The classical diffusion theory cannot explain the temperature kink of the activation energy and the anomalous isotopic effect observed in the hydrogen atom migration in BCC metals. We present a theory based on the equations of quantum statistical mechanics that permits interpreting both these phenomena completely. We consider three possible mechanisms for an elementary act of hydrogen diffusion in metals: the over-barrier hopping, the thermally activated tunnel transition, and the tunneling due to decay of a local deformation near the hydrogen atom.
Rate constant for the escape of light particles from the potential minimumMost of the quantum theories of hydrogen diffusion in metals [1]-[5] are based on the concept of the hopping conductivity of small-radius polarons [6]. The essential drawbacks of the polaron theory concerning hydrogen atom (HA) diffusion problems have been discussed in numerous papers, including [7]. Our goal here is to present a completely different approach to this problem, an approach sufficiently close to the basic concept of chemical kinetics [8].We consider the diffusion migration of light impurities in the one-dimensional crystal model. For the model potential, we use the potential of a symmetric well with two cells such that the distance between their minimums is d. The total system in this model can be divided into three subsystems: a thermostat including the lattice and electrons {1}, a light particle in the left-hand potential well {2}, and a light particle in the right-hand potential well {3}. The localized states of light particles at the interstitial sites of the crystal correspond to the equilibrium distribution in the configuration space. Such particles migrate jumplike because the lifetime of a particle at the temperature β −1 1 ∼ 10 3 K is 10 −8 to 10 −9 sec in order of magnitude, while the time of motion through the potential barrier is 10 −13 sec. It is clear that the total system under these conditions is sufficiently close to thermodynamic equilibrium. In the case of a weak particle-thermostat interaction, the general expression for the rate constant (RC) for the escape of particles from the potential minimum can be written as [9]We use the system of units where = k B = 1. Here, Ω is the eigenfrequency of particle oscillation in the well (subsystem {2} or {3}), ω s = Ωs is an energy level in the harmonic well, γ s = ω s /Ωτ 1 is the decay,
Planar channeled particles (protons, helium ions, etc.) are considered as an individual thermodynamic subsystem. A statistical operator for the nonequilibrium system under conditions of multiple electron scattering and an energy-momentum balance equation are obtained on the basis of the nonequilibrium statistical thermodynamics. The formalism presented is applied to analyze the transverse quasitemperature of the channeled particle subsystem in steady state, its quasiequilibrium energy distribution, and the diffusion coefficient of the particles.Les particules mouvant dans le regime canale (protons, helium ions etc.), sont consideres comme un subsysteme thermodynamique individuel. L'operateur statistique et Equation de balance de I'energie-impulsion de dispersion electronique multiple est deduit sur la base de la thermodynamique statistique nonequilibre. Le formalisme presente est employ6 dans l'analyse de la quasitemperature transversale de subsystkme des particules en etat stationnaire et dans l'analyse de sa distribution energetique quasiequilibre et du coefficient de diffusion des particules.
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