The behavior of the isothermal viscosity as a function of heattreatment time was measured by continuous recording of the elongation of the fiber. Special care was taken to begin the measurements within the first minute after insertion of the fiber into the hot furnace. It is estimated that the fibers reached the heat-treatment temperature in less than 2 minutes. The measurements were then continued for times lasting up to 150,000 minutes. Some fibers were loaded immediately, and others were heat-treated for different time periods before the load was applied in order to determine the delayed elastic effects. Several measurements were conducted at the same temperature, but with different loads in order to detect stress-dependent behavior. In both glasses, the structure appeared to grow in size during the isothermal heat treatments. The volume fractions of each phase remained constant throughout the measurements. The volume fractions of durable to soluble phase are 50:50 and 55:45 for Type I and Type II glasses, respectively. The change in etching solution necessary for the analysis of the structure in the Type II samples indicated that the chemical composition of the phases may have changed during the heat treatments as a function of both temperature and treatment duration. This question is deferred to another report [17] where the chemical durability of the samples is measured as a function of heat-treatment time and temperature. Further analysis of the micrographs indicated that the interconnectivity remained high throughout the microstructure growth. These results, when taken together, suggest that we are observing primarily the rearrangement stage of the phase separation process. It is now necessary to ascribe a microstructure size to each micrograph and analyze the change of this quantity with heat-treatment time and temperature. An easily measured quantity, as shown before, is the distance between consecutive phase changes. However, in order to remain consistent with out previous work on the subject [7,13], let us determine a correlation length to characterize the phases. This is done through a correlation function, G(r), which represents the increased probability due to phase separation of going a distance r from any point and remaining within the same phase. The distance between phase changes, I, is therefore defined as: Using a probability function previously shown to describe these systems well [Ref. 7]: where G G(r) = G exp [−r2/2^2] (2) is a constant and A is the correlation length, we obtain the following relationship: A = 0.63 r . (3) The isothermal time dependence of the correlation length, A, may be readily calculated from the measured dependence of r on heattreatment time and temperature. The data for the Type I glass were reported in Ref. 13. Those for the Type II glass are shown in figure 10. Both glasses follow a 1/3 power dependence of structure size on time, generally expressed as [18]: with the time and size at which this 1/3 power-law behavior begins (A and t) sufficiently smaller than the values reported that they may be ignored. Near the transition temperature, the diffusion coefficient, D, can be expressed in terms of a mobility term and the chemical potential with the following result: 2 (5) where D is a constant; t is the time; T is the temperature; Tc is the transition temperature, and E2 is the activation energy controlling the diffusion process by which the phase rearrangement is occurring. The parameters of the fit of the data to this equation are as follows: Since bulk diffusion through the fluid phase is likely to be the rate controlling step, as indicated by the 1/3 power relationship of Eq. 5 between time and size, then we may assume that it is characterized by an activation energy whose value is E, 2° The isothermal viscosity measured at this laboratory for the two glasses under consideration is shown in figures 11 and 12. It is interesting to note in passing that despite the large viscosity differences between the two glasses above and at the transition temperature (fig. 1), the range of temperatures for which the viscosity is suitably measured by the fiber elongation method is the same, 540-660°C. Figures 11 and 12 show that the isothermal viscosity increases by as much as five orders of magnitude over the heat-treatment times studied. Before correlating this increase to microstructure development, we must identify the effect of the elastic response from application of Fig. 11. Composite illustration of the isothermal viscosity |