HR: 16:45h
AN: DI44A-04 INVITED    [Abstracts]
TI: Some Theoretical Issues on the Equation of State of Silicate Melts
AU: * Karato, S
EM: shun-ichiro.karato@yale.edu
AF: Yale University, 210 Whitney Avenue, New Haven, CT 06520, United States
AU: Jing, Z
EM: Zhicheng.jing@yale.edu
AF: Yale University, 210 Whitney Avenue, New Haven, CT 06520, United States
AB: Properties of silicate melts, particularly their densities under deep Earth conditions (i.e., the equation of state), are critical to the understanding of evolution of terrestrial planets. However, the inspection of the existing experimental data reveals fundamental differences in the mechanisms of compression between melts and solids that poses important questions as to the interpretation and applications of experimental data on compression of melts to Earth science problems. Common to all complex liquids, the X-ray studies of radial distribution function (RDF) show the presence of short-range-order (SRO) but absence of long-range-order (LRO). Furthermore, the classic analysis by Bottinga-Weill (1970) showed that a silicate melt can be modeled as a mixture of oxide components, where the (partial) molar volumes of component oxides are close to those of solid counterparts. However, the observed RDF indicates that the bond-length of "oxide component" does not shrink as much as expected from the volume reduction under compression. Also the observed bulk moduli for individual "oxide" components in melts are much less than those of solid counterparts, indicating that much of the compression occurs through the geometrical rearrangement of oxide units. In addition, RDF and NMR observations show that in many silicate melts, coordination numbers of oxygen surrounding cations increase (continuously) with pressure. These two types of structural changes at different scales, namely the geometrical rearrangement of oxide units and the coordination changes of individual oxide units themselves, contribute significantly to the compression of silicate melts. We present a simple model to incorporate these structural details in the equation of state of silicate melts. We find that the coordination change affects the internal energy (and the vibrational entropy) whereas the geometrical arrangement of oxide units contributes to the configurational entropy. Consequently, the former affects the effective compressibility of silicate melts, while the latter affect the thermal component of equation of state such as the Grüneisen parameter and the temperature dependence of bulk modulus. We will discuss the implications of the present model for the validity of ideal mixing model.
DE: 3611 Thermodynamics (0766, 1011, 8411)
DE: 3919 Equations of state
SC: Study of the Earth's Deep Interior [DI]
MN: 2007 Fall Meeting