  We examine the role of an imposed epitaxial strain e in enhancing or
depressing the spinodal instability of an alloy thin film. Since the alloy film
starts with an imposed strain, phase separation offers a mechanism to relieve
it, but only when the film is elastically inhomogeneous. With
composition-dependence of elastic modulus given by y, and that of lattice
parameter by {\eta}, our simulations using the Cahn-Hilliard model show (and
analytical results for early stages confirm) that, for (ey/{\eta}) > 0, the
imposed strain adds to the driving force for phase separation, decreases the
maximally growing wave length, and expands the coherent spinodal in the phase
diagram. Further, when (ey/{\eta}) > 0.372, it expands to even outside of
chemical spinodal. Phase separation produces islands of elastically softer
(harder) phase with (without) a favorable imposed strain. These results are in
agreement with experimental results in GeSi thin films on Si and Ge substrates,
as well as in InGaAs films on GaAs substrates.
