Combined use of oxide and fluoride solid electrolytes for the measurement of Gibbs energy of formation of ternary oxides:System Bi-Ca-O

Phase equilibrium studies of the ternary system Bi-Ca-O at 1000 K and ambient pressure indicate that all the ternary oxides lie along the pseudo-binary line $Bi_2O_3-CaO$. Four ternary oxides, $Bi_2Ca_2O_5$, $Bi_6Ca_4O_{13}$, $Bi_2CaO_4$ and $Bi_{14}Ca_5O_{26}$ and two phases of variable composition $(\delta and \beta)$ are identified. The chemical potential of CaO in two-phase fields of the pseudo-binary $Bi_2O_3-CaO$ is determined as a function of temperature using solid state cells based on single crystal $CaF_2$ as the electrolyte. The chemical potential of $Bi_2O_3$ in the two-phase fields is measured using cells incorporating $(Y_2O_3)ZrO_2$ as the solid electrolyte. The standard Gibbs free energy of formation of each ternary oxide from the binary oxides is calculated independently from the chemical potentials of CaO and $Bi_2O_3$ in two-phase fields on either side of the compound composition. The independent assessments agree closely; the maximum difference in the value of $?G_f^0$ $(Bi_{2m}Ca_nO_{3m+n})/(m+n)$ is 170 J/mol of the component binary oxides. The results are discussed in the light of the phase diagram and compared with calorimetric and free energy measurements reported in the literature. The combined use of emf data from cells incorporating fluoride and oxide electrolytes enhances the reliability of derived data. Free energies of formation of ternary oxides from component binary oxides are given by the following equations: $Bi_2Ca_2O_5: ?G_{f,ox}^0(J/mol) = -43800+5.79 T (±900)Bi_6Ca_4O_{13}:?G_{f,ox}^0(J/mol) = -109800+7.04 T (±2300)Bi_2CaO_4: ?G_{f,ox}^0(J/mol) = -31910+2.31 T (±650)Bi_{14}Ca_5O_{26} ?G_{f,ox}^0(J/mol) = -184560+12.76 T (±4320)Bi_{1.4}Ca_{0.3}O_{2.4} (?): ?G_{f,ox}^0(J/mol) = -12290(±300) at 900 K; Bi_{1.56}Ca_{0.22}O_{2.56} (?): ?G_{f,ox}^0(J/mol) = -9890(±180)$ at 900 K