Configurational Contribution to the Compression of Silicate Liquids

Melting of silicates in the deep interior of planets has likely played an important role in their evolution. The segregation of silicate melts is controlled by the density contrast between melts and residual solids. Stolper et al. (1981) hypothesized that melts might be denser than their residues at high pressures due to the much larger compressibility of liquids than that of solids. Although the large compressibility of liquids is supported by ultrasonic measurements and static compression experiments using sink/float method, the compression mechanism of liquids is still not well understood. In general, equation of state of a material can be obtained by taking the volume derivative of the Helmholtz free energy. For a solid, free energy has two contributions, the potential energy of a static lattice, and the vibrational free energy (thermal contribution). Thus bulk modulus (the second derivative of free energy) of a solid at T=0 K is determined by the potential energy, while the vibrational part gives the temperature dependence. However, under compression atoms in a liquid can undergo structural rearrangement in addition to the uniform shortening of interatomic distances. Therefore another term, the configurational contribution, must be included in the liquid free energy. It is this contribution that leads to the different compression mechanism for liquids. In this work, we analyzed elastic properties determined by Brillouin spectroscopy, ultrasonic velocity measurements, and static compression experiments on solids, glasses, super- cooled liquids, and liquids for several silicate compositions including CaMgSi2O6, CaAl2Si2O8, Fe2SiO4, etc. We find that in the bulk modulus-density log-log plot (the slope of this plot is the Grüneisen-Anderson parameter), data for solids, glasses, and super-cooled liquids fall on the same straight line, while data for relaxed liquids fall on a distinctly different line. This means that the compression mechanisms for super-cooled liquids, glasses, and solids are essentially the same. Their differences in bulk modulus are mainly due to the volume difference (or bond length difference). However, unlike super-cooled liquids and glasses, configurational rearrangement plays an important role for the relaxed compression of liquids, which makes the bulk modulus of liquids further smaller. The percentages of configurational contribution to the total compressibility for different silicate liquids are then compared with the configurational entropy of the liquids to shed some light on the theoretical model of liquid compression.