NASA TN D-6980 APPLICATION OF THERMODYNAMICS TO SILICATE CRYSTALLINE SOLUTIONS
i FOREWORD iii ACKNOWLEDGMENTS v SYMBOLS ix 1 THERMODYNAMIC RELATIONS IN CRYSTALLINE SOLUTIONS 1 2 THERMODYNAMIC STABILITY OF A SOLUTION 11 3 COMPOSITION OF COEXISTING PHASES 15 4 MEASUREMENT OF COMPONENT ACTIVITIES BY ANALYSIS OF PHASE DIAGRAMS 25 5 MEASUREMENT OF COMPONENT ACTIVITY USING COMPOSITION OF COEXISTING MINERALS 35 6 ORDER-DISORDER IN Fe-Mg SILICATES 39
Some Applications of Thermodynamics to Coexisting Minerals of Variable Composition. Examples: Orthopyroxene-Clinopyroxene and Orthopyroxene-Garnet
Consideration is given to the relationship between the chemical potential of a species and its concentration in solids of the type (A, B, C)M and (A, B)(C, D)qM, where A, B, C, D, and M are chemical species. On this basis the distribution coefficient is derived for different combinations of chemical mixtures. For coexisting phases α = (A, B)M, and β = (A, B)N, the distribution coefficient with reference to species A is \documentclass{aastex}
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\begin{document}$$K_{D} = \frac{X^{\alpha}_{A}(1-X^{\beta}_{A})}{(1 - X^{\alpha}_{A})X^{\beta}_{A}} = \frac{f^{\alpha}_{B} f^{\beta}_{A}}{f^{\alpha}_{A} f^{\beta}_{B}} \frac{\lambda^{BM}_{B} \lambda^{AN}_{A}}{\lambda^{AM}_{A} \lambda^{BN}_{B}},$$\end{document} where X = A /(A + B), the terms in f denote activity coefficients, and the terms in λ denote absolute activities. For coexisting phases α = (A, B, C)M and β = (A, B,Ç)N the distribution coefficient with reference to A has a similar form and is now dependent on the B: C ratio in either phase. The pressure dependence and temperature dependence of the distribution coefficient can be expressed by the equations: \documentclass{aastex}
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\begin{document}$$K_{D\,2}= K_{D\,1}\ {\mathrm{exp}}\left[\frac{( - V^{\alpha}_{A} + V^{\alpha}_{B} + V^{\beta}_{A} - V^{\beta}_{B})(P_{2}-P_{1})}{RT}\right],$$\end{document} and \documentclass{aastex}
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\begin{document}$$K_{D\,2}= K_{D\,1}\ {\mathrm{exp}}\left[\frac{(H^{\alpha}_{A} - H^{\alpha}_{B} - H^{\beta}_{A} + H^{\beta}_{B}) \left(\frac{1}{T_{1}} - \frac{1}{T_{2}}\right)}{R}\right],$$\end{document} where P = pressure, T = absolute temperature, R is the gas constant, and the terms in V denote partial molar volumes and those in H, partial molar enthalpies. The coexistence of natural orthopyroxene and clinopyroxene is considered as an example of two phases of the type (A, B)M and (A, B)N. KD is evidently independent of X, indicating that both phases are ideal mixtures. In rocks of presumed metamorphic crystallization, \documentclass{aastex}
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\begin{document}$$K_{D} \simeq 0.54$$\end{document} and in rocks of presumed igneous crystallization, \documentclass{aastex}
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\begin{document}$$K_{D} \simeq 0.73$$\end{document}. The difference in KD is attributed to a difference in crystallization temperature. The coexistence of natural orthopyroxene and garnet is considered as an example of two phases of the type (A, B, C, D)M and (A, B, C, D)N. With reference to Mg, KD is correlative with the Mn-concentration in garnet. This relationship provides empirical confirmation of the chemical theory.
Crystallographic and Magnetic properties of the systems lithium ferrite-aluminate and lithium ferrite-gallate
Abstract Measurements of the saturation magnetization σ against temperature have been carried out for the systems Li0.5Fe2.5-aAlaO4 and Li0.5Fe2.5-aGaaO4(0 ⩽ a ⩽ 2.5), which have an ordered spinel structure. From the σ-T curves the saturation moments were obtained, and from these it was possible to calculate the trivalent cation distribution, since X-ray diffraction shows that the Li+ ions are always on octahedral sites. For small values of a Al3+ is substituted mainly on octahedral sites, whereas Ga3+ mainly enters the tetrahedral sites. It is argued that in spinels a certain preference for tetrahedral sites exists which increases in the sequence Al3+, Fe3+, Ga3+. All Neel's anomalous σ-T curves have been found in the system Li0.5Fe2.5-aAlaO4.