Theory of excitation bands of hydrogen in bcc metals and of their observation by neutron scattering

Abstract

I consider the possibility that the excited-state oscillator wave functions of dilute hydrogen in bcc metals overlap sufficiently with nearest-neighbor occupancy sites so as to produce hydrogenic energy bands, analogous to electronic energy bands in narrow-band semiconductors. The theory is motivated by the experiments of Magerl et al. as well as the earlier observation of ground-state tunnel splitting by Wipf et al., demonstrating quantum coherence in the motion of the hydrogen, despite the necessity of correlated motion by the surrounding metal atoms. Because of the latter complication, the relevant overlap integrals are not calculated from first principles. The band structures are given for the first (nondegenerate) and second (doubly degenerate) excitations ${\omega }_{\mathrm{I}}$ and ${\omega }_{\mathrm{II}}$ of the local oscillators, modulo a few irreducible overlap integrals, which are then determined by comparison with experiment. The fact that the experimental bandwidths for inelastic neutron scattering from dilute hydrogen in V, Nb, and Ta satisfy $\Gamma \left(\mathrm{V}\right)>\mathrm{}\Gamma \left(\mathrm{Nb}\right)>\mathrm{}\Gamma \left(\mathrm{Ta}\right)$ at room temperature (Rush, Magerl, and Rowe) finds a natural explanation in the theory. It is shown that the ${\omega }_{\mathrm{I}}$ and ${\omega }_{\mathrm{II}}$ bandwidths satisfy $\frac{\Delta E_{\mathrm{II}}}{\Delta E_{\mathrm{I}}}=\left(\frac{H_{\mathrm{II}}}{H_{\mathrm{I}}}\right)\Upsilon$, where $H_{\mathrm{I}}$ and $H_{\mathrm{II}}$ are irreducible overlap integrals and $\Upsilon$ is an (almost) universal constant for H in bcc metals, determined (essentially) by the geometry of the tetrahedrally coordinated hydrogen occupancy sites. On the basis of the band structure that I obtain, I estimate that $\Upsilon \simeq \frac{3}{4}$. Based upon physical reasoning, the relation $\left(\frac{H_{\mathrm{II}}}{H_{\mathrm{I}}}\right)={\left(\frac{{\omega }_{\mathrm{II}}}{{\omega }_{\mathrm{I}}}\right)}^2$ is proposed. Given the (model-consistent) empirical result, $\frac{{\omega }_{\mathrm{II}}}{{\omega }_{\mathrm{I}}}\simeq 2^{\frac{1}{2}}$, this leads to the prediction $\frac{\Delta E_{\mathrm{II}}}{\Delta E_{\mathrm{I}}}\simeq \frac{3}{2}$, to be compared with the neutron-measured ratios $\frac{{\Gamma }_{\mathrm{II}}}{{\Gamma }_{\mathrm{I}}}=1.3\mathrm{} \mathrm{and} 2.0$ for dilute hydrogen trapped at O and N impurities in Nb metal at $T=4\mathrm{} \mathrm{and} 10$ K, respectively. The variation in

Keywords

• MSUB
• NEUTRON
• OCCUPANCY SITES
• BAND STRUCTURES
• BCC METALS
• IRREDUCIBLE OVERLAP INTEGRALS

This publication has 4 references indexed in Scilit:

• Local hydrogen vibrations in Nb in the presence of interstitial (N,O) and substitutional (V) impurities
  Physical Review B, 1983
• DETECTION OF IMPURITY TUNNELING IN SOLIDS VIA COHERENT PHONON COUPLING AND DIRECT NEUTRON SCATTERING
  Le Journal de Physique Colloques, 1981
• Theory of neutron scattering from hydrogen in metals involving transitions to excited tunnel-split states
  Physical Review B, 1981
• Neutron-Spectroscopic Evidence for Hydrogen Tunneling States in Niobium
  Physical Review Letters, 1981

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