[en] A surface-sensitive X-ray line shape analysis of the ordering process in Cu3Au(001) has been performed following a rapid temperature quench from the disordered phase into the ordered phase. We study the temporal evolution of ordered domains in the subsurface region. We find distinct and anisotropic antiphase domain patterns in the unstable and metastable growth mode. This leads to rather unusual surface-induced coarsening schemes. (orig.)