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Phase relations in the system NaAlSiO4–MgAl2O4 were determined at 11–30 GPa at 1273–1873 K, using multianvil apparatus. At 1873 K, calcium-ferrite solid solution in the compositional range of (1 − x)NaAlSiO4·xMgAl2O4 (0 ≤ x ≤ 0.3) is formed above 17 GPa, and hexagonal aluminous phase is stable in the compositional range of 0.5 ≤ x ≤ 0.7 above 13.5 GPa. The hexagonal aluminous phase becomes nonstoichiometric with increasing MgAl2O4 component from x = 0.5 due to substitution mechanisms involving cation vacancy. In the composition of 0.3 ≤ x ≤ 0.5, Na-rich calcium-ferrite and Mg-rich hexagonal aluminous phase coexist. In 50%NaAlSiO450%MgAl2O4 composition (mol%), MgAl2O4 spinel + NaAlSi2O6 jadeite + α-NaAlO2 reacts to form a single hexagonal phase (see Reaction (1)) at 13–14 GPa at 1273–1873 K. In 67%MgAl2O433%CaAl2O4 composition, MgAl2O4 spinel + CaAl2O4 calcium ferrite changes to a single hexagonal phase (see Reaction (2)) at 13–14 GPa at 1273–1673 K. The two hexagonal phases of Na0.5Mg0.5Al1.5Si0.5O4 and Mg0.67Ca0.33Al2O4 are stable up to at least 30 GPa at 1873 K. By high-temperature drop-solution calorimetry, enthalpies at 298 K of Reactions (1) and (2) to form hexagonal phases were obtained to be 54.6 ± 1.6 and 36.8 ± 2.3 kJ/mol, respectively. Isobaric heat capacities (Cp) and entropies (S°298) of hexagonal phases of Na0.5Mg0.5Al1.5Si0.5O4 and Mg0.67Ca0.33Al2O4 were calculated by Kieffer models, based on Raman spectra and Cp measured by a differential scanning calorimeter. The calculated S°298 of hexagonal phases of Na0.5Mg0.5Al1.5Si0.5O4 and Mg0.67Ca0.33Al2O4 are 86.7 and 88.0 J/(mol K), respectively. Using the above enthalpies and entropies, P–T boundaries for formation of Na0.5Mg0.5Al1.5Si0.5O4 and Mg0.67Ca0.33Al2O4 hexagonal phases from the low-pressure phase assemblages were calculated. The calculated boundaries are generally consistent with high-pressure experimental data within the errors. The measured enthalpies and molar volumes suggest that hexagonal phase of Na0.5Mg0.5Al1.5Si0.5O4 would transform to calcium ferrite at pressure in the upper half of the lower mantle. [Copyright &y& Elsevier]