Calculation of the Viscosity of Nuclear Waste Glass Systems
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CALCULATION OF THE VISCOSITY OF NUCLEAR WASTE GLASS SYSTEMS
R. SHAH, E.C. BEHRMAN AND D. OKSOY Institute for Ceramic Physics New York State College of Ceramics at Alfred University Alfred, NY 14802 ABSTRACT Viscosity is one of the most important processing parameters and one of the most difficult to calculate theoretically, particularly for multicomponent systems like nuclear waste glasses. Here, we propose a semi-empirical approach based on the Fulcher equation, involving identification of key variables, for which coefficients are then determined by regression analysis. Results are presented for two glass systems, and compared to results of previous workers and to experiment. We also sketch a first-order statistical mechanical perturbation theory calculation for the effects on viscosity of a change in composition of the melt. INTRODUCTION Viscosity and its dependence on temperature and composition is the single most important variable in glass processing. Viscosity determines the rate of melting of the raw feed, the rate of gas bubble release(fining), the rate of homogenization, and thus, the quality of final product. There are three basic groups of viscosity theories[1,21. The largest group is that of a purely empirical relationships, such as power series in T or l/T, exponential functions of 1/T or T, and sums and/or quotients of these. While these may be rationalized on theoretical grounds, the rationalizations are only that: the connections to microscopic reality are tenous at best. The seccond group of theories is based on Arrhenius model, in which flow is imagined to be a classical barrier crossing process, the rate thermally activated: 0 = n` = exp(-# A G,,0)
(1)
where q• = n-1, the reciprocal of viscosity, is the fluidity, AG!,G,is the free energy of activation for viscous flow, and B is the inverse absolute temperature in units of Boltzmann's constant, kB. The simplest version of this theory assumes that AS,,i, and AE,,,, (where AG,,i, = T A S,,,o + AE,,,,) are both independent of temperature (so that a plot of log(77) vs. l/T is linear.) In general this is not true for glasses: the temperature dependence can be much stronger. At this point such theories must rely entirely on empirically determined constants to express the temperature dependence of zliEj,. The third group of theories is based on the idea of "free volume"[3] Flow is dependent on there being space for the molecules to move into. The viscosity r1 is then a function of the difference between the liquid volume at temperature T, VT and the volume at some reference temperature T. < T, V.: 77= ?7(VT - VI,,T). T. is generally taken to be the glass transition temperature. The usual procedure is to Mat. Res. Soc. Symp. Proc. Vol. 176. c1990 Materials Research Society
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assume that VT = V,,[1 + a(T - T.)], where a is the coefficient of expansion. This leads to the Fogel-Fulcher-Tammann equation[2,4]: logst7= -A + B/(T - T,,)
(2)
where A, B and To are constants. This equation fits remarkably well over a wide range of viscosities. The above e
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