Debye Temperature and Quantum Diffusion of Hydrogen in Body-Centered Cubic Metals

Abstract

Diffusion of deuterium in potassium is studied herein. Mass transfer is controlled predominantly by the mechanism of overbarrier atomic jumps at temperatures 120–260 K and by the tunneling mechanism at 90–120 K. These results together with literature data allowed us to determine conditions under which the quantum diffusion of hydrogen in metals can be observed, which is a fundamental problem. It is established that in metals with a body-centered cubic lattice tunneling can be observed only at temperatures below the Debye temperature θD solely for metals with θD < 350 K. Predictions are made for metals in which quantum diffusion of hydrogen can be experimentally registered. Metals for which such results cannot be obtained are specified as well. Among them are important engineering materials such as α-Fe, W, Mo, V, and Cr.

Interstitial diffusion of hydrogen in M7C3 (M=Cr,Mn,Fe)

“…Fe and Pd) below room temperature may require the employment of classical transition state theory with quantum corrections to capture the effects of H tunneling [37,38]. In the present work, we opted to ignore such quantum effects for three reasons: (i) Acceptable agreement between experimental and classically computed data for H diffusion in several metals has been previously reported in the literature [39], (ii) Cr 7 C 3 is characterized by a generally high Debye temperature -of the order of 730 K [40] -while H tunneling is expected primarily for systems with the Debye temperature below 350 K [41], and finally (iii) the quantum effects are either negligible in many systems, such as Ni [37], TiAl [42], VC, TiC, NbC, TaC [43], and Mo with additions of 3d, 4d, and 5d transition metals [44], or contribute up to 15% of the total binding energy [45], rendering them insensitive to the general trends in H diffusion.…”

Strong Increase of Tunneling Rate of Hydrogen in Indium in the Presence of Vacancies

“…Experiments were carried out using two modes of the accelerating technique of nuclear reactions and the technique of isochronous annealings. The D 1 values, i.e., for a high concentration of radiation defects, were determined by the online technique of nuclear reactions, NRAOL. ,, In this case, the D measurements are performed upon continuous irradiation of a specimen with deuterons, and in this mode, the concentration of defects increases with time, which makes it possible to obtain the D values for specimens containing radiation defects. The NRAOL technique is briefly described in Section ; earlier it was applied for measuring the coefficients of classical and quantum diffusion of deuterium in sodium, potassium, and indium. ,, …”

“…The D values were found when treating the dependences c ( x , t ) via solving the diffusion equations for the initial and boundary conditions realized in the experiments; for the NRAOL and NRA techniques, they are given in Sections and . The description of accelerating techniques is presented in more detail. ,, …”

“…The NRAOL technique is briefly described in Section 3.2; earlier it was applied for measuring the coefficients of classical and quantum diffusion of deuterium in sodium, potassium, and indium. 3,4,8 To obtain values of D 2 for specimens with a low or virtually zero concentration of radiation defects, a two-stage experimental scheme was employed. At the first step, the NRAOL technique was used at the temperature 77 K, which led to the formation of radiation defects in the indium specimens.…”

“…Diffusion in solids is governed by two mechanisms: tunneling and overbarrier jumps; yet, the data on classical diffusion predominate, whereas the quantum diffusion was investigated only for hydrogen isotopes at low temperatures. − As for the classical diffusion, one of the main scientific interests is focusing on the experiments related to the vacancy impact on the diffusion coefficients. Such experiments present information about the concentration and types of point defects in crystals and energy barriers for atomic migration in the crystal lattice.…”