Thin films of In0.81Ga0.19As/InP, grown by molecular beam epitaxy and imaged by in vacuo scanning tunneling microscopy, are observed to possess surfaces that consist of multiple reconstruction domains; small anisotropic regions of beta 2(2x4) in a matrix of a disordered (nx3) reconstruction. The shape and size distribution of these domains is consistent with anisotropic elastic relaxation at the domain boundaries. The boundary energy anisotropy varies with the growth temperature, indicating that the configurational entropy along the [110] direction is higher than for the [110].