A two-dimensional Monte Carlo approach of phase separation in binary a
lloys with internal elastic energy has been developed. Based on the st
andard Ising model, this approach considers both the binding potential
and the internal elastic interaction between two species, which are a
ssumed to decay respectively with the distance via power functions. It
has been found that the phase separation exhibits quite different dyn
amics from the current mode which only takes into account the binding
potential interaction. This dynamics is characterized by strong lattic
e anisotropy of the microstructure and structure function, periodicall
y modulating correlation functions and an exponent of the late stage c
oarsening kinetics much smaller than 0.33 as well, demonstrating the c
rucial role played by the elastic interaction in dynamics of phase sep
aration.