Diffusion controlled growth of hydrogen clusters in metals

We show that a simple diffusion controlled growth, with subsequent aggregation, mean field theory accounts numerically for the growth of hydrogen clusters in certain metals (e.g. V, Nb, Zr, etc.). We also calculate the percolation threshold for the formation of an “infinite” aggregate both analytically and by a Monte Carlo simulation in a cubic lattice. The results are comparable and seem to correspond to the observed physical behavior.     

Diffusion hall effect in compensated metals

Analytical investigation is made of the electron-hole diffusion in compensated media like semimetals, which takes place under crossed electric and magnetic fields. It is shown that the diffusion of carriers causes a transverse field effect different to the usual Hall one, if the conducting medium is bounded. The transverse voltage due to this effect increases almost linearly with the magnetic field (H), and changes its sign according to the polarity of H. This voltage is observable even for bulk specimens for which the usual size effect is negligible, but its appearance is easily masked in the presence of impurities. A detailed discussion is made for bismuth, considering a non-parabolic model for the electron Fermi surface. The transverse voltage is found to be very sensitive to the surface recombination velocity of the carriers as well as to the impurity concentration.     

Diffusion of hydrogen in heterogeneous systems

The effective long-range long-time tracer diffusivity D_eff for interstitial diffusion of hydrogen through heterogeneous systems was studied theoretically for model systems consisting of isolated grains of material G embedded in a matrix of material M. Different solubilities of hydrogen in these two materials as well as different diffusivities are allowed for. Additionally, modified diffusion barriers at the phase boundaries were included in the diffusion model. The effect of different sizes, arrangements, and forms of the grains was also considered. D_eff was determined by Monte Carlo (MC) simulations on simple lattice models of the systems described above. An equilibrium distribution of hydrogen atoms among the two constituent materials was assumed. Our main interest was focused on whether and how D_eff may be related to mesoscopic or macroscopic quantities characterizing the heterogeneous system and its constituent materials, such as the volume fractions of the two materials, the fraction of lattice sites in the immediate vicinity of the phase boundary, the hydrogen concentrations c_G and c_M in the grains and in the matrix and the respective hydrogen diffusivities D_G(c_G) and D_M(c_M). In order to obtain good estimates for these relations in terms of analytic formulas, we attempted to model a heterogeneous system by a network of diffusion elements connected in series and in parallel, in analogy to an electric network. The properties of the basic connections, in parallel and in series, were studied on layered structures, for which analytic expressions for D_eff could be derived. The network formulas for different grain–matrix systems were tested by comparing with results of MC simulations. In general, the network formulas describe the corresponding MC results for D_eff fairly well. It was found that differences in the hydrogen solubilities in the two phases as well as modified energy barriers at the phase boundaries may have dramatic effects on D_eff. Received: 19 September 2000 / Accepted: 6 November 2000 / Published online: 9 February 2001     

Diffusion and collective motions in liquid metals

Collective oscillations in thermal equilibrium are shown to represent only a small fraction of the degrees of freedom of a liquid metal, the important fraction being associated to uncorrelated motions of the atoms. The present paper, however, justifies the basic interest for these oscillations in the theory of diffusion. In fact, they can be explained in the framework of a collective coordinate formulation, where the relevant Fourier components of the pair potential are only those corresponding to the wavevectors of the collective modes. Since the matrix elements for atomic scattering processes are proportional to the Fourier coefficients, it follows that, in this formulation, the only important processes are collisions where the wavevector change of an atom is a wavevector of the collective modes. A reduction in the number of these modes, as produced by a temperature rise, implies a reduction in the scattering processes and, subsequently, of the resistance presented by the liquid to the motion of a diffusing atom. This explains the strong rise with temperature of the self-diffusion coefficient, as recently observed in liquid lithium. Perturbation theory can be used to account for those Fourier components, which have been neglected in the above formulation. In this case, the results are fully consistent with the theory of diffusion developed earlier [M. Omini, Phil. Mag. 86 1643 (2006)].     

Diffusion of muonium and hydrogen in diamond

Jump rates of muonium and hydrogen in diamond are calculated by quantum transition-state theory, based on the path-integral centroid formalism. This technique allows us to study the influence of vibrational mode quantization on the effective free-energy barriers DeltaF for impurity diffusion, which are renormalized with respect to the zero-temperature classical calculation. For the transition from a tetrahedral (T) site to a bond-center (BC) position, DeltaF is larger for hydrogen than for muonium, and the opposite happens for the transition BC-->T. The calculated effective barriers decrease for rising temperature, except for the muonium transition from T to BC sites. The calculated jump rates are in good agreement with available muon spin rotation data.     

Theory of incoherent hydrogen diffusion in metals

Hydrogen migration in a one-dimensional model of the bcc lattice is examined using the double-time Green functions, for temperatures at which the migration mechanism is mainly due to the thermally activated tunnelling of a proton. In deriving the coefficient of incoherent hydrogen diffusion, allowance is made for the lattice distortion around the hydrogen and for the two-phonon scattering processes. It is shown that the observed temperature break in the activation energy of incoherent hydrogen diffusion in bcc metals is the result of the change in the mechanism responsible for an elementary diffusion process near the Debye temperature, anmely, it is the result of the transition from “passive” to “active” transport.     

Diffusion of hydrogen into V-Mo-Zr alloys

The diffusion coefficient of hydrogen into two alloys of the V-Mo-Zr system is measured using technique based on the static Gorskii effect during bending. The diffusion activation energy U and the preexponential factor D₀ in Arrhenius's relation are determined from the temperature dependence of the diffusion coefficient. Unusually high values of U and D₀ are found for the alloys compared with pure vanadium, due to doping with zirconium, although the value of the diffusion coefficient does not change very much. An explanation of this result is proposed based on the assumption that traps exist in the alloys which have a high coupling energy with the hydrogen atoms.V. D. Kuznetsov Siberian Institute of Applied Physics, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 100–106, May, 1993.     

Diffusion constant and surface states of positrons in metals

Positron lifetime spectra and angular correlation curves for seven fine-grained powders of Fe, Co, Ni, and W are analyzed. From the lifetime data, the positron diffusion constant in metals atT=300°K was found to beD ₊=(1.0±0.5)×10^?2 cm² sec^?1. Evidence is presented that positrons are trapped in metal surface states.     

Diffusion behavior of transition metals in field-assisted ion-exchanged glasses

The use of ion-exchange techniques for doping silicate glasses with transition metals has attracted much attention in the last decades for its potential in several applications, namely, light waveguides technology, luminescent materials, and for the possibility to realize systems in which metal nanocluster formation is controlled by suitable post-exchange techniques. In this framework, the control of metal distribution inside the glass is a central issue for both the understanding of the incorporation process and for the definition of effective preparation protocols. In this experiment, metallic films (Ag, Cu, Au, Co) were deposited onto the substrates by the rf-sputtering technique. Metal ions then penetrate to substitute glass alkali by means of field-assisted ion-exchange, realized at different temperature and electric field values. In particular, we present in this paper the Au doping of silicate glasses, successfully realized for the first time with this method. The gold diffusion profiles, as measured by Secondary Ion Mass Spectrometry (SIMS), indicate that the migration depends on the experimental parameters (temperature and electric field), but also on the local structure, as well as on chemical phenomena occurring at the metal/glass interface.     

Trends in hydrogen chemisorption on transition metals

A systematic study of H adsorption on the close-packed surfaces of the transition metals in the 3d and 4d series is presented. The effect of the TM d band on the chemisorption bond is investigated, by embedding a cluster of TM muffin tins at the surface of an effective jellium-like medium. It is found that the broad and incomplete H/jellium resonance is narrowed, shifted down and made to contain more electrons as a result of hybridization with the TM d states. These effects are larger in the case of the 4d metals, thus indicating a greater participation in the chemisorption bond of the d electrons for these metals than for the 3d metals. Calculation of one-electron energy differences on going from the H on jellium system to that of H on the TM cluster are presented. Trends for the one-electron energy differences are compared to trends in experimental chemisorption energy. H adsorption in the three-fold hollow site with no secondlayer TM atom below the H site is favoured for the hcp metals, while no discernible preference between the two hollow sites is recorded for the fcc metals, with the exception of Rh where the site with no second-layer TM atom below is preferred.     

Diffusion and solubility of some interstitial impurities in deformed metals

Summary The problem of impurity diffusion accompanying segregation phase nucleation on dislocations has been studied using the approximation of the local equilibrium with respect to the impurity distribution between the volume solution and dislocation regions. It has been shown that the known experimental data on diffusion and solubility of some interstitial impurities in cold-worked b.c.c. and f.c.c. metals and alloys can be described in the framework of the dislocation trap model. The characteristics of the impurity segregation regions near dislocations have been obtained from the treatment of the diffusion and solubility data for the systems. On the basis of the crystallographic and thermodynamic considerations the possibility of the existence of such segregation phase regions along dislocations in the systems in question has been shown.     

Diffusion of positive muons and other light particles in metals

The paper gives a survey of the principal techniques available for the experimental determination of the diffusivityD ⁺(T) of positive muons in crystals (Gurevich technique, trapping, longitudinal muon-spin relaxation, transverse muon-spin relaxation in superconductors) and discusses their strengths and weaknesses. The main theoretical ideas of the quantum theory of diffusion are outlined and the distinction between different mechanisms is emphasized. It is argued that at high temperaturesT the so-called adiabatic regime with a preexponential factor of the diffusivity of the order of magnitude _D d ² ( _D = Debye frequency of the host crystal,d=jump distance of the muons) always exists. In the fcc metals and in the case of¹H in Nb it is followed by a so-called Flynn-Stoneham regime at intermediate temperatures, whereas for ⁺ in Nb and-Fe such a regime is not observed. Instead, in these cases the adiabatic regime appears to go over directly to the few-phonon regime of incoherent tunnelling between adjacent ground states, leading to the one-phononD ⁺ ~T law at low temperatures.The metal best-studied with regard to muon diffusion,-Fe, is used to illustrate the theoretical analysis of experimental results in some detail. In an Appendix the theoretical expressions required for the quantitative determination ofD ⁺ by the Gurevich technique are collected.