Combined experimental and computational investigation of thermodynamics and phase equilibria in the CaO–TiO₂ system

Abstract

Phase relations in the CaO–TiO2 system are of considerable interest in geology, metallurgy, and ceramics. Despite a number of studies of phase equilibria in the CaO–TiO2 system, there are still some open questions regarding the stability of intermediate compounds. In this work, a series of specimens with different CaO:TiO2 ratios were prepared by solid‐state reaction. The heat capacities of Ca3Ti2O7 and Ca4Ti3O10 from 300 to 1073 K were measured by differential scanning calorimetry and their formation enthalpies from the component oxides at 298 K were measured by high temperature oxide melt solution calorimetry. Using phase diagram information and thermodynamic data from the literature and the present measurements, thermodynamic optimization of the CaO–TiO2 system was carried out by the CALPHAD technique. The phase diagram and the thermodynamic properties of the CaO–TiO2 system were calculated using the obtained thermodynamic database, which clarify the stable and metastable phase equilibria of the system. The thermodynamic stability of the various compounds was discussed.

Thermochemistry of the ZrO2–SrO System: From enthalpies of formation and heat capacities of the compounds to the phase diagram

“…The reason for this difference is not clear. Overall our measured data agree with the NKR calculations well, as has been seen in other mixed oxide compounds . Thus we consider the NKR approximation to be generally adequate and useful for the ZrO 2 –SrO system.…”

“…Dash et al obtained these values by assuming the entropies of formation of Sr 4 Zr 3 O 10 from the component oxides at 298 K to be 20 J/mol·K and that of Sr 3 Zr 2 O 7 to be 15 J/mol·K, which are analogous to the values for Ca 4 Ti 3 O 10 (18.5 J/mol·K) and Ca 3 Ti 2 O 7 (14.8 J/mol·K) in the CaO–TiO 2 system . These values were different from those (16.7 and 26.2 J/mol·K respectively) recently suggested by Gong et al No experimental thermodynamic data for Sr 2 ZrO 4 were found in the literature, except for the estimated enthalpy of formation (−2364.6 kJ/mol) and entropy at 298 K . Dash et al calculated the entropy of Sr 2 ZrO 4 at 298 K to be 171.8 J/mol·K by assuming the entropy of formation of Sr 2 ZrO 4 from the component oxides at 298 K to be 10 J/mol·K.…”

“…26 It was reported that Sr 2 ZrO 4 exhibits a first order transition at 1203 K. 27 Literature data on the thermodynamic properties of Sr 4 Zr 3 O 10 , Sr 3 Zr 2 O 7 , and Sr 2 ZrO 4 are scarce. [28][29][30][31] Using a high-temperature Calvet calorimeter, Banerjee et al 28 32 These values were different from those (16.7 and 26.2 J/mol·K respectively) recently suggested by Gong et al 33 No experimental thermodynamic data for Sr 2 ZrO 4 were found in the literature, except for the estimated enthalpy of formation (−2364.6 kJ/mol) 19 and entropy at 298 K. 19 Dash et al 19 calculated the entropy of Sr 2 ZrO 4 at 298 K to be 171.8 J/ mol·K by assuming the entropy of formation of Sr 2 ZrO 4 from the component oxides at 298 K to be 10 J/mol·K.…”

“…They are liquid, C SS (cubic ZrO 2 ‐based solid solution), T SS (tetragonal ZrO 2 ‐based solid solution), M SS (monoclinic ZrO 2 ‐based solid solution), and RS SS (rocksalt SrO‐based solid solution). To be compatible with our series work on oxide ceramics [], a regular substitutional solution model was used to describe the liquid and solid solution phases, the Gibbs energy for the liquid was expressed by Redlich‐Kister polynomials as Equation ().where H SER is the abbreviation of (1− x )H ZrO2 SER + x H SrO SER , R is the gas constant, x is the mole fraction of SrO. The interaction parameters a 0 , b 0 , a 1 and b 1 were to be optimized.…”

“…Overall our measured data agree with the NKR calculations well, as has been seen in other mixed oxide compounds. 33 Thus we consider the NKR approximation to be generally adequate and useful for the ZrO 2 -SrO system. In evaluating this system by CALPHAD, see below, we prefer to use the NKR approximation for heat capacities of ternary compounds for several reasons.…”