General Concepts of Crystallization: Some Recent …
11
evolution and relaxation at the limiting case of Hookean solids as we did expect it
from above mentioned general considerations. Obviously, some other factors have
to be accounted for if one would like to obtain the correct limiting behavior. We will
return to this problem here somewhat later.
3 Some Other Topics of Current Interest
Utilizing CNT and the described above methods, several other topics have been
addressed in recent years, in particular, (i) the specification of the location of the
maxima of nucleation and growth rates and the rates of overall crystallization both
for temperature and pressure-induced phase formation [27, 28], (ii) the relevance of
fragility concepts and the glass transition temperature for the understanding of crystallization in glass-forming melts [29], (iii) the effects of decoupling of diffusion and
viscosity on crystallization, in general, and crystal growth, in particular [30], (iv) the
analysis of the relation between the average time of formation of the first supercritical
nucleus, the time-lag in nucleation, and the steady-state nucleation rate [31]. In [27,
28], a set of equations for determining temperature or pressure of the maximum nucleation, growth, and overall crystallization rates of glass-forming liquids is derived and
analyzed. In [29], it is shown that the classical fragility concepts can be of relevance
for the understanding of crystallization only if several severe conditions are fulfilled
which are rarely met. However, a modification of the classical definition of fragility
is shown to turn out to be highly useful in application to crystallization. In addition,
general relations are derived correlating the maximum of the crystal nucleation rate
and the glass transition temperature in its conventional definition as proposed long
ago by Tammann (T g corresponding to a viscosity 10
12 Pa s). In [30], a relation is
derived allowing one to correlate the decoupling temperature with the glass transition
temperature and the fragility of the liquid. All results are confirmed by experimental
data. In [31], general expressions are derived for the description of the correlations
between average time of formation of the first supercritical nucleus, time-lag in
nucleation, and the steady-state nucleation rate. The results have been employed by
us in the proof of the absence of a pseudo-spinodal in melt crystallization performed
in [13–15]. The existence of a pseudo-spinodal in melt crystallization characterized
by intensive nucleation processes was suggested by Kauzmann [11] as a possible
way of resolution of the Kauzmann paradox. It is discussed widely up to now and
was recently even denoted as “another vital concept related to supercooled liquids,
which is not known within the glass research community” [32]. Consequently, the
analysis of this topic and the proof of the absence of such pseudo-spinodal curve
with the properties assigned to it by Kauzmann are not merely of historical interest.
The results obtained in [31] have been employed also in the analysis of the interplay
between stress development and stress relaxation in crystallization of highly viscous
glass-forming melts. In particular, it gives a confirmation of the basic assumption,
Eq. 18, utilized in the analysis of the interplay of stress evolution and stress relaxation.
11
evolution and relaxation at the limiting case of Hookean solids as we did expect it
from above mentioned general considerations. Obviously, some other factors have
to be accounted for if one would like to obtain the correct limiting behavior. We will
return to this problem here somewhat later.
3 Some Other Topics of Current Interest
Utilizing CNT and the described above methods, several other topics have been
addressed in recent years, in particular, (i) the specification of the location of the
maxima of nucleation and growth rates and the rates of overall crystallization both
for temperature and pressure-induced phase formation [27, 28], (ii) the relevance of
fragility concepts and the glass transition temperature for the understanding of crystallization in glass-forming melts [29], (iii) the effects of decoupling of diffusion and
viscosity on crystallization, in general, and crystal growth, in particular [30], (iv) the
analysis of the relation between the average time of formation of the first supercritical
nucleus, the time-lag in nucleation, and the steady-state nucleation rate [31]. In [27,
28], a set of equations for determining temperature or pressure of the maximum nucleation, growth, and overall crystallization rates of glass-forming liquids is derived and
analyzed. In [29], it is shown that the classical fragility concepts can be of relevance
for the understanding of crystallization only if several severe conditions are fulfilled
which are rarely met. However, a modification of the classical definition of fragility
is shown to turn out to be highly useful in application to crystallization. In addition,
general relations are derived correlating the maximum of the crystal nucleation rate
and the glass transition temperature in its conventional definition as proposed long
ago by Tammann (T g corresponding to a viscosity 10
12 Pa s). In [30], a relation is
derived allowing one to correlate the decoupling temperature with the glass transition
temperature and the fragility of the liquid. All results are confirmed by experimental
data. In [31], general expressions are derived for the description of the correlations
between average time of formation of the first supercritical nucleus, time-lag in
nucleation, and the steady-state nucleation rate. The results have been employed by
us in the proof of the absence of a pseudo-spinodal in melt crystallization performed
in [13–15]. The existence of a pseudo-spinodal in melt crystallization characterized
by intensive nucleation processes was suggested by Kauzmann [11] as a possible
way of resolution of the Kauzmann paradox. It is discussed widely up to now and
was recently even denoted as “another vital concept related to supercooled liquids,
which is not known within the glass research community” [32]. Consequently, the
analysis of this topic and the proof of the absence of such pseudo-spinodal curve
with the properties assigned to it by Kauzmann are not merely of historical interest.
The results obtained in [31] have been employed also in the analysis of the interplay
between stress development and stress relaxation in crystallization of highly viscous
glass-forming melts. In particular, it gives a confirmation of the basic assumption,
Eq. 18, utilized in the analysis of the interplay of stress evolution and stress relaxation.