The free energy of formation of Mg₂TiO₄ (synthetic qandilite), an inverse spinel with configurational entropy

Synthetic qandilite (Mg₂TiO₄) is an inverse spinel in which random mixing of Mg and Ti on the octahedral site should give rise to a configurational entropy of 11.5 J K^-1 mol^-1. The free energy of formation of Mg₂TiO₄ has been determined from the location of the univariant reaction MgTiO₃ + MgO = Mg₂TiO₄ in pressure-temperature space between 0 and 20 kbar; together with literature data for MgTiO₃ and MgO, the results give S^o_(298K)= 111.2 ± 0.6 J K^-1 mol^-1 for Mg₂TiO₄. This entropy is only 7.6 ± 0.9 J K^-1 mol^-1 more than the calorimetrically determined value of 103.6 ± 0.7 J K^-1 mol^-1. The discrepancy implies either considerable short-range order of Mg and Ti in Mg₂TiO₄, or perhaps an error in the high-temperature heat-capacity data for MgTiO₃ caused by disordering in this substance.