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Solid solutions Ca1-xGdxF2+x for 3 × 10−7≤ x ≤10−1 have been studied by electron paramagnetic resonance (EPR) and ionic thermal currents (ITC). The EPR experiments show the presence of two single-ion sites a cubic and a tetragonal Gd3+ center which co-exist with comparable abundances for intermediate impurity concentrations. The cubic center predominates at very low and high concentrations. Seven different relaxation processes have been identified from the ITC spectra and the variation of their intensity vs. x was measured. The absolute concentrations of the cubic and nn Gd3+ dipoles were calculated. The scavenging of interstitial fluorines by the neutral clusters explains both the abundance of cubic sites at high concentration and the variety of orientable clusters detected by ITC.

Solid solutions Ca1 x-yLuxGdy F2+x+y for 10−4 ≤ x ≤ 2 × 10−2 and y=0.0001 have been studied by electron paramagnetic resonance (EPR) and ionic thermal currents (ITC). It has been found that the ITC spectrum from 77 to 420 K is very weak and the main peak is attributed to the relaxation of both Lu3+-F− x and Gd3+F− i nn dipoles. No polarizable clusters are present in the temperature range explored here. The EPR spectra show the presence of Gd3+ tetragonal and cubic centers due to the local and non local compensation, respectively. The continuous decrease in the molar fraction of Gd3+ tetragonal centers together with the low concentration of Lu nn dipoles is an evidence of the existence at these low and intermediate concentrations of large clusters such as the cubo-octahedral hexamer which has been proposed for CaF2 crystals very highly doped with small trivalent cations.

To study the different populations of defects existing in Ba1-x Gd x F2+x solid solutions for x ranging from 0.0001 to 0.1, comparative Ionic Thermal Currents (ITC) and Electron Paramagnetic Resonance (EPR) experiments have been performed. In the as-grown crystals weak trigonal centers assigned to the nnn Gd3+-F i − dipoles coexist at all concentrations with Gd3+ in cubic sites. The variation of the number of these nnn dipoles as a function of x found with the two series of experiments is a strong indication of the existence of larger clusters in the crystals. The appearance of new relaxation peaks in the low temperature zone of the ITC spectra is correlated to the formation of these aggregates together with the observed variation in the number of cubic sites. An association energy of 0.41 eV of the nnn dipole is calculated from the equilibrium of associated and free defects. The less doped crystals were treated thermally at 1223 K and variable amounts of O2− ions diffused into the samples creati...

A Monte Carlo computing procedure is presented for evaluating the set of parameters which characterize the superhyperfine interaction in electron-nuclear spin coupled systems. The method is illustrated in the determination of the components T/sub /// and Tperpendicular to of the interaction tensor Tto or from together with the linewidth Delta Hp-p of each of the superhyperfine transitions present in the electron paramagnetic resonance spectrum given by a cubic Gd3+ centre in CaF2 recorded at room temperature. The different steps followed to simulate the 'annealing' of the system are described in detail together with the shortcuts proposed in order to minimize the computing time taken for the procedure to converge to the best set of parameters. This method is applicable even if no good estimates are available for the initial set of parameters as these are usually taken as zero. This modern approach to the complicated problem of fitting the superhyperfine structure to the theoretical expressions is shown to be the best alternative and even if it is time consuming it can be easily run on a microcomputer.

Ionic thermocurrent (ITC) and electron paramagnetic resonance (EPR) experiments have been performed on solid solutions of the type Ba1−xYxF2+x, 0.0001≤x≤0.05, additionally doped with a small fixed molar concentration, equal to 10−4 , of Gd3+ acting as paramagnetic probes. It is shown that the more abundant polarizable defect is the next nearest neighbor (nnn) dipole, Y3+−Fi−, whose molar concentration reaches a maximum for x∼0.005. Also, the EPR experiments show the coexistence of cubic and trigonal Gd3+ centers for the whole x range studied here. The variation of the population of these two paramagnetic centers peaks around x=0.0002 and the fraction of their relative abundances deduced from the observed EPR intensity is almost constant. The existence of several weaker lines evidences the presence of Gd3+ ions in additional sites to the cubic and trigonal ones. The comparison of the results obtained from the ITC and EPR techniques indicates the presence of Y3+ in larger clusters than the simple nnn dipole. To explain the variation of the abundance of the trigonal center at low Y3+ concentrations, a mechanism is proposed for the creation of the clusters formed by the trapping of an extra Fi− by either the Y3+ or the Gd3+ nnn dipoles. The existence of clustering among the trivalent ions in this system is supported by the variation of the linewidths of the EPR lines as x increases. These linewidths do not increase linearly with x but rather present a saturation effect at high x values. This indicates that a high doping levels the yttrium ions are not mainly dispersed in the lattice as nnn dipoles, but rather they are forming higher clusters whose interaction with the Gd3+ trigonal centers is small. The ITC results show that most of the clusters are either not polarizable or present a very small dipolar moment. As all the evidence presented here indicates that clustering is important in these crystals, one can conclude that the behavior of the high temperature ITC peak is best understood if it is attributed to an interfacial polarization around the dislocations of the crystal and not to a space charge effect.

A series of poly(alpha-n-alkyl beta-L-aspartates) which are nanophase self-assembled comb-like polymers has been studied by dielectric spectroscopy in a broad frequency range (10(-2) < or = nu < or = 3 x 10(6) Hz), with n-alkyls side chains of various lengths, 10 < or = n < or =18. In every member of the series the same relaxations were identified after the decomposition of the experimental isothermal trace in up to three peaks with relaxation times distributions. The strength, width and average relaxation time for all the relaxation modes were determined for each material. Besides the local low temperature, Arrhenius modes, two relaxation modes, alpha and alpha(PE), present a cooperative character whose dynamics are not affected by the side chains melting. The alpha(PE) relaxation is a polyethylene-like glass transition of the amorphous side chains and its dynamics is strongly dependent on the n value due to the increasing restrictions imposed by the self-assembled confinement. The strength of the alpha(PE) relaxation mode increases as the lateral chains loose their 2D order. The restricted chopstick motion of the rigid rods is thought to be the origin of the alpha mode; this motion is hindered at temperatures where the cage size decreases as a result of the increasing disorder with temperature.

The thermal transitions in amorphous and semicrystalline Bisphenol A Polycarbonate (BPA-PC) have been studied by the thermally stimulated depolarization currents technique. The dielectric relaxations at low temperature, /spl beta/ band, are carefully analyzed by the direct signal analysis in order to decompose the complex peak in elementary excitations in an energy interval, whose inverse frequency factors and contribution to polarization are best fitted to the experimental trace. The complex peak is shown to be composed by 3 main relaxations and their behavior is compared as the free volume in the material is varied, either by thermal treatments and/or by increasing the degree of crystallinity. It is shown that the observed behavior is compatible with a cooperative molecular motion of several repeating units along the chain for the first two relaxations, the third one being a more localized reorientation mechanism. The high temperature zone of the dielectric spectrum shows, in addition to the intense relaxation corresponding to the glass transition, a space charge peak due to the relaxation of the accumulated free carriers near the electrodes.

The TSDC spectra of LLDPE functionalized with diethylmaleate polar groups has three main peaks labeled /spl alpha/, /spl beta/ and /spl gamma/ with decreasing temperature. The /spl gamma/ and /spl beta/ relaxations have been alternatively attributed in the literature to the manifestation of the glass rubber transition, and to a localized conformational bond rotation perturbed by the environment. The /spl alpha/ relaxation has been related to processes occurring in the crystalline phase. These peaks have been carefully recorded and the /spl gamma/ peak also shows a broad shoulder on its low temperature side. We analyzed these relaxations using the Simulated Annealing Direct Signal Analysis (SADSA) procedure where we decompose each peak into its elementary excitations which are monoenergetic and have either an Arrhenius or Vogel-Fulcher relaxation time dependence. This model is fitted to the experimental curves by utilizing Monte Carlo Simulated Annealing method and the result is the energy spectra for the relaxations. In particular the clean /spl gamma/ peak was found to have Vogel-Fulcher relaxation times and the sub-/spl gamma/ shoulder could only be fitted using Arrhenius relaxation times, confirming that the /spl gamma/ transition is indeed the T/sub g/ relaxation and that at these low temperatures both localized motions of the polar groups and cooperative motions of the chain occur.

Thermally stimulated depolarization currents, TSDC, experiments have been performed on a series of poly(styrene)-b-poly(butadiene)-b-poly(epsilon-caprolactone) triblock copolymers SBC with different proportions of the poly(epsilon-caprolactone) crystallizable block, PCL. The morphology of the segregated microphases varies with the PCL content and has been observed by transmission electron microscopy. The crystallinity of the PCL block is estimated by wide angle x-ray scattering, WAXS. The relaxation times distribution is extracted by a numerical decomposition of the TSDC spectra and it is shown that this distribution is not significantly changed on going from the homopolymer to the triblock copolymer with 16 wt % to 77 wt % of PCL in the original samples. Better segregation of the mesophase structure is reached when the samples are annealed at 413 K and important variations in the TSDC and WAXS spectra are observed as a result of the thermal treatment. For the S09B14C77 triblock copolymer the results obtained can be explained by postulating the existence of a rigid amorphous phase in the PCL block. Such rigid amorphous phase is located between the core-shell cylinders formed by the other blocks [with poly(styrene)(PS) as core and poly(butadiene)(PB) as shell] and is constrained by undulated lamellae of crystalline PCL material. In the case of S35B15C50 triblock copolymer, an important amount of diffuse PS-PCL interphase where the homopolymers are mixed must be present before annealing. The results for the material with the less abundant PCL block are explained as a result of the confinement in nanotubes of PCL surrounded by PB embedded in a vitreous PS matrix. Broadband dielectric experiments on these same materials confirm the results obtained by TSDC spectroscopy.

A new application of the simulated annealing Monte Carlo procedure is presented and applied to the extraction of the relaxation time distribution from dielectric spectroscopy either in time or frequency domain. This decomposition method named simulated annealing direct signal analysis~SADSA!, is applied to computer generated curves, e(t), e8(v), and e9(v), by using the most widely accepted empirical distributions. The discretized distribution fits exactly the analytical expression which can be evaluated in these cases for the set of parameters used in the simulation. Also, both distribution functions are found to be identical which proves that the method is certainly converging to the right solution in both cases. Experimental results on amorphous poly~aryl ether ether ketone! for e(t), e8(v), and e9(v) are analyzed with SADSA and the obtained relaxation time distribution is used to go from time to frequency domain and reciprocally. The results are compared to those obtained by assuming a Havriliak–Negami profile for the distribution function. © 2000 American Institute of Physics, Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICIT G97-000594). Comunidad de Madrid 07N/0063/1998! and to DGICYT (Grant No. PB 94-0049) Spain. FPI program of the Spanish Ministry of Science and Culture (MEC).

Comparative Thermally Stimulated Polarization and Depolarization studies have been carried out on SrF 2 crystals doped with lanthanum up to molar concentrations of 5x10 −2 and to temperatures of 500K. The first three peaks, attributed to nearest-neighbour dipoles and to clusters built with this basic unit (L-shaped La 3+ -F i2 − and the gettered 2:2:2 dimer) and the first high temperature peak are accurately reproduced in both spectra proving the dipolar origin of these relaxations. A fifth band at high temperature is present in the ITC spectrum but not in the TSP run where it is replaced by a steep increase in the current. The behaviour of this peak is studied and it is concluded that it is related to the relaxation of space charges accumulated near the electrodes.

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.

A Monte Carlo computing procedure different from the standard least-squares fitting method is presented for evaluating the set of parameters which best fit the effective spin Hamiltonian. The parameter g and the electric-field parameters blm are fitted using the experimental data obtained from the electron paramagnetic resonance (EPR) spectra. This method is very powerful as regards decision making so that the labelling of the quantum levels involved in a transition is optional in most cases. The different steps in the simulated 'annealing' program are described in detail and a sample calculation is given for Gd3+ in a CaF2 matrix when it is located in tetragonal or cubic sites. This centre was chosen as the results obtained can be compared with previous determinations reported in the literature by using more conventional fitting procedures. This method is applicable even when the off-diagonal elements of the effective spin Hamiltonian matrix are large. The use of Monte Carlo optimisation methods, even if time consuming, is a modern approach that is easily available as it can be run on a microcomputer; this offers clear advantages for fitting the EPR data.

Lanthanum doped SrF2 single crystals with concentrations ranging from 10−4 to 5 × 10−2 (in molar fraction) were studied by ionic thermal currents and thermally stimulated polarization techniques from 77 to 500 K. Current peaks identified with a La3+-F i -nearest-neighbour dipole (A), an L-shaped La3+-F i2- Complex (B), and higher clusters (C) were found by both techniques. A higher temperature peak (D), which presented an anomalous behaviour, was found at temperatures which depended on the doping level of the crystal and the thermal treatment. Additional experiments, done with different polarizing conditions, various sample thicknesses and mechanical treatments, were performed in order to elucidate the origin of this higher temperature peak. The new evidence reported here agrees better with the dislocation polarization model rather than the idea of surface accumulation of charges near the electrodes. A fifth peak is found when the sample is polarized at higher temperatures which is possibly due t...

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.

The ionic conductivity of NaCl crystals highly doped with SrCl2(10−5 ≤ c ≤ 2 × 10−2, expressed in molar fraction) has been measured from room temperature to the melting point. In this wide range of concentration a unique value for the migration energy for the cation vacancy has been found: 0.75 ± 0.02 eV. With this value all the parameters for the creation and motion of lattice defects have been determined. Simple association theory could not explain the observed results. The Debye–Huckel approach was used to account for the observed absence of association at high temperature. Quenching experiments from high temperatures were performed on these doped crystals and a saturation limit of 8 × 10−4 was found for the dilution of dipoles in the matrix. The effect of clustering of these dipoles was followed by quenching from different annealing temperatures.

A new ITC peak in highly doped NaCl crystals was detected at high temperature (318 K). By studying the behaviour of this peak after adequate thermal treatments, we are able to show that it is due to the precipitates of the Suzuki phase present in the crystal.

The dielectric permittivity of semi crystalline polyvinylidene fluoride (PVDF) in the /spl alpha/ phase, has been studied from 10 to 300 K at frequencies ranging from 10/sup 2/ to 1/spl times/10/sup 5/ Hz. The degree of crystallinity was varied from 50 to 60% by using different casting procedures and its value determined by Differential Scanning Calorimetry. The /spl alpha//sub a/ relaxation corresponding to the glass transition of the amorphous PVDF is intense and its maximum shifts from 241 to 273 K as the frequency and the crystallinity vary. The Vogel-Fulcher equation was used to model the dependence of the relaxation time on temperature and to calculate the activation energy, T/sub 0/ and /spl tau//sub 0/. The Williams-Landel-Ferry model was also applied and no deviations near the glass transition temperature were observed. The experimental values of /spl epsi/'' as a function of frequency and for several temperatures were used to obtain the Universal Dielectric Response of the material. It is shown that the spectral shape parameters are m=0.58 and n=0.80 for the normalized plot. >

The relaxation behavior of high density polyethylene functionalized with diethylmaleate has been determined by dynamic mechanical method and thermally stimulated depolarization technique. The transitions observed have been related to the structural parameters as well as the α-olefin comonomer content and degree of grafting, and compared with previous TSDC results on LLPE functionalized with the same polar group. The lowest relaxation is composed of a sub-γ and a γ mode assigned to localized motions of the polar groups and to the glass transition (at 137 K), respectively. The β-relaxation intensity grows with the grafting degree in agreement with its assignment to motions taking place in the interfacial regions. The behavior of the α-mode with different content of diethylmaleate has confirmed its dependence with the crystallite size.