Thermodynamic mixing properties of Mg(Al, Cr)₂O₄ spinel crystalline solution at high temperatures and pressures

Abstract

Three Al-Cr exchange isotherms at 1,250°, 1,050°, and 796° between Mg(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 25 kbar pressure. Starting from gels of suitable bulk compositions, close approach to equilibrium has been demonstrated in each case by time studies.

Using the equation of state for (Al, Cr)₂O₃ crystalline solution (Chatterjee et al. 1982a) and assuming that the Mg(Al, Cr)₂O₄ can be treated in terms of the asymmetric Margules relation, the exchange isotherms were solved for Δ G ^*, $W_{G,{\text{ MgAl}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}}$ and $W_{G,{\text{ MgCr}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}}$. The best constrained data set from the 1,250° C isotherm clearly shows that the latter two quantities do not overlap within three standard deviations, justifying the choice of asymmetric Margules relation for describing the excess mixing properties of Mg(Al, Cr)₂O₄ spinels. Based on these experiments, the following polybaric-polythermal equation of state can be formulated: $\begin{gathered} G_{\text{m}}^{{\text{ex}}} = (1 - X_{{\text{MgCr}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}} ){\text{ }}X_{{\text{MgCr}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}} [W_{G,{\text{ MgCr}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}} + \hfill \\ (W_{{\text{MgCr}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}} - W_{G,{\text{ MgCr}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}} ){\text{ }}X_{{\text{MgCr}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}} ] \hfill \\ {\text{with }}W_{G,{\text{ MgAl}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}} = 19,686 + 0.0182{\text{ }}P + 0.463{\text{ }}T,{\text{ and}} \hfill \\ {\text{ }}W_{{\text{MgCr}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}} = 23,894 + 0.0504{\text{ }}P + 1.964{\text{ }}T \hfill \\ \end{gathered}$, P expressed in bars, T in K, G ^ex_m and W ^Sp_G,i in joules/mol.

Temperature-dependence of G ^ex_m is best constrained in the range 796–1,250° C; extrapolation beyond that range would have to be done with caution. Such extrapolation to lower temperature shows tentatively that at 1 bar pressure the critical temperature, T _c, of the spinel solvus is 427° C, with dT_c/dP≈1.3 K/kbar. The critical composition, X _c, is 0.42 $X_{{\text{MgCr}}_{\text{2}} {\text{O}}_{\text{4}} }^{{\text{Sp}}}$, and changes barely with pressure.

Substantial error in calculated phase diagrams will result if the significant positive deviation from ideality is ignored for Al-Cr mixing in such spinels.