Theory of incoherent hydrogen diffusion in metals

Kashlev, Yu. A.

doi:10.1016/0378-4371(84)90027-x

Cited by 3 publications

(7 citation statements)

References 16 publications

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“…A detailed analysis of the situation in the theory of hydrogen diffusion at the beginning of the 1990s, as well as of the contradictions related to the analogy between HA migration and polaron motion, is described in our literature survey contained in [23]. Taking these difficulties into account here, we do not use the concept of the conductivity of small-radius polarons but use Prigogine's and Bak's ideas [8].…”

Section: 3mentioning

confidence: 97%

“…Therefore, the rigid lattice model and hence the Condon approximation [4] cannot be used to writeJ 23 . If we use the HA transmission coefficient less than unity [5], then we obtain the simplest version…”

Section: Ha Over-barrier Hopping In Fcc Metalsmentioning

confidence: 99%

“…Calculating the total energy then reduces to minimizing functional (16) with the normalization condition for the wave function ϕ(R) taken into account. Because the test wave function must not have nodes, it is convenient to choose the hydrogen-like wave function of the 1S-state, namely, ϕ (1) = γ 3/2 π −1/2 e −γR , for this function.…”

Section: Ha Tunnel Transitions Due To Decay Of Bcc-lattice Local Defomentioning

confidence: 99%

“…Relation (24) then acquires the additional factor 1 + Ker(β 1 ∆E 1 /2, 2), where the second term gives a small correction to the first term. Second, according to the classification in [16], the under-barrier transitions of an HA with the RC given by (24) should be called "active" jumps. In this case, any transitions with the RC given by (19) can be called "passive" jumps.…”

Section: Thermally Active Tunnel Transitions In Bcc Metalsmentioning

confidence: 99%

“…We do not give this cumbersome expression here, but we note that the functional E λ [ψ (2) ] has a minimum to which the stationary excited state of subsystem {2} corresponds. Calculating ∆E 1 with the change in elastic deformation energy (15b) taken into account reduces to minimizing the difference of functionals of form (16): (2) ] − E λ [ψ (1) ] .…”

Section: Thermally Active Tunnel Transitions In Bcc Metalsmentioning

confidence: 99%

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Three Regimes of Diffusion Migration of Hydrogen Atoms in Metals

Kashlev

2005

Theor Math Phys

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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,

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Section: 3mentioning

confidence: 97%