Electrical conductivity and chemical diffusion coefficient measurements in single crystalline nickel oxide at high temperatures

Electrical conductivity measurements on nickel oxide have been performed at high temperatures (1273 K<T< 1673 K) and in partial pressures of oxygen ranging from Po₂ = 1.89 × 10^?4 atm to Po₂ = 1 atm. The $\text{po}{}_2{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}$ dependence of the conductivity decreases from about $\text{1}\text{4}$ for Po₂ = 1 atm to smaller values for lower partial pressures of oxygen. The activation enthalpy for conduction increases for decreasing oxygen partial pressures (from 22.5 kcal mol^?1 at Po₂ = 1 atm to 26.0 kcal mol^?1 for Po₂ = 1.89 × 10^?4 atm). This behaviour can be explained by the simultaneous presence of singly and doubly ionized nickel vacancies, with different energies of formation.Furthermore, chemical diffusion coefficient measurements have been performed in the same temperature range, using the conductivity technique, and leading to the result:

$\text{D}\text{?}\text{= 0.244 exp (?}\text{36,600}\text{RT}\text{) cm}{}^2\text{s}{}^{\mathrm{?1}}$

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Electrical conductivity of pure and doped α-ferric oxides

Electrical conductivities of αFe₂O₃ containing 1 2, 2 3 and 3 8 mol% CdO were measured in the temperature range of 300 to 1300°C at Po₂'s of 10^?9 to 10^?1 atm Plots of log $\text{σ}\text{vs}\text{1}\text{T}$ at constant Po₂'s were found to be linear with an inflection at temperatures around 500°C and higher Po₂'s than 1 × 10^?4 atm. The activation energies obtained by the least-squares method were 1 34 eV for the intrinsic region and 0 51 eV for the extrinsic region on αFe₂O₃ doped with 38 mol% CdO The extrinsic conductivities disappeared at lower Po₂'s than 1 × 10^-4atm, and the intrinsic conduction appeared on the specimens investigated The electrical conductivities decreased with increasing amount of CdO doping The predominant defects in this system are believed to be interstitial Fe² for the intrinsic region and oxygen vacancies for the extrinsic region.     

Diffusion of titanium in slightly reduced rutile

The self-diffusion of ⁴⁴Ti in slightly reduced rutile. TiO_2?δ, was measured along the c axis over the temperature range of 1000–1100°C between 0.2 and 1 × 10^?18atm. oxygen pressure. These measurements enabled the determination of the defect structure of TiO_2-δ for 0.02 ?gd ? 0.001. For oxygen pressures between 1 × 10^?13 and 1 × 10^?16atm. at 1058.4°C random tetravalent titanium atoms are the predominant defects evident from self-diffusion. The enthalpy of motion was determined as ΔH_m = 57.03 ± 4.9% kcal/mole. From the activation energy at 1.69 × 10^?16atm., the enthalpy of formation for tetravalent titanium interstitials was determined as ΔH_f = 276 ± 15.6% kcal/mole.For oxygen pressures less than 1 × 10^?16atm. at 1058.4°C, the tracer diffusion coefficient shows a continuous decline as the oxygen pressure is lowered. Comparisons with thermogravimetric studies and consideration of the similarity in structure between nonstoichiometric point defect phases and the first homologous series phase indicate that the order-disorder transition retains a considerable degree of short range order below the critical concentration in the form of Wadsley defects.     

Silver-tracer diffusion in Cu2O

The diffusion of¹¹⁰Ag in Cu₂O has been measured by a serial-sectioning technique as a function of temperature (700–1132°C) and oxygen partial pressure (6 × 10^?6 ?8 × 10^?2 atm). The data are fit to the defect model for Cu₂O developed by the authors in the preceding paper. Silver ions have a larger impurity-vacancy binding free energy and/or a larger jump frequency for the singly charged cation vacancies relative to that for the neutral cation vacancies. The activation enthalpies for the diffusion of copper and silver ions in Cu₂O are nearly equal, but the absolute value of D¹_Ag is about three times larger than D¹_Cu even though the silver ion is 31% larger than the copper ion.     

Isotope effect for cation diffusion in CoO

The simultaneous diffusion of ⁵⁵Co and ⁶⁰Co has been measured in CoO as a function of equilibrium oxygen pressure in the range 10^?9 < po₂ < 1 atm at 1200°C. The slope of the log D¹_Co vs logpo₂ plot changes from a value of about $\text{1}\text{4}$ at high po₂ to about $\text{1}\text{5}$ at low po₂, in agreement with the extensive measurements of Dieckmann. The isotope effect is independent of po₂, which suggests that diffusion by defect clusters, interstitial Co ions and impurity-induced defects is not important in the present measurements. Conductivity, diffusion, stoichiometry and isotope-effect results are consistent with diffusion by neutral, singly charged, and doubly charged vacancies; the relative contributions from the various vacancies varies with po₂.     

Diffusion of 55Fe in Fe2O3 single crystals

The diffusion of ⁵⁵Fe has been measured parallel to the c axis of Fe₂O₃ single crystals at temperatures in the range 708–1303°C and at an oxygen activity of unity. The tracer penetration profiles were determined using sectioning techniques. For temperatures above 900°C the tracer diffusion coefficient is given byD¹(Fe) = 1.6 × 10⁹ exp[?6.0 (eV)/kT] cm² s^?1 and below 900°C by 2.8 × 10^?9 exp[?1.8 (eV)kT]. The high-temperature behaviour is probably characteristic of pure Fe₂O₃, whereas diffusion at lower temperatures may be influenced by impurities. The most likely defects responsible for diffusion of Fe are iron interstitials and, for oxygen, oxygen vacancies, and the observed activation energies are discussed in terms of the properties of these defects. The diffusion data and defect models have been used to predict the rate of growth of Fe₂O₃ and indicate that outward Fe diffusion is the dominant transport process. Previously published data for Fe₂O₃ growth in a variety of experimental situations have been corrected to a single rate constant using a model for multilayer growth. The corrected data are all in good agreement but are approximately two orders of magnitude greater than predicted from diffusion data, which suggests that grain boundary diffusion controls the growth of Fe₂O₃ in practice.     

Diffusion and correlation effects in iron-doped CoO

The diffusion of ⁵⁹Fe and ⁶⁰Co has been measured in pure CoO and dilute iron-doped CoO, (Co_1?cFe_cO, as a function of temperature (1000–1400°C) and oxygen partial pressure P_{o2), (10^?7 ≦ Po2 ≦ 0 21 atm) The enhancement factors for the diffusivities of iron and cobalt are nearly identical, which suggests that the primary cause of the enhancement is the increased concentration of charge-compensating cation vacancies with the addition of iron. The Fe ions dissolved in CoO appear to exist as a mixture of Fe²⁺ and Fe³⁺ ions, the fraction of iron ions in the three-plus state decreases with decreasing Po2 The simultaneous diffusion of ⁵²Fe and ⁵⁹Fe has been measured as a function of (itpo; at 1200°C The correlation factor for Fe impurity diffusion determined from the isotope-effect measurements is about the same as that for self-diffusion in CoO at high (itPo2} (2 × 10^?3 ≦ p_o2 ≦ 0 21 atm), but increases slightly with decreasing p_O2 Both the enhancement-effect and isotope-effect experiments suggest that the nearestneighbor interactions between Fe ions and vacancies is small, and that the dissolved Fe ions do not have strongly bound electron holes.     

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.     

Defect structure of lanthanum-doped calcium titanate

The defect structure of lanthanum-doped polycrystalline calcium titanate was investigated by measuring the oxygen partial pressure (10⁰–10^?18 atm.) dependence of the electrical conductivity at 1000° C and 1050°C. Two types of charge compensation were observed, namely electronic and ionic. For P₀₂ < 10^?15 atm. the carrier concentration was fixed by the amount of lanthanum (donor) added and the conductivity was found to be independent of oxygen partial pressure (electronic compensation). For higher oxygen partial pressure conditions (P₂₂ > 10^?13 atm.) the extra charge of the lanthanum was compensated by doubly ionized calcium vacancies (ionic compensation). In the ionic compensation region, a model involving a shear structure is discussed.     

The influence of chromium on the defect structure and their mobility in nonstoichiometric cobaltous oxide

Defect structure and the mobility of point defects in pure metal deficient cobalt oxide (Co_1−yO) and in Co_1−yO-Cr₂O₃ solid solutions have been studied as a function of temperature (1223-1573 K) and oxygen pressure (10-10⁵ Pa) using microthermogravimetric techniques. It has been shown that the predominant defects in pure and Cr-doped cobaltous oxide are singly ionized cation vacancies, and 3% at of dopant is high enough to fix the concentration of predominant defects in such solid solutions on a constant level being much higher than in pure Co_1−yO. Re-equilibration rate measurements have demonstrated that the chemical diffusion coefficient and thereby the mobility of point defects in pure Co_1−yO is concentration independent, strongly suggesting that in spite of rather high their concentration no interactions and clustering of defects is to be expected. On the other hand, in Cr-doped cobaltous oxide, re-equilibration rate measurements have shown, that in this case the defect structure is more complicated, although singly ionized cation vacancies seem to be still predominant defects.     

Diffusion of oxygen vacancies in yttrium iron garnet investigated by dynamic conductivity measurements

In yttrium iron garnet, Y₃Fe₅O₁₂, the oxygen vacancy concentration at high temperatures depends on the partial oxygen pressure. Due to the electron donating nature of the vacancies, changes in the oxygen vacancy concentration can be measured by electrical conductivity measurements. We discuss a dynamic method for studying the diffusion of oxygen vacancies by measurements of the time dependence of the electrical conduction after a change in the oxygen partial pressure has taken place. It is shown that the interpretation of the measurements is straightforward if the relative change in conductivity remains small (? 10%). Measurements were performed on single crystals and on polycrystalline samples at temperatures 900–1400°C. The samples were made n-type by substitution with Si or p-type by substitution with Ca, Zn or Pb. The partial oxygen pressure was changed between 1 and 0.1 atm. For all samples the diffusion coefficient D of the oxygen vacancies can be represented by $\text{D = A}\text{exp}\text{(?}\text{Q}\text{kT}\text{)}$, where A = 8400 cm²s^?1 and Q = 2.90 eV. It is shown that the activation energy of 2.90 eV is due to the migration enthalpy of the vacancies only.     

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.     

Diffusion of sulfur in nickel oxide single crystals

The diffusion of sulfur in nickel oxide single crystals has been investigated over the temperature range from 1000 to 1250°C. The measured data were found to deviate markedly from the error function complement dependence for diffusion from a constant source. The deviation is attributed to the migration of sulfur by the “double mode simultaneous diffusion mechanism.” The faster mode diffusion is suggested to be via nickel vacancies, and the slower mode diffusion is suggested to be via oxygen vacancies. The diffusivities for faster mode are given by D_f = 2.94 exp[? 86.6 kcal/RT] cm² sec^?1 and, the slower mode, D_s = 1.08 × 10^?9 exp [?32.8 kcal/RT]cm²sec^?1.     

Diffusion and point defects in Cu2O

The diffusion of⁶⁴Cu in Cu₂O has been measured by a serial-sectioning technique as a function of temperature (700–1153°C) and oxygen partial pressure (10^?6?8 × 10^2&#x0304; atm). The oxygen-partial-pressure and temperature dependencies of D¹_Cu suggest that both neutral and singly charged copper vacancies contribute to cation self-diffusion. A defect model involving both neutral and singly charged copper vacancies, electron holes, and singly charged oxygen-interstitial ions is developed and fit to the tracer-diffusion data, the electrical-conductivity data (Maluenda et al.), and the stoichiometry data (O'Keeffe and Moore). The resulting defect data are quantitatively consistent with the chemical-diffusion data (Maluenda et al.) and with a correlation factor $\text{f}{}_{\mathrm{v}}\text{=}\text{2}\text{3}$. The defect data are also quantitatively consistent with the high-temperature oxidation studies of copper metal (Iguchi et al.) and with the copper vacancy being 10 times more mobile than the oxygen-interstitial ion at 10002C.     

Die Diffusionskoeffizienten und mittleren freien Weglängen der geladenen und neutralen Radon-Folgeprodukte in Luft

The knowledge of the diffusion coefficients of radioactive atoms and ions in air is very important in a number of investigations on and computations of the attachment of radon decay products to aerosol particles. In this work measurements of the diffusion coefficients of neutral and charged²¹²Pb atoms are reported. The values found areD ₀=(7.6±0.4)·10^?2cm²s^?1 for neutral atomsD=(5.0±0.3)·10^?2cm²s^?1 for charged atoms The used method of measurement allowed to determine these constants 1–5 seconds after the formation aged²¹²Pb atoms, so that a “cluster” formation was improbable. The mean free path for neutral (λ₀=(4.9±0.3)·10^?6cm) and charged (λ=(3.2±0.2)· 10^?6cm) lead 212 atoms in air were computed from the measured diffusion coefficients. All obtained results were compared with values, calculated from theory.     

Defect sites in thin films of germanium dioxide irradiated with silicon ions

Optical transmission spectra of GeO₂ films irradiated with silicon ions and subjected to postimplantation annealing in the regime of silicon nanocrystal formation are analyzed. It is shown that point defects form in the films after irradiation with doses D ～ 10²⁰ m^?2: germanium electron centers, neutral oxygen vacancies, and Ge²⁺ centers, which have been annealed at a temperature of 1000°C for an hour. At D ≥ 1 × 10²¹ m^?2, more complex defects arise in the films, which are only partially annealed under the same conditions.     

Quasi-elastic scattering due to fast oxygen diffuson in yttria stabilized zirconia

Evidence for fast oxygen diffusion at high temperatures in single crystal ZrO₂ containing 12 mol % Y₂O₃ is presented from quasi-elastic light scattering data. Lattice vacancies are responsible for the enhanced ionic diffusion and the structural disorder. In the temperature range investigated we estimate the barrier activation energy for the jumping of oxygen vacancies to be 0.25 eV. At 1500°K the jump time is ～ 4 × 10^?12 sec., the diffusion constant is ～ 3.26 × 10^?5 cm²/sec. and the conductivity is ～ 0.24 (Ωcm)^?1.     

On the thermal conductivity of glasses

We estimate the numerical contribution of the interaction between like defects in glasses for the linewidth (? T^?1₂) obtained in acoustical experiments. This interaction gives origin to a diffusion process with a very large diffusion constant (D = 10^?5 cm² sec^?1). The thermal conductivity due to this diffusion process is calculated. Its temperature dependence is also obtained.     

An electrochemical study on the substituted spinel LiMn1.95Cr0.05O4

Cyclic voltammetry, galvanostatic charge?Cdischarge technique, potentiostatic intermittent titration technique (PITT), and electrochemical impedance spectroscopy (EIS) were used to study the behavior of a LiMn_1.95Cr_0.05O₄ (substituted lithium?Cmanganese spinel) electrode in nonaqueous electrolytes at 25 °C. Quantitative and qualitative changes of the electrode transport parameters as functions of lithium concentration were analyzed. Several equivalent circuits are discussed; the results obtained by different methods are compared. The PITT and EIS results are in good agreement; the chemical diffusion coefficient D varies within 10^?14?C10^?9 cm² s^?1 depending on the lithium content in the Li_xMn_1.95Cr_0.05O₄ electrode.     

Electrochemical determinations of the chemical diffusion coefficient and non-stoichiometry in AgCl

Measurements were made of the electronic conductivities, σ_e and σ_h, of AgCl as a function of P_Cl2 and of the chemical diffusion coefficient of n-type and p-type AgCl, respectively, in the temperature range of 360–440°C by means of the improved dc polarization technique. The deviation from stoichiometry, δ, in the formula Ag_1+δCl was calculated from the measured electronic conductivities and chemical diffusion coefficients. It was found that δ ranges from -10^?4 to 10^?6 according to P_Cl2. Based on the determined δ values, the imperfection equilibrium in AgCl are discussed.