VOLUME AND ENTROPY SYSTEMATICS OF MATERIALS AT HIGH PRESSURES AND TEMPERATURES BY HEATED DIAMOND-ANVIL ENERGY-DISPERSIVE TECHNIQUES (THERMODYNAMICS, TIN, EQUATIONS STATE)

The temperatures and pressures throughout most of the mantle are generally above those normally achieved for in situ experimental work. Thus, it has been necessary to use extrapolations based on various thermodynamic assumptions to convert the data from the laboratory conditions to those appropriate for the Earth's mantle. An experimental technique utilizing a heated diamond-anvil cell and energy-dispersive x-ray diffraction (EDXRD) has been developed whereby molar volumes and molar entropies at elevated pressures and temperatures can be obtained. This technique minimizes the extrapolations to mantle conditions.;The entropy-volume systematics of tin (Sn) have been studied by utilizing these techniques. 39 volume determinations that span the P-T stability field of Sn((beta)) were fitted to 25 different equations, constituting 18 possible equations of state. Over the range of 25(DEGREES)C to 310(DEGREES)C and 0 to 9.4 GPa, the preferred equation of state is: V/V(,0) = 0.9973 - 1.77 x 10('-2)P + 4.94 x 10('-4)P('2) + 6.38 x 10('-5)T + 1.04 x 10('-7)T('2) - 7.13 x 10('-6)PT. The data require the ratio (alpha)/(beta) decrease with decreasing volume and the isochores be concave towards the pressure axis. The isentropes for Sn((beta)) are concave toward the temperature axis for entropies greater than 51 J/K-mole.;The Sn((beta)) melting curve is approximately parallel to the Sn((beta)) isentropes, indicating melting which results from a critical state of disorder. However, the Sn(II) melt curve appears to be subparallel to the Sn(II) isochores resulting from a critical volume where atomic collisions take place. Based on the volume and entropy systematics at the invariant point, the molar volume and entropy of Sn(L) at 308(DEGREES)C and 2.87 Gpa were determined to be 1.677 J/bar and 65.17 J/K-mole, respectively.;Modifications to a megabar diamond-anvil cell were made allowing in situ x-ray diffraction measuresments to 500(DEGREES)C. The use of EDXRD techniques and a high brilliance x-ray generator simplify the geometry and reduce the data collection time to about one hour. Two cup heaters within a toroid wound heater are used to control the temperature and the temperature gradient within the cell. With this configuration temperatures can be reproduced to (+OR-) 3(DEGREES)C. A hollow cylinder device applies the force to the lever arm of the cell and is used to change pressure without disturbing the x-ray alignment. These modifications allow for continuous and independent variation of pressure and temperature.