Three Regimes of Diffusion Migration of Hydrogen Atoms in Metals

Abstract

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,

In-situ nuclear reaction analysis

“…Существуют всего два механизма миграции атомов в твердых телах: надбарьерные прыжки атомов (классический механизм) и туннелирование (квантовый). Почти все опытные данные по диффузии относятся к классическому механизму миграции, однако в случае атомов легких элементов большой практический и теоретический интерес представляют диффузионные данные для квантового механизма миграции [14][15][16][17]. Они актуальны для теорий диффузии, квантовой химии, низкотемпературных технологий и астрофизики, прежде всего для водорода в связи с его участием во многих природных и технологических процессах.…”

“…Метод NRA предполагает облучение образцов на ускорителе и регистрацию продуктов ядерных реакций, протекающих во время облучения, между ускоренными частицами и содержащимися в образцах атомами легких элементов. Примерами таких реакций являются 18 О(p,) 15 N и 16 O(d,p 1 ) 17 . Oни иллюстрируют изотопную чувствительность методики.…”

Quantum Diffusion of Deuterium in Sodium

“…Quantum tunneling governs the rate of chemical and biological reactions at cryogenic temperatures. Particularly, diffusion of hydrogen on metal surfaces − and in metals − was a subject of many experimental and theoretical studies. The results of those studies are important for the development of quantum theories of diffusion, surface chemistry and physics, catalysis, astrophysics, and various low-temperature technologies.…”

Molecular dynamics simulation of hydrogen atom diffusion in crystal lattice of fcc metals

“…It is well known that the distinguishing features of hydrogen diffusion in metals, compared to other heavier interstitial atoms, in addition to exceptionally low activation energy, is the quantum nature of diffusion at low temperatures which is manifested in pure crystals up to room temperature [2,5,8]. For instance, at superlow temperatures a predominantly quantum diffusion mechanism is possible, which consists of under-barrier quantum tunneling of hydrogen atoms between the neighboring interstitial sites.…”

“…With increased temperature and imperfections of the crystal lattice, the contribution from the under-barrier diffusion is sharply decreased and the classical over-barrier mechanisms are predominantly realized. At temperatures above the room temperature, hydrogen diffusion occurs via overbarrier mechanisms [2,5,8]. This allows us to investigate diffusion of light interstitial atoms by classical molecular dynamics at comparatively high temperatures.…”