Influence of hydrogen on electron-phonon coupling and intrinsic electrical resistivity in zirconium: A first-principles study

Abstract

This paper presents the first-principles calculation of the electron-phonon coupling and the temperature dependence of the intrinsic electrical resistivity of the zirconium-hydrogen system with various hydrogen concentrations. The nature of the anomalous decrease in the electrical resistivity of the Zr-H system with the increase of hydrogen concentration (at high concentrations of H/Zr>1.5) is studied. It was found that the hydrogen concentration, where the resistivity starts to decrease, is very close to the critical concentration of the δ-ε phase transition. It is shown that the tetragonal lattice distortion due to the δ-ε phase transition of the Zr-H system eliminates imaginary phonon frequencies and the strong electron-phonon coupling of the δ phase and, as a result, leads to the reduction of the electrical resistivity of the Zr-H system at a high hydrogen concentration.

Modified Ziman Resistivity Formula Valid for the Case of the Fermi Level Near a Band Edge

“…It indicates the relevance of the large-angle scattering during the electronic transport process. In previous literature, − such a factor often takes an alternative form as Q ( mk + q , nk ) = [ 1 − v mk + q · v nk | v nk | 2 ] by which the anisotropy of electronic transport is partially ignored in the ZRF. Further, if we assume that the Fermi surface is isotropic, then the modes of the velocities in the initial and final states are the same; only in this situation can eq be obtained from eq , or they are equivalent.…”

“…However, for many actual materials with relatively complicated crystal structures, such a numerical solution is much expensive. As a parallel approach to the iteration solution of the BTE, the so-called Ziman resistivity formula (ZRF) was often employed to study the intrinsic resistivity of metallic materials in previous literature. − Such a formula was originally developed by Ziman by means of variational solution of the BTE; then, it was generalized to the case of complicated Fermi surfaces by Allen. , Consequently, the ZRF is suitable for the first-principles study on the intrinsic resistivity of realistic materials. Unlike the iteration solution of the BTE, the ZRF gives an explicit expression of the intrinsic resistivity in terms of the e-ph coupling spectral function.…”

“…What is more, in most cases the latter requires less computational cost than the former. However, it should be noticed that starting from the BTE, some additional approximations are exerted to reach the final form of the ZRF, which often went unrecognized when it was adopted for numerical calculations in recent works. − ,, In such a context, there is a need to test the validity of the ZRF before employing it to perform numerical calculations on any actual materials.…”

First-principles calculations on the intrinsic resistivity of realistic metals: a case study of monolayer V2N

“…The Ziman resistivity formula derived from a variation of BTE in the presence of e-ph scattering was proposed by Ziman, 2 followed by Allen's generalization to more realistic cases, including the complicated Fermi surface formed by multiple bands. [3][4][5] Thus far, the Ziman formula has been widely employed to assess the intrinsic resistivity of realistic metals on the level of first-principles calculations, [6][7][8][9][10] but still has not provided convincing proof of validity. Solving the BTE with the aid of a numerical iteration method has only been realized in recent years, [11][12][13] and is currently the most accurate numerical approach.…”