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Melting and subsolidus relations in the system K2SO4MgSO4CaSO4 were studied using heating-cooling curves, differential thermal analysis, optics, X-ray diffraction at room and high temperatures and by quenching techniques. Previous investigators were unable to study the binary MgSO4CaSO4 system and the adjacent area in the ternary system because of the decomposition of MgSO4 and CaSO4 at high temperatures. This problem was partly overcome by a novel sealed-tube quenching method, by hydrothermal synthesis, and by long-time heating in the solidus. As a result of this study, we found: (1) a new compound, CaSO4??3MgSO4 (m.p. 1201??C) with a field extending into the ternary system; (2) a high temperature form of MgSO4 with a sluggishly reversible inversion. An X-ray diffraction pattern for this polymorphic form is given; (3) the inversion of ??-CaSO4 (anhydrite) to ??-CaSO4 at 1195??C, in agreement with grahmann; (1) (4) the melting point of MgSO4 is 1136??C and that of CaSO4 is 1462??C (using sealed tube methods to prevent decomposition of the sulphates); (5) calcium langbeinite (K2SO4??2CaSO4) is the only compound in the K2SO4CaSO4 binary system. This resolved discrepancies in the results of previous investigators; (6) a continuous solid solution series between congruently melting K2SOP4??2MgSO4 (langbeinite) and incongruently melting K2SO4??2CaSO4 (calcium langbeinite); (7) the liquidus in the ternary system consists of primary phase fields of K2SO4, MgSO4, CaSO4, langbeinite-calcium langbeinite solid solution, and CaSO4??3MgSO4. The CaSO4 field extends over a large portion of the system. Previously reported fields for the compounds (K2SO4??MgSO4??nCaSO4), K2SO4??3CaSO4 and K2SO4??CaSO4 were not found; (8) a minimum in the ternary system at: 740??C, 25% MgSO4, 6% CaSO4, 69% K2SO4; and ternary eutectics at 882??C, 49% MgSO4, 19% CaSO4, 32% K2SO4; and 880??, 67??5% MgSO4, 5% CaSO4, 27??5% K2SO4. ?? 1967.