Tellurite And Fluorotellurite Glasses For Active And Passive

4. Thermal properties and glass stability; MDO 95
where Ft = fraction transformed, kc = time independent, temperature dependent rate
constant, and m = mechanism constant. If we assume homogeneous nucleation (i.e. no
impurity surfaces) and that crystalline regions grow as spheres, m = 4. For different
assumptions, m can vary from 1 to 4. Therefore, we can fit experimental data to the
model and statements can be made about the crystallisation mechanism. However
homogeneous nucleation is unusual in glasses, and heterogeneous nucleation typically
occurs at the glass / crucible interface in the DTA. When DTA runs are performed on
glass lumps and compared to traces run on powdered samples (higher surface area) of the
same composition and thermal history, if homogeneous nucleation is occurring, then the
crystallisation exotherm will move to a lower temperature in the powdered sample.
Glass samples can be held at a series of isothermal temperatures in the DTA around
the crystallisation region and the fraction transformed calculated by the method described
above. Equation (4.1) can be rearranged:
m
ln( 1−
Ft ) = −k
ct
(4.2)
ln( − ln( 1−
)) = ln k + mln
t
(4.3)
Ft c
A plot of ln(-ln(1–Ft)) vs. lnt, should take the form of a straight line and kc and m can be
obtained for each temperature (y = mx + c, where m ≡ m = gradient and c ≡ lnkc = y-axis
intercept). The gradients (and hence m) should be identical for each isothermal
temperature, presuming the crystallisation mechanism does not change. The rate constant
is generally taken to have Arrhenius temperature dependence [3]: