A new approach to parameterize the viscosity-temperature relationships
of silicate melts is applied to a data set for 28 aluminosilicate melts
based on a haplogranitic chemistry. The approach is based on the introduction
of a crossover temperature T_{c}. Such a crossover temperature
has been predicted by the recently developed mode coupling theory (MCT)
and neutron and light scattering experiments in simple liquids have demonstrated
that a critical temperature T_{c} can be clearly identified at
temperatures above the glass transition temperature (T_{g}). For
simple liquids, this temperature divides a fluid regime with a power-law
temperature dependence of viscosity from a viscous regime with a Vogel-Fulcher-Tammann
temperature dependence of viscosity. Up to now the question has remained
open as to whether MCT can also be applied to strong glass formers (i.e.
silicate melts).

A widely discussed classification, based on the temperature dependence
of viscosity, was introduced by Angell. Plotting the logarithm of the viscosity
(η) as a function of the reduced temperature
T_{g}/T, where T_{g} is the glass transition temperature
(η = 10^{12 }Pa s), the authors obtained
curves exhibiting different degrees of non-Arrhenian behaviour. Nearly
straight (Arrhenian) lines are observed for highly polymerized network
glasses (e.g. SiO_{2}), whereas strong deviations from Arrhenian
behaviour are found in particular for systems with non-directional interatomic/intermolecular
bonds (e.g. molten salts or simple organic liquids). In a restricted temperature
range above T_{g} the different curves in the η
= η(T_{g}/T) plot are well interpolated
by the Vogel-Fulcher-Tammann equation (VFT) η
∝ exp[DT_{0}/(T-T_{0})],
and the parameter D may be considered as a measure of the non-Arrhenian
behaviour, i.e. the "fragility". Alternatively a model independent determination
of fragility has been introduced by using the slope in plot of log τ
versus T_{g}/T at T_{g} , where τ
is the average relaxation time and T_{g} the glass transition temperature
at τ = 100 s.

Influenced by MCT, Rössler has proposed a scaling procedure in
order to provide a master curve for the temperature dependence of η.
First, log_{10}(η/η_{Tg})
is plotted as function of (T_{g}-T)/T where η_{Tg}
is the viscosity at the calorimetric determined glass transition temperature
T_{g}. Next, the temperature interval (T_{c}-T_{g})/
T_{c }is scaled to 1 for each glass former. This is accomplished
by multiplying the abscissa with F ≡ T_{c}
/(T_{c}-T_{g}), i.e. log_{10}(η
/η _{Tg}) is plotted versus F(T_{g}-T)/T.
This procedure is carried out for the reference system o-terphenyl for
which T_{c} is well known. For all other compositions T_{c}
is determined by visual inspection in such a way that the viscosity curves
coincide with the curve for o-terphenyl over a temperature range as large
as possible by varying T_{c}. Fig. 3.7-1 shows the master plot.
The viscosity data of all systems studied over a range of 10 orders of
magnitude, comprising fragile and strong glasses, follow approximately
a master curve. Between T_{c} and T_{g}, the non-Arrhenius
character of all curves is quite similar. This implies that parameter D
has an universal value, rather than being a measure of non-Arrhenian behaviour.
In contrast the parameter m, which quantifies the slope of the

Fig. 3.7-1: The master plot. The crosses refer to viscosity data of haplogranitic melt compositions. Tan (α ) ≅ 14 represents the slope of the master curve at T |

relaxation time vs. T_{g}/T at T_{g}, can be used. Because
the scaling procedure (of the master plot) leads to a master curve very
close to T_{g} , F must be related to m. From the master plot we
find that the slope at T_{g} is about 14 (see straight line in
Fig. 3.7-1). Thus we find the relationship: m ≅
14*F. Introducing the fragility m via the master plot, we obtain improved
values for m, and systematic trends appear, when m is now plotted as a
function of the melt structure parameter (i.e. NBO/T). In addition T_{c}
can be related to cationic properties such as electronegativity. The success
of the master plot raises the possibility that a universal viscosity behaviour
exists for all liquids between T_{c} and T_{g} and supports
the idea that a well-distinguished crossover temperature exists in the
melt. Further experiments (e.g. light scattering) will clarify whether
T_{c} as defined by the master plot may be identified with the
critical temperature defined in MCT.

Bayerisches Geoinstitut, Universität Bayreuth, 95440 Bayreuth, Deutschland

Tel: +49-(0) 921 55 3700 / 3766, Fax: +49-(0) 921 55 3769, E-mail: bayerisches.geoinstitut(at)uni-bayreuth.de

Tel: +49-(0) 921 55 3700 / 3766, Fax: +49-(0) 921 55 3769, E-mail: bayerisches.geoinstitut(at)uni-bayreuth.de