Ti⁴⁺ in silicate melts: Energetics from high-temperature calorimetric studies and implications for melt structure

The drop solution calorimetric method was used to determine the enthalpy of solution of rutile (ΔH_sol) in silicate melts. High-temperature (1760 K) in situ calorimetric data show that ΔH_SOl is a strong function of melt composition. For potassium endmember melts, potassium disilicate, and trisilicate, ΔH_sol increases (from 28-48 kJ/mol) as TiO₂ concentration increases. For calcium disilicate melts ΔH_sol is constant (69 kJ/mol). For mixed potassium-calcium compositions, Δ_sol is more exothermic than for the calcium endmember but remains constant at 43.9 kJ/mol. The enthalpy of solution of rutile at 1760 K and the enthalpy of mixing at 978 K derived from lead borate solution calorimetry for Ti-bearing potassium aluminosilicate glasses have been used to model the homogeneous equilibria among Ti species in the potassium-bearing melts. The energetics of Ti speciation were used to predict quantitatively the excess heat capacity of titanium-bearing silicate melts previously observed by Lange and Navrotsky (1993), suggesting that heat capacities, mixing properties, and rutile solubility are all controlled by the temperature and composition dependence of the same set of homogenous equilibria among titanium species in the melts. Though knowing the exact microscopic nature of these species is not necessary for macroscopic thermodynamic modeling, the model is consistent with a gradual variation with composition and temperature in mid-range order involving five-coordinated titanyl groups and alkali atoms as proposed by Farges et al. (1996a,b,c).