The delocalization of H over pairs or more extendend sets of tetrahedral sites in Nb, Ta and V has been the object of several experimental and theoretical investigations over more than 20 years, and still open questions remain. When H is trapped by an interstitial impurity (I = O, N, C), it delocalizes itself over pairs of sites and all the experimental observations fit well within the existing two-level system (TLS) model with non-adiabatic interaction with the conduction electrons. The case of trapping within the more symmetrical environment of a substitutional impurity (S = Ti, Zr) is compatible with H delocalization also over the four sites of a face of the cubic cell, or over a <111> ring of 6 sites. The S-H pair has been mainly studied by anelastic spectroscopy (dynamic elastic moduli, whose imaginary part is the elastic energy absorption), and only recently by neutron spectroscopy. The anelastic spectra of S-H exhibit a much more complex phenomenology than those of I-H, and a four-level system (FLS) model has been developed in order to explain the dependence of the intensities of the acoustic absorption peaks on the symmetry of the applied stress, on the H isotope mass and on the impurity concentration. However, most of these features are explained in terms of transitions between the 1st and 4th levels of the FLS, which correspond to those of a TLS; therefore, such results are also compatible with TLS with parameters close to those of the I-H pairs, and do not provide a conclusive evidence on the geometry of the tunnel system (TS). Also the neutron spectroscopy measurements from Ti-H pairs yield ambiguous results, and the analysis of the H excited states suggest a multilevel tunnel system, but do not distinguish between FLS or other geometries, like the 6 site ring. New acoustic spectroscopy measurements on single crystals and polycrystalline samples with Zr/Ti concentrations around 0.1% and H/D concentrations as low as 0.01% finally provide clear evidence of the delocalization of H in FLS. In fact, a major problem with all the previous experiments is that the elastic interactions between S impurities with concentrations as low as 0.4% are strong enough to destroy the symmetry of most of the sets of sites surrounding the S atoms. Instead, the new anelastic spectra at the lowest impurity contents contain additional peaks, around 6 K and 100 K at 40 kHz, which arise from the undistorted traps. The combined analysis of the peaks due to the H dynamics within the TS and those arising from the slower reorientation among different TS, unambiguously demonstrate that H delocalizes itself over a face of the cube containing the S atoms, and not over a ring of 6 sites. Both the new peak at ~6 K and another peak at ~1.5 K arise from transitions between eigenstates of the FLS, due to the scattering of the conduction electrons and the interaction with phonons. The peak at ~1.5 K is due to transitions between the 1st and 4th levels, whose energies depend quadratically on strain ? for ? ? 0, and in fact the peak has vanishing intensity for very symmetric TS. Instead, the intensity of the peak at 6 K is finite also in the limit of infinite impurity dilution, and therefore it involves the 2nd and 3rd levels, which depend linearly on strain. Even though the correct analysis of the dynamics of TLS formed by the I-H pairs requires a theoretical framework much more advanced than the simple Fermi Golden rule, it is shown that the latter simple minded approach can explain the features of the new peak at 6 K. In particular, the high temperature of the maximum indicates a much slower transition rate with respect to the 1-4 transitions of the 1.5 K peak. In addition, its narrow shape is incompatible with the temperature dependence expected from the prevalent interaction with the conduction electrons in the superconducting state, and instead indicates a law of the type ??? ~ T5. This is explainable in terms of the selection rules for the FLS, which prohibit first-order transitions for the 2nd and 3rd eigenstates, both for the interaction with phonons and for the scattering of the conduction electrons. The relaxation of such levels would occur at a much slower rate thanks to multi-phonon transitions.
Geometry and dynamics of four-site tunnel systems of H in substitutional Nb alloys at extremely low dilution
F Cordero;
2001
Abstract
The delocalization of H over pairs or more extendend sets of tetrahedral sites in Nb, Ta and V has been the object of several experimental and theoretical investigations over more than 20 years, and still open questions remain. When H is trapped by an interstitial impurity (I = O, N, C), it delocalizes itself over pairs of sites and all the experimental observations fit well within the existing two-level system (TLS) model with non-adiabatic interaction with the conduction electrons. The case of trapping within the more symmetrical environment of a substitutional impurity (S = Ti, Zr) is compatible with H delocalization also over the four sites of a face of the cubic cell, or over a <111> ring of 6 sites. The S-H pair has been mainly studied by anelastic spectroscopy (dynamic elastic moduli, whose imaginary part is the elastic energy absorption), and only recently by neutron spectroscopy. The anelastic spectra of S-H exhibit a much more complex phenomenology than those of I-H, and a four-level system (FLS) model has been developed in order to explain the dependence of the intensities of the acoustic absorption peaks on the symmetry of the applied stress, on the H isotope mass and on the impurity concentration. However, most of these features are explained in terms of transitions between the 1st and 4th levels of the FLS, which correspond to those of a TLS; therefore, such results are also compatible with TLS with parameters close to those of the I-H pairs, and do not provide a conclusive evidence on the geometry of the tunnel system (TS). Also the neutron spectroscopy measurements from Ti-H pairs yield ambiguous results, and the analysis of the H excited states suggest a multilevel tunnel system, but do not distinguish between FLS or other geometries, like the 6 site ring. New acoustic spectroscopy measurements on single crystals and polycrystalline samples with Zr/Ti concentrations around 0.1% and H/D concentrations as low as 0.01% finally provide clear evidence of the delocalization of H in FLS. In fact, a major problem with all the previous experiments is that the elastic interactions between S impurities with concentrations as low as 0.4% are strong enough to destroy the symmetry of most of the sets of sites surrounding the S atoms. Instead, the new anelastic spectra at the lowest impurity contents contain additional peaks, around 6 K and 100 K at 40 kHz, which arise from the undistorted traps. The combined analysis of the peaks due to the H dynamics within the TS and those arising from the slower reorientation among different TS, unambiguously demonstrate that H delocalizes itself over a face of the cube containing the S atoms, and not over a ring of 6 sites. Both the new peak at ~6 K and another peak at ~1.5 K arise from transitions between eigenstates of the FLS, due to the scattering of the conduction electrons and the interaction with phonons. The peak at ~1.5 K is due to transitions between the 1st and 4th levels, whose energies depend quadratically on strain ? for ? ? 0, and in fact the peak has vanishing intensity for very symmetric TS. Instead, the intensity of the peak at 6 K is finite also in the limit of infinite impurity dilution, and therefore it involves the 2nd and 3rd levels, which depend linearly on strain. Even though the correct analysis of the dynamics of TLS formed by the I-H pairs requires a theoretical framework much more advanced than the simple Fermi Golden rule, it is shown that the latter simple minded approach can explain the features of the new peak at 6 K. In particular, the high temperature of the maximum indicates a much slower transition rate with respect to the 1-4 transitions of the 1.5 K peak. In addition, its narrow shape is incompatible with the temperature dependence expected from the prevalent interaction with the conduction electrons in the superconducting state, and instead indicates a law of the type ??? ~ T5. This is explainable in terms of the selection rules for the FLS, which prohibit first-order transitions for the 2nd and 3rd eigenstates, both for the interaction with phonons and for the scattering of the conduction electrons. The relaxation of such levels would occur at a much slower rate thanks to multi-phonon transitions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
