Bull. Minéral.
(1983), 106, 99-105
Application of a percolation model to supercooled liquids with a tetrahedral structure
by José TEIXEIRA (1), H. Eugene STANLEY* (2), Yan BOTTINGA (3) and Pascal RICHET (4)
(1) Laboratoire de Physique Thermique (E.R.A. 365 du CNRS) ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France.
(2) Center for Polymer studies** and Department of Physics Boston University, Boston, MA 02215, U.S.A.
(3) Laboratoire de Géologie et de Géochimie, (E.R.A. 888 du CNRS), Université de Nice, Parc Valrose,
06034 Nice Cedex, France.
(4) Laboratoire de Géochimie et Cosmochimie (LA 196 du CNRS), Institut de Çhysique du Globe, Université de Paris VII,
4 place Jussieu, 75230 Paris Cedex 05, France.
Application d' un modèle de percolation aux liquides surfondus dont la structure est tétrciédrique .
I. -Introduction
Liquid water at low temperatures and liquid silica have various characteristic properties in common, which are usually considered to be anomalous for li¬ quids, see for example Kanno and Angell (1980). The reason for this similarity is that both liquids have a three dimensional open network structure consisting of interconnected tetrahedra. In water four hydrogen atoms are tetrahedrally arranged around an oxygen (see Eisenberg and Kauzmann, 1969, for a review) while in the case of silica each silicon atom is sur¬ rounded by four oxygen atoms (Mozzi and Warren, 1969 ; Nukui et al., 1978). Dilute aqueous solutions at low temperature and silicate liquid show the same arrangement.
The anomalous properties of liquid water are quite prominent at temperatures below 0 °C. We refer the reader to the review by Angell (1982) for more de¬ tails. Here we limit the discussion to those aspects, which H20 and Si02 have in common. At 1 atm. pressure liquid water and silica at their melting point are more dense than the solid phase with which each is in equilibrium. The densities of liquid HzO and
*) John Simon Guggenheim Memorial Fellow, 1980-1981.
**) Supported, in part, by grants from ONR, NSF, and ARO.
Si02 in the neighbourhood of their melting points in¬ crease with increasing temperature over a restricted temperature interval at 1 atm. In this temperature re¬ gion the coefficients of thermal expansion become ne¬ gative. For pure water, the existence of a density ma¬ ximum close to 4 °C is of course well known, for silica such a maximum has been reported at approximately 1,550 °C by Bruckner (1964). The viscosity of pure wafer and dilute aqueous solutions at low temperatures decreases initially when pressure is applied (Kestin et al., 1977 ; Agayev, 1980 ; Correia et al., 1980). It is' unknown how the viscosity of liquid silica varies with pressure, but liquid silicates show a viscosity decrease with pressure (Kushiro, 1977, 1981 ; Scarfe et al., 1979), when the concentration of network modifying elements is not too large.
These anomalous effects and others for water have been explained qualitatively by Stanley (1979), Stan¬ ley and Teixeira (1980) and Stanley et al. (1981), who applied percolation theory. It seems reasonable to at¬ tempt to explain the properties of liquid silica and silicates in the same way. Besides, this theory may also be of use to interpret the chemical properties and their composition dependence of liquid silicate solu¬ tions, because Dron (1979a, \919b) has shown that the Masson polymerization scheme for binary silicate melts (Masson, 1965 ; Masson, 1977) is a limiting case of a more general scheme, which can be straight¬ forwardly derived from percolation theory.
