Epitaxial effects on coherent phase diagrams of alloys

We present a cluster-based description of coherent binary or pseudobinary alloys and predict and contrast bulk and epitaxial composition-temperature phase diagrams and excess thermodynamic functions. This formalism addresses in a unified way phenomena characteristic of coherent epitaxial solids, including the following: for phase-separating alloys (whose constituents are insoluble in bulk below a miscibility-gap temperature), (i) epitaxial ordered phases not present in the bulk phase diagram and (ii) a stabilization of the disordered phase to far lower temperatures; and for all alloys, (iii) epitaxial changes of order-disorder transition temperatures and (iv) the pinning (``lattice latching'') of the composition near where an epitaxial alloy is lattice matched to a given substrate. We illustrate these effects for Cu_1-x{Au}ₓ$, a typical ``ordering'' alloy (with stable ordered compounds in bulk) and for ${GaAs}ₓSb_1-x, a typical ``phase-separating'' alloy. Using a simple thermodynamic description of the reactions describing molecular-beam epitaxy growth of a coherent epitaxial isovalent semiconductor alloy, we demonstrate that composition pinning persists even in this growth method, and compare with available experiments.