challenge presented by this particular alloy system is that the wavelength of the decomposition is at the nanometre scale. The scale of the microstructure is too small to expect the continuum approximations of the Cahn - Hilliard approach to apply, and, indeed, we show that the approach fails to describe the kinetics of the experimentally observed decomposition. On the other hand it has already been established in our earlier work that the dynamic Ising model describes the kinetics of this decomposition remarkably well. In this paper we show that the Penrose model of spinodal decomposition can also account for the kinetics quantitatively. The Penrose model is deterministic and is essentially a mean-field approximation to the dynamic Ising model. In addition we show that the form of the initial distribution of amplitudes of compositional variations within the high-temperature random alloy has a significant effect on the subsequent kinetics of phase separation.