ALBERT

Notes: By appropriate fitting of conductive-system frequency-response data for two different ionic materials over ranges of temperature and ionic concentration, it is shown how dispersion associated entirely with ionic motion and that leading to nearly constant dielectric loss (NCL) can be unambiguously distinguished and separated. The latter is clearly associated with polarization of the bulk material, and in the limit of zero mobile-ion concentration NCL appears to approach zero, yielding only a bulk dielectric constant, cursive-epsilonD∞0, one that is frequency-independent over the usual immittance-spectroscopy experimental range. For nonzero ionic concentration, however, dielectric NCL appears and can be represented by a small-exponent constant phase element (CPE) complex power law in frequency. This part of the full response may be modeled either by a CPE that includes all bulk dielectric dispersion or, more plausibly, by cursive-epsilonD∞0 and a CPE representing only incremental bulk dispersion associated with coupling between ionic motion and bulk polarization. In this case, interestingly, precise power-law dependencies of various dielectric parameters on ionic concentration are established but need theoretical explanation. Fitting of the ionic part of the total dispersion with three different Kohlrausch–Williams–Watts models leads to dependencies of their different β-shape parameters and dielectric quantities on temperature and on ionic concentration and strongly suggests that the widely used original-modulus-formalism dispersion fitting model is incorrect and should be replaced by a corrected version. © 2002 American Institute of Physics.

Notes: Oxygen isotope shifts on the 13C chemical shifts and carbon isotope shifts on the 17O chemical shifts in carbon monoxide and carbon dioxide are reported. Using models developed by Jameson, shielding derivatives with respect to bond lengths can be calculated using the measured isotope shifts. For carbon monoxide, the derivatives were calculated to be [∂σ (13C)/∂r]e =−456±15 ppm/A(ring) and [∂σ (17O)/∂r]e =−1150±130 ppm/A(ring). Although earlier coupled Hartree–Fock calculations give a much lower value for [∂σ (17O)/∂r]e, recent ab initio calculations for carbon monoxide agree very well with our experimental results. Furthermore, the observed 18O/16O iostope shift is similar to values measured previously for a series of metal carbonyls. For carbon dioxide the iostope shift gives [∂σ (13C)/∂r]e =−214±17 ppm/A(ring) which is in excellent agreement with the value obtained from a recent variable temperature gas phase NMR study. In addition, scalar spin–spin coupling constants, 1J(13C,17O) were measured to be 16.4±0.1 Hz in carbon monoxide and 16.1±0.1 Hz in carbon dioxide. To our knowledge, these are the first directly measured carbon–oxygen coupling constants to be reported in the literature. From general trends in the periodic table, it seems likely that the sign of these coupling constants is positive.

Notes: Conductivity exhibiting power-law frequency response with an exponent of unity leads to frequency-independent dielectric loss. Such constant-loss (CL) behavior is not physically realizable over a nonzero frequency range, and approximate expressions that have been used to represent it are inconsistent with the Kronig–Kramers relations. Response models are proposed and investigated that do satisfy these relations and can lead to very close approximation to CL over many frequency decades, as often observed at low temperatures in ionic conductors such as glasses. Apparent CL response is shown to arise from the series connection of a constant-phase complex-power-law element (CPE), with exponent δ (0〈δ(very-much-less-than)1), and a frequency-independent dielectric constant, cursive-epsilonU. Two physically disparate situations can lead to such a series connection. The first involves bulk CPE response in series with an electrode-related, double-layer blocking capacitance involving a dielectric constant cursive-epsilonS. Then, apparent CL behavior may be associated with localized ionic motion in the bulk of the material. The second (mirror-image) situation involves CPE response associated with ionic motion in or at an electrode in series with a capacitance such as the bulk high-frequency-limiting total dielectric constant cursive-epsilon∞ or the pure-dielectric quantity cursive-epsilonD∞. The present model is used to simultaneously fit both the real and imaginary parts of data derived from measurements on a sodium-trisilicate glass at 122 K. This data set exhibits power-law nearly constant loss for cursive-epsilon′(ω) and apparent CL for cursive-epsilon″(ω). The magnitude of the CL closely satisfies a simple equation involving only δ and cursive-epsilonU. Further, for the electrode-power-law situation, estimated values of limiting-high-frequency dielectric constants turn out to be more consistent with bulk values established at much higher temperatures where nearly constant loss is no longer a dominant part of the response. Data at −0.5°C are also analyzed with a more complicated composite model, one that is a generalization of both of the above approaches, and nearly constant loss bulk, not electrode, power-law effects in both cursive-epsilon′(ω) and cursive-epsilon″(ω) are isolated and quantified. For this data set it is shown that electrode effects are important at both ends of the frequency range.© 2001 American Institute of Physics.

Notes: Three weighted, complex nonlinear least-squares methods for the deconvolution of dielectric or conducting system frequency-response data are described and applied to synthetic data and to dielectric data of n-pentanol alcohol, water, and glycerol. The first method represents a distribution of relaxation times or transition rates by an inherently discrete function. Its inversion accuracy and resolution power are shown to be limited only by the accuracy of the data when the data themselves arise from a discrete distribution involving an arbitrary number of spectral lines. It is shown that those inversion methods employed here which allow the relaxation times to be free variables are much superior to those where these quantities are fixed. Furthermore, free-τ methods allow unambiguous discrimination between discrete and continuous distributions, even for data with substantial errors. Contrary to previous conclusions, discrete distributions were determined for both n-pentanol alcohol and water. A complex, continuous distribution estimate was obtained for glycerol. Algorithms for all approaches are incorporated in a readily available computer program. Serious problems with some previous dielectric inversion methods are identified. Finally, several possibilities are mentioned that may allow greater inversion resolution to be obtained for complex nonlinear least-squares estimation of continuous distributions from noisy data. © 1995 American Institute of Physics.

Notes: Problems with scaling of conductive-system experimental Mdat″(ω) and σdat′(ω) data are considered and resolved by dispersive-relaxation-model fitting and comparison. Scaling is attempted for both synthetic and experimental M″(ω) data sets. A crucial element in all experimental frequency-response data is the influence of the high-frequency-limiting dipolar-and-vibronic dielectric constant cursive-epsilonD∞, often designated cursive-epsilon∞, and not related to ionic transport. It is shown that cursive-epsilonD∞ precludes scaling of Mdat″(ω) for ionic materials when the mobile-charge concentration varies. When the effects of cursive-epsilonD∞ are properly removed from the data, however, such scaling is viable. Only the σ′(ω) and cursive-epsilon″(ω) parts of immittance response are uninfluenced by cursive-epsilonD∞. Thus, scaling is possible for experimental σ′(ω) data sets under concentration variation if the shape parameter of a well-fitting model remains constant and if any parts of the response not associated with bulk ionic transport are eliminated. Comparison between the predictions of the original-modulus-formalism (OMF) response model of 1972–1973 and a corrected version of it that takes proper account of cursive-epsilonD∞, the corrected modulus formalism (CMF), demonstrates that the role played by cursive-epsilonD∞ (or cursive-epsilon∞) in the OMF is incorrect. Detailed fitting of data for three different ionic glasses using a Kohlrausch–Williams–Watts response model, the KWW1, for OMF and CMF analysis clearly demonstrates that the OMF leads to inconsistent shape-parameter (β1) estimates and the CMF does not. The CMF KWW1 model is shown to subsume, correct, and generalize the recent disparate scaling/fitting approaches of Sidebottom, León, Roling, and Ngai. © 2001 American Institute of Physics.

Notes: A new universality has been recently proposed by Lee, Liu, and Nowick [Phys. Rev. Lett. 67, 1559 (1991)] for dispersion in high-resistivity crystalline and disordered solids which posits that the real part of the conductivity σ' exhibits ωγ frequency response, with γ=1 over an appreciable temperature range. To investigate this surprising conclusion in further detail, several powerful analysis methods were applied to Lee and co-worker's ac relaxation data for single-crystal NaCl doped with Zn2+. In the past, no significant information has been obtained from the σ‘ data. Complex nonlinear least-squares fitting was used to analyze simultaneously both parts of the admittance data, Y(ω)=Y'(ω)+iY‘(ω), with several conductive-system response models. The dispersive part of the response is here generally very small compared to the low-frequency-limiting conductance, G0 and capacitance. New forms of the Barton, Nakajima, and Namikawa relation were derived and shown to be applicable for the data and the most appropriate model. Contrary to previous work, analysis and interpretation in terms of conductive-system dispersion, rather than dielectric dispersion, led to new results which vitiate the new universality assumption. Arrhenius plotting of G0(T) yielded a curved line, but a split of R0≡G−10≡R∞+ΔR, into the undispersed high-frequency-limiting part R∞ and the strength of the dispersed part ΔR, showed that while both quantities were separately thermally activated, R∞ exhibited a large, abrupt entropy transition near 363 K. From these results the vacancy migration activation energy was estimated to be 0.695 eV, and the R∞ vacancy-association activation energy changed from about 0.66 eV below the transition to about 0.56 above it, suggesting a transition from nearest-neighbor association to next-nearest-neighbor association.

Notes: X-ray reflectivity measurements were made on Si(001) crystals containing a delta-doping layer of Sb atoms a few nanometers below the surface. The measurements show the Sb doping profile to be abrupt towards the substrate side of the sample and to decay towards the surface with a characteristic decay length of 1.01 nm.

Notes: Three empirical equations introduced by Jonscher to represent the imaginary part of the small-signal frequency response of dielectric materials and termed "universal dielectric response'' by him are generalized in three ways. The equations may be applied in normalized form at the impedance level as well as at the usual complex dielectric constant level, defining the response of conducting rather than dielectric materials. They are generalized to include real as well as imaginary parts where possible. A unified dielectric or conductive distribution-of-activation-energies (DAE) physical model is proposed whose predictions agree remarkably well with those of all the Jonscher universal dielectric response equations as well as with many other common dielectric response equations. The new model, unlike previous small-signal response models, leads to quantitative predictions for the temperature dependence of the power-law frequency exponent appearing in the ubiquitous constant-phase-response frequency region of the total response.

Notes: New expressions are presented, simplified, and discussed for the small-signal-frequency response of systems involving distributions of activation energies with either exponential or Gaussian probability densities. The results involve the possibility of separate but related thermal activation of energy-storage and energy-loss processes, and apply to the response of both dielectric and conductive systems. Response with a Gaussian distribution of activation energies (GDAE) may be either symmetric or asymmetric in log frequency, and typical GDAE responses are compared with those associated with several exponential distributions of activation-energy (EDAE) models, using complex nonlinear least-squares fitting. The GDAE model does not lead to the frequently observed fractional-exponent power-law response in time or frequency as does the EDAE; thus, the GDAE cannot fit any EDAE response well which involves an appreciable range of such behavior, but it is found that, conversely, the general EDAE model can often fit a GDAE response very well overa wide frequency range. Recent (KBr)0.5(KCN)0.5 dielectric data covering a range from T=13.7 to 34.7 K are analyzed with the Cole–Cole, EDAE, and GDAE models, and the GDAE is found to yield the best overall fits. The results of the GDAE fits are analyzed in detail to illustrate the application of the GDAE model to real data. Contrary to the conclusions of an earlier analysis of the same data using an idealized, symmetric, and approximate GDAE model, we find that much of the data are better fit by a somewhat asymmetric, exact GDAE model which may involve a temperature-independent, finite-width Gaussian probability density. The present analysis suggests an alternative to the earlier results and suggestions that the width of the probability-density distribution increases with decreasing temperature and that the activation energies or barrier heights themselves depend linearly on temperature. The present data fit yield estimates of the lower limit of the temperature independent distribution of activation energies E0 and of the more or less central activation energy E1, but only set a lower limit for the value of the maximum activation energy of the distribution, E∞. There is some evidence from the fitting that there may be a glasslike transition below about 4 K, but other effects outside the GDAE model may intervene before that temperature region is reached.

Notes: When the small-signal ac frequency response of a dielectric or conductive system is known, either functionally or as data, it is shown that the corresponding response of an associated conductive or dielectric system may be immediately obtained through the use of new duality relations. A specific model is considered which involves thermally activated capacitance and/or resistance, with an activation energy probability density exponentially dependent on energy. Previous frequency response analyses of such a continuously distributed model involve inadequate approximations and lead to erroneous predictions. Correct immittance results are presented in three ways: analytically, by means of complex plane plots, and through the use of three-dimensional perspective plots. Results are given in general form but apply to both dielectric and conductive systems which involve the same functional dependence on activation energies. Low- and high-frequency-limiting responses for a given system are found to be associated with the same simple equivalent circuit. In intermediate frequency ranges a power-law frequency response somewhat like that of the constant phase element may occur. Differences between the power-law exponents for dielectric and conductive systems are clarified, and the types of possible temperature dependence of the exponents explored. Exponent values are not limited to the range between zero and unity. The overall response of the present normalized three-parameter model is similar to that often found experimentally for both dielectric and conductive systems and similar to but more general than that of other normalized distributed-element (two-parameter) models such as that of Williams and Watts and that of Davidson and Cole.