THE MAGNESIOWUSTITE: IRON EQUILIBRIUM AND ITS IMPLICATIONS FOR THE ACTIVITY-COMPOSITION RELATIONS OF (MG,FE)2SIO4 OLIVINE SOLID SOLUTIONS

Abstract

The chemical potential of oxygen (µO2) in equilibrium with magnesiowustite solid solution (Mg, Fe)O and metallic Fe has been determined by gas-mixing experiments at 1,473 K supplemented by solid-cell EMF experiments at lower temperatures. The results give:<formula form="DISPLAY" disc="MATH">% MathType!MTEF!2!1!+- % feaafaart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaacaWG1cGaae4tamaaBaaaleaacaaIYaaabeaakiaacIcacaqG % RbGaaeOsaiaab+cacaqGTbGaae4BaiaabYgacaGGPaGaeyypa0Jaam % yTaiaab+eadaWgaaWcbaGaaGOmaaqabaGccaGGOaGaamysaiaadEfa % caGGPaGaey4kaSIaaGOmaiaacIcacaWGybWaaSbaaSqaaiaab2eaca % qGNbGaae4taaqabaGccaGGPaWaaWbaaSqabeaacaaIYaaaaOGaai4w % aiaacIcacaaI1aGaaiOlaiaaiEdacaaI2aGaey4kaSIaaG4maiaac6 % cacaaI0aGaaG4naiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacqGH % sislcaaIZaaaaOGaamivaiaacMcacqGHRaWkcaaIWaGaaiOlaiaais % dacaaIXaGaaiikaiaaiodacqGHsislcaaI0aGaamiwamaaBaaaleaa % caqGnbGaae4zaiaab+eaaeqaaOGaaiykaiaac2faaaa!6CE4! $$ \mu {\rm{O}}_2 ({\rm{kJ/mol}}) = \mu {\rm{O}}_2 (IW) + 2(X_{{\rm{MgO}}} )^2 [(5.76 + 3.47 \times 10^{ - 3} T) + 0.41(3 - 4X_{{\rm{MgO}}} )] $$ </formula>where IW refers to the Fe-"FeO" equilibrium. The previous work of Srecec et al. (1987) and Wiser and Wood (1991) agree well with this equation, as does that of Hahn and Muan (1962) when their reported compositions are corrected to a new calibration curve for lattice parameter vs. composition. The amount of Fe3+ in the magnesiowustite solid solution in equilibrium with Fe metal was determined by Mossbauer spectroscopy on selected samples. These data were combined with literature data from gravimetric studies and fitted to a semi-empirical equation:<formula form="DISPLAY" disc="MATH">% MathType!Translator!2!1!AMS-alt LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaacaWGybWaaSbaaSqaaiaabAeacaqGLbWaaWbaaWqabeaacaaI % ZaGaey4kaScaaSGaae4tamaaBaaameaacaaIXaGaaiOlaiaaiwdaae % qaaaWcbeaakiabg2da9iaacIcacaaIXaGaeyOeI0IaamiwamaaBaaa % leaacaqGnbGaae4zaiaab+eacaaMc8oabeaakiaacMcadaahaaWcbe % qaaiaaiodacaGGVaGaaGOmaaaakiaacUfacaaIWaGaaiOlaiaaigda % caaIWaGaaG4maiabgkHiTiaaicdacaGGUaGaaGOmaiaaicdacaaIZa % GaamiwamaaBaaaleaacaqGnbGaae4zaiaab+eaaeqaaOGaey4kaSIa % aGimaiaac6cacaaIYaGaaGymaiaaiodacaGGOaGaamiwamaaBaaale % aacaqGnbGaae4zaiaab+eaaeqaaOGaaiykamaaCaaaleqabaGaaGOm % aaaakiaac2faaaa!64D4! $$ X_{{{\text{Fe}}^{{3 + }} {\text{O}}_{{1.5}} }} = (1 - X_{{{\text{MgO}}\,}} )^{{3/2}} [0.103 - 0.203X_{{{\text{MgO}}}} + 0.213(X_{{{\text{MgO}}}} )^{2} ] $$</formula>These results were then used to reassess the activity-composition relations in (Mg, Fe)2SiO4 olivine solid solutions at 1,400 K, from the partitioning of Mg and Fe2+ between olivine and magnesiowustite in equilibrium with metallic Fe experimentally determined by Wiser and Wood (1991). The olivine solid solution is constrained to be nearly symmetric with <formula form="INLINE" disc="MATH">% MathType!MTEF!2!1!+- % feaafaart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaacaWGxbWaa0baaSqaaiaab2eacaqGNbGaaeylaiaabAeacaqG % LbaabaGaae4BaiaabYgaaaGccqGH9aqpcaaIYaGaaiOlaiaaiAdaca % aMe8+aaSGbaeaacaqGRbGaaeOsaaqaaiaab2gacaqGVbGaaeiBaaaa % aaa!49E9! $$ W_{{\rm{Mg - Fe}}}^{{\rm{ol}}} = 2.6\;{{{\rm{kJ}}} \mathord{\left/ {\vphantom {{{\rm{kJ}}} {{\rm{mol}}}}} \right. \kern-\delimiterspace} {{\rm{mol}}}} $$</formula>, with a probable uncertainty of less than ±0.5 kJ/mol (one standard deviation). The results also provide a useful constraint on the free energy of formation of Mg2SiO4.