Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 128

This equation holds for a system that forms a new phase on cooling, i.e., Δ T is the su-
percooling. If the new phase is formed on heating, as in systems with the inverse solu-
bility, Δ T would become the superheating, i.e., T − T 0 . Then Eq. 3.85 would change to:

2

EE AT
B

1 2 T

T

(3.86)

0

=+ + .

D

2 2 3

( ) ( )

∆ T ∆

As mentioned earlier, Eq. 3.83 is not the only form of the temperature dependence
of the solubility. A change of the form of this dependence would result in changing
the final equation for the temperature-dependent activation energy. For instance, the
use of an alternative form: [ 145 ]

ln xZBT = ′ + ′

(3.87)

yields the following equation for the supersaturation:

ln SBTTBT = ′ −=′

0

( ) ∆ . (3.88)

Replacing the supersaturation in Eq. 3.82 with the right-hand side of Eq. 3.88 fol-
lowed by taking the derivative (Eq. 3.85) gives rise to the temperature-dependent
activation energy of the following form:

EE A
B TT TT

3 2

(3.89)

=+ ′ − .

D

2 2 3

( )

2

( )

∆ ∆

Again, Δ T in this equation is the supercooling and it holds for systems that form a
new phase on cooling. For systems that form a new phase on heating, Δ T would be
the superheating, and the second term in the brackets would change its sign.
Equations 3.85 and 3.86 can be used to predict the behavior of the experimental
activation energy (Fig. 3.55 ). It is easy to demonstrate that the expression in the

Fig. 3.55 Temperature
dependence of the activation
energy for the processes of
the new phase formation on
heating and on cooling

one phase
↓
two phases

cooling

E=E D

E=0

two phases
↑
one phase

heating

T