EQUATIONS OF STATE FOR THE POLYMORPHS OF TIN AND IRON-ORTHOSILICATE DETERMINED BY IN SITU ENERGY-DISPERSIVE X-RAY DIFFRACTION IN A HEATED DIAMOND-ANVIL PRESSURE CELL. (VOLUMES I AND II) (FAYALITE, SPINEL)

Energy-dispersive x-ray diffraction of powdered samples in a heated diamond-anvil pressure cell allows the in situ measurement of the molar volume of crystalline materials at simultaneously elevated temperature and pressure. The most complete and precise P-V-T data sets currently available, including those produced in this study, can be adequately modeled by a temperature-corrected Murnaghan equation incorporating six or fewer refinable parameters.;Twenty-one molar volume determinations for fayalite and 13 determinations for (gamma)-Fe(,2)SiO(,4) (spinel), all at 400(DEGREES)C, constitute the first elevated-temperature static compression isotherms for any silicate minerals. Murnaghan regressions through these data yield values of 103.3 GPa and 8.12 respectively for the isothermal bulk modulus (K(,T)) and its pressure derivative (K(,T)('')) for fayalite and 148.8 GPa and 7.37 for (gamma)-Fe(,2)SiO(,4). Compared to literature room-temperature compressibility data, these elevated-temperature isotherms yield -5.64 x 10('-2) GPa/deg and +3.1 x 10('-3) deg('-1) respectively for ((PAR-DIFF)K/(PAR-DIFF)T) and ((PAR-DIFF)K'/(PAR-DIFF)T) for fayalite and -13.1 x 10('-2) GPa/deg and +4.8 x 10('-3) deg('-1) for (gamma)-Fe(,2)SiO(,4). When equivalent P-V-T data for the magnesium end-member polymorphs become available, this data can be used to predict the phase equilibria within one of the most important chemical subsystems in the earth's mantle, the (Mg,Fe)(,2)SiO(,4) solid solution.;Forty molar volume determinations for the high-pressure phase of metallic tin, Sn(II), form the basis for the first experimentally-determined P-V-T equation of state for any non-quenchable phase. The isochores for Sn(II) are concave toward the pressure axis; their slope varies from approximately 120 deg/GPa at the Sn((beta))--Sn(II)--Sn(melt) triple point at 308(DEGREES)C and 2.9 GPa to approximately 290 deg/GPa at the room-temperature Sn((beta))--Sn(II) transition at 9.4 GPa. Used in conjunction with Cavaleri's (1984) P-V-T data for Sn((beta)), this Sn(II) data reveals that (DELTA)V for the Sn((beta))--Sn(II) reaction remains remarkably constant at approximately -0.135 J/MPa/mol whereas (DELTA)S increases from +2.15 J/deg/mol at room-temperature to +7.15 J/deg/mol at the triple point. The molar volume and entropy of Sn(melt) at the triple point were determined to be 16.113 J/MPa/mol and 81.91 J/deg/mol, respectively, indicating that (DELTA)S along the Sn((beta)) melt curve remains very nearly constant whereas (DELTA)V decreases by approximately 31% from room-pressure to the triple point.