Real-time small-angle x-ray scattering study of the early stage of phase separation in the SiO2-BaO-K2O system.

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Time-resolved small-angle x-ray scattering was used to study the early stage of phase separation in a silicate system. Scattering patterns were acquired in real time as a sample was quenched in situ from a temperature ${\mathit{T}}_{1}$ in the single-phase region directly to a temperature ${\mathit{T}}_{2}$ in the two-phase region and held isothermally. This was made possible by using a high-intensity synchrotron x-ray source, a fast position-sensitive detector, a sample heater capable of rapid quenches, and a sample composition chosen to give good scattering contrast and relatively slow kinetics. The composition studied, 90 mol% ${\mathrm{SiO}}_{2}$, 5 mol% BaO, and 5 mol% ${\mathrm{K}}_{2}$O, undergoes subliquidus phase separation at temperatures below 1021 K to form alkali-oxide-rich and alkali-oxide-poor amorphous phases. The temperatures used were ${\mathit{T}}_{1}$=1074 K and ${\mathit{T}}_{2}$=1014, 995, 970, and 950 K. While the resultant data agree qualitatively with the linearized thermodynamics of the Cahn-Hilliard-Cook (CHC) theory of spinodal decomposition (i.e., the structure factor changes exponentially with time at each wave number), they do not agree with the simple diffusive kinetics used in the CHC theory. The data are in very good agreement with a modified theory incorporating diffusion-induced-flow (DIF) kinetics, in which one considers both the generation of stress arising from unequal mobilities of the diffusing species and the relaxation of this stress through deformation. Values of the material parameters as a function of temperature obtained from fits of the DIF theory to the data are in reasonable agreement with independent measurements and estimates based on a regular-solution model. For amorphous systems in particular, these results provide direct evidence that viscous flow is the rate-limiting step for the interdiffusion of network-forming and network-modifying species over the short length scales involved in the early stage of phase separation.