General Concepts of Crystallization: Some Recent …
13
It follows that the two terms in the right-hand side of Eq. 26 are of different signs.
Utilizing in addition the relation [36]:
dη
d p
T
= −
κ T (T, p)
α T (T, p
dη
dT
p
(28)
we obtain with Eq. 6:
dg
dT
isochronal
= −
h m
T m
+ v m
κ T (T, p)
α T p (T, p)
(29)
Consequently, if for the systems under consideration Eq. 29 yields values of the
derivative nearly equal to zero, the mentioned result posed by Adrjanowicz et al. [33,
34] is easily understandable in terms of CNT and does not require any assumptions
going beyond it. A detailed analysis of this topic in application to the systems studied
by mentioned authors we consider as highly interesting.
4 Beyond Classical Nucleation Theory: Some Possible
Directions of Its Further Development
In order to describe quantitatively correctly experimental data in the whole range
of pressure and temperature, several generalizations of classical concepts have been
advanced like the decoupling of diffusion and viscosity (or relaxation), the effect of
the size of the “structural units” on crystallization, the possible effect of heterogeneous structure of glass-forming liquids on crystal nucleation, the account of deviations of the properties of critical clusters from the properties of the newly evolving
stable or metastable macroscopic phases, the account of deviations of the state of
the glass-forming melt from metastable equilibrium states. In the present section, we
will discuss some of them in more detail.
4.1 Properties of Critical Clusters Versus Properties
of the Newly Evolving Macroscopic Phases
One of the basic assumptions of CNT supported by Gibbs’ theory consists of the
assumed independence of the properties of critical clusters on the degree of deviation
from equilibrium. This assumption is in a variety of cases in conflict with alternative
theoretical approaches like density functional computations, computer simulations,
and experimental data [37, 38]. It has been questioned immediately after the formulation of CNT and attempted to be overcome inside the framework of Gibbs theory
(Scheil, Hobstetter, see [6, 39, 40]). This critique finally led then to the rediscovery of
13
It follows that the two terms in the right-hand side of Eq. 26 are of different signs.
Utilizing in addition the relation [36]:
dη
d p
T
= −
κ T (T, p)
α T (T, p
dη
dT
p
(28)
we obtain with Eq. 6:
dg
dT
isochronal
= −
h m
T m
+ v m
κ T (T, p)
α T p (T, p)
(29)
Consequently, if for the systems under consideration Eq. 29 yields values of the
derivative nearly equal to zero, the mentioned result posed by Adrjanowicz et al. [33,
34] is easily understandable in terms of CNT and does not require any assumptions
going beyond it. A detailed analysis of this topic in application to the systems studied
by mentioned authors we consider as highly interesting.
4 Beyond Classical Nucleation Theory: Some Possible
Directions of Its Further Development
In order to describe quantitatively correctly experimental data in the whole range
of pressure and temperature, several generalizations of classical concepts have been
advanced like the decoupling of diffusion and viscosity (or relaxation), the effect of
the size of the “structural units” on crystallization, the possible effect of heterogeneous structure of glass-forming liquids on crystal nucleation, the account of deviations of the properties of critical clusters from the properties of the newly evolving
stable or metastable macroscopic phases, the account of deviations of the state of
the glass-forming melt from metastable equilibrium states. In the present section, we
will discuss some of them in more detail.
4.1 Properties of Critical Clusters Versus Properties
of the Newly Evolving Macroscopic Phases
One of the basic assumptions of CNT supported by Gibbs’ theory consists of the
assumed independence of the properties of critical clusters on the degree of deviation
from equilibrium. This assumption is in a variety of cases in conflict with alternative
theoretical approaches like density functional computations, computer simulations,
and experimental data [37, 38]. It has been questioned immediately after the formulation of CNT and attempted to be overcome inside the framework of Gibbs theory
(Scheil, Hobstetter, see [6, 39, 40]). This critique finally led then to the rediscovery of