Phonons neutron scattering

Phonon Neutron scattering (cm ) Raman scattering (cm" ) Raman bound state (cm" ) Average (cm )... 

In contrast to the Raman scattering results a temperature-dependent softening of the mode is observed between 300 and 5 K in phononic neutron scattering (Reichart and Niicker 1983). This has been attributed by Thalmeier (1984) to the temperature dependence of the vertex corrections, which have to be taken into account in higher-order perturbation theory. The vertex corrections yield a temperature-dependent renormalization of the phonon frequency proportional to the difference in occupation of the F and Fg CEF levels. 

Logan et al. (1970) measured the inelastic incoherent neutron scattering from a crystalline sample of benzene at temperatures in the range 77-270°K They found qualitative agreement at low temperatures with the one-phonon neutron scattering cross section calculated from G(v) of Nakamura and Miyazawa (1969). 

Figure 4 Schematic vector diagrams illustrating the use of coherent inelastic neutron scattering to determine phonon dispersion relationships, (a) Scattering m real space (h) a scattering triangle illustrating the momentum transfer, Q, of the neutrons in relation to the reciprocal lattice vector of the sample t and the phonon wave vector, q. Heavy dots represent Bragg reflections.

If the displacements of the atoms are given in terms of the harmonic normal modes of vibration for the crystal, the coherent one-phonon inelastic neutron scattering cross section can be analytically expressed in terms of the eigenvectors and eigenvalues of the hannonic analysis, as described in Ref. 1. 

Figure 3 Phonon dispersion curves obtained by inelastic neutron scattering revealing precursor behaviour prior to the 14M transformation in Ni-AI. The dip at q = 1/6 [110] (a) deepens upon cooling and (b) shifts under an external load .

The density of states (DOS) of lattice phonons has been calculated by lattice dynamical methods [111]. The vibrational DOS of orthorhombic Ss up to about 500 cm has been determined by neutron scattering [121] and calculated by MD simulations of a flexible molecule model [118,122]. 

The Debye temperatures of stages two and one were determined by inelastic neutron scattering measurements [33], The total entropy variation using equation 8 is in the order of about 2 J/(mol.K). Although smaller in value, such variation accounts for 10-15% of the total entropy and should not be neglected. We are currently carrying on calculations of the vibrational entropy from the phonon density of states in LixC6 phases. 

The phonon branch that is suspected to interact strongly with the charge by the ARPES measurement, namely the zone-boundary Cu-0 bondstretching LO phonon branch (Fig. 1), was found by inelastic neutron scattering to show unusual temperature dependence [8],... 

Essentially similar spectra were observed for other diborides. The only difference was a degradation of maxima with bias rise, taking into account their purity and increased EPI, which leads to the transition from the spectroscopic to the non-spectroscopic (thermal) regime of the current flow [33]. The positions of the low-energy peaks are proportional to the inverse square root of the masses of the d metals [33], as expected. For NbE>2 and TaE>2 the phonon density of states (DoS) is measured by means of neutron scattering [34], The position of phonon peaks corresponds to the PC spectra maxima (Fig. 5). Because Nb and Zr have nearly the same atomic mass, it is suggested that they should have similar phonon DoS. 

Inelastic neutron scattering (INS) measurements have been successfully used to study dynamical phenomena such as molecular or lattice vibrations in pristine C60 [43] and a variety of fullerides [44-48]. When INS spectra are collected on instruments with a large energy window, it is possible to observe all phonon modes including the molecular vibrations and the generalised phonon density-of-states (GDOS) can be directly calculated. 

Figure 2.1. Dispersion of phonons in a deuterated anthracene crystal (S. L. Chaplot et al., 1982). Upper part calculated spectra. Lower part dispersion measured by neutron scattering. The Raman-active modes at k = 0(F) are marked R, and have symmetry /4,(S) or Bt(A). Note the weak dispersion of the lower R mode along c. ... 

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