Thermodynamics of Mg–Al Order-Disorder Reaction in MgAl2O4-Spinel: Constrained by Prolonged Annealing Experiments at 773–1123 K

Abstract

MgAl2O4-spinel has wide industrial and geological applications due to its special structural and physical–chemical features. It is presumably the most important endmember of complex natural spinel solid solutions, and therefore provides a structural model for a large group of minerals with the spinel structure. There exists a well known but still inadequately understood phenomenon in the structure of MgAl2O4-spinel, the Mg–Al cations readily exchanging their positions in response to variations of temperature, pressure, and composition. A large number of experiments were performed to investigate the Mg–Al cation order-disorder process usually quantified by the inversion parameter x (representing either the molar fraction of Al on the tetrahedral T-sites or the molar fraction of Mg on the octahedral M-sites in the spinel structure), and some thermodynamic models were thereby constructed to describe the x-T relation. However, experimental data at some key T were absent, so that the different performance of these thermodynamic models could not be carefully evaluated. This limited the interpolation and extrapolation of the thermodynamic models. By performing some prolonged annealing experiments with some almost pure natural MgAl2O4-spinel plates and quantifying the x values with single-crystal X-ray diffraction technique, we obtained some critical equilibrium x values at T down to 773 K. These new x-T data, along with those relatively reliable x values at relatively high T from early studies, clearly indicate that the CS94 Model (a model constructed by Carpenter and Salje in 1994) better describes the Mg–Al cation order-disorder reaction in MgAl2O4-spinel for a wide range of T. On the basis of the CS94 Model, a geothermometer was established, and its form is T-closure = 21362 × x3 − 12143 × x2 + 6401 × x − 10 (T-closure standing for the closure temperature of the Mg–Al cation exchange reaction). This geothermometer can be used to constrain the thermal history of the geological bodies containing MgAl2O4-spinel.

Thermodynamic Properties of MgAl2O4 Spinel at High Temperatures and High Pressures

“…Lattice parameters of MgAl 2 O 4 spinel at ambient pressure conditions have been measured using X-ray diffraction [19,20,22,23] and neutron diffraction [24][25][26] from room temperature to ~1900 K, and the values at the low-temperature range were provided by Grimes and Al-Ajaj [21] (Table 1, Figure 1). Although previous investigations reported that the order-disorder transition would affect the volume as well as the thermal expansion of MgAl 2 O 4 spinel [11,17,20,[43][44][45], due to the limitations of the method used in this study, we assume that the ordering state of the cations does not affect the volume. Therefore, we converted the lattice parameters of MgAl 2 O 4 spinel from the published literature [19][20][21][22][23][24][25][26] (Table 1) to the unit-cell volumes, then analyzed the values via the EoSfit software [46] and fit them using the empirical formula recommended by Fei [47].…”

“…that the order-disorder transition would affect the volume as well as the thermal expansion of MgAl2O4 spinel [11,17,20,[43][44][45], due to the limitations of the method used in this study, we assume that the ordering state of the cations does not affect the volume. Therefore, we converted the lattice parameters of MgAl2O4 spinel from the published literature [19][20][21][22][23][24][25][26] (Table 1) to the unit-cell volumes, then analyzed the values via the EoSfit software [46] and fit them using the empirical formula recommended by Fei [47].…”