A new approach to the equation of state of silicate melts: An application of the theory of hard sphere mixtures

摘要

A comparison of compressional properties of silicate solids, glasses, and liquids reveals the following fundamental differences: (1) Liquids have much smaller bulk moduli than solids and glasses and the bulk moduli of various silicate melts have a narrow range of values; (2) Liquids do not follow the Birch's law of corresponding state as opposed to solids and glasses; (3) The Grüneisen parameter increases with increasing pressure for liquids but decreases for solids; (4) The radial distribution functions of liquids show that the interatomic distances in liquids do not change upon compression as much as solids do. The last observation indicates that the compression of silicate melts occurs mostly through the geometrical arrangement of various units whose sizes do not change much with compression, i.e., the entropic mechanism of compression plays a dominant role over the internal energy contribution. All of the other three observations listed above can be explained by this point of view. In order to account for the role of the entropic contribution, we propose a new equation of state for multi-component silicate melts based on the hard sphere mixture model of a liquid. We assign a hard sphere for each cation species that moves in the liquid freely except for the volume occupied by other spheres. The geometrical arrangement of these spheres gives the entropic contribution to compression, while the Columbic attraction between all ions provides the internal energy contribution to compression. We calibrate the equation of state using the experimental data on room-pressure density and room-pressure bulk modulus of liquids. The effective size of a hard sphere for each component in silicate melts is determined. The temperature and volume dependencies of sphere diameters are also included in the model in order to explain the experimental data especially the melt density data at high pressures. All compressional properties of a silicate melt can be calculated using the calibrated sphere diameters. This equation of state provides a unified explanation for most of compressional behaviors of silicate melts and the experimental observations cited above including the uniformly small bulk moduli of silicate melts as well as the pressure dependence of Grüneisen parameters. With additional data to better constrain the key parameters, this equation of state will serve as a first step toward the unified equation of state for silicate melts.