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The existence of a distribution of relaxation times has been widely used to describe the relaxation function versus frequency in glass-forming liquids. Several empirical distributions have been proposed and the usual method is to fit the experimental data to a model that assumes one of these functions. Another alternative is to extract from the experimental data the discrete profile of the distribution function that best fits the experimental curve without any a priori assumption. To test this approach a Monte Carlo algorithm using the simulated annealing is used to best fit simulated dielectric loss data, ${\ensuremath{\varepsilon}}^{\ensuremath{''}}(\ensuremath{\omega}),$ generated with Cole-Cole, Cole-Davidson, Havriliak-Negami, and Kohlrausch-Williams-Watts (KWW) functions. The relaxation times distribution, $G(\mathrm{ln}(\ensuremath{\tau})),$ is obtained as an histogram that follows very closely the analytical expression for the distributions that are known in these cases. Also, the temporal decay functions, $\ensuremath{\varphi}(t),$ are evaluated and compared to a stretched exponential. The method is then applied to experimental data for $\ensuremath{\alpha}$-polyvinylidene fluoride over a temperature range $233 \mathrm{K}l~Tl~278 \mathrm{K}$ and frequencies varying from 3 MHz to 0.001 Hz. These data show the existence of two relaxation processes: the fast segmental ${\ensuremath{\alpha}}_{a}$ process associated with the glass transition and a ${\ensuremath{\alpha}}_{c}$ mode, which is slower and due to changes in conformation that can occur in the crystalline regions. The experimental curves are fitted by the simulated annealing direct signal analysis procedure, and the relaxation times distributions are calculated and found to vary with temperature. The decay function is also evaluated and it shows clearly its bimodal character and a good agreement with a KWW function with a temperature dependent $\ensuremath{\beta}$ for each mode. The relaxation plots are drawn for each mode and the Vogel-Tammann-Fulcher and Arrhenius parameters are found. The fragility parameter for polyvinylidene flouride (PVDF) is found to be 87, which characterizes this polymer as a relatively structurally strong material.

The combined results obtained on ${\mathrm{Ca}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Gd}}_{\mathit{x}}$${\mathrm{F}}_{2+\mathit{x}}$ and ${\mathrm{Ca}}_{1\mathrm{\ensuremath{-}}\mathit{x}\mathrm{\ensuremath{-}}\mathit{y}}$${\mathrm{Lu}}_{\mathit{x}}$${\mathrm{Gd}}_{\mathit{y}}$${\mathrm{F}}_{2+\mathit{x}+\mathit{y}}$ solid solutions by ionic thermal currents and electron paramagnetic resonance techniques are presented for a wide range of x values. The ${\mathrm{Gd}}^{3+}$ ions are located in tetragonal and cubic sites, and in a variety of at least nine polarizable entities in the single-doped solid solutions whose range of existence and relaxation parameters have been precisely determined. In the double-doped crystals the ${\mathrm{Gd}}^{3+}$ probes are in constant concentration (y=0.0001) while the ${\mathrm{Lu}}^{3+}$ ions detected in the temperature range explored here constitute a very small fraction of the nominal concentration of the sample. The differences observed are accounted for by a scavenging of ${\mathrm{F}}_{\mathit{i}}^{\mathrm{\ensuremath{-}}}$ by clusters of increasing size in the single-doped matrix and by the existence of cubo-octahedra hexamers existing from very low doping levels in the double-doped crystals.

Thermally stimulated depolarization [ionic thermal current (ITC)] and thermally stimulated polarization current (TSPC) methods are compared, and the results obtained for ${\mathrm{SrF}}_{2}$ crystals doped with La are reported in this paper. It is shown that for normal dipolar peaks such as the low-temperature relaxation caused by the movement of the interstitial ${\mathrm{F}}_{\mathrm{i}}^{\mathrm{\ensuremath{-}}}$ bound to a ${\mathrm{La}}^{3+}$ cation to form a nearest-neighbor dipole, both techniques give the same information, provided that for the ITC case, the polarization temperature is below the temperature range where the very intense and somewhat anomalous high-temperature peak occurs. For an ITC experiment a current reversal is observed in the high-temperature tail of the dipolar peak if the sample is polarized at a temperature above the high-temperature peak. This current reversal, typical of a TSPC peak, is clearly observed and its height is useful in determining the effective polarization field applied to the sample when an ITC run is performed. The presence of the current reversal indicates the existence of a frozen-in polarization due to processes occurring in the high-temperature part of the relaxation spectrum. Also, information on the origin of the observed relaxation processes at high temperature can be deduced from a comparison of the two spectra.

Concentrated solid solutions ${\mathrm{Ba}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{La}}_{\mathrm{x}}$${\mathrm{F}}_{2+\mathrm{x}}$, x\ensuremath{\le}0.492, are studied by means of thermally stimulated depolarization [ionic thermal current (ITC)] or polarization [thermally stimulated polarization current (TSPC)] techniques. At high temperature two peaks are reported whose maxima shift to lower temperatures as x increases. The energies calculated for these relaxation processes are compared to the enthalpies deduced from conductivity measurements. The first high-temperature peak, D, has been already reported in a more restricted concentration range and has been attributed to either a space-charge accumulation near the electrodes or the polarization of the dislocations present in the crystal.We show here that it is the highest-temperature peak reported here for the first time and labeled as peak E which is best related to the displacement of free interstitial fluorines through the bulk of the crystal; that is, to the building up of a space charge near the electrodes. At low concentrations the behavior of peaks D and E is understood if the Debye-H\"uckel interaction energy among unassociated defects is taken into account. For the more concentrated region (x\ensuremath{\gtrsim}0.05), the enhanced ionic motion model proposed to explain the variation of the ionic conductivity slopes as a function of x also applies here; the parameters present in the model are calculated and are found to be in agreement with those previously reported. The energy difference observed between peaks D and E is almost constant for x\ensuremath{\ge}0.05. This energy difference equal to 0.08 eV is attributed to the binding energy of the interstitial fluorines forming the dislocation charge cloud to the dislocation line. TSPC experiments are carried out on the same crystals and they show that peak D is present in all the TSPC spectra, thus confirming the localized displacement of the charges, while the highest-temperature peak E is replaced by a steep increase of the ionic current. Therefore, the origin of peak E observed in ITC must be attributed to the accumulation of charges near the electrodes; that is, the build up of the space-charge layer.

A computer program has been written to analyze ionic-thermal-current (ITC) peaks. The reorientation energy is assumed to have a distribution of width $\ensuremath{\sigma}$ around a mean value ${E}_{0}$. The relaxation parameters ${E}_{0}$, $\ensuremath{\sigma}$, ${\ensuremath{\tau}}_{0}$ and the number of dipoles ${N}_{D}$ are calculated by two different methods. One set is obtained after a least-squares fitting of the experimental data was performed and another set by matching a set of experimental parameters chosen with a certain criterion. The two methods are applied to analyze Sr${\mathrm{F}}_{2}$:La ITC spectra in the cases of the monoenergetic model, the Lorentzian, and the Gaussian energy distribution. The Gaussian distribution for the reorientation energy gives the most credible results, provided that the curves are efficiently cleaned. Only in this case do the two methods converge to the same set of relaxation parameters; the value of $\ensuremath{\sigma}$ is then an increasing function of the nominal concentration and not of ${N}_{D}$. The origin of the curve broadening is discussed in terms of dipole-dipole interaction, and it is shown that this effect alone is not responsible for the energy distribution. Moreover, evidence of the presence of satellite peaks on each side of the main relaxation peak is presented. These satellite peaks explain the need of analyzing only efficiently cleaned curves for obtaining reliable results.