The dynamic structure factor S(q, tv) of electrons in Li-metal single crystals for q~~ [100], q~~[ 110],and q~~[ 111]with 0.28 a.u. & q & 1.4 a.u. was measured with 1-eV resolution by using inelastic scattering of synchrotron x radiation from DORIS II (Doppel-Ring Speicheranlage). Mainly for q & q, (q, is the plasmon cutoff vector) the fine structure of S(q, co) exhibits a strong dependence on the direction of the momentum transfer q. This crystal-lattice-induced peak structure is connected with minima of the combined density of states as due to band gaps across Bragg planes and can be interpreted as zone-boundary collective states within the limits of a two-band approximation.Comparison of the experimental results with model calculations of S(q,co), going beyond the random-phase approximation (RPA) by means of local-field corrections and also taking into account momentum-dependent lifetime effects for the inhomogeneous case (including band-structure effects) led to the following conclusions: (1) Most of the fine structure of S(q,co) is induced by the interaction of electrons with the ion lattice. (2) The overall shape of the S(q, co) spectra, mainly their strong deviation from corresponding homogeneous RPA results, is dominated by the momentum dependence of the inverse lifetime of quasiparticles with a steep rise at momentum po which makes possible decay of quasiparticle states into a plasmon. (3) The influence of exchange and correlation on S(q, co) via a local-field correction factor is found to be appreciable.A second source of experimental evidence for the dynamical structure factor is inelastic x-ray scattering.Thus further difficulties on the experimental side of the problem with S(q, to} of simple metals arise from the limitations of conventional x-ray source experiments, which are connected both with low photon flux in the scattered beam and low-energy resolution of the x-ray measurements compared with electron-energy-loss experiments. Even when using high-power rotating-anode generators, both the energy resolution of inelastic x-ray scattering ex-1986 The American Physical Society 33 DYNAMIC STRUCTURE OF ELECTRONS IN Li METAL: periments performed so far and the signal-to-background ratio are limited by the requirement of using unmonochromatized characteristic x-ray lines with rather large natural width and contaminated by bremsstrahlung.On the other hand, the x-ray measurements are much less influenced by multiscattering events, so that the spectra can give dirmt evidence of the full shape of S(q,co). , is a fine structure with at least two peaks (double-peak structure), where one peak exhibits nearly no dispersion and the other one follows roughly the free-electron RPA peak. This "universal double peak structure, " which has been interpreted by Platzman and Eisenbergers as an indication of an incipient Wigner electron lattice, has prompted much theoretical
The d.c. conductivity of NaI has been measured in the intrinsic and extrinsic temperature regions. The formation energy Es for the Schottky defects and the energy Em+ for the cation vacancy migration have been determined. The Em+ value has been found to be slightly higher than that required for the motion of the 'bound' vacancy in the system NaI + Ca++. The formation energy Es obtained is smaller than that of NaF, NaCl, and NaBr as was expected.
The dynamic structure factor S(q, co) of electrons in Be metal was measured with 1-eV resolution by means of inelastic scattering of synchrotron x radiation both on single crystals for a large number of difFerent directions of q (among others, q~~g, oo, g"v, g,o"goo,) and on polycrystalline samples with 0.45 a.u. &q &1.69 a.u. The experimental results were compared with model calculations, which go beyond the random-phase approximation. The overall shape of experimental S(q, co) can be understood when taking into account appropriately both state-dependent quasiparticle lifetime and local-field corrections. The strongly q-orientation-dependent fine structure of S(q, e) can be interpreted as being due to excitation gaps, which are generated by transitions to final states on Bragg planes. This type of fine structure can be utilized to get information about the band structure in a very direct manner. There is every indication that also the less q-orientation-dependent fine structure found in experimental S{q,co) is induced by ion-electron interaction, although another origin (electron-electron interaction) cannot be ruled out completely.
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