For pt.I see ibid., vol.4, p.138 (1989). The phonon modes are calculated for superlattices over the whole surface Brillouin zone for both GaSb-InAs and GaAs-AlAs systems. Three distinct types of phonon modes are identified, characterised by their overlap with the bulk phonon bands in the constituent media, including purely interface modes for the GaSb-InAs system. Off the Brillouin zone centre, mode mixing is seen.