ALBERT

Notes: We report the successful growth of pseudomorphic, trigonal structured HoF3 insulating layers, stable at room temperature, on the Si(111) surface. Normally the tysonite structure is only stable at temperatures above 1070 °C [R. E. Thoma and G. D. Brunton, Sov. Phys. Crystallogr. 18, 473 (1966)]. A phase transition to the lower-temperature orthorhombic structure is observed for a thickness of around 12 A(ring), consistent with the relaxation of elastic strain in the insulating layer.

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: 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: Given a fitting model, such as the Kohlrausch–Williams–Watts (KWW)/stretched-exponential response, three plausible approaches to fitting small-signal frequency or time-response data are described and compared. Fitting can be carried out with either of two conductive-system formalisms or with a dielectric-system one. Methods are discussed and illustrated for deciding which of the three approaches is most pertinent for a given data set. Limiting low- and high-frequency log–log slopes for each of the four immittance levels are presented for several common models; cutoff effects are considered; and an anomaly in the approach to a single-relaxation-time Debye response for one of the conductive-system approaches is identified and explained. It is found that the temporal response function for the most appropriate conductive-system dispersion (CSD) approach, designated the CSD1, one long used in approximate form for frequency-response data analysis, does not lead to stretched-exponential transient behavior when a KWW response model is considered. Frequency-domain fitting methods and approaches are illustrated and discriminated using 321 and 380 K Na2O–3SiO2 data sets. The CSD1 approach using a KWW model is found to be most appropriate for fitting these data exceedingly closely with a complex nonlinear least-squares procedure available in the free computer program LEVM. Detailed examination and simulation of the approximate, long-used CSD1 modulus fitting formalism shows the unfortunate results of its failure to include separately the effects of the always present high-frequency-limiting dielectric constant, εD∞. The stretched-exponential exponent, β, associated with this fitting approach has always been misidentified in the past, and even after its reinterpretation, the result is likely to be sufficiently approximate that most physical conclusions derived from such fitting will need reevaluation. © 1997 American Institute of Physics.

Notes: The conclusion [K. L. Ngai, A. K. Rajagopal, R. W. Rendell, and S. Teitler, Phys. Rev. B 28, 6073 (1983)] that simple exponential decay is a nonviable model for electrical relaxation, because it fails to satisfy the fundamental Paley–Wiener Fourier transform criterion, is shown by direct analysis to be inapplicable to small-signal electrical relaxation situations. Thus, not only is exponential decay and its associated single-relaxation-time Debye frequency response a valid model for relaxation, but, by extension, all distributions of relaxations times and energies which use a superposition of simple exponentials or Debye functions are also acceptable descriptions of relaxation phenomena. Reasons why the earlier conclusion is nonviable in the present context are discussed. © 1997 American Institute of Physics.

Notes: The ionic conductivity of glassy, fast-ion-conducting materials can show non-Arrhenius behavior and approach saturation at sufficiently high temperatures [J. Kincs and S. W. Martin, Phys. Rev. Lett. 76, 20 (1996)]. The Ngai coupling model was soon applied to explain some of these observations [K. L. Ngai and A. K. Rizos, Phys. Rev. Lett. 76, 1296 (1996)], but detailed examination and generalization of the coupling model suggested the consideration of a related, yet different, approach, the cutoff model. Although both the coupling and cutoff models involve a shortest nonzero response time, τc, and lead to single-relaxation-time Debye response at limiting short times and high frequencies, they involve different physical interpretations of their low- and high-frequency response functions. These differences are discussed; the predictions of both models in the frequency and time domains are compared; and the utility of both models is evaluated for explaining the non-Arrhenius conductivity behavior associated with the dispersed frequency response of zAgI+(1−z)[0.525Ag2S+0.475B2S3:SiS2] glass for z=0 and 0.4. The cutoff approach, using simulation rather than direct data fitting, yielded semiquantitative agreement with the data, but similar analysis using the coupling model led to poor results. The coupling model leads to an appreciable slope discontinuity at the τc transition point between its two separate response parts, while the cutoff model shows no such discontinuity because it involves only a single response equation with a smooth transition at τc to limiting single-relaxation-time response. The greater simplicity, utility, and generality of the cutoff model suggest that it should be the favored choice for analyzing high-conductivity data exhibiting non-Arrhenius behavior. © 1998 American Institute of Physics.

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: 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: 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.