Low temperature tunnelling and quantum diffusion of hydrogen Nb(NH)x

Excited-state vibrational tunnel splitting of hydrogen trapped by nitrogen in niobium

“…Moreover, the resulting ground-state splitting of 0.22 meV is in good agreement with the experimental peak energy of ≈ 0.18 meV observed for the more dilute Nb(NH) 0.0005 trap system [21]. It should be noted that our simple model does not consider the effects of concentration-dependent strains on the observed tunnelling levels [18,21], but these effects are expected to be relatively small and will have little impact on the excited-state tunnel splitting. Further, despite the success of our relatively simple one-dimensional model in reproducing the key features of this tunnelling system, we stress that our potential is only meant to represent the dominant one-dimensional effects of the actual three-dimensional H potential.…”

“…The barrier height for this potential is approximately 330 meV, which also is a reasonable value. Moreover, the resulting ground-state splitting of 0.22 meV is in good agreement with the experimental peak energy of ≈ 0.18 meV observed for the more dilute Nb(NH) 0.0005 trap system [21]. It should be noted that our simple model does not consider the effects of concentration-dependent strains on the observed tunnelling levels [18,21], but these effects are expected to be relatively small and will have little impact on the excited-state tunnel splitting.…”

“…Hydrogen trapped by interstitial oxygen impurities in NbO x H y (y ≈ x) has been widely studied by specific heat [7][8][9] (and ultrasonic or anelastic measurements [10][11][12][13][14][15]), which provided the first evidence of quantised H motions at very low temperatures. Subsequently, direct measurement of ground-state tunnelling transitions of ∼ 0.1-0.2 meV for H trapped by O [16][17][18][19][20], N [21], and C interstitial impurities [22] as well as Ti substitutional impurities [23] has been achieved by cold-neutron spectroscopy. These results and related local diffusion studies at higher temperatures have been associated with non-adiabatic coupling of hydrogen to the conduction electrons (Kondo effect) [5,6,18,20].…”

“…The width and shape of this distribution is dependent on the dopant concentration. Decreasing this concentration is known to narrow the energy-shift distribution function, as evidenced by the sharpening of ground-state tunnelling peaks [18,21].…”

Real-time detection of hydrogen absorption and desorption in metallic palladium using vibrating wire method

“…[1][2][3] It is difficult to reach a full understanding of H absorption and diffusion because of the remarkable quantum mechanical properties of H, [4][5][6][7][8][9] which arise because it is the lightest of all atoms. H diffusion in metals due to quantum tunneling (QT), which is one of the most fundamental concepts in quantum mechanics, has been studied in a variety of experiments [10][11][12][13] such as quasi-elastic neutron scattering [14][15][16] and nuclear magnetic resonance. 17,18) Most studies on QT of H discuss the temperature dependence of the reaction rate or the relaxation time for samples hydrogenating at high temperatures.…”