Nonequilibrium statistical thermodynamics of channeled particles: Thermal particles

Kashlev, Yu. A.; Sadykov, N. M.

doi:10.1007/bf02557149

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…A direct jump from the O-position at the cube center to the O-position at the midpoint of an edge cannot be realized, because it is necessary to overcome a much greater potential barrier in this case. We substitute η 1 (ζ) from (8a) in (9). Moreover, we replace the matrix element of the transition {2} → {3} in (9) with the matrix elementJ 23 of the over-barrier hopping.…”

Section: Ha Over-barrier Hopping In Fcc Metalsmentioning

confidence: 99%

“…In the case ξ 1, we can assume that α(ρ) 1 and hence r s. Second, in the semiclassical approximation, ω s and r can be replaced with the continuous variables ε and r = β 1 ε. To ensure rapid convergence of the series in s in expression (1), we use the change of variables successfully applied in [8] and [9]. Namely, we replace s with the discrete variable η r , which is a root of the transcendental equation and whose explicit form is given below.…”

Section: Rate Constant For the Escape Of Light Particles From The Potmentioning

confidence: 99%

“…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] …”

Section: Rate Constant For the Escape Of Light Particles From The Potmentioning

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: Ha Over-barrier Hopping In Fcc Metalsmentioning

confidence: 99%

Section: Rate Constant For the Escape Of Light Particles From The Potmentioning

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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“…In turn, the CP distribution p(E ⊥ ) is also a non-Maxwellian function truncated, as shown in Fig. 1a, in the range of large transverse energies, i.e., at E ⊥ = ω s0 = ω h s 0 [20]. If p(E ⊥ ) andp(E s ) are compared, then it is obvious that the shapes of the CP and NS energy distributions coincide completely.…”

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confidence: 94%

Balance equation and the quasitemperature of channeled particles in equilibrium

Kashlev

2009

Theor Math Phys

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Using the methods of nonequilibrium statistical thermodynamics, we obtain the equation for the transverse energy and momentum balance for fast atomic particles moving in the planar channeling regime. Based on the solution of this equation, we obtain an expression for the transverse quasitemperature in the quasiequilibrium in terms of the basic parameters of the theory. We show that the equilibrium quasitemperature of channeled particles is established because of particle diffusion in the space of transverse energies (subsystem "heating"), the dissipative process ("cooling"), and the anharmonic effects of particle oscillations between the channel walls (the redistribution of energies over the oscillatory degrees of freedom is the internal thermalization of the subsystem). According to the estimates for particles with an energy of the order of 1 MeV, the quasitemperature values are in the characteristic temperature range for a low-temperature plasma.1. The concept of quasitemperature as the modulus of the equilibrium distribution of an isolated subsystem of particles (quasiparticles, spins) is successfully used in the case of systems far from complete thermodynamic equilibrium. We list several characteristic examples of the application of this concept:• quasitemperature in the presence of interactions between particles (quasiparticles, spins);• quasitemperature in the case of weak interactions between some (translational, internal) degrees of freedom when the corresponding relaxation processes are independent;• quasitemperature in the presence of interactions of particles with a heat bath and of an additional energy exchange between the internal degrees of freedom of the subsystem.The first case is typical for the subsystem of nuclear spins isolated from the lattice when spins pass to the internal quasiequilibrium because of the spin-spin interaction. In this case, the probability that the subsystem is in a given energy state is described by the Boltzmann distribution [1]. The second case is realized in a plasma [2], [3] when the modulus of the distribution over all degrees of freedom except the translational one is the effective electron temperature. More precisely, the distribution of heavy particles (ions, neutral particles) over the translational degrees of freedom is determined by the temperature of the heavy plasma component, while the modulus of the distribution over all the other degrees of freedom is the electron temperature. The third case is directly related to "hot" atoms moving in crystalline solids, including high-energy channeled particles (CPs) [4], [5]. The planar channeling effect can be considered from the standpoint of nonequilibrium statistical thermodynamics because the CPs constitute an independent thermodynamic subsystem.

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Kashlev

2002

Theoretical and Mathematical Physics

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Nonequilibrium statistical thermodynamics of channeled particles: Thermal particles

Cited by 4 publications

References 14 publications

Three Regimes of Diffusion Migration of Hydrogen Atoms in Metals

Three Regimes of Diffusion Migration of Hydrogen Atoms in Metals

Balance equation and the quasitemperature of channeled particles in equilibrium

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