Tellurite And Fluorotellurite Glasses For Active And Passive
Tellurite And Fluorotellurite Glasses For Active And Passive Tellurite And Fluorotellurite Glasses For Active And Passive
2. Literature review; MDO 17 conductivity. However, it cannot explain all phenomena, such as property effects thought to be due to short range ordering, and the glass formation in some novel systems also contradict the criteria of this theory. The kinetic theory of glass formation provides a more satisfactory explanation of glass formation of known systems, but the structural theories are still valid and widely used [2]. 2.2.2.4. Dietzel and field strength By extending Goldschmidt’s original consideration of glass formation to radius and charge of the constituent atoms / ions, Dietzel classified elements according to their field strength, Fs. This considers the forces (attraction / repulsion) between cations and anions in the glass [2]. F s τ c = ( ra + rc 2 ) (2.1) where τc is the valence of the cation, r the ionic radius of the cation (c) or anion (a). Using Zachariasen’s classification, ions can be catagorised into three field strength groups, Fs = 0.1 to 0.4 (network modifiers), Fs = 0.5 to 1 (intermediates), and Fs = 1.4 to 2 (network formers) [2]. On cooling a binary melt with cations of approximately the same field strength, phase separation or crystallisation of the pure oxide phases is normally seen (e.g. SiO2-P2O5, SiO2-B2O3, B2O3-P2O5). To form a single stable crystalline compound normally requires ∆Fs > 0.3. As ∆Fs increases, so does the number of possible stable compounds, and the
2. Literature review; MDO 18 tendency to form a glass. For a binary system, glass formation is likely for ∆Fs > 1.33 [2]. Again, this theory can usefully categorise glass forming ability in conventional systems, but not universally. 2.2.3. Kinetic theory of glass formation Glass formation has been shown in materials of a wide variety of compositional, bonding, and structural types. Therefore, considering how rapidly a vapour or liquid must be cooled to avoid a detectable volume fraction of crystallisation (10 -6 0.0001 %) can be a useful way of characterising its glass forming ability [2]. If nucleation frequencies, i (in s -1 ), and growth rates, u (in cm.s -1 ), are known as functions of temperature, equation (2.2) can be used to plot a time-temperature-transformation (TTT) diagram. π 3 −6 3 4 10 = iu t (2.2) where it is the frequency of nucleation with time, and u 3 t 3 the growth in three dimensions with time [2]. However, it is important to note that current theories of homogeneous nucleation in glasses are not able to predict accurately the observed homogeneous rates, and can be many orders of magnitude disparate [7]. From the measured TTT plot, it is possible to obtain the time at each temperature before a significant fraction of the undercooled melt has devitrified. These plots have a ‘nose’ shape with the temperature at the apex of the nose where crystallisation is most rapid. This nose shape arises, as the tendency for crystallisation will be initially enhanced thermodynamically on melt
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2. Literature review; MDO 17<br />
conductivity. However, it cannot explain all phenomena, such as property effects thought<br />
to be due to short range ordering, and the glass formation in some novel systems also<br />
contradict the criteria of this theory. The kinetic theory of glass formation provides a<br />
more satisfactory explanation of glass formation of known systems, but the structural<br />
theories are still valid and widely used [2].<br />
2.2.2.4. Dietzel and field strength<br />
By extending Goldschmidt’s original consideration of glass formation to radius and<br />
charge of the constituent atoms / ions, Dietzel classified elements according to their field<br />
strength, Fs. This considers the forces (attraction / repulsion) between cations and anions<br />
in the glass [2].<br />
F<br />
s<br />
τ c<br />
=<br />
( ra<br />
+ rc<br />
2<br />
)<br />
(2.1)<br />
where τc is the valence of the cation, r the ionic radius of the cation (c) or anion (a).<br />
Using Zachariasen’s classification, ions can be catagorised into three field strength<br />
groups, Fs = 0.1 to 0.4 (network modifiers), Fs = 0.5 to 1 (intermediates), and Fs = 1.4 to<br />
2 (network formers) [2].<br />
On cooling a binary melt with cations of approximately the same field strength, phase<br />
separation or crystallisation of the pure oxide phases is normally seen (e.g. SiO2-P2O5,<br />
SiO2-B2O3, B2O3-P2O5). To form a single stable crystalline compound normally requires<br />
∆Fs > 0.3. As ∆Fs increases, so does the number of possible stable compounds, and the
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