Initial-value solutions for spinodal decomposition in ternary solids

The establishment of a Fourier decomposable initial value representation of spinodal decomposition in a ternary alloy requires that the 2 X 2 diffusion (D) and gradient energy (G) matrices be simultaneously brought to the diagonal, or equivalently that they commute. The three sub-matrices involving solution thermodynamics, mobility and gradient terms are examined within standard atomic models with the view to establishing conditions for commutability within shallow spinodal states. Establishing that this condition is thermodynamically and kinetically feasible, though far from general, we explore the special case where the G-matrix is homothetic, implying that G is diagonal with equal eigenvalues. Within this specialization we demonstrate the trend whereby composition vector components of arbitrary fluctuations which parallel the near critical point tielines rapidly dominate the growth manifold, and this in parallel with the expected independent trend for fastest growing wave number selection.