We studied the vibrational modes of H-doped nanocrystalline Pd H͞Pd # 0.04͒ by neutron spectroscopy, using the small H content as a probe for a separate determination of the vibrations of Pd atoms at surfaces and/or grain boundaries. We find that these atoms are responsible for the additional low-frequency modes which are characteristic for nanocrystalline materials, and that their local vibrational density of states is essentially linear in frequency. The Pd atoms within grains do not noticeably contribute to the additional low-frequency modes. [S0031-9007 (98)06873-2] PACS numbers: 61.82.Rx, 61.72.Ji, 63.50. + xThe vibrational density of states (VDOS) of nanocrystalline (nano) materials shows, at low frequencies, an increase against coarse-grained material. This increase is established experimentally by neutron [1-5] and resonant nuclear-g-ray spectroscopy [6], as well as in theoretical calculations [7,8]. However, real atomistic understanding requires knowing whether the additional low-frequency modes in nanostructured materials reflect dominantly vibrations of atoms (i) within grains, (ii) at grain boundaries, or (iii) at surfaces. This question is not answered by the experimental and one of the theoretical [7] studies above since they do not differentiate between (identical) atoms at different local positions. Only a very recent theoretical calculation [8] shows that surface atoms cause in fact low-frequency modes.This paper reports on a neutron spectroscopy study on two H-doped nano-Pd samples ͑H͞Pd # 0.04͒, in which the small H content was a probe for a separate determination of the vibrations of Pd atoms at surfaces and/or grain boundaries. Our results show that these Pd atoms cause additional modes at low frequencies, with a local VDOS essentially linear in frequency, whereas the Pd atoms within grains do not noticeably contribute to these low-frequency modes.The vibrations of a given atom are described by the spectral density ͗u 2 ͑v, T ͒͘ of its temperature-dependent vibrational displacements or by its local VDOS f͑v͒ (T is the temperature and R0 f͑v͒ dv 1͒. The relation between ͗u 2 ͑v, T ͒͘ and f͑v͒ is [9] ͗u 2 ͑v, T ͒͘ f͑v͒ 3h coth͑hv͞2k B T ͒ 2Mv ,
We studied by neutron spectroscopy H tunnelling states in Nb below the superconducting transition temperature in both the superconducting and normal-conducting electronic state. Our results prove the direct (nonadiabatic) interaction between tunnelling states and conduction electrons. The electronic coupling parameter is derived independently of the damping (relaxation) of the tunnelling states and of the renormalization of the tunnelling matrix elements.
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