Lattice dynamics, measurement

Rose-Petruck C, Jimenez R, Guo T, Cavalleri A, Siders CW, Raksi E, Squier JA, Walker BC, Wilson KR, Barty CPJ (1999) Picosecond-milliangstrom lattice dynamics measured by ultrafast X-ray diffraction. Nature 398 310-312... 

Recently, we hav measured the surface phonon dispersion of Cu(l 10) along the rx, rF, and F5 azimuth of the surface Brillouin zone (Fig. 13) and analyzed the data with a lattice dynamical slab calculation. As an example we will discuss here the results along the TX-direction, i.e. the direction along the close-packed Cu atom rows. 

The obtained Ao gi = 5.7 x 10 is even larger than the value of Acr (Cu) X (= 4.7 X 10 A ), and of the hypothetical Co—Cu crystal with intermediate elastic properties than bulk cobalt and copper (4.1 x lO" A ). The derived effect of the effect of the lower coordination of the surface atoms on the mean-square relative displacement (perpendicular vs. parallel motions) is 1.4 times larger amplitude of the perpendicular vs. parallel motions, in agreement with lattice dynamics calculations. This SEXAFS study has produced a measure of the surface effect on the atomic vibrations. This has been possible due to the absence of surface or adsorbate reconstruction (i.e. no changes in bond orientations with respect to the bulk) and of intermixing. 

Pandit and King (1982) and Bathe et al. (1984) presented measurements using transducer techniques, which are somewhat different from the accepted values of Kiefte et al. (1985). The reason for the discrepancy of the sonic velocity values from those in Table 2.8 and above is not fully understood. It should be noted that compressional velocity values can vary significantly depending on the hydrate composition and occupancy. This has been demonstrated by lattice-dynamics calculations, which showed that the adiabatic elastic moduli of methane hydrate is larger than that of a hypothetical empty hydrate lattice (Shpakov et al., 1998). 

Two of the more direct techniques used in the study of lattice dynamics of crystals have been the scattering of neutrons and of x-rays from crystals. In addition, the phonon vibrational spectrum can be inferred from careful analysis of measurements of specific heat and elastic constants. In studies of Bragg reflection of x-rays (which involves no loss of energy to the lattice), it was found that temperature has a strong influence on the intensity of the reflected lines. The intensity of the scattered x-rays as a function of temperature can be expressed by I (T) = IQ e"2Tr(r) where 2W(T) is called the Debye-Waller factor. Similarly in the Mossbauer effect, gamma rays are emitted or absorbed without loss of energy and without change in the quantum state of the lattice by... 

Complementary spin-lattice relaxation measurements corroborate the observations made using the 2H line-shape measurements. Based on these measurements the low temperature relaxation times are dramatically shorter in the intercalated sample as compared to the bulk, indicating enhanced polymer re-orientation dynamics in the intercalated samples. Furthermore, the temperature dependence of the relaxation time in the bulk and intercalated sample show dramatic differences. While the relaxation time for the intercalated sample passes smoothly from low to high temperatures, the bulk sample shows a break between the crystalline state and melt state, with the melt state relaxation times at least one order of magnitude faster than those observed in the intercalated sample at the same temperature. 

In NMR work, spin-lattice relaxation measurements indicated a non-exponential nature of the ionic relaxation.10,11 While this conclusion is in harmony with results from electrical and mechanical relaxation studies, the latter techniques yielded larger activation energies for the ion dynamics than spin-lattice relaxation analysis. Possible origins of these deviations were discussed in detail.10,193 196 The crucial point of spin-lattice relaxation studies is the choice of an appropriate correlation function of the fluctuating local fields, which in turn reflect ion dynamics. Here, we refrain from further reviewing NMR relaxation studies, but focus on recent applications of multidimensional NMR on solid-ion conductors, where well defined correlation functions can be directly measured. 

The surface Fuchs-Kliewer modes, like the Rayleigh modes, should be regarded as macroscopic vibrations, and may be predicted from the bulk elastic or dielectric properties of the solid with the imposition of a surface boundary condition. Their projection deep into the bulk makes them insensitive to changes in local surface structure, or the adsorption of molecules at the surface. True localised surface modes are those which depend on details of the lattice dynamics of near surface ions which may be modified by surface reconstruction, relaxation or adsorbate bonding at the surface. Relatively little has been reported on the measurement of such phonon modes, although they have been the subject of lattice dynamical calculations [61-67],... 

Ultraviolet Raman spectroscopy has emerged as a powerful technique for characterization of nanoscale materials, in particular, wide-bandgap semiconductors and dielectrics. The advantages of ultraviolet excitation for Raman measurements of ferroelectric thin films and heterostructures, such as reduced penetration depth and enhanced scattering intensity, are discussed. Recent results of application of ultraviolet Raman spectroscopy for studies of the lattice dynamics and phase transitions in nanoscale ferroelectric structures, such as superlattices based on BaTiOs, SrTiOs, and CaTiOs, as well as ultrathin films of BaTiOs and SrTi03 are reviewed. 

In contrast, neutron spectroscopy is a more powerful probe, its results are directly proportional to the phonon density of states (DOS) (see Fig. 2) which can be vigorously calculated by lattice dynamics (LD) and molecular dynamics (MD). Applying these simulation techniques provide an excellent opportunity for constructing and testing potential functions. Because optical selection rules are not involved, INS measures all modes (IR/Raman measure the modes at the Brillouin Zone (BZ) q = 0, see Fig. 2) and is particularly suitable for studying disordered systems (or liquids). It hence provides direct information on the hydrogen bond interactions in water and ice. 

O /O isotope ratio measurements for laboratory hydrate 1983 - First molecular and lattice dynamic calculations of hydrates 1983 - Confirmation of low thermal conductivity values of hydrates... 

There have been several measurements of the lattice dynamics of quartz by inelastic neutron scattering. Early results showed that the soft mode in the high-temperature phase is overdamped (Axe 1971). Other work on RUMs at wave vectors not directly associated with the phase transition showed that on cooling through the phase transition the RUMs rapidly increase in frequency since they are no longer RUMs in the low-temperature phase (Boysen et al. 1980). The most definitive study of the RUMs associated with the phase transition was that of Dolino et al. (1992). 

There has been one lattice dynamics study of leucite by inelastic neutron scattering (Boysen 1990). The low-energy dispersion curves were measured for the high-temperature cubic phase along a few symmetry directions in reciprocal space. The results... 

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