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).     

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: .     

Defects and diffusion in MnO

Diffusional transport of manganese through MnO scales has been studied at temperatures from 900–1200°C by means of a novel diffusion/evaporation method and by the two-stage oxidation (Rosenburg) method. In the phase field of Mn_1?vO near the MnO₃O₄ phase boundary the manganese self-diffusion coefficient and the concentration of defects is concluded to be proportional to . The concentration of defects increases with decreasing temperature at constant partial pressure of oxygen. In this non-stoichiometry range Mn_1?yO has properties similar to wüstite, Fe_1?yO, and it is concluded that the important cation defects are defect clusters. The results may be explained assuming that the defect clusters consist of four vacancies on octahedral sites and one interstitial on a tetrahedral site. Values for the concentration of defects, the self-diffusion of manganese ions and of the defects have been calculated. For the phase field near the M/MnO phase boundary it is concluded that Mn-interstitials predominate.     

Method for studying metal ion self-diffusion in some inorganic compounds

A method for studying metal ion self-diffusion in oxides (or other inorganic compounds) is described. The method involves oxidation of an appropriate metal to form a dense, single-layered scale of the lowest valent oxide (e.g. MnO on Mn). The specimen is then treated in high vacuum, and the evaporation of metal diffusing through the scale is measured. From the rates of metal diffusion/evaporation as a function of scale thickness information about the defect structure is obtained. The metal ion self-diffusion coefficient is determined from the rate of metal transport (evaporation) through a scale with known thickness. The requirements and limitations of the method are discussed. The use of the method is illustrated for Mn self-diffusion in MnO at 1100°C. The self-diffusion coefficient of Mn in MnO is proportional to the square root of the oxygen pressure, , in t MnO phase field near the MnO/Mn₃O₄ phase boundary. It is also tentatively concluded that the predominating defects near the Mn/MnO phase boundary are manganese interstitials.     

A search for integrable two-dimensional hamiltonian systems with polynomial potential

We report the results of a search for all integrable hamiltonian systems of type $\text{H = (}\text{1}\text{2}\text{)p}{}_{\mathrm{x}}{}^2\text{+ (}\text{1}\text{2}\text{)p}{}_{\mathrm{y}}{}^2\text{+ V(x,y)}$, where V is a polynomial in x and y of degree 5 or less and the second invariant is a polynomial in p_x and p_y of order 4 or less. Both classical and quantum integrability are discussed.     

Ionic-electronic conductors based on lithium-containing oxide bronzes

Lithium-containing oxide bronzes Li_xV_2?yM_yO₅-β (M=Mo or W) have been studied in wide range of temperature (25–550°C) and composition (0.22?x?0.47, 0?y?0.25) as prospective ionic-electronic conductors. By coulometric titration tecknique, $\text{Δ}\text{G}{}_{\mathrm{<mtext>Li</mtext>}}$, $\text{Δ}\text{H}{}_{\mathrm{<mtext>Li</mtext>}}$ and $\text{Δ}\text{S}{}_{\mathrm{<mtext>Li</mtext>}}$ have been found and ordering of the lithium ions within the channel structure Li_xV₂O₅-β has been discussed depending on composition and temperature. The chemical diffusion coefficient for lithium D?_Li has been measured by potentiometric technique on hot-pressed ceramic samples. The lithium self-diffusion coefficient D_Li and partial lithium-ionic conductivity have been calculated.     

A piezomodulation study of the absorption edge and Mn++ internal transition in Cd1−xMnxTe,a prototype of diluted magnetic semiconductors

We report the first piezomodulation spectrum of Cd_1?xMn_xTe. Signatures of the exciton transition and the internal transition of Mn⁺⁺ are identified. The opposite signs of these signatures are attributed to the positive pressure coefficient of the direct interband transition as contrasted to a negative pressure coefficient for the ${}^6\text{A}{}_1\text{→}{}^4\text{T}{}_1$ transition causing the Mn⁺⁺ feature.     

Dissociation activation barrier and heat of chemisorption: A morse-type analytical approach

The activation barrier ΔE¹_ABfor dissociation AB → A + B on transition-metal surfaces is analyzed within an additive Morse-type approach based on the bond-order conservation. It is shown that $\text{Δ}\text{E}{}^1{}_{\mathrm{AB}}\text{=}\text{D}{}_{\mathrm{AB}}\text{?(}\text{Q}{}_{\mathrm{A}}\text{+}\text{Q}{}_{\mathrm{B}}\text{+}\text{Q}{}_{\mathrm{A}}\text{Q}{}_{\mathrm{B}}\text{/(}\text{Q}{}_{\mathrm{A}}\text{+}\text{Q}{}_{\mathrm{B}}\text{)}$ where D_AB is the gas-phase dissociation energy and Q_A(Q_B) is the heat of atomic chemisorption. Estimates of $\text{Δ}\text{E}{}^1\text{for H}{}_2\text{, N}{}_2\text{, O}{}_2$, and NO are shown to be in reasonable agreement with experiment. The two-dimensional potential diagram of the metal-AB interactions is defined analytically and discussed in some detail.     

Three-nucleon results for separable potentials modelled on the Reid soft-core potential

Using a solution to the inverse scattering problem we have generated phase-equivalent separable potentials in the ${}^1\text{S}{}_0$ and ${}^3\text{S}{}_1\text{?}{}^3\text{D}{}_1$ states, which have nearly the same singlet UPA form factors and deuteron parameters (E_D, P_D, Q_D, A_S and $\text{A}{}_{\mathrm{D}}\text{A}{}_{\mathrm{S}}$) as the Reid soft-core potential. We compare our results for the binding energy of the triton and the neutron-deuteron doublet scattering length with the corresponding values for the Reid soft-core potential.     

Predissociation and Λ-doubling in the even-parity Rydberg states of the nitrogen molecule

Predissociations in the y¹Π_g and $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Rydberg states of N₂ (configurations $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{4pσ}$ and $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{3pπ}$, respectively) and their likely causes, are discussed. Peaking of rotational intensity at unusually low J values, without sharp breaking off, is interpreted as due to case c^? or case cⁱ predissociation. Λ doubling in the y state, attributed to interactions with the $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state and with another, ¹Σ⁺, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, here labeled x′, is obtained. It is concluded that the predissociation in the Π⁺ levels of the y state is an indirect one mediated by the interaction with x′ coupled with predissociation of x′ by a ${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state dissociating to ${}^4\text{S +}{}^2\text{P}$ atoms: combined, however, with perturbation of the y state by the k¹Π_g Rydberg state (configuration $\text{3σ}{}_{\mathrm{g}}{}^{\mathrm{?1}}\text{4dπ}$), whose Π⁺ levels are completely predissociated.     

The mechanism of 5D3−5D4 cross-relaxation in Y3Al5O12: Tb3+

The ${}^5\text{D}{}_3\text{?}{}^5\text{D}{}_3$ cross-relaxation of YAG:Tb³⁺ has investigated by analysis of the ⁵D₃ decay curve as a function of Tb³⁺ concentration. This technique is a more sensitive test of the mechanism than relative intensity measurements alone. It is shown that the relaxation is predominantly dipole-dipole in character (R₀ ～ 1.3nm), and insensitive to temperature. The population of the ⁵D₄ state following high energy excitation occurs almost entirely via cross-relaxation from the ⁵D₃ state.     

Non affinity of Fe2+ for B sites in iron thiochromites and compared band structures of oxides and sulfides spinels

Departure from stoichiometry in vapor grown FeCr₂S₄ was studied using Mössbauer spectroscopy. The paramagnetic Mössbauer spectra give evidence of two singlets and two doublets which correspond respectively to A site Fe²⁺ ? Fe³⁺, Fe^II in T_d symmetry and in symmetry lower than T_d. The following ionic distribution has been deduced:

$\text{(Fe}{}^{\mathrm{2+}}{}_{\mathrm{1?y}}\text{Fe}{}^{\mathrm{3+}}{}_{\mathrm{y}}\text{)|Cr}{}^{\mathrm{3+}}{}_{\mathrm{2?x}}\text{□}{}_{\mathrm{x}}\text{|S}{}_{\mathrm{4?z}}\text{□}{}_{\mathrm{z}}$

Compounds in the system Fe_1+xCr_2?xS₄ have been studied for 0 ? x ? 0.1. The spectra are solved assuming Fe^II in A site with T_d symmetry, A site Fe^II with lower symmetry and B site Fe³⁺. No Fe²⁺ appears in B site. These features are discussed in terms of schematic band structures implying single electron narrow bands. The non-affinity of Fe²⁺ for B sites of iron thiochromites is discussed in relation with B site Cr²⁺ level.     

Overtone bands of 14N16O and determination of molecular constants

The wavenumbers of the rotation-vibration lines of ¹⁴N¹⁶O are reported for the (2-0) and (3-0) bands. The full set of spectroscopic constants for the three bands (1-0), (2-0), and (3-0) has been determined with the method developed by Albritton, Schmeltekopf, and Zare for merging the results of separate least-squares fits. The vibrational constants ω_e, ω_ex_e, ω_ey_e, and the vibrational dependence of the rotational constants have been deduced. The apparent spin-orbit constant $\text{A}\text{?}{}_{\mathrm{<mtext>v</mtext>}}$ and its centrifugal correction $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext>}}$ (including the spin-rotation constant) have a vibrational dependence of the following form: $\text{A}\text{?}{}_{\mathrm{v}}\text{=}\text{A}\text{?}{}_{\mathrm{e}}\text{? α}{}_{\mathrm{A}}\text{(v +}\text{1}\text{2}\text{) + γ}{}_{\mathrm{A}}\text{(v +}\text{1}\text{2}\text{)}{}^2$ and $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>v</mtext>}}\text{=}\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>e</mtext>}}\text{? β}{}_{\mathrm{A}}\text{(v +}\text{1}\text{2}\text{) + δ}{}_{\mathrm{A}}\text{(v +}\text{built+1}\text{2}\text{)}{}^2$; the values of the constants in these two equations have been determined.     

Cation self-diffusion and the isotope effect in Mn1−δO

Diffusion of ⁵⁴Mn in Mn_1?δO single crystals has been measured by a serial sectioning technique as a function of temperature (1000–1500°C) and deviation from stoichiometry (0.00003 < δ < 0.12). The value of m in the expression varies from about 6 at low Po₂ at all temperatures to a value approacing 2 at high Po₂ and high temperatures, thus suggesting that diffusion occurs by doubly charged vacancies at low Po₂ with increasing contributions from singly charged and neutral vacancies as Po₂ (and vacancy concentration) increases. For δ near 0.1, the values of D fall below the values extrapolated from smaller defect concentrations. The isotope effect for cation self-diffusion was measured by simultaneous diffusion of ⁵²Mn and ⁵⁴Mn in Mn_1?δO (0.0004 < δ < 0.116) at 1300 and 1500°C. The measured values of fΔK are independent of temperature within experimental error, and decrease from a value of 0.70 at low defect concentrations to 0.37 for large values of δ. The isotope-effect results suggest that diffusion occurs by single non-interacting vacancies at low defect concentrations; defect-defect interactions become important for δ ? 0.01. The defect-defect interactions may involve essentially individual defects or may result in defect clusters; the similarity between the present isotope-effect results and those for Fe_1?δ0 suggests that defect clustering plays a significant role in mass transport in Mn_1?δO at large values of δ.     

Theory of the self-diffusion (spin diffusion) coefficient of an electron gas

The self-diffusion (spin-diffusion) coefficient D of an electron gas is investigated by means of a proper connected diagram expansion which treats a collision in a medium (rather than in vacuum) in a natural manner. By calculating real and virtual interaction processes to the order e⁴ (second order in interaction strength), we obtain

for a non-degenerate gas where n₀ represents the density. The square-root density (n₀) dependence is noteworthy. In the calculation, no cut-off limiting low momentum transfer in collision is introduced; the screening effect which is important at higher densities, is neglected.     

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.     

Electronic density of levels in a disordered system

Three-, two-, and one-dimensional disordered systems with randomly distributed, purely repulsive scattering centers, known as Lorentz models, are studied in the low energy limit [1]. Using a functional integral representation and a version of the “replica trick”, we have found in the D-dimensional system the density of electronic levels of the form

$\text{n(E)=b}{}_0\text{Eγ}\text{exp}\text{(?b}{}_1\text{E}{}^{\mathrm{<mtext>?(</mtext><mtext>D</mtext><mtext>2</mtext><mtext>)</mtext>}}\text{+b}{}_2\text{E}{}^{\mathrm{<mtext>?(</mtext><mtext>D</mtext><mtext>2</mtext><mtext>)+1</mtext>}}\text{+·+b}{}_{\mathrm{D}}\text{E}{}^{\mathrm{<mtext>?(</mtext><mtext>1</mtext><mtext>2</mtext><mtext>)</mtext>}}\text{)(1+O(}\text{E}\text{))}$

and the constants b₀, b₁,…, b_D, and γ have been determined.     

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.     

Bounded diffusion in solid solution electrode powder compacts. Part II. The simultaneous measurement of the chemical diffusion coefficient and the thermodynamic factor in LixTiS2 and LixCoO2

Two electrochemical methods - involving the application of a long-time galvanostatic current pulse and a small potentiostatic voltage step to a M/M_xSSE cell - are presented. From the overvoltage, respectively current response the chemical diffusion coefficient ($\text{D}{}_{\mathrm{M}}{}^{\mathrm{+}}$) and the thermodynamic factor (? ln a/? ln c) are obtained. The methods have been applied to the cells: Li/1M·LiClO₄ in propylenecarbonate/Li_xTi_1.03S₂ 0.05 < x < 0.95, T = 20°C; and Li_xCoO₂ 0.10 < × < 1, T = 20°C. From the application of the current pulse/voltage decay method it followed: $\text{D}{}_{\mathrm{<mtext>Li</mtext>}}{}^{\mathrm{+}}\text{(}\text{Li}{}_{\mathrm{x}}\text{Ti}{}_{1.03}\text{S}{}_2\text{) = 1?4 × 10}{}^{\mathrm{?8}}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$, with a slight tendency to increase with decreasing x; $\text{D}{}_{\mathrm{<mtext>Li</mtext>}}\text{C}\text{(}\text{Li}{}_{\mathrm{x}}\text{CoO}{}_2\text{) = 2?40 × 10}{}^{\mathrm{?9}}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$, decreasing with decreasing x. These values are among the highest found for solid state Li⁺-ion diffusion, and will be closely evaluated and compared with data reported by other workers. The x-dependence of the thermodynamic factor, determined from kinetic data, for Li_xTi_1.03S₂ (x = 0.05-0.95) and Li_xCoO₂ (x = 0.60-1.00) is in accordance with a simple thermodynamic model. Unlike for Li_xTi_1.03S₂, the thermodynamic factor for Li_xCoO₂, determined from the EMF-x relation, cannot be accounted for by this model. Furthermore, a fast, but crude method to determine the average chemical diffusion coefficient in Li_xTi_1.03S₂ and Li_xCoO₂ is discussed.