Equation of state of ZnAl2O4 spinel constrained by new in situ synchrotron powder X-ray diffraction data

Reliable thermodynamic properties of ZnAl2O4 spinel (gahnite) are essential for pressure (P)–temperature (T) estimation of metamorphism involving Zn. However, its equation of state (EoS), particularly its thermal expansion behavior, remains poorly constrained. In this study, pure ZnAl2O4 spinel was synthesized, and its unit-cell volume was measured by in situ synchrotron powder X-ray diffraction at ambient pressure from 30 to 1100 K. The unit-cell volume increased systematically with temperature between 70 and 1100 K, whereas a slight decrease (negative thermal expansion) was observed between 30 and 55 K. An abrupt volume increase occurred between 55 and 70 K. No significant cation inversion between the tetrahedral and octahedral sites was detected throughout the investigated temperature range. The volume (V)–T data obtained in this study were combined with previously published hydrostatic P–V data and adiabatic bulk moduli to derive a self-consistent thermoelastic EoS. Several EoS formulations were evaluated, and a thermal-pressure EoS combining the third-order Birch–Murnaghan EoS with the Mie–Grüneisen–Debye EoS provides the best fit to the combined datasets. The analysis yielded the following EoS parameters: V0 = 39.7895(7) cm3/mol, KT0 = 208(3) GPa, K′T0 = 5.4(11), θD0 = 927(15) K, γ0 = 1.21(3), and q = 3.0(8). The EoS has the properties at room conditions of αV0 = 1.65(3) × 10−5 K−1 and KS0 = 209(3) GPa. The obtained αV0 is lower than most previous experimental estimates but consistent with recent lattice-dynamical calculations. Because previous V–T datasets were limited to temperatures above room temperature, inclusion of low-temperature data enables reproduction of the physically required curvature of αV(T) toward the third-law limit. Comparison with MgAl2O4 spinel reveals nearly identical expansion coefficients below ∼400 K, but systematically larger values for ZnAl2O4 spinel at higher temperatures. This divergence reflects competition between enhanced vibrational driving forces arising from low-frequency Zn-dominated optical modes and the relatively high bulk modulus associated with partial covalent character of the Zn–O bond. Despite the larger mass of Zn, the Debye temperature exceeds that of MgAl2O4 spinel, indicating significant bond stiffening. These results demonstrate that Zn incorporation modifies the thermoelastic behavior of spinel and that neglecting Zn may lead to systematic bias in P–T estimates of Zn-bearing metamorphic systems.