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
Distribution of Magnesium and Iron between Orthopyroxene and Calcic Pyroxene in Natural Mineral Assemblages
Distribution coefficients with reference to Mg-Fe exchange and Mn-(Mg, Fe) exchange have been computed for sixty-four calcic pyroxene-orthopyroxene (or pigeonite) combinations from a variety of rocks. The distribution coefficient with reference to Mg-Fe exchange is denned as \documentclass{aastex}
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\begin{document}$$K_{D({\mathrm{Mg-Fe}})}\equiv\frac{X_{{\mathrm{MgSiO}}_{3}}}{1-X_{{\mathrm{MgSiO}}_{3}}} \cdot\frac{1-X_{{\mathrm{MgCaSi}}_{2}{\mathrm{O}}_{6}}}{X_{{\mathrm{MgCaSi}}_{2}{\mathrm{O}}_{6}}}$$\end{document}, where \documentclass{aastex}
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\begin{document}$$X_{{\mathrm{MgCaSi}}_{2}{\mathrm{O}}_{6}}$$\end{document} are mole fractions. In twenty-five high-grade metamorphic rocks the coefficient ranges from 0.51 to 0.65, and in fourteen rocks known or presumed to have crystallized from silicate melt, from 0.65 to 0.86. Two anomalous values were found. In ultramafic nodules in basaltic rock, the coefficient tends to approach unity more closely than in any other rocks. The distribution coefficient with reference to Mn-(Mg, Fe) exchange is variable to the extent that a correlation with temperature or pressure is not possible at present. A tentative equilibrium diagram may be constructed to illustrate the response of the Mg-Fe distribution coefficient to variations in temperature and pressure.
Importance of intrasublattice magnetic interactions and of substitutional ion type in the behavior of substituted yttrium iron garnets
The results of measurements at moderate to high magnetic fields on a large number of nonmagnetic ion substituted yttrium iron garnets suggest that intrasublattice interactions play an important role in determining their spontaneous magnetizations and Curie temperatures. It is shown that the system {Y 3−x Ca x }[Fe 2 ](Fe 3−x Si x )O 12 is continuously related to the system {Y 3−x Ca x }[Zr x Fe 2−x ](Fe 3 )O 12 or {Y 3 }[Sc x Fe 2−x ](Fe 3 )O 12 . It is concluded that in these systems the tetrahedral-tetrahedral (d-d) antiferromagnetic interactions are stronger than octahedral-octahedral (a-a) antiferromagnetic interactions. The changes in magnetic structure from an ideal ferrimagnet, yttrium iron garnet, to an end-member in which there are at least short-range antiferromagnetic interactions (i.e., in {Ca 3 }[Fe 2 ](Si 3 )O 12 or a hypothetical {YCa 2 }[Zr 2 ](Fe 3 )O 12 ) should bear an analogy to the crystal chemical changes. It is therefore proposed that when substitution is made exclusively in one sublattice, the moments of the Fe3+ ions in that sublattice remain parallel (as in the Yafet-Kittel theory), while the weakened average a-d interactions and the intrasublattice interactions lead to random canting of the Fe3+ ion moments of the other. This tendency occurs as soon as substitution begins. On continued substitution, a point is reached beyond which canting increases much more rapidly with increasing substitution. In this region, the intrasublattice interactions dominate the a-d interactions, but it is probable that the canting continues to be random.