Correlation effects in tracer diffusion and ionic conductivity

In this paper a conceptual link between the tracer correlation factor and the physical or conductivity correlation factor is explored in detail. As an aid to the discussion Monte Carlo simulation is used to calculate diagonal and cross phenomenological transport coefficients. It is shown that the tracer correlation factor can be regarded as a conductivity correlation factor and that the question of the formal correlation factor status of the conductivity correlation factor is meaningless.     

Correlation factor in tracer diffusion for high tracer concentrations

The meaning of cross terms in the Onsager equation for diffusion in multicomponent systems is clarified based on the Path Probability method of irreversible statistical mechanics. The problems involved in increasing the concentration of tracer atoms in tracer diffusion experiments are discussed. Some comments on the correlation function approach with respect to the present problem are also added.     

Electrical conductivity and tracer diffusion in sodium germanate glasses

Measurements of the electrical conductivity using ac complex impedance techniques and the tracer diffusion coefficient of ²²Na have been performed in a series of (x)Na₂O(1?x) GeO₂ glasses (where 0.0006 ? x ? 0.156). The compositional form of the Haven ratios, calculated from these data, have been interpreted in terms of a single defect model which considers a number of distinctly different jump frequencies for the alkali ion; the magnitude of these different jump frequencies is determined by the proximity of the diffusing alkali ion to a charge-compensating center within the glass network. Attractive interactions between the positive alkali ions and the negative charge-compensating centers cause successive jump directions of the alkali ions to become correlated. In the sodium germanate glasses the negatively-charged centers probably correspond to the six-fold coordinated sites formed upon addition of alkali oxide to GeO₂. These negatively-charged trapping centers correspond to non-bridging oxygen sites in alkali silicate glasses.     

Ionic conductivity and tracer diffusion in a lattice containing random traps

A model where the lattice contained a number of randomly distributed traps equal to the number of diffusing particles was investigated rigorously. Monte Carlo methods were used to determine the relevant correlation factors in the tracer diffusion and ionic conductivity. It was found that the temperature dependence of the correlation factors contributed a relatively small component to the activation energy of the overall transport process. The relevance of the findings to atomic transport in fluorite-related oxides containing divalent dopant ions is commented on.     

Correlation effects in the diffusion and electrical conductivity of an interacting lattice gas

A simple and effective self-consistent scheme is proposed for the determination of the average potentials which allows thermodynamic functions and other characteristics of lattice systems in equilibrium to be calculated with high accuracy and short computing time. This scheme has been used for analysis of the expressions for the coefficients of diffusion and electrical conductivity obtained on the basis of the modern statistical theory of nonequilibrium processes. Results of the simulations are correlated with the data of Monte Carlo simulations obtained using parallel vector algorithms on a Cray TZE computer of the Max Plank Society (Germany).     

About ionic conductivity/diffusion relationships in yttria doped zirconia

The values of the oxygen self-diffusion coefficients (measured using¹⁸O tracer) are compared to the ionic conductivity (measured by impedance spectroscopy) of 9.5 mol% yttria doped zirconia single crystals in the temperature range 240–800 °C in air. Electrical conductivity measurements in polycrystals, exhibiting a grain boundary contribution to the ionic conductivity, are furthermore discussed in the frame of a “brick/boundary model”. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16–22, 2001.     

Correlation between I-Ag distance and ionic conductivity in AgI fast-ion-conducting glasses

A large number of AgI-based fast-ion-conducting glasses have been investigated by K-iodine extended x-ray absorption fine structure spectroscopy (EXAFS) measurements at liquid nitrogen temperature. A general correlation between the I-Ag distance measured by EXAFS and the glass activation energy for dc ionic conductivity has been found out: glasses with longer I-Ag distances display higher ionic conductivity, independently from the chemical composition of their host glassy matrix. This behavior can be related to the progressive increase of the "pathway volume" for ionic conduction.     

The relationship between chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice

The theoretical model developed by Lidiard was extended to describe the relationship between the chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice.It is shown that the relationship between the chemical diffusion coefficient, D, and the tracer diffusion coefficient, D¹, is D = 2D¹ if the migration of dimers is the principal mechanism of transport and for the migration of trimers D = 3D¹ if the concentration of impurity ion is relatively small. These relationships are valid regardless of the charge of the aliovalent or lattice ions.The chemical diffusion coefficients of Cr³⁺ in Cr-doped MgO were determined for three different temperatures, 1656, 1717 and 1768K, and for the concentration region 2.5×10^?2?2.8×10^?1 mole% Cr₂O₃. Using previously determined values for the tracer diffusion coefficient of ⁵¹Cr in Cr-doped MgO it was found that for the temperature and concentration region investigated D = (2.00±0.17)D¹ which indicates that diffusion proceeds primarily by the migration of dimers.     

Entropy and ionic conductivity

It is known that the ionic conductivity can be obtained by using the diffusion constant and the Einstein relation. We derive it here by extracting it from the steady electric current which we calculate in three ways, using statistics analysis, an entropy method, and an entropy production approach.     

Correlation and isotope effects for cation diffusion in magnetite

The simultaneous diffusion of ⁵²Fe and ⁵⁹Fe has been measured in Fe₃O₄ as a function of equilibrium oxygen partial pressure (10^?9 <p_o2 < 10^?4 atm) at 1200°C. The p_o2 dependence of D goes through a minimum near 10^?6 atm in agreement with earlier data of Dieckmann and Schmalzried. Comparison of the isotope effect results with correlation-factor calculations suggests that at p_o2 γ 10^?6, diffusion occurs predominantly by vacancy jumps between the normally occupied octahedral sites on the spinel lattice; jumps between tetrahedral sites probably play a lesser role. At p_o2< 10^?6 atm, diffusion occurs by an interstitialtype mechanism involving the simultaneous migration of two atoms. Five of the seven interstitialcy jumps considered in our correlation-factor calculations are consistent with the experimental results.     

Chromium tracer diffusion in NiO crystals

Diffusion of ⁵¹Cr in NiO single crystals in air has been studied by the tracer-sectioning technique. In the temperature range 1192–1642°C, the diffusion coefficient can be expressed by the Arrhenius expression D=D_oexp(-Q/RT), with D_o=(8·6±1·2)×10^?3 cm²/sec and Q=67·4±1·1 kcal/mole. The use of a high specific-activity tracer and a special configuration for the diffusion anneal prevented the self-dopling effect found by Seltzer and the evaporation of chromium from the sample surface. The present results, in conjunction with published results on nickel self-diffusion in NiO and interdiffusion in the NiO?Cr₂O₃ system, are used to determine a chromium ion-vacancy binding energy of about 5 kcal/mole in pure NiO.     

Influence of grain sizes on the ionic conductivity and the chemical diffusion coefficient in copper selenide

Ionic conductivity and chemical diffusion coefficient have been studied for superionic polycrystalline Cu_1.75Se copper selenide within the temperature interval 300–500 K. An increase in ionic conductivity with an grain size increase is observed. In our opinion, this fact is caused by lower activation energy for the bulk diffusion than that for the grain boundary diffusion.     

High ionic conductivity in new fluorine compounds of tin II. I. On PbSnF4: Relation between structure and conductivity

The structural determination of the monoclinic form of PbSnF₄ shows a cationic network as in the fluorite structure. The high value of the F^? mobility seems to be correlated to a great number of vacancies in the anionic network.     

Correlation effects in diffusion in a two sublattice structure

With a Monte Carlo method we have investigated tracer and conductivity (physical) correlation factors in the simple cubic lattice gas with two f.c.c. inequivalent sublattices and self exclusion by the atoms. Except at very low temperatures, excellent agreement was found between our results for the conductivity correlation factor and Richard's approximate treatment. At an occupation of 0.5 the Haven Ratio exhibits the characteristic discontinuity found recently in other lattice gases which give ordered arrangements. On the concentration axis at low temperature we found another discontinuity in the Haven Ratio. All of these discontinuities are associated with changes in mechanism.     

Electronic and ionic conductivity in CaTiO3

The present work describes the electrical conductivity of undoped CaTiO₃ in terms of the electrical conductivity components corresponding to electrons, electron holes and ionic charge carriers in the temperature range 973 K — 1323 K and under controlled oxygen partial pressure (10 Pa — 72 kPa). These data are considered in terms of the transference numbers of the respective charge carriers. It appears that the ionic conductivity component assumes maximum at the n-p transition when the ionic transfer number reaches 50% of the total conductivity value at 1323 K. The present study also includes the determination of the activation energy of the conductivity component related to ions (162.1 kJ/mol), electrons (134.2 kJ/mol) and electron holes (86.2 kJ/mol). The data obtained in this work indicate that undoped CaTiO₃ exhibits a substantial level of ionic conduction that cannot be ignored in a quantitative analysis of electrical conductivity data.     

Simultaneous tracer diffusion and interdiffusion in a sandwich-type configuration to provide the composition dependence of the tracer diffusion coefficients

In this paper, a new formalism of a combined tracer and interdiffusion experiment for a binary interdiffusion couple is developed. The analysis requires an interdiffusion couple that initially contains a thin layer of tracers of one or both of the constituent elements at the original interface of the couple (sandwich interdiffusion experiment). This type of interdiffusion experiment was first performed in 1958 by J.R. Manning. The theoretical analysis presented in this paper is based on a newly developed phenomenological theory of isotopic interdiffusion combined with the Boltzmann–Matano formalism. This new analysis now provides the means to obtain the composition dependent interdiffusion coefficient and tracer diffusion coefficients simultaneously from analysis of the interdiffusion and tracer profiles in a single sandwich interdiffusion experiment. The new analysis is successfully applied to the results of Manning’s original ‘sandwich interdiffusion’ experiment in the Ag–Cd system (six couples in total) and is validated with an independent determination of the Ag and Cd tracer diffusion coefficients by Schoen using the conventional thin film technique. Suggestions for further development of the sandwich interdiffusion experiment and analysis to the case of multicomponent alloys are provided.     

Study of cation tracer diffusion in NaF

Cation tracer diffusion coefficients were measured in pure NaF crystals in the intrinsic ionic conductivity range (876–970 °C). The results can be rationalized satisfactorily in terms of contributions to the observed Na tracer diffusivities arising from both free vacancies and neutral vacancy pairs, the latter contribution amounting to about 53 per cent of the total Na diffusion at the highest measuring temperature. The best-fit defect parameters derived in an earlier conductivity study [21] from this laboratory on similar NaF crystals give for the free vacancy contribution D_v^*(Na) = 4·25 exp (?2·21 eV/kT) cm²s^?1. A combination of these D_v^*(Na) values with the present diffusion data yields for the vacancy-pair contribution D_p^*(Na) = 1·15 × 10⁸exp (?4·04 eV/kT) cm²s^?1. Comparison of the present findings with published values of the anion tracer diffusion coefficient in NaF showed that D_p^* (F) is 2·3 to 4·4 times larger than D_p^*(Na) over the temperature range of our observations, the difference between the two contributions increasing with decreasing temperature. When approximate account is taken of the temperature-dependence of the two pair correlation factors, this last result indicates that the anion jumps into the vacancy pair occur with a higher frequency, and increasingly so at lower temperatures, than do those involving the cations.     

Luminescence and ionic conductivity of bariumfluorochloride

The luminescence and ionic conductivity of pure and doped BaFCl crystals are reported. The ionic conductivity occurs mainly via chloride ion vacancies, whereas the efficient, yellow luminescence is ascribed to oxygen impurities (O′_F).