Phase-Field Modeling of Spinodal Decomposition

As a special case of microstructure evolution model, spinodal decomposition does not consider interactions between phases, and the elastic energy is dominated by chemical misfit instead of phase misfit. Gradient term in spinodal decomposition is calculated by chemical gradient instead of order parameter gradient. As a result, order parameter evolution (the Eq. 11 in Phase-Field Modeling of Precipitation) is not relevant and only Cahn-Hilliard (the Eq. 12 in Phase-Field Modeling of Precipitation) dynamics needs to be solved. The formula of elastic energy in spinodal decomposition is constructed as:

(1)

When spinodal decomposition is simulated, the gradient term will be replaced by using concentration field instead of phase field:

(2)

where κ_j is the gradient energy coefficient.

In spinodal decomposition, a homogeneous solid solution decomposes into two or more isostructural phases which are different in composition. Certain wavelength of decomposition grows faster than the other wavelengths owing to thermodynamic driving force and kinetic factors. By linearizing the Cahn-Hillard equation for a binary alloy, the maximally growing wavelength in the initial stages of the decomposition can be calculated by

(3)

where κ is the gradient energy coefficient and f '' is the second derivative of Gibbs free energy.

Table 1 lists the symbols used in the phase-field models.