Phase relations in the system NaAlSiO 4 –MgAl 2 O 4 were determined at 11–30GPa at 1273–1873K, using multianvil apparatus. At 1873K, calcium-ferrite solid solution in the compositional range of (1−x)NaAlSiO 4 ·xMgAl 2 O 4 (0≤x≤0.3) is formed above 17GPa, and hexagonal aluminous phase is stable in the compositional range of 0.5≤x≤0.7 above 13.5GPa. The hexagonal aluminous phase becomes nonstoichiometric with increasing MgAl 2 O 4 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%NaAlSiO 4 50%MgAl 2 O 4 composition (mol%), MgAl 2 O 4 spinel+NaAlSi 2 O 6 jadeite+α-NaAlO 2 reacts to form a single hexagonal phase (see Reaction (1)) at 13–14GPa at 1273–1873K. In 67%MgAl 2 O 4 33%CaAl 2 O 4 composition, MgAl 2 O 4 spinel+CaAl 2 O 4 calcium ferrite changes to a single hexagonal phase (see Reaction (2)) at 13–14GPa at 1273–1673K. The two hexagonal phases of Na 0.5 Mg 0.5 Al 1.5 Si 0.5 O 4 and Mg 0.67 Ca 0.33 Al 2 O 4 are stable up to at least 30GPa at 1873K. By high-temperature drop-solution calorimetry, enthalpies at 298K of Reactions (1) and (2) to form hexagonal phases were obtained to be 54.6±1.6 and 36.8±2.3kJ/mol, respectively. Isobaric heat capacities (C p ) and entropies (S° 298 ) of hexagonal phases of Na 0.5 Mg 0.5 Al 1.5 Si 0.5 O 4 and Mg 0.67 Ca 0.33 Al 2 O 4 were calculated by Kieffer models, based on Raman spectra and C p measured by a differential scanning calorimeter. The calculated S° 298 of hexagonal phases of Na 0.5 Mg 0.5 Al 1.5 Si 0.5 O 4 and Mg 0.67 Ca 0.33 Al 2 O 4 are 86.7 and 88.0J/(molK), respectively. Using the above enthalpies and entropies, P–T boundaries for formation of Na 0.5 Mg 0.5 Al 1.5 Si 0.5 O 4 and Mg 0.67 Ca 0.33 Al 2 O 4 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 Na 0.5 Mg 0.5 Al 1.5 Si 0.5 O 4 would transform to calcium ferrite at pressure in the upper half of the lower mantle.