Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 123

predicted by the Turnbull-Fisher model (Fig. 3.50 ). The transition from the form
II to the form I demonstrates positive values of E ʱ that decrease with increasing ʱ,
which is expected because the measurements are done on heating so that ʱ increases
monotonously with increasing T . Similarly, for the transition from the form I to the
form II that is measured on cooling, E ʱ is expected to be negative and to increase
with increasing ʱ (i.e., with decreasing T ) toward 0.
The obtained E ʱ dependencies (Fig. 3.51 ) are converted to the E ʱ versus T depen-
dencies by replacing each value of ʱ with the mean temperature related to it. The
resulting dependencies (Fig. 3.52 ) look quite similar to the theoretical ones derived
from the Turnbull-Fisher model (Fig. 3.50 ). We can now try to fit the theoretical E ʱ
versus T dependence (Eq. 3.45) to the experimental one. For simplicity, we assume
that the E D and A parameters of Eq. 3.45 remain the same for the forward (heating)
and reverse (cooling) transition. The value of T 0 can also be used as a fit parameter.
This would permit estimating the position of the equilibrium transition temperature,
which, as explained earlier, is hard to measure experimentally. The resulting fit sug-
gests that T 0 is ~ 396 K (~ 123 ﾰC). This places the equilibrium transition tempera-
ture much closer to the onset of the transition measured on heating (128 ﾰC) than to
the one measured on cooling (113 ﾰC; Fig. 3.47 ). Also, the fit yields an estimate for
the activation energy of diffusion, E D = 63 2 kJ mol −1 . This value falls in the range
of the activation energies measured [ 144 ] by nuclear magnetic resonance (NMR)
for translational diffusion of ammonium ion in the phases I and II of ammonium
nitrate.
The solid-solid transitions are a new application area of isoconversional meth-
ods. Their full potential in this area is yet to be discovered.

Fig. 3.52 Fitting E versus
T data ( points ) to Eq. 3.45
( solid lines )

600

500

400

300

200

Cooling:
phase I hase II

Heating:
phase II

100

→

→

phase I

0

-100

-200

-300

385 390 395 400 405

T / K