Estimation of liquidus temperatures for multicomponent silicates from activation energies for viscous flow
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I. INTRODUCTION
IT is well known that the viscosities of liquids increase with decreasing temperatures. In multicomponent systems, as the solid phase separates at and below the liquidus temperatures, the viscosities exhibit non-Newtonian behavior. The viscosities of multicomponent slags show a sharp viscosity increase near and below the liquidus temperature, even in the absence of non-Newtonian behavior. It is interesting to examine whether the viscosities can in some way be related to the prenucleation situation in the liquid state (prior to mush formation) and, therefore, to the thermodynamic liquidus temperatures, which is the focus of the present article. A knowledge of the liquidus temperatures is extremely important for metallurgical operations. Experimental measurements of the liquidus temperatures of slags are difficult, since slags invariably supercool. Consequently, in differential thermal analysis (DTA) measurements, the exothermic peak associated with the solid separation at the liquidus temperature occurs at much lower temperatures. During the heating mode, the compositional inhomogenities would make the results somewhat uncertain. It is hoped that the present article may offer a method of estimating the liquidus temperatures of slags from viscosity data. The approach is to relate the temperature dependency of the activation energy to ionic association behavior and, in turn, to try to correlate this to the liquidus temperature. II. THEORITICAL BACKGROUND A. The Viscous Flow The viscous flows of liquids depend upon the mobility of the species in the systems (atoms, molecules, or ions),
S. SEETHARAMAN, Professor, and DU SICHEN, Associate Professor, are with the Department of Metallurgy, Royal Institute of Technology, SE100 44 Stockholm, Sweden. S. SRIDHAR, Research Associate, is with the Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890. K.C. MILLS, Professor, is with the Department of Materials, Imperial College of Science, Technology and METALLURGICAL AND MATERIALS TRANSACTIONS B
which, in turn, depends upon the nature of the chemical bond and the configuration of the species in the liquid. Thus, for slags, viscosity is a function of the interionic forces that are dependent on the sizes and charges of the ions involved. Stronger forces would lead to an increase in the viscosities. It is commonly known that, for silicate melts with high silica contents, the anions exist in a polymerized state and that bonds are broken and smaller units formed with the addition of metal cations. The viscosities of silicates decrease drastically with the addition of alkali oxides up to about 10 to 20 mol pct, which has been attributed to the decreasing degree of polymerization of the silicate network.[1] From an atomistic point of view, when a liquid is approaching the freezing point, the ordering in the system is expected to increase. Darken and Gurry[2] attributed this phenomenon to nonrandom thermal agitation in the stable liquid at temperatures above the liquidus
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