Self-trapping of positively charged particles in metals

It is shown that the existence of a metastable state in which positrons in metals are “self-trapped” by strong interaction with the lattice gives rise to an anomalous temperature dependence in positron annihilation properties. The “intermediate” temperature variation of the shape of the annihilation photon line discovered by MacKenzieet al. is well accounted for by this mechanism; alternative interpretations in terms of thermal expansion effects may be refuted. This result calls for considerable revision of some of the published monovacancy formation energies obtained from positron annihilation measurements. Approximate criteria for the existence and the metastability of a selftrapped state of positively charged particles in metals are given. It is found that metastable self-trapping may occur for positrons; hydrogen isotopes and positive muons should be self-trapped in configurations that are always stable relative to the Bloch-wave states of these particles.     

The effect of chain reactions on the diffusion of absorbates

A chain reaction mechanism is developed that can dramatically increase the predicted diffusion coefficient as a function of coverage for thermally activated submonolayer coverages of adsorbates weakly chemisorbed on surfaces. The key idea is that when a diffusing adatom encounters another adatom it will tend to forward scatter it (due to the channeling effect of the periodic potential of the substrate lattice) thus increasing the effective mean free path. The enhancement effect can be quite dramatic at large adsorbate coverages. The formalism is essentially that of a Markoffian random walk on a lattice which allows for “billiard ball” type collisions. A general formalism for calculating the chemical diffusion tensor for an unspecified lattice is developed. The diffusion tensor is then related to the effective diffusion coefficient measured by the field emission fluctuation method. The special case of the two-dimensional rhombic lattice with two adsorbate species is worked out and shown to agree qualitatively with theoretical predictions of the coverage dependence of the diffusion coefficient with the experimental data for hydrogen and deuterium on W(110)[1].     

Quantum theory of impurity migration in crystals

A quantum theory of impurity migration in crystals is proposed. The impurity state is taken in the form of a wave packet constructed out of its Bloch states in the host lattice. Its time evolution is studied including its interaction with the host lattice phonons. A correspondence is established between the classical diffusion equation and the time evolution of the probability density arising out of the impurity wave packet. The diffusion coefficient D_T and trapping rate γ_T are related to the imaginary part of the energy shift of the impurity caused by its interaction with phonons. The detailed calculations are carried out using second order perturbation theory for the energy shift. The Debye model for the host lattice and effective mass approximation for the impurity band are used. At low temperature D_T is found to be proportional to_T3/2, and at high temperature the Arrhenius formula of Vineyard is obtained. The estimated migration energy for μ⁺ migration in bcc metals agrees reasonably with the experimental values.     

Quantum theory of atom-surface scattering: Incommensurate and fluid adsorbates

The problem of atomic scattering from adsorbate-covered surfaces, treated earlier for the case of commensurate overlayers, is considered again in the eikonal approximation for incommensurate lattice phases and for fluid phases. Stochastic methods are employed and for a specific model (hard bosses on a plane) it is shown how the statistical and geometric problems can be separately solved. In order to explain the meaning of the coherent and incoherent scattering contributions a time-dependent theory is introduced and it is shown that the incoherent “elastic” scattering is in fact weakly inelastic and (for classical diffusion with diffusion coefficient D) has an energy width of the order ?DQ², where Q is the parallel momentum transfer. The problem of the decay of substrate diffraction intensities when the coverage of random impurities is increased is also discussed.     

Two-polaron energy diffusion in a 1D lattice of hydrogen bonded peptide units

A generalized Pauli master equation is established for describing the vibrational energy flow in a 1D lattice of hydrogen bounded peptide units. A Lang-Firsov transformation is applied so that the relevant excitations are small polarons corresponding to vibrational excitons dressed by virtual phonons. A special attention is thus paid to characterize the energy transfer mediated by two polarons. At biological temperature, it is shown that the polaron-phonon coupling is sufficiently strong to prevent any coherent motion. The polaron-polaron interaction occurring in such a nonlinear lattice does not affect the long time behavior of the energy flow which results from the diffusion of two independent polarons. This diffusive motion originates from the competition between two contributions related to phonon mediated transitions (incoherent contribution) and to dephasing limited coherent motion (coherent contribution).     

Polarization bremsstrahlung of heavy charged particles in a polycrystal

Polarization bremsstrahlung (PBS) of a fast ion scattered in a polycrystalline medium is calculated and analyzed with allowance for the contributions from the coherent and incoherent channels of the process. It is shown that scattering of a projectile from the crystal lattice of the target is responsible for typical features of the PBS spectrum. For example, PBS is suppressed (as compared to radiation emitted by a single atom) in the low-frequency part of the spectrum, where coherent PBS dominates. In the intermediate spectral region, a step structure is formed as a result of “elimination” of the contribution from the reciprocal lattice vector with a preset magnitude to the coherent component of the process. Finally, incoherent PBS dominates in the high-frequency part of the spectrum and the process occurs as in the case of a single atom. These spectral peculiarities of PBS are determined by the structure of the target and depend on the velocity of the projectile and the emission angle, and can be observed in experiments dealing with radiation emitted by fast charged particles in thin polycrystalline films.     

Lattice self-diffusion in plastic pivalic acid (acid 2.2 dimethyl propanoic)—III: Computer calculation of the correlation factor for various tracer self diffusion mechanisms. Discussion of these mechanisms

The correlation factors ? for lattice self-diffusion of tracers involving mono or divacancies have been calculated in “plastic” pivalic acid. The peculiarities of the crystalline structure have been taken into account. Dimers (molecules linked by 2 hydrogen bondings) induce short range order, but no long range order. The local order changes at the frequency ω_R with which hydrogen bondings break. ? has been obtained using the encounter model and the Monte Carlo method. It has been supposed that hydrogen bondings never break during an encounter. The calculation gives the upper limit of ? for ω_m = nω_R, where n ? 2 and ω_m is the frequency of migration of the defect. The asymptotic value of ? for n→∞ is also obtained. Two diffusion mechanisms for monovacancies as well as for divacancies have been considered. All these mechanisms are strongly correlated. In every case, dimers induce low values of ?. Other experimental data concerning point defects and diffusion in pivalic acid are discussed. Lattice self-diffusion should be due mainly to relaxed monovacancies migrating according to mechanism 1 (exchange of the monovacancy with one of the two molecules forming a dimer). This mechanism is characterised by 0.38 ? ? ? 0.57. Some contribution of divacancies, noticeable above 301K, is not incompatible with experimental data in the whole plastic range.     

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.     

The effect of substitutional impurity atoms on the diffusivity of an interstitial species

A model has been developed to treat the problem of the effect of substitutional solute elements on the diffusion of an interstitial species. The calculation applies only to cases where the substitutional solute creates “antitrapping” sites, whose energies are higher than the “normal” interstitial sites in the defect-free solvent lattice.The model predicts that, for sufficiently “high” antitrapping sites, there will be substantially no effect of composition or even solute atom type on the mobility of the interstitial species even up to about 20 atm% of substitutional solute.It is also possible for a given substitutional solute to act both as an accelerator or retarder with respect to the diffusivity of the interstitial species, depending upon temperature.     

Electrotransport in a coherent metal-hydrogen system

The growth and decay kinetics of macroscopic hydrogen density modes in single crystals of niobium excited by an applied electric field was measured. The samples were prepared in-situ as to prevent incoherent precipitations. At a low hydrogen concentration (c=0.04 H/Nb) the diffusion coefficient and the effective charge agree well with results from experiments using polycrystalline samples. At a high hydrogen concentration (c=0.28 H/Nb) the electrotransport experiments could be extended into the unstable region of the incoherent phase diagram. The spinodal temperature obtained from the concentration amplitude (350±12 K) is significantly lower than the incoherent spinodal temperature. Important difficulties in evaluating electrotransport experiments at high hydrogen concentrations are discussed.     

Reaction-diffusion processes in the “adsorbate-substrate” system

We obtain a chain of quantum kinetic reaction-diffusion-type equations for “adsorbate-substrate” system taking into account the coupling of a light particle with a metallic surface, the adsorbate surface diffusion by the tunnelling mechanism and the occurrence of bimolecular chemical reactions. We calculate the temperature dependence of the kinetic kernels related to the diffusion coefficients and the reaction rates. It is shown that one can alter the temperature dependence of the reaction rates by changing the “adsorbate-substrate” coupling. It is also shown that the mean field terms contribute to the activation energies of the reaction rates, while their contribution to the activation energies of the diffusion coefficients vanishes.     

Effect of anharmonic longitudinal and transverse vibrations with wave vector k = (2/3)(1, 1, 1) on the structural stability of β-Zr under pressure

The pressure and temperature dependences of the frequencies of a strongly anharmonic longitudinal and a transverse vibrational mode with wave vector k = (2/3)(1, 1, 1) in β-Zr are studied. The frequencies are calculated by solving a set of stochastic Langevin differential equations with a thermal bath of the white-noise type. In the calculations, a two-mode effective potential is used. This potential is found in the framework of the density-functional theory using the “frozen-phonon” model and assuming that the contribution from the electron entropy to the free energy is dependent on the atomic displacements. Based on the calculated pressure and temperature dependences of the spectral density of transverse vibrations, the region of stability of the bcc phase of zirconium is determined for pressures up to 35 GPa, and the result is in good agreement with the experimental data. The bcc lattice is found to be unstable with respect to atomic displacements characteristic of vibrations with wave vector k = (2/3)(1, 1, 1). This instability is of importance not only in the β → ω transition but also in the β → α transformation, which is observed to occur at pressures less than 5 GPa.     

The Haven ratio of Ag ion in α-AgI by Monte Carlo method

The temperature dependence of the Haven ratio of Ag ion in α-AgI is computed by a Monte Carlo method under the following assumptions: (1) Ag ions travel on the non-Bravais lattice points formed by 12(d) sites of bcc by I ions. (2) The pair interaction between two Ag ions consists of a Coulomb term. (3) A caterpillar mechanism is introduced in a proper way. It is confirmed that there exist the correlation in successive jump of ions in diffusion process even for a disordered crystal such as α-AgI. The Haven ratio derived from the present calculation is in good agreement with the experimental one.     

Hyperfine fields amd electronic structure of non-magnetic impurities in iron

Hyperfine fields of non-magnetic impurities in iron are calculated using the local-density formalism in an embedded cluster model. The hyperfine fields are seen to result from a delicate balance between negative exchange polarized “bound-paired” states and positive “unpaired-band” contributions. Pressure and temperature dependence and effects due to lattice relaxation are discussed.     

Lattice-assisted proton hopping in oxides at low temperatures

Stimulated diffusion of protons in oxides such as ABO₃ crystals and rutile TiO₂ is discussed in the context of quantum Brownian motion. A self-consistent lattice-assisted proton hopping (LAPH) model is developed by going from white noise (characteristic of the standard stochastic theory of superionic conduction) to colored noise in the Markovian limit. This model differs from the commonly used ion jump models in that the hydrogen diffusion rate prefactor is identified as a quantity proportional to the frequency of phonon assistance. Application of the quantum fluctuation–dissipation theorem suggests that the dynamic activation energy for diffusion is a function of a bath-mode frequency. The LAPH model can predict enhanced rates of barrier jumping at room temperature compared to thermally activated proton diffusion. This indicates that low-temperature solid oxide devices are potential candidates for use in hydrogen energy research. The LAPH model offers a valid explanation for the mechanism of high protonic mobility recently observed for TiO₂ in a picosecond transient pump-probe experiment. This unexpected dominant lattice relaxation channel must be considered as a new classical-like (but low-temperature) proton transfer mechanism. For vibration-assisted protonic jumps to occur at low temperature, the phonon assistance must be classified as a low-frequency vibration specific to each lattice.     

The thermodynamics of Pd-Au-H ternary solid solutions

The solubility of hydrogen in PdAuH ternary solutions in equilibrium with H gas at atmospheric pressure has been measured in the temperature range 625–1250 K and in Pd-Au “binary solvents” containing up to 80 At % of Au Concomitant elastic measurements have provided data which enable the partial thermodynamic functions of the H atoms deduced from the solubility measurements to be converted so as to refer to a hypothetical Pd-Au lattice of constant specific volume The resulting “volume corrected” functions have been discussed in terms of the cell model for ternary solutions and have been shown to vary with temperature and Au concentration in a manner in accord with this model.     

Ordering kinetics in bcc alloys with allowance for diffusion processes

The kinetics of inhomogeneous ordering in binary bcc substitution alloys of arbitrary stoichiometry is considered with the account for for diffusion processes. A system of kinetic equations describing the joint evolution of the occupancies of two sublattices of a bcc lattice is derived using a phenomenological approach. It is shown that, even within the mean-field approximation, this approach allows one to describe simultaneously the processes of establishment of the long-range order and diffusion of the alloy components. Numerical analysis of the obtained system of equations showed that quick onset of long-range order first occurs, which is followed by slow diffusion of the alloy components.