# What, well above the melting temperature of

What, then, is glass
transformation behavior? We traditionally discuss glass transformation behavior
on the basis of either enthalpy or volume versus temperature diagrams, such as
that shown in Fig.1.2. Since enthalpy and volume behave in a similar fashion,
the choice of the ordinate is somewhat arbitrary. In either case, we can
envision a small volume of a liquid at a temperature well above the melting
temperature of that substance. As we cool the liquid, the atomic structure of
the melt will gradually change and will characteristic of exact temperature at
which the melt is held. Cooling to any temperature below the melting
temperature of the crystal would normally result in the conversion of the
material to the crystalline state, with the formation of a long range, periodic
atomic arrangement.

If this occurs, the enthalpy
will decrease abruptly to the value appropriate for the crystal. Continued
cooling of the crystal will result in a further decrease in enthalpy due to the
heat capacity of the crystal. If the liquid can be cooled below the melting
temperature of the crystal without crystallization, a supercooled liquid is
obtained. The structure of the liquid continues to rearrange as the temperature
decreases, but there is no abrupt decrease in enthalpy due to discontinuous
structural rearrangement. As the liquid is cooled further, the viscosity
increases. This increase in viscosity eventually becomes so great that the
atoms can no longer completely rearrange to the equilibrium liquid structure,
during the time allowed by the experiment. The structure begins to lag behind
that which would be present if sufficient time were allowed to reach
equilibrium. The enthalpy begins to deviate from the equilibrium line,
following a curve of gradually decreasing slope, until it eventually becomes
determined by the heat capacity of the frozen liquid, i.e., the viscosity
becomes so great that the structure of the liquid becomes fixed and is no
longer temperature-dependent. The temperature region laying between the limits
where the enthalpy is that of the
equilibrium  liquid  and
that of the frozen solid, is known as the glass transformation  region. The frozen liquid is now a glass.

Since the temperature where the enthalpy
departs from the equilibrium curve is controlled by the viscosity of the liquid,
i.e., by kinetic factors, use of a slower cooling rate will allow the enthalpy
to follow the equilibrium curve to a lower temperature. The glass
transformation region will shift to lower temperatures and the formation of a
completely frozen liquid, or glass, will not occur until a lower temperature.
The glass obtained will have a lower enthalpy than that obtained using a faster
cooling rate. The atomic arrangement will be that characteristic of the
equilibrium liquid at a lower temperature than that of the more rapidly cooled
glass. Although the glass transformation actually occurs over a temperature
range, it is convenient to define a term which allows us to express the
difference in thermal history between these two glasses. If we extrapolate the
glass and supercooled liquid lines, they intersect at a temperature defined as
the fictive temperature. The structure of the glass is considered to be that of
the equilibrium liquid at the fictive temperature. Although the fictive
temperature concept is not a completely satisfactory method for characterizing
the thermal history of glasses, it does provide a useful parameter for
discussion of the effect of changes in cooling rate on glass structure and
properties.

Finally, we need to define a term,
which, while commonly used, has only a vague scientific meaning. As indicated
above, the glass transformation occurs over a range of temperatures and cannot
be characterized by any single temperature. It is, however, convenient to be
able to use just such a single temperature as an indication of the onset of the
glass transformation region during heating of a glass. This temperature, which
is termed either the glass transformation temperature, or the glass transition
temperature, (Tg) , is rather vaguely defined by changes in either thermal
analysis curves or thermal expansion curves. The values obtained from these two
methods, while similar, are not identical. The value obtained for Tg, is also a
function of the heating rate used to produce these curves. Since Tg, is a
function of both the experimental method used for the measurement and the
heating rate used in that measurement, it cannot be considered to be a true
property of the glass. We can, however, think of Tg, as a useful indicator of
the approximate temperature where the supercooled liquid converts to a solid on
cooling, or, conversely, of which the solid begins to behave as a viscoelastic
solid on heating Shelby (1997).