The study of radiation effects in solids is important for the development of ＇radiation-resistant＇ materials for fission-reactor applications＇. The effects of heavy-ion irradiation in the isostructural orthosilicates zircon (ZrSiO4), hafnon (HfSiO4) and thorite (ThSiO4) are particularly important because these minerals are under active investigation for use as a waste form for plutonium-239 resulting from the dismantling of nuclear weapons(2-4). During ion irradiation, localized ＇cascades＇ of displaced atoms can form as a result of ballistic collisions in the target material, and the temperature inside these regions may for a short time exceed the bulk melting temperature. Whether these cascades do indeed generate a localized liquid state(5-8) has, however, remained unclear. Here we investigate the irradiation-induced decomposition of zircon and hafnon, and find evidence for formation of a liquidlike state in the displacement cascades. Our results explain the frequent occurrence of ZrO2 in natural amorphous zircong(9-12) Moreover, we conclude that zircon-based nuclear waste forms should be maintained within strict temperature Limits, to avoid potentially detrimental irradiation-induced amorphization or phase decomposition of the zircon.