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)     

Catalytic decomposition of DCOOD studied by reactive scattering of a modulated DCOOD nozzle beam by a polycrystalline platinum surface in ultra high vacuum

The catalytic decomposition of formic acid by a polycrystalline platinum surface was studied by use of modulated molecular beam techniques with mass spectrometric phasesensitive detection. Kinetic information about elementary surface reaction steps was obtained. The formation of CO₂ was found to be a monomolecular, whereas that of D₂ was a bimolecular process. The resulting reaction mechanism may be described as follows:

The rate constants in dependence from the surface temperature t₀ are $\text{η = 7.1 × 10}{}^3\text{exp}\text{(?}\text{9.9}\text{RT}{}_0\text{kcal/mole}\text{),}$ The sticking probability η is provided by the temperature dependence of the intensity of the nonreactive scattered formic acid molecules; the rate constants k_d1 and k_d2 are derived from the measured phase shift between reactive and nonreactive scattered particles. From the phase angle ?, the average surface residence time τ of the intermediates is computed: 3.7 ? τ_DCOO ? 0.41 msec (418 ? T₀ ? 505 K), 31.8 ? τ_D ? 11.6 msec (418 ? T₀ ? 460 K). The difference between τ_D and τ_DCOO is because of the different molecularity of desorption.     

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.     

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

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

.     

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^?.     

Chemical diffusion in CoO

Equilibration kinetics of CoO have been studied over the range 1–10^?5 atm oxygen pressure and 900–1300°C by both thermogravimetric and electrical conductivity techniques. The former technique gives excellent agreement with theory based on bulk diffusion and results in a chemical diffusion coefficient given by, $\text{D}\text{?}\text{= 4.8×10}{}^{\mathrm{?3}}\text{exp (?22,500/RT)}$ cm${}^2\text{sec}$. The defect diffusion coefficient (Dinvinco) is equal to $\text{i}\text{?}\text{tD}\text{2}$. No dependence of ?tD on defect concentration was observed. The electrical conductivity technique qualitatively supports these results.     

The hopping motion of the self-trapped exciton in NaCl

The decay kinetics and the yield of the π luminescence from the lowest triplet state of the self-trapped exciton have been studied in NaCl containing Li⁺ ions. It is found that the π luminescence band which is observed at 6K is replaced by a luminescence band peaked at 3.34 eV above 77K. The 3.34 eV luminescence band is ascribed to the recombination of the relaxed exciton trapped by a Li⁺ ion, (V_ke)_Li. The decay of the π luminescence induced by an electron pulse and the time change of the luminescence from (V_ke)_Li are explained in terms of the characteristic equation of the diffusion-limited reaction of the lowest triplet self-trapped excitons with the Li⁺ ions. From the analysis of the dependence of the decay rate of the π luminescence on temperature and on the Li⁺ concentration, we found the diffusion constant D of the lowest triplet self-trapped exciton in NaCl to be given by with $\text{D}{}_0\text{= 2.13 × 10}{}^{\mathrm{?3}}\text{cm}{}^2\text{s}$ and E₀ = 0.13 eV. The present result can be regarded as the first clear experimental evidence for the hopping diffusion of the self-trapped exciton in alkali halides. The obtained values of E_a and D₀ are discussed using the small polaron theory. The effect of the anharmonicity on the hopping of the self-trapped excitons is suggested to be significant.     

Mixed conduction in Cr-doped GaAs

Hall-effect and magnetoresistance measurements have been carried out in GaAs : Cr as functions of magnetic field strength (B = 0–18kG) and temperature (T = 125–420°K). Independent solutions for the mobilities, μ_n and μ_p, and the carrier concentrations, n and p, are obtained from the basic mixed-conductivity equations. These quantities, as well as the intrinsic carrier concentration, n_i are then calculated as a function of temperature for one sample, and subsequent analysis yields the following values in the range T = 360–420°K: an acceptor (presumably Cr) energy E_A = 0.69±0.02eV (from the valence band); the bandgap energy E_g = E_g0 + αT, with E_go = 1.48±0.02eV, $\text{α ? 3.2 × 10}{}^{\mathrm{?4}}\text{eV}\text{°}\text{K}$; $\text{μ}{}_{\mathrm{n}}\text{= 2700± 100}\text{cm}{}^2\text{V}\text{sec}$, decreasing slightly with temperature; = 350± 50 $\text{cm}{}^2\text{V sec}$; and an acceptor-to-donor concentration ratio, itN_A/N_D?8. The electron mobility appears to be limited by neutral impurity scattering, with N_A ? 2 × 10¹⁶cm^?3. Several other samples were also investigated but as a function of temperature only (at B = 0). At room temperature both positive (p-type) and negative (n-type) Hall coefficients were observed.     

Self-diffusion of manganese in manganous sulphide

The self-diffusion coefficient of manganese in manganous sulphide has been calculated as a function of temperature and sulphur vapour pressure. It has been shown that near the Mn/MnS phase boundary Mn self diffusion occurs by means of interstitial or interstitialcy mechanism and D_Mn is the following function of temperature and sulphur vapour pressure: . At higher sulphur pressures manganese diffuses via doubly ionized cation vacancies and analogous pressure and temperature dependence can be described by the following empirical equation: .     

Cation self-diffusion and the isotope effect in Fe2O3

Self-diffusion of ⁵⁹Fe parallel to the c axis in single crystals of Fe₂O₃ has been measured as a function of temperature (1150–1340°C) and oxygen partial pressure (2 × 10^?3 ? p_O2 ? 1 atm) The temperature dependence of the cation diffusivity in air is given by the expression

$\text{D}{}_{\mathrm{<mtext>Fe</mtext>}}{}^1\text{= (1.9}{}_{\mathrm{?1.4}}{}^{\mathrm{+5.2}}\text{× 10}{}^9\text{exp}\text{(?}\text{141.4 ± 4.0 kcal/mole}\text{RT}\text{)}\text{cm}{}^2\text{/}\text{s}$

.The unusually large value of D₀ is interpreted in terms of the values of the preexponential terms in the reaction constants for the creation of defects in Fe₂O₃. The oxygen-partial-pressure dependence of the diffusivity indicates that cation self-diffusion occurs by an interstitial-type mechanism The simultaneous diffusion of ⁵²Fe and ⁵⁹Fe has been measured in Fe₂O₃. The small value of the isotope effect suggests that iron ions diffuse by an noncollinear interstitialcy mechanism, which is consistent with the crystal structure of Fe₂O₃.     

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.     

Nuclear spin-lattice relaxation of Co59 in CoB

We report the result of the Co⁵⁹ nuclear spin-lattice relaxation time T₁ measurements in the diamagnetic monoboride CoB. The analysis of the data, in the 4.2–300 K temperature range, allows us to separate three contributions to the relaxation rate: first a Korringa process, (T_1KT)^?1= 0.21 sec^?1K^?1 (in good agreement with the temperature independent isotropic Knight shift) from which we deduced the Co⁵⁹ hyperfine constant A=6.2 ×10^?6eV, second an impurity contribution independent of temperature and third a quadrupolar term, $\text{T}{}^{\mathrm{?1}}{}_{\mathrm{1Q}}\text{=3560 (}\text{T}\text{θ}{}_{\mathrm{D}}\text{)}{}^2\text{E(}\text{T}\text{θ}{}_{\mathrm{D}}\text{) sec}{}^{\mathrm{?1}}$, which is predominant at high temperature and well explained by the Van Kranendonk theory. It seems that it was the first time that such a quadrupolar effect was detected in a metallic compound. A remarkable coherency between Lundquist's three bands model and our experimental results has to be noted.     

Optical detection of triplet excitons in GaS

Optically detected magnetic resonance has been used to investigate exciton recombination in the layered semiconductor GaS. Five triplet exciton resonances have been observed all with the same g-value of g_ex6 = 2.006 ± 0.002 but with different zero field splittings:

$\text{D}{}^{\mathrm{I}}\text{= + 0.013 cm}{}^{\mathrm{?1}}\text{, D}{}^{\mathrm{II}}\text{= + 0.024 cm}{}^{\mathrm{?1}}\text{, D}{}^{\mathrm{III}}\text{= + 0.025 cm}{}^{\mathrm{?1}}$

,

$\text{D}{}^{\mathrm{IV}}\text{= + 0.075 cm}{}^{\mathrm{?1}}\text{, D}{}^{\mathrm{V}}\text{= + 0.010 cm}{}^{\mathrm{?1}}$

. The resonances from the high energy wing are remarkably narrow and we believe that this may be the first observation of resonance from free indirect excitons.     

The examination of the Faraday effect and location of the Cr level in Cr doped PbTe

Faraday effect, absorption coefficient and Hall effect have been examined in Cr doped PbTe single crystals. The effective masses of carriers m_F and then values of effective masses at the bottom of conductivity band m_F(0) have been calculated. It is shown that m_F in Cr doped PbTe is comparable with m_F in n-type PbTe not doped with chromium, with the same free carrier concentration, and the relative temperature variation of m_F(0) corresponds to relative variation of Eg. In the absorption spectrum the additional absorption maximum is found at the energy 0.11–0.14 eV. The long-wave side of the peak is shifted towards longer waves as the temperature is increased. Calculation shows that chromium level is located in the conduction band at ΔE = 0.11 eV in the limit T → 0, and is shifted down towards the bottom of the conduction band with a constant rate of $\text{0.8 × 10}{}^{\mathrm{?4}}\text{eV}\text{K}$ within the temperature range of 4.4–300 K and $\text{3.3 × 10}{}^{\mathrm{?4}}\text{eV}\text{K}$ within the temperature range 300–800 K.     

Transport processes in NaCl single crystals doped with a trivalent cation; solubility,association and migration of Y3+

The self-diffusion coefficient of ²²Na⁺ and the ionic conductivity are measured as a function of temperature in NaCl single crystals doped with labelled yttrium ions, as well as the diffusion coefficient of ⁸⁸Y³⁺. We give the theoretical equations for the transport processes in the alkali halides doped with a trivalent cation; These are derived from the theory of the crystals doped with divalent cations. Solubility of YCl₃ in NaCl is accurately determined through a radioactive technique. The free enthalpy of solubility of free Y³⁺ is: (2.91?13 kT) eV. A good fit of the whole set of data is obtained by treating the association between Y³⁺ ions and vacancies by the single equation $\text{K}{}_2\text{= 12}\text{exp}\text{(-9.5)}\text{exp}\text{(}\text{1.17}\text{kT}\text{)}$. The jump frequency of Y³⁺ is $\text{w}{}_2\text{= 1.37 × 10}{}^{13}\text{exp}\text{(-}\text{0.98}\text{kT}\text{)}\text{sec}{}^{-1}$. The results are compared to those characterising the divalent foreign cations.     

Electron-hole interaction in the presence of excitons

We calculate the effective electron-hole interaction V_re in the presence of an exciton gas, which reads in real space:

$\text{V}{}_{\mathrm{re}}\text{(r)=}\text{?e}{}^2\text{r}\text{{1+}\text{∑}\text{i=1}\text{4}\text{(?1)}{}^{\mathrm{i}}\text{C}{}_{\mathrm{i}}\text{exp}\text{(?Z}{}_{\mathrm{i}}\text{r}\text{a}\text{}}$

The parameters C_i and Z_i are given explicitly for GaAs. For this material, we show the binding energy of the exciton is weakly modified so long as $\text{8πR}{}_0\text{?}{}_{\mathrm{ex}}\text{a}{}_0{}^3\text{kT?1}$. (R₀, exciton Rydberg, a₀ exciyon radius, ?_ex exciton density, T temperature).     

Diffusivity permeability and solubility of hydrogen in platinum

The permeability time-lag method has been used to measure the temperature dependence of the diffusivity of hydrogen in platinum in the temperature range 558–936°C. In this temperature range the diffusivity D was found to be represented by the Arrhenius relation,

$\text{D = (6.47±1.73) × 10}{}^{\mathrm{?7}}\text{exp}\text{?}\text{Q}\text{RT}\text{m}{}^2\text{sec}$

where $\text{Q =}\text{26.3 ± 2.3}\text{kJ}\text{mol}$.Measurements of the absolute permeation flux in the steady state condition yield values for the permeability coefficient and the solubility. The solubility values obtained from the permeability flux determinations show discrepancies when compared to solubilities determined by direct equilibration techniques. This discrepancy is briefly discussed.     

Heat capacity of [Ni(OCH3)(acac)(CH3OH)]4 from 0.4 to 285 K: Spin interaction and tunnel-splitting of internal rotation of methyl group

The heat capacity of the tetranuclear nickel cluster complex, tetrakis [μ₃-methoxo-2,4-pentanedionato (methanol) nickel (2)], has been measured from 0.4 to 285 K. Contrary to the previous prediction by Bertrand et al.[6], that this complex exhibits an intercluster ferromagnetic spin coupling, the present heat capacity measurement shows no indication of the spin-ordering effect caused by the intercluster interaction at least down to 0.4 K. Instead, a heat capacity anomaly centered around 1.5 K with a shoulder at 0.5 K has been observed. This anomaly is well accounted for in terms of both a level splitting of the ground S = 4 state due to a uni-axial crystalline anisotropy and a tunnel-splitting of the rotational levels of methyl groups. The intracluster spin exchange constant J and the single-ion zero-field splitting parameter D are determined to be $\text{J}\text{hc}\text{= 7.0 cm}{}^{\mathrm{?1}}$ and $\text{D}\text{hc}\text{= 3.65 cm}{}^{\mathrm{?1}}$ (h being the Planck constant and c the speed of light in a vacuum). The temperature dependence of the effective Bohr magneton [6] is also satisfactorily accounted for on the basis of this model. The tunnel-splitting δ of the lowest rotational level of the four methyl groups belonging to methoxides is estimated to be $\text{δ}\text{hc}\text{= 0.4–0.7 cm}{}^{\mathrm{?1}}$ and the corresponding potential barrier V_o is found to be V_o = 1.9–1.5 kJmol^?1.     

Self-diffusion of C in single crystals of NBCx

The self-diffusion coefficients of ¹⁴C in NbC_x single crystals have been measured as a function of composition in the temperature range 1900–2315 K, and can be represented by the expressions

$\text{D}{}^1{}_{\mathrm{C}}\text{(}\text{NbC}{}_{0.868}\text{) = (2.59}{}_{\mathrm{?1.07}}{}^{\mathrm{+1.82}}\text{)}\text{exp}\text{(?}\text{100.42 ± 2.2}\text{kcal}\text{mol}\text{RT}\text{)}\text{cm}{}^2\text{s}$

$\text{D}{}^1{}_{\mathrm{C}}\text{(}\text{NbC}{}_{0.834}\text{) = (7.44}{}_{\mathrm{?4.14}}{}^{\mathrm{+9.36}}\text{)}\text{exp}\text{(?}\text{105.0 ± 3.3}\text{kcal}\text{mol}\text{RT}\text{)}\text{cm}{}^2\text{s}$

$\text{D}{}^1{}_{\mathrm{C}}\text{(}\text{NbC}{}_{0.766}\text{) = (2.22}{}_{\mathrm{?1.04}}{}^{\mathrm{+1.98}}\text{) × 10}{}^{\mathrm{?2}}\text{exp}\text{(?}\text{76.02 ± 2.7}\text{kcal}\text{mol}\text{RT}\text{)}\text{cm}{}^2\text{s}$

The lower values of the activation energy and the pre-exponential term in NbC_0.766 are attributed to a change in the path of C mass transport from that of an octahedral-tetrahedral-octahedral mechanism in NbC_0.868 and NbC_0.834 involving a C-metal divacancy mechanism. The effect of lattice geometry and the electronic charge distribution on the diffusion mechanism is also discussed.     

Trapping probabilities and desorption energies of alkali atoms on a clean and an oxygen covered tungsten (110) surface

Alkali atoms were scattered with hyperthermal energies from a clean and an oxygen covered (θ ≈ 0.5 ML) W(110) surface. The trapping probability of K and Na atoms on oxygen covered W(110) has been measured as a function of incoming energy (0–30 eV) and incident angle. A considerable enhancement of trapping on the oxygen covered surface compared to a clean surface was observed. At energies above 25 eV there are still K and Na atoms being trapped by the oxygen covered surface. From the temperature dependence of the mean residence time τ of the initially trapped atoms the pre-exponential factor τ₀ and the desorption energy Q were derived using the relation: $\text{τ = τ}{}_0\text{exp}\text{(}\text{Q}\text{kT}{}_{\mathrm{<mtext>s</mtext>}}\text{)}$. On clean W(110) we obtained for Li: $\text{τ}{}_0\text{= (8 ±}\text{8}\text{4}\text{) × 10}{}^{\mathrm{?14}}\text{sec}$, Q = (2.78 ± 0.09) eV; for Na: τ₀ = (9 ± 3) × 10^?14 sec, Q = (2.55 ± 0.04) eV; and for K: τ₀ = (4 ± 1) × 10^?13 sec, Q = (2.05 ± 0.02) eV. Oxygen covered W(110) gave for Na: τ₀ = (7 ±3) × 10^?15 sec, Q = (2.88 ± 0.05) eV; and for K: $\text{τ}{}_0\text{= (1.3 ±}\text{0.9}\text{0.6}\text{) × 10}{}^{\mathrm{?14}}\text{sec}$, Q = (2.48 ±0.05) eV. The adsorption on clean W(110) has the features of a supermobile two-dimentional gas; on the oxygen covered W(110) adsorbed atoms have the partition function of a one-dimen-sional gas. The binding of the adatoms to the surface has a highly ionic character in the systems of the present experiment. An estimate is given for the screening length of the non-perfect conductor W(110):k_s^?1≈ 0.5 Å.