Kinetics of refractory fiber glass devitrification Page: 2 of 26
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wt = wt fraction glass = %G/100
w. = wt fraction crystal = 1-wg
p, = density of the crystal = 1/E(w;/p)
where w; = wt fraction of each crystal phase
and p, = density of each crystal phase present.
pT = density at time (t) and temperature (T) = [wjpg +.(w.)E(w;/pi)]'
and f. = volume fraction crystallized = w.(p;/p)
Using equation (5), and the devitrification data for the three commercial refractory fibers [Lo
1991], the volume fraction crystallized, f.,, at a given time (15 - 1800 s) and temperature (1366
K to 1700 K) was calculated (see Table 1). The volume fraction crystallized at each time was
plotted in the form of equation (2) and n and k were calculated from the slope and intercept for
each temperature. The rate constant and temperature data was plotted in the form of equation
(4), and the activation energy and frequency factor were calculated from the slope and intercept.
Figure 1 and Figure 2 illustrate this for the ACS fiber. This procedure is the same as that
outlined by Speyer [1994. p.66].
These equations are also applied to non-isothermal analyses such as differential thermal
analysis (DTA). In a DTA study, the temperature may be increased at a constant rate and the
temperature of the sample, relative to a reference, is measured. Crystallization is observed as
an exothermic peak. Some assumptions are necessary for this application to be valid. The
major assumption is that nucleation is completed at some lower temperature than that at which
crystal growth occurs. Bansal et al. [1983] derive the following equation (equation (6)) for the
analysis of this data:
1n(TG) - ln(E/R) - In(v) + (E/R)T (6
where Tp = crystallization temperature (exothermic peak),
a = crystallization rate,
R = ideal gas constant,
E = activation energy, and
v = kinetic frequency factor.
Thus, a plot of ln('") vs. l/T should give a line with a slope of (E/R) and an intercept of
ln(E/R)-ln(v).
1700 K = 1427*C = 2600*F
1589 K = 1316*C = 2400*F
1477 K = 1204*C = 2200*F
1366 K = 1093*C = 2000*F.2
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Curtis, J.M. & DePoorter, G.L. Kinetics of refractory fiber glass devitrification, article, December 31, 1995; United States. (https://digital.library.unt.edu/ark:/67531/metadc665080/m1/2/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.