Equations of state of Plagioclase Feldspars

Abstract

The volume variation with pressure of seven intermediate plagioclase feldspars has been determined by high-pressure single-crystal X-ray diffraction. The bulk moduli of plagioclases for a 3rd-order Birch-Murnaghan EoS can be described by the following pair of equations: % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaacaWGlbWaaSbaaSqaaiaadsfacaaIWaaabeaakiabg2da9iaa % iwdacaaI0aGaaiOlaiaaigdadaqadaqaaiaaiodaaiaawIcacaGLPa % aacqGHRaWkcaaIWaGaaiOlaiaaiodacaaI5aWaaeWaaeaacaaIXaaa % caGLOaGaayzkaaGaamiwamaaBaaaleaacaWGbbGaamOBaaqabaGcca % qGGaGaaeOzaiaab+gacaqGYbGaaeiiaiaadIfadaWgaaWcbaGaamyq % aiaad6gaaeqaaOGaeyipaWJaaeynaiaabcdaaaa!5476! $$ K_{{T0}} = 54.1{\left( 3 \right)} + 0.39{\left( 1 \right)}X_{{An}} {\text{ for }}X_{{An}} < {\text{50}} $$ % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaacaWGlbWaaSbaaSqaaiaadsfacaaIWaaabeaakiabg2da9iaa % iwdacaaI5aGaaiOlaiaaiwdadaqadaqaaiaaiodacaGGUaGaaGymaa % GaayjkaiaawMcaaiabgUcaRiaaicdacaGGUaGaaGOmaiaaiodadaqa % daqaaiaaisdaaiaawIcacaGLPaaacaWGybWaaSbaaSqaaiaadgeaca % WGUbaabeaakiaabccacaqGMbGaae4BaiaabkhacaqGGaGaamiwamaa % BaaaleaacaWGbbGaamOBaaqabaGccqGH+aGpcaqG1aGaaeimaaaa!55EC! $$ K_{{T0}} = 59.5{\left( {3.1} \right)} + 0.23{\left( 4 \right)}X_{{An}} {\text{ for }}X_{{An}} > {\text{50}} $$ with % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! <![CDATA[% MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaaceWGlbGbauaadaWgaaWcbaGaaGimaaqabaGccqGH9aqpcaaI % 1aGaaiOlaiaaiIdaaaa!3E7A! $${K}'_{0} = 5.8$$ for plagioclase with X An <20 and % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! <![CDATA[% MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaaceWGlbGbauaadaWgaaWcbaGaaGimaaqabaGccqGH9aqpcaaI % ZaGaaiOlaiaaikdaaaa!3E72! $${K}'_{0} = 3.2$$ for X An >35. These parameters can also be used in a Murnaghan EoS to describe the volume variation of plagioclase feldspars up to pressures of 3 GPa. For a Murnaghan EoS with % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! <![CDATA[% MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaaceWGlbGbauaadaWgaaWcbaGaaGimaaqabaGccqGH9aqpcaaI % 0aaaaa!3D05! $${K}'_{0} = 4$$ , the values of the bulk moduli can be described by a single equation, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafaart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaacaWGlbWaaSbaaSqaaiaadsfacaaIWaaabeaakiabg2da9iaa % iwdacaaI3aGaaiOlaiaaiEdadaqadaqaaiaaiAdaaiaawIcacaGLPa % aacqGHRaWkcaaIWaGaaiOlaiaaikdacaaI0aWaaeWaaeaacaaIXaaa % caGLOaGaayzkaaGaamiwamaaBaaaleaacaWGbbGaamOBaaqabaaaaa!4B20! $$ K_{{T0}} = 57.7{\left( 6 \right)} + 0.24{\left( 1 \right)}X_{{An}} $$ , with a small loss in the accuracy of the predicted volumes up to pressures of 3 GPa.