Spinodal decomposition in amorphous systems

Abstract

The theory of spinodal decomposition in amorphous systems is extended to include the effect of internal stress due to coherency strain. A quantitative treatment is developed for the kinetics of internal stress relaxation via plastic deformation. The general solution for the evolution of the composition and internal stress distributions during the early stage of spinodal decomposition is derived for a system obeying the visco-elastic constitutive relations of a Maxwell solid. A kinetic equation for the structure factor is obtained for the limiting case in which coherency strain is relatively large. In this case, it is found that plastic deformation to relieve internal stress can become the rate-limiting step in the evolution of Fourier components having large wavenumbers. The predicted shape of the structure factor as a function of wavenumber, time, and temperature can be very different from that obtained when the kinetics of internal stress relaxation are neglected. The theory is expected to be particularly applicable to amorphous systems in which the species of interest have very different mobilities, and can explain the discrepancies found in previous analyses of scattering data for the lead-aluminum-borate system and alkali-silicate systems.