Nonisothermal Kinetics of Spinel Crystallization in a HLW Glass
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D.G. CASLER AND P. HRMA Pacific Northwest National Laboratory, Richland, WA 99352, [email protected] ABSTRACT Nonisothermal kinetics of spinel crystallization in a high-level waste (HLW) glass was predicted using Mehl-Avrami-Johnson-Kolmogorov equation coefficients from isothermal data. The volume
fraction of spinel was determined as a function of time, temperature, and cooling rate. The results were verified experimentally. Also predicted was the spatial distribution of spinel in a HLW glass canister. Finally, a parameter study was performed, and an empirical equation was proposed relating the final spinel volume fraction in glass to dimensionless numbers for cooling rate, phase equilibrium, and crystallization kinetics. INTRODUCTION
Spinel is a product of an interaction between Cr203 , Fe 20 3, NiO, FeO, and other oxides, which
are present in most high-level waste (HLW) streams at Hanford and Savannah River [1-6]. Spinel
formation in the HLW glass melter may plug the melter spout, and spinel accumulation may obstruct the bottom drain and interfere with the flow of glass within the melter [7]. For the majority of HLW streams, spinel formation in the HLW melter limits the waste fraction in glass. Though precipitation of spinel in the glass outside the melter is harmless [8], the information on spinel concentration distribution within the waste glass canister is required for waste form acceptance [9]. In this paper, spinel crystallization kinetics for nonisothermal temperature histories is predicted
using isothermal kinetic data and compared with measured values. Also, the concentration distribution of spinel in a glass canister is estimated using an empirically determined time-
dependent temperature field. Finally, an empirical approximation equation is formulated for the final concentration of spinel in HLW glass as a function of cooling rate and the equilibrium and kinetic parameters of spinel crystallization. THEORY
The equilibrium volume fraction of spinel in molten glass, C0 , is a function of temperature, T, glass composition, and redox (the partial pressure of oxygen, Po2 ). As a previous study [ 10] showed, spinel equilibrium can be approximated by the equation C0 =cmax{1-exp[-BL(T-1 -TZ')}}1(1 where Cmax and BL are composition-dependent coefficients and TL is the liquidus temperature.
Spinel crystallization kinetics can be represented by the differential equation dC / dt = nk(Co - C)[-ln(1 - C / Co)](n-I'/n
(2)
where C is the spinel volume fraction in molten glass, n is the Avrami exponent, t is time, and
(3) k = koexp(-Bk / T) is the crystallization rate coefficient approximated by an Arrhenius function; ko and B, are constants. Eq. (2) is based on the Johnson-Mehl-Avrami-Kolmogorov equation [11-13] for isothermal crystallization, C = C 0 {l - exp[-(kt)n]I, which was verified for spinel in a HLW glass
by Reynolds and Hrma [10], who have shown that, unlike clinopyroxene [14], spinel nucleates without a measurable incubation period. CALCULATIONS AND EXPERIMENTAL VERIFICATION Spinel Crystallizat
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