Heats of formation for several crystalline polymorphs and pressure-induced amorphous forms of AMo₂O₈ (A = Zr, Hf) and ZrW ₂O₈

The enthalpies of drop solution (ΔH_ds) for several polymorphs of ZrW₂O₈ (cubic, orthorhombic, trigonal, and amorphous), ZrMo₂O₈ (cubic, trigonal, monoclinic, and amorphous), and HfMo₂O₈ (cubic, trigonal, and amorphous) have been measured in molten 3Na₂O·4MoO₃ at 975 K. Using the values of ΔH_ds for the binary oxides, we calculated enthalpies of formation from the oxides at 298 K. Monoclinic ZrMo ₂O₈ is the only polymorph examined that is enthalpically stable relative to the binary oxides (ΔH_f,ox = -5.1 ± 3.5 kJ/mol), and even that stability is marginal. The ΔH_f,ox values for cubic and trigonal ZrMo₂O₈ are 45.2 ± 5.3 and 32.2 ± 4.5 kJ/mol, respectively; for cubic and trigonal HfMo ₂O₈, 55.8 ± 3.1, and 46.5 ± 3.6 kJ/mol, respectively; and for cubic, orthorhombic, and trigonal ZrW₂O ₈, 64.8 ± 2.8, 50.6 ± 3.0, and 49.8 ± 4.1 kJ/mol, respectively. Therefore, these phases are either entropically stabilized and/or their formation/persistence is kinetically controlled. The enthalpies of formation from the oxides, at ambient pressure, for the amorphous phases recovered after compression of the cubic polymorphs in a multianvil press are more positive than those of the crystalline polymorphs: 98.9 ± 5.0 kJ/mol for ZrMo₂O₈, 102.0 ± 6.3 kJ/mol for HfMo ₂O₈, and 127.8 ± 5.5 kJ/mol for ZrW ₂O₈. The entropies of the amorphous phases are probably greater than those for the cubic ones and thus the pressure-induced amorphous phase can be entropically (as well as volumetrically) favored, and the pressure-induced amorphization boundary probably has a negative P-T slope. Nevertheless, these amorphous phases could be metastable with respect to more dense crystalline polymorphs, either in the P-T range where they are observed or at higher pressure.