We investigate, via computer simulations, coherent phase segregation i
n a microscopic model alloy consisting of A and B atoms of unequal siz
es on a square lattice. The effective Hamiltonian, obtained by minimiz
ation over the displacement of the atoms from their lattice positions,
contains long range linear elastic interactions that cause the precip
itates to be highly anisotropic. Under external load they acquire ''wa
vy'' long sides and align parallel to one of the axes. Their size, mea
sured by the reciprocal of the number of A-B bonds, grows approximativ
ely as t(1/3).