Neutron inelastic scattering phonons

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 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],... 

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. 

In the metallic state below about 150 K a set of diffuse streaks was found in X-ray studies as shown in Fig. 18 which suggests the onset of the periodic lattice distortion with = 0.295 b having no correlation among them perpendicular to the one-dimensional b-axis [55,56]. Corresponding to these x-ray streaks inelastic neutron scattering studies revealed the decrease in the phonon frequency for the wave vector = 0.295 b with decreasing temperature as shown in Fig. 19 [60]. This soft phonon is considered to be frozen out at the metal-insulator transition temperature 53 K causing the superstructure described above. This type... 

C. K. Loong et ai, High-Energy Oxygen Phonon Modes and Superconductivity in Bai j,Kj,Bi03 An Inelastic-Neutron-Scattering Experiment and Molecular-Dynamics Simulation, Phys. Rev. Lett. 62, 2628-2631 (1989). 

Regarding both vibrational (phonon) and magnetic (magnon) excitations, the finite particle size imposes an upper wavelength limit. This can be detected in measurements that probe the excitation spectra up to large wavelengths (e.g., inelastic neutron scattering) and it affects the thermodynamic properties of the nanoparticles. 

Table III with the preceding columns. The new results calculated with the ab initio potential agree very well with the frequencies from inelastic neutron scattering (Kjems and Dolling, 1975) and from infrared and Raman spectroscopy (Thi6ry and Fabre, 1976 Fondire et al., 1981) for all types of modes. Also the phonon dispersion relations, displayed in Fig. 4, are in good agreement with the neutron-scattering data. Since most of the lattice modes are actually mixed libron-phonon modes, this indicates that the translation-rotation coupling is correctly included in the RPA formalism.

Fig. 4. Calculated (TDH) dispersion curves for a-N2, for phonon-libron modes propagating along the [110] direction. The circles correspond to inelastic neutron scattering data measured at T = 15 K by Kjems and Dolling (1975).

Phonon wings are probably the most important band shaping processes in inelastic neutron scattering spectroscopy and this theme is developed in later chapters. The intensity arising from the vth internal transition and remaining at the band origin, coq, is termed the zero-phonon-band intensity, often found in the literature as Sq. From Eq. (2.62), for R = 0... 

R. Mukhopadhyay S.L. Chaplot (2002). Chem. Phys. Lett., 358,219-223. Phonon density of states in tetrabromoethylene lattice dynamic and inelastic neutron scattering study. 

J. Tomkinson G.J. Kearley (1989). J. Chem. Phys., 91, 5164-5169. Phonon wings in inelastic neutron scattering spectroscopy the harmonic approximation. 

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