Chemical diffusion measurements in single crystalline cuprous oxide

Using electrical conductivity measurements in the temperature range 650–1100°C and for oxygen pressure greater than 10^?6atm., the variation of the chemical diffusion coefficient in cuprous oxide with temperature has been determined as:

$\text{D}\text{?}\text{= 1.2 10}{}^{\mathrm{?3}}\text{exp}\text{(}\text{? 7800}\text{RT}\text{)}\text{cm}{}^2\text{sec}{}^{\mathrm{?1}}$

.Taking into account the nature of the prevailing defects in cuprous oxide one can show that $\text{D}\text{?}\text{?D}{}_{\mathrm{<mtext>Cu</mtext>}}\text{[V}{}^{\mathrm{x}}{}_{\mathrm{<mtext>Cu</mtext>}}\text{]}$. This relation permits the results to be compared with those determined by tracer diffusivities. Using a value for the enthalpy of formation of non ionized copper vacancies in the range 12–16 kcal mol^?1, the results are shown to be in agreement with the value of the activation enthalpy for self-diffusion of copper of 24 kcal mol^?.     

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:

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

.     

A study of oxygen self-diffusion in the C-direction of rutile using a nuclear technique

Oxygen-18 has been used as a tracer to study diffusion in the c-direction of rutile single crystals in the temperature range 1173–1473K. The distribution of the tracer was determined by means of a nuclear technique. The diffusion coefficient can be represented in this temperature range by the equation $\text{D = 2.4 × 10}{}^{\mathrm{?6}}\text{exp}\text{?}\text{(2.826 ± 0.05) × 10}{}^5\text{RT}\text{m}{}^2\text{s}{}^{\mathrm{?1}}$. A diffusion coefficient obtained at 1673 K using a different technique agrees well with the value obtained by extrapolation from the other results. Consideration of the results from specimens with different impurity concentrations leads to the conclusion that the diffusion which has been studied is extrinsic.The results obtained in this investigation are in good agreement with those of Haul and Dümbgen[l] and (by extrapolation) Gruenwald and Gordon [2] but not with those of Doskocil and Pospisil[3] and Bagshaw and Hyde[4].     

Diffusion of water in additively colored potassium iodide crystals

The diffusion of water into additively colored potassium iodide has been studied in the range 15–45°C. Penetration depths, measured by decrease in the F-band absorption, increase with $\text{t}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The diffusion coefficient, D = 0·58 exp (?6496/T) cm² sec^?1 agrees very well with that determined by other workers. The Henry's law constant, $\text{K =}\text{C}{}_0\text{p}{}_{\mathrm{w}}\text{= 1·3 × 10}{}^9\text{exp}\text{(+4882/T)}\text{cm}{}^{\mathrm{?3}}\text{torr}{}^{\mathrm{?1}}$ implies a water concentration of C₀ ? 10¹⁷ molecules per cm³ in the surface of KI crystals in equilibrium with an environment at 25°C and 35 per cent relative humidity. The large C₀ makes penetration very rapid. Diffusion occurs by interstitial migration of water molecules with an entropy of activation of 9.4 cal/mol deg and an enthalpy of activation of 12·9 kcal/mol.     

Chemical diffusion in nonstoichiometric chromium sulfide,Cr2+yS3

Using the re-equilibration kinetic method the chemical diffusion coefficient in nonstoichiometric chromium sesquisulfide, Cr_2+yS₃, has been determined as a function of temperature (1073–1373 K) and sulphur vapour pressure (10?10⁴ Pa). It has been found that this coefficient is independent of sulphur pressure and can be described by the following empirical equation: $\text{D}\text{?}\text{Cr}{}_{\mathrm{2+y}}\text{S}{}_3\text{=50.86}\text{exp(-39070 cal/mole/}\text{RT)}\text{(cm}{}^2\text{s}{}^{\mathrm{?1)}}$. It has been shown that the mobility of the point defects inCr_2+yS₃ is independent of their concentration and that the self-diffusion coefficient of chromium in this sulfide has the following function of temperature and sulphur pressure: . (cm²s^?1).     

Diffusion and point defects in TiO2−x

The self-diffusion of ⁴⁴Ti has been measured both parallel to and perpendicular to the c axis in rutile single crystals by a serial-sectioning technique as a function of temperature (1000–1500°C) and oxygen partial pressure (10^?14 ? 1 atm). The oxygen-partial-pressure dependence of. D¹_Ti indicates that cation selfdiffusion occurs by an interstitial-type mechanism and that both trivalent and tetravalent interstitial titanium ions may contribute to cation self-diffusion. At p_o2 = 1.50 × 10^?7 atm where impurity-induced defects are unimportant,

$\text{D}{}^1{}_{\mathrm{<mtext>Ti</mtext>}}\text{(∥c)=}\text{6.50}\text{+1.33}\text{?1.11}\text{exp}\text{?}\text{(66.11±0.56}\text{kcal}\text{mole}\text{RT}\text{cm}{}^2\text{S}$

and

$\text{D}{}^1{}_{\mathrm{<mtext>Ti</mtext>}}\text{(⊥c)=}\text{4.55}\text{+1.78}\text{?1.28}\text{exp}\text{?}\text{(64.08±0.99)}\text{kcal}\text{mole}\text{RT}\text{cm}{}^2\text{S}\text{.}$

In the intrinsic region, the ratio D¹_Ti (⊥c)/D¹_Ti(∥c) was found to increase from 1.2 to 1.6 as the temperature decreased from 1500 to 1000°C. Computations based upon the defect model of Kofstad (involving the atomic defects Ti^..._iTi^...._iand V^.._o), of Marucco etal. (Ti^...._i and V^.._o), and of Blumenthal etal. (Ti^..._i and Ti^...._i) are compared with the experimental data on deviation from stoichiometry, electrical conductivity, cation self-diffusion and chemical diffusion in TiO_2?x. These comparisons provide values of the defect concentrations, cation-defect diffusivities, electron mobility and reasonable values of the correlation factor for cation diffusion by the interstitialcy mechanism. Only the model of Kofstad is inconsistent with the data.     

Lithium mobility in the layered oxide Li1−xCoO2

The Li⁺-ion chemical diffusion coefficient in the layered oxide Li_0.65CoO₂ has been measured to be $\text{D}\text{?}\text{= 5 × 10}{}^{\mathrm{?12}}$ m² s^?1 by three independent techniques: (1) from the Warburg prefactor, (2) from the transition frequency for semi-infinite to finite diffusion lengths in steady-state ac-impedence measurements and (3) from a modified Tubandt method that uses ac-impedance data to distinguish interfacial and surface-layer resistances from the bulk resistance of the sample. This value and a small increase in D? with (1 ? x) in Li_1?xCoO₂, 0.45 < (1 ? x) < 0.80, compare favorably with the $\text{D}\text{?}\text{= 5}\text{to}\text{7 × 10}{}^{-12}\text{m}{}^2\text{s}{}^{-1}$ obtained by Honders for this system with pulse techniques. A qualitative discussion is presented as to why this composition dependence and why D? for this system is a factor of five larger than that for Li⁺-ion diffusion in Li_xTiS₂.     

Diffusion and ionic conductivity in sodium beta alumina

Measurements of sodium tracer diffusion (D_t) and ionic conductivity (σ) have been made on the same single crystals of sodium beta-alumina of composition 1.23 Na₂0.11 Al₂O₃. The σ- measurements were made over the temperature 390–660 K using reversible (liquid sodium) electrodes. A fit to the conductivity data gives $\text{σT = 2470}\text{exp}\text{(?0.142}\text{eV}\text{kT}\text{)Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}\text{K}$. The D_t, measurements employed two techniques, i.e. nondestructive profiling over the temperature range 210–750 K and cation exchange over the temperature range 505–970 K. The results of the two techniques were in close agreement and can be expressed as $\text{D = 2.12 ×10}{}^{\mathrm{?4}}\text{exp}\text{(?0.169}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}{}^{\mathrm{?1}}$ for T>520K and $\text{D = 2.45 × 10}{}^{\mathrm{?4}}\text{exp}\text{(?0.164}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}\text{470}\text{K}$. The “transition” region between 470 and 520 K is not observed in the conductivity measurements. Silver cation exchange was used to determine the number of mobile sodium ions. A comparison of D_t and σ data yielded a Haven ratio that is temperature dependent, ranging in value from 0.45 at 870 K to 0.35 at 370 K.     

Simultaneous diffusion of calcium and strontium in KCl single crystals

Concentration dependent diffusion coefficients for ⁴⁵Ca²⁺ and ⁸⁵Sr²⁺ in purified KCl were measured using a sectioning method. KCl was purified by an ion exchange — Cl₂?HCl process and the crystals grown under $\text{1}\text{6}$ atmosphere of HCl. The tracers were purified on small disposable ion exchange columns to remove precessor and daughter impurities prior to use in a diffusion anneal. Isothermal diffusion anneals were made in the temperature range from 451% to 669%C. At temperatures above 580%C (the lowest melting eutectic in this system) diffusion was from a vapor source: below 580%C surface depositied sources were used. The saturation diffusion coefficients. enthalpies and entropies of impurity-vacancy associations were calculated using the common ion model for simultaneous diffusion of divalent ions in alkali halides. In KCl the saturation diffusion coefficients D_S(ca) and D_s(Sr) are given by

$\text{D}{}_{\mathrm{s}}\text{(Ca) = 9.93 × 10}{}^{\mathrm{?5}}\text{exp(?0.592}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}$

(1) and

$\text{D}{}_{\mathrm{s}}\text{(Sr) = 1.20 × 10}{}^{\mathrm{?3}}\text{exp(?0.871}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}$

(2) for calcium and strontium, respectively. The Gibbs free energy of association of the impurity vacancy complex in KCl for calcium can be represented by

$\text{Δg(Ca) = ?-0.507 eV + (2.25 × 10}{}^{\mathrm{?4}}\text{eV}\text{\%K}\text{)T}$

(3) and that for strontium by

$\text{Δg(Sr) = ?0.575 eV + (2.90 × 10}{}^{\mathrm{?4}}\text{eV}\text{\%K}\text{)T}$

. (4)     

Stark mixing spectroscopy in cesium

We present a new technique for selectively populating excited states which are inaccessible by dipole excitation from the ground state. The method uses a static electric field to introduce a component of a dipole-allowed state into the state of interest. We have applied the method to cesium to measure lifetimes and a Stark mixing coefficient. The results are $\text{τ(6}{}^2\text{D}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)=64(2) ns}$, $\text{τ(7}{}^2\text{D}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)=92.5(15) ns}$, and <6²D_{$\text{5}\text{2}$}|;ez |7²P_{$\text{3}\text{2}$}>/(E_7P?E_6D)=0.7(3)×10^?3 where is in kV/cm. 141     

Electrical conductivity of the system Y2O3CeO2

The electrical conductivity of the system Y₂O₃CeO₂ was measured in the temperature range 500–1100°C and P_o2 range 10^–7?10^?1 atm. Possible defect models were suggested on the basis of conductivity data, which were investigated as a function of temperature and of P_o2. The observed activation energies were 0.40 eV and 1.79 eV in the low- and high-temperature regions, respectively. The observed conductivity dependences on P_o2 were in the temperature range 500–750°C and at temperatures from 750–1100°C. It is suggested that the system Y₂O₃CeO₂ shows a mixed ionic plus hole conduction due to an O^″_i defect and an electronic hole conduction due to a V^'''_Y defect in the low- and high-temperature regions, respectively.     

Electromigration of cadmiun in lead

The electromigration of cadmium in lead up to a concentration of 510 at ppm Cd was measured at constant temperatures between 250 and 290°C by the steady state method and also by a somewhat novel transient technique; the latter required shorter running time and also gave additional information, namely the chemical diffusion coefficient, D_ch. From the steady state runs the observed effective charge number was Z¹_ss = + 2.5 ± 0.3 for the lowest concentration. The positive value was apparently the result of the counterflowing of the lead in a vacancy-interstitial pair mechanism. The temperature dependence of Z¹ is described by $\text{Z}{}^1\text{= (0.5 ± 2.4) + (0.9 ± 1.1)}$$\text{10}{}^{\mathrm{?4}}\text{ρ}$ and both the wind force and the electrostatic Z_el appear to be small. The Z¹_ss, appeared to increase slightly with concentration. The transient measurements were in general less precise, but were consistent with the steady state results within their experimental accuracy. The values of $\text{D}{}_{\mathrm{ch}}\text{D}{}^1$ appeared to be unity within the same accuracy for a range of composition up to 510 at ppm Cd. To a standard dissociation model for impurity mobility we have added a rather extended atomic exciton mechanism to help explain the diffusion kinetics.     

Vacancy diffusion in magnetite

The chemical diffusion coefficient in a single crystal of magnetite was measured by observing the relaxation of deviations from stoichiometry responding to a stepwise change in oxygen partial pressure between 1300 and 1450°C. The chemical diffusion coefficient was proportional to $\text{(?}\text{In}\text{δ}\text{?}\text{In}\text{p}{}_{\mathrm{o2}}\text{)}{}^{\mathrm{?1}}$. The vacancy diffusion coefficient was calculated with the help of nonstoichiometric data and was found to be independent of the vacancy composition. The value of D_v was

$\text{D}{}_{\mathrm{v}}\text{= (0.14 ± 0.08)}\text{exp}\text{(?}\text{(32,500 ± 1800)}\text{RT)}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$

.     

Reorientational motion of the OH− ion in cubic sodium hydroxide

The rotational motion of the OH^? ion was studied in cubic NaOH at 575 K with quasielastic incoherent neutron scattering. The data are compared to two simple models yielding values for the radius of rotation R, the translational mean square displacement 〈u²〉_H, the rotational jump rate τ^?1 and the rotational diffusion coefficient D_R. The following parameter values are obtained: (a) rotational jump model: $\text{R = 0.95}\text{A}\text{?}$, $\text{〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.052}\text{A}\text{?}{}^2\text{, τ}{}^{\mathrm{?1}}\text{= 2}\text{meV}$, (b) rotational diffusion model: $\text{R = 0.99}\text{A}\text{?}\text{, 〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.046}\text{A}\text{?}{}^2\text{, D}{}_{\mathrm{R}}\text{= 0.72}\text{meV}$.     

Electrical transport and magnetic properties of Nd2(WO4)3

Measurements of the molar magnetic susceptibility (X_m) of a powdered sample of Nd₂(WO₄)₃ in the temperature range 300–900 K, and the electrical conductivity (σ) and dielectric constant (?$\text{)}\text{?}$ of pressed pellets of the compound in the temperature range 4.2–1180 K are reported. X_m obeys the Curie-Weiss law with a Curie constant C= 3.13 K/mole, a paramagnetic Curie temperature θ= ?60 K and a moment of Bohr magnetons, p= 3.49 for the Nd³⁺ ion. The electrical conductivity data can be explained in terms of the usual band model and impurity levels. Both the σ and ?$\text{\$}\text{?}$data indicate some sort of phase transition round 1025 K. The conductivity follows Mott's law $\text{σ = A exp (?B/T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{)}$ in the temperature range $\text{200 < T < 3000}\text{K with}\text{B = 45.00 (}\text{K}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{and}\text{A = 1.38 × 10}{}^{\mathrm{?5}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$. The dielectric constant increases slowly up to 600 K, as is usual for ionic solids. The increase becomes much faster above 600 K, which is attributed to space-charge polarization of thermally generated charge carriers.     

Iron diffusion and electrical conductivity in magnesio-wüstite solid solutions (Mg,Fe)O

Diffusion of ⁵⁹Fe and electrical conductivity in magnesio-wüstite solid solution (Mg_xFe_1?x)O with x = 0.26 and 0.5 have been measured as a function of temperature and oxygen partial pressure. For both solid solutions, the results show that at 1100°C the diffusivity D of ⁵⁹Fe is directly proportional to $\text{p}{}_{\mathrm{o2}}{}^{\mathrm{<mtext>1</mtext><mtext>6</mtext>}}$, whereas the electrical conductivity σ is directly proportional to $\text{p}{}_{\mathrm{o2}}{}^{\mathrm{<mtext>1</mtext><mtext>3.4</mtext>}}$. At a given temperature and oxygen partial pressure, the value of D decreases with an increase in MgO concentration in the solid solution. The results are discussed in terms of the coexistence of variously ionized cation vacancies and their change in concentration with MgO additions.     

Electrical conductivity of LiNbWO6

The electrical conductivity of polycrystalline LiNbWO₆, which has a trirutile structure, was studied by the ac impedance method and dc resistance measurement. From the results, the following is clear; LiNbWO₆ is a lithium ionic conductor, its electrical conductivity at 150°C is $\text{1.8 × 10}{}^{\mathrm{?6}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$ and the electronic transference number is about 0.03.     

Analysis of the 2770-Å emission system in I2

A weak emission spectrum of I₂ near 2770 Å is reanalyzed and found to to minate on the A(1u³Π) state. The assigned bands span v″ levels 5–19 and v′ levels 0–8. The new assignment is corroborated by isotope shifts, band profile simulations, and Franck-Condon calculations. The excited state is an ion-pair state, probably the 1g state which tends toward $\text{I}{}^{\mathrm{?}}\text{(}{}^1\text{S) +}\text{I}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_1\text{)}$. In combination with other results for the A state, the analysis yields the following spectroscopic constants: T″_e = 10 907 cm^?1, $\text{D}$″_e = 1640 cm^?1, ω″_e = 95 cm^?1, $\text{R″}{}_{\mathrm{e}}\text{= 3.06}\text{A}\text{?}$; T′_e = 47 559.1 cm^?1, ω′_e = 106.60 cm^?1, $\text{R′}{}_{\mathrm{e}}\text{= 3.53}\text{A}\text{?}$.     

Oscillator strengths in the Cameron system of carbon monoxide

Relative oscillator strengths in the Cameron system of CO(a³Π ← X¹Σ) have been observed in absorption for six bands (υ′ = 0–5, υ″ = 0) with the result, normalized to the absolute (0, 0) band measurement of Hasson and Nicholls, $\text{?}{}_{00}\text{= (1.62±0.07) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{10}\text{= (1.96±0.09) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{20}\text{= (1.41±0.04) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{\mathrm{3\; 0}}\text{= (0.72±0.03) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{40}\text{= (0.31±0.02) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{50}\text{= (0.14±0.01) × 10}{}^{\mathrm{?7}}$. The density of CO was modulated with a motor-driven vacuum valve and synchronous fluctuations (?1 per cent) in the transmitted intensity detected with a lock-in amplifier. Peak pressure in the 21 cm absorption cell was approximately 10 torr. A curve of growth analysis was used to correct saturation effects by less than 3 per cent.     

Decays of charmed mesons via color-octet decays of the c-quark

We unify the color-octet weak transitions first studied in cq? annihilation models with the coherence structure of c-quark decay models. We find then, with a dominant c-quark decay contribution, $\text{2.3,?}{}_{\mathrm{\tau }}\text{(}\text{D}{}^{\mathrm{+}}\text{)}\text{τ(}\text{D}{}^0\text{)?3.0}$ and τ(D⁺)≈7.5×10^?13 s, not inconsistent with the trends in the experimental results.