Phase Separation by Spinodal Decomposition in the Tetragonal System

Coherent spinodal curves for the [001] and [100] directions were calculated for the system TiO₂-SnO₂. Inside the [001] spinodal curve, the crystalline solutions decomposed by a modulated phase composed of TiO₂-rich and SnO₂-rich plates perpendicular to the [001] direction. No modulation of structure was observed at compositions and temperatures between the [001] coherent spinodal and the equilibrium curve. The kinetics of the decomposition showed that the wavelength of the modulation decreased in the early stages of the separation, reaching minimum observable values of approximately 110 Å at 925°C, 170 Å at 1000°C, and 240 Å at 1150°C. In the second stage when the coherency was lost, the wavelength increased. Theoretical calculations to find the elastic free energy/unit volume to cause fluctuation of composition in the spinodal process were worked out for the tetragonal system. The calculations were done for an arbitrary direction and involved elastic constants. The theoretical prediction and the experimental results for the system TiO₂-SnO₂ agreed well.