Thermodynamics of a stressed alloy with a free surface: Coupling between the morphological and compositional instabilities

We demonstrate how a unified thermodynamic treatment of the morphological and compositional instabilities of a nonhydrostatically stressed alloy with a free surface, describing quantitatively how, when combined, these instabilities modify each other, leads to results differing deeply from those obtained by considering independently each instability. Provided its stress-free unit-cell volume depends on composition, any such alloy is unstable with respect to a range of joint surface undulations and composition modulations. This new morphological-compositional (MC) instability, whose occurrence thus only requires an atomic-size difference between the alloy constituents, is driven by the reduction of the elastic energy with respect to either the case of pure surface undulation or that of pure composition modulation. The domain of existence of the MC instability is determined as a function of temperature and modulation wave number. To each modulation wave number corresponds a particular critical temperature under which the system is unstable and, to each temperature, a particular critical wave number. Unstable joint undulations and modulations exist at any temperature, so that the overall critical temperature is infinite. Any such alloy should thus tend to decompose at any temperature, provided adequate mass-transport processes operate. The overall critical wave numbers always larger than its counterpart for the pure morphological instability and also infinite in some cases. The elastic state of the modulated alloy is calculated, and we show that the composition modulations with the lowest energy are exponentially attenuated normally to the free surface. Possible experimental manifestations of the MC instability in semiconductor alloys are discussed.