Bulk-to-surface precipitation and surface diffusion of carbon on polycrystalline nickel

The time evolution of the KLL Auger spectrum of carbon as a function of temperature is used to derive the kinetics of the surface diffusion and bulk-to-surface precipitation of carbon on polycrystalline nickel. The results show that the activation energy for the surface diffusion of carbon atoms on polycrystalline nickel is 6.9 ± 0.6 $\text{kcal}\text{mole}$, and the activation energy for bulk-to-surface precipitation is 9.4 ± 0.6 $\text{kcal}\text{mole}$. The dependence on the surface diffusion coefficient D_s (cm²s^?1), on the absolute temperature T can be represented, over the experimental temperature range, 350–425° C, by: $\text{ln}\text{D}{}_{\mathrm{s}}\text{= 10.27 ?}\text{3568}\text{T}$.     

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.     

The application of XPS to the determination of the kinetics of the co oxidation reaction over the Ir(111) surface

The coverages of adsorbed oxygen and CO on an Ir(111) surface have been determined using X-ray photoelectron spectroscopy (XPS) during the steady-state catalytic production of CO₂. Correlating the coverages of the reacting adsorbates with the rate of CO₂ production allows the kinetics of the CO oxidation reaction to be determined. The reaction is found to obey a Langmuir-Hinshelwood rate expression of the form , where R_CO2 is the rate of CO₂ production, k⁰ is the pre-exponential factor of the reaction rate coefficient, [CO] and [O] are the surface coverages of CO and oxygen, respectively, and E_a is the activation energy for the oxidation reaction. The activation energy for this catalytic oxidation reaction is found to be approximately 9 $\text{kcal}\text{mole}$.     

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.     

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.     

Softening of surface phonons in the (100) plane of Nb3Sn

The propagation of the surface acoustic mode in the (001) plane is investigated as a function of the temperature dependent elastic moduli of Nb₃Sn in the cubic phase. For the [100] and [110]-directions a softening of the surface mode velocity ν_s is found to follow the softening of the velocity ν_T2 of the bulk shear mode T₂A. It is shown that for the [100]-direction the ratio $\text{(}\text{ν}{}_{\mathrm{s}}\text{ν}{}_{\mathrm{T2}}\text{)}$ tends to ?2 at the structural phase transition. The question is discussed of whether the softening of the surface mode can be observed with Brillouin scattering from opaque surfaces.     

Diffusional transport in manganous sulphide

Using a novel diffusion-evaporation method, the self-diffusion coefficient of manganese in manganous sulphide has been determined as a function of temperature (1073–1373 K) in equilibrium with the metallic phase. It has been shown that the activation energy of this process at constant sulphur activity amounts to 269 kJ/mol and the self-diffusion coefficient is the following function of temperature and sulphur vapour pressure: . Diffusion of Mn²⁺ cations in Mn_1+yS proceeds via the interstitialcy mechanism and the activation enthalpy of successive jumps of these defects, δH_m is equal to 118 kJ/mol. It has been demonstrated that the mobility of interstitial cations in the Mn_1+yS lattice does not depend on their concentration and the diffusion coefficient of these defects has the following function of temperature: D_i=0.759 exp(-118 kJ/mol/RT).     

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.     

NMR study of hydrogen diffusion in uranium hydride

The diffusion of hydrogen in uranium hydride is studied employing the NMR technique. From measurements of spin-spin relaxation time T₂, the activation energy for hydrogen diffusion in β-UH₃ is determined to be $\text{E}{}_{\mathrm{a}}\text{= (19.25 ± 0.4)}\text{kcal}\text{mole}$ and the preexponential factor to be A₀ ≈ 5 × 10¹⁴ Hz. It is shown that these results are in fair agreement with spin-lattice relaxation time T₁ data. Assuming that hydrogen diffusion proceeds via vacancies whose concentration is temperature dependent, it is concluded that E_a is the sum of the energies of vacancy formation and barrier height, and that A₀ contains an entropy change factor. Using vacancy concentration data calculated by Libowitz, we estimate the barrier height energy to be E_b ≈7 kcal/mole. Using a value for the frequency of hydrogen vibration v₀ determined from inelastic neutron scattering by Rush et al., we estimate the entropy change due to vacancy formation and the hydrogen atom jump to be about $\text{S}\text{k}{}_{\mathrm{B}}\text{≈3}$. Similar measurements on samples containing less hydrogen than is needed to compose stoichiometric UH₃, show that the rate of diffusion is enhanced by the presence of excess metal in the sample. The jump frequency at 500°K in UH₃ is found to be approximately 10⁶ Hz while for the two-phase samples of H/U = 2.8 and 2.5, it is larger by a factor of about 3 and 3.5, respectively.     

Surface self-diffusion studies on the (111) surface of vanadium

The temperature dependence of the surface self-diffusion coeffiecient of vanadium was investigated experimentally under ultra-high vacuum conditions by using the sinusoidal profile decay technique. The rates of decay of profiles were measured in situ by using the laser diffraction technique. These diffusion studies were carried out on the (111) plane and the diffusion direction on this plane was controlled to be 〈2&#x0304;11〉. For the temperature range 1374–1521 K, the results were found to follow the relationship: $\text{D}{}_{\mathrm{<mtext>s</mtext><mtext>(111)</mtext>}}\text{〈}\text{2}\text{?}\text{11〉 = 66}\text{exp}\text{[?48,000)RT]}\text{cm}{}^2\text{/}\text{s}$. A comparison of activation energy with a pairwise potential model shows that a significant lattice relaxation is present when an atom occupies the saddle point configuration. Saddle point energies for various body centered cubic metals, calculated from the experimental data on surface diffusion, have been shown to vary linearly with the heat of vaporization.     

Heat capacity and thermodynamic properties of α-Fe2O3 in the region 300–1050 K. antiferromagnetic transition

The heat capacity of synthetic α-Fe₂O₃ has been measured in the range 300–1050K by adiabatic shield calorimetry with intermittent energy inputs and temperature equilibration in between. A λ-type transition, related to the change from antiferro- to paramagnetism in the compound, is delineated and a maximum heat capacity of about 195 JK^?1 mole^?1 is observed over a 3 K interval around 955 K. Values of thermodynamic functions have been derived and C_P (1000K), [H⁰(1000K)-H⁰(0)], and [S⁰(1000K)-S⁰(0)] are 149.0JK^?1 mole^?1, 115.72 kJ mole^?1, and 252.27 JK^?1 mole^?1, respectively, after inclusion of earlier low-temperature results [X⁰ (298.15K)-X⁰(0)]. The non-magnetic heat capacity is estimated and the thermodynamic properties of the magnetic transition evaluated. The results are compared with spin-wave calculations in the random phase approximation below the Néel temperature and the Oguchi pair model above. An upper estimate of the total magnetic entropy gives 32.4JK^?1 mole^?1, which compares favorably with that calculated for randomization of five unpaired electron spins on each iron, ΔS = 2R ln 6 = 29.79 JK^?1 mole^?1 for α-Fe₂O₃. The critical exponent α in the equation $\text{C}{}_{\mathrm{m}}\text{= (}\text{A}\text{α}\text{) [(|T}{}_{\mathrm{<mtext>n</mtext>}}\text{?T|/T}{}_{\mathrm{<mtext>n</mtext>}}\text{)?1]}{}^{\mathrm{?\alpha }}\text{+ B}$ is ?(0.50±0.10) below the maximum and 0.15±0.10 above, for T_n = 955.0K. The high temperature tail is discussed in terms of short range order.     

Cation self-diffusion in disordered VOx

The diffusion of ⁴⁸V in disordered VO_x, crystals has been measured by a serial-sectioning technique as a function of temperature (1100–1500°C) over the homogeneity range 0.78 < x < 1.28. The temperature dependence of the cation tracer diffusivity at each fixed composition is characterized by an Arrhenius behavior in the temperature range 1100–1500°C. The Arrhenius parameters decrease rather sharply near the stoichiometric composition as the composition increases from the metal-rich to the metal-deficient regime; the activation energy for diffusion decreases from ~71 $\text{kcal}\text{mole}$ to ~48 $\text{kcal}\text{mole}$, and the frequency factor decreases by nearly two orders of magnitude (from ~5 $\text{cm}{}^2\text{s}$ to ~0.05 $\text{cm}{}^2\text{s)}$. It is concluded that the significant difference in the cation self-diffusion behavior between the metal-rich and the metal-deficient VO_x may be attributed to the significant differences in the defect structures of the two regimes. The various possible diffusion mechanisms are explored, and comparisons of the cation diffusion behavior in VO_x, with that of the related transition-metal monoxides TiO_x and Fe_1?δO are made. It is concluded that the experimental results for the entire composition range are consistent with the process of diffusion occurring by the migration of monovacancies in equilibrium with defect clusters, the nature of the clusters being different for x < 1 and x #62;; 1.     

Dynamical properties of colloidal systems: III. Collective and self-diffusion of interacting charged particles

The formalism, developed in two earlier papers, for the dynamics of interacting Brownian particles is applied to a system of charged spherical particles in solution. Memory-type transport equations are derived for the propagators of collective and self-diffusion. The memory function for collective diffusion can be related, in the hydrodynamic limit, to the viscosity of the “fluid” of Brownian particles. The memory functions are calculated for a Debye-Hückel system, from an experimentally determined static structure factor S(k), and for an overdamped one-component plasma (OCP). In the two latter cases satisfactory agreement is found with dynamical light scattering results on solutions of polystyrene spheres; in particular, the deviation of the dynamical structure factor from a simple exponential decay can be related to memory effects. With regard to self-diffusion the velocity autocorrelation function, the mean square displacement of one particle and from it the self-diffusion coefficient D_s are calculated. Using S(k) for an actual system, $\text{D}{}_{\mathrm{s}}\text{≈}\text{1}\text{3}\text{D}{}_0$ is obtained, where D₀ is the free diffusion constant. The calculations on the basis of the overdamped OCP-model show that the dynamical properties of the experimentally investigated systems of charged polystyrene spheres can be described by this model for a wide range of scattering angles.     

Self-diffusion of 95Nb in single crystals of NbCx

The self-diffusion of ⁹⁵Nb in single crystals of NbC_0.868, NbC_0.834 and NbC_0.766 has been studied in the range of 2370–2660K. The diffusion coefficients are composition independent and can be described by the expression:

$\text{D}{}^1{}_{\mathrm{Nb}}\text{= (4.54}{}^{\mathrm{+\; 2.85}}{}_{\mathrm{?1.75}}\text{) exp(?}\text{(140.0 ±2.4}\text{kcal}\text{mole}\text{)}\text{RT)}\text{cm}{}^2\text{sec}$

An analysis of the results indicates that Nb diffuses by an (0-0) mechanism, just as a pure metal diffuses in a f.c.c. lattice, wherein the atom migrates from its lattice position directly to an analogous vacant site. As this process involves the energies of both migration and Nb vacancy formation, the slower diffusion rates of this species, relative to that of C whose mechanisms of transport involve only the energy of migration, are thus explained.     

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: .     

Surface cyclotron resonance in Si under uniaxial stress

The cyclotron resonance of inversion-layer electrons on (100)p-type Si is found to depend sensitively on an externally applied compressive stress. At low temperatures (T ? 10 K) we observe a considerable increase of the cyclotron mass m¹_c with stress S along the [001] direction. The effect is most strongly observed at low electron densities n_s. For $\text{S～1.5 × 10}{}^9\text{dyne}\text{cm}{}^2$ and n_s～2 × 10¹¹cm^-2 we obtain $\text{m}{}^1{}_{\mathrm{c}}\text{～0.4 m}{}_0$ instead of the expected 0.2m₀. Along with this change of $\text{m}{}^1{}_{\mathrm{c}}$ a strong narrowing of the resonance is noted. Raising the temperature gives an additional n_s- dependent increase of $\text{m}{}^1{}_{\mathrm{c}}$.     

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).     

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

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

.