Coherent Inelastic Scattering

Inelastic coherent scattering measurements using single crystals may focus on selected modes. For triple-axis spectroscopy, the work of Shirane et al. sets the standard by which most other smdies can be gauged (Figures 7 and 8). For additional examples, see the monograph by Shirane, Shapiro and Transquada. Measured phonon densities of... 

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. 

The scattering of neutrons by any molecular system can be elastic or inelastic, coherent or incoherent. The elastic coherent scattering of a labeled polymer in a background matrix can be extracted from the data in a properly designed experiment. 

Table II Space- and Time-Resolved Measurements from Inelastic Light Scattering. All methods are suitable for nonequilibrium conditions. Here, RS refers to Raman scattering, CARS to coherent anti-Stokes Raman spectroscopy, and RIKES to Raman-induced Kerr effect.

Onufrieva F., and Pfeuty P., (2002). Spin dynamics of a two-dimensional metal in a superconducting state Application to the high-Tc cuprates Phys. Rev. B 65 054515 Manske D., Eremin I., and Bennemann K.H., (2001). Analysis of the resonance peak and magnetic coherence seen in inelastic neutron scattering of cuprate superconductors A consistent picture with tunneling and conductivity data. Phys. Rev. B 63 054517. 

Dorner, B., Coherent inelastic neutron scattering in lattice dynamics, in Tracks in Modern Physics, Vol. 93. Springer, Berlin, 1982. 

Neutron time-of-flight spectra for molded polyetrafluoroethylene at six temperatures between 10° C and 100 C are reproduced in Fig. 9 (27). Unlike polyethylene and polypropylene, neutron scattering from poly-tetrafluoroethylene is expected to be mainly coherent. Thus, peaks may occur in the inelastic spectrum due to coherent scattering from individual lattice planes. However, measurements as a function of scattering angle... 

Coherent Inelastic Scattering.—Inelastic neutron collisions with the solid can excite phonon modes (collective vibrations) and if the coherently scattered component can be detected variation with direction within the solid, i.e. the phonon dispersion curve, can be determined. This technique is well established for bulk solids and has been used recently to examine the properties of small particles (carbon black). 

Inelastic collisions are dealt with in a very detailed paper by Prins which has only just appeared, in which the coherent scattered waves starting from the atoms are given a phase displacement as compared with the primary wave. This phase displacement is chosen in such a way that by interference the scattered waves weaken the primary wave traversing them to the exact extent required by the absorption coefficient. The deviation of the refractive index from unity also enters into this in a complicated way. With certain assumptions about... 

Inelastic collisions have also been dealt with recently in a detailed paper by Bethe. The results, however, refer only to fast electrons and to the diffraction caused by a single atom. The continuous background formed by the electrons which are scattered inelastically falls off much more steeply, according to this theory, than the coherently scattered de Broglie waves. Thus when the angle of deviation is large we are more or less in a position to neglect it in experiments. 

As well as the coherent scattering, which has the same wavelength as the incident waves, an atom scatters waves of reduced wave-length. The intensity of these waves is not included in the formulae (I) and (2). For X-rays falling on a hydrogen atom, the total intensity scattered inelastically, due both to Raman effect and Compton effect, is given by the formula... 

Leake, J. A.. W. B. Daniels, J. J. Skalyo, B. C. Frazer, and G. Shirane 1969, Lattice dynamics of neon at two densities from coherent inelastic neutron scattering . Phys. Rev. 181 1251-1260. 

B. Domer (1982). Coherent Inelastic Neutron Scattering in Lattice Dynamics, Springer Tracts In Modem Physics, vol. 93, Springer-Verlag, Berlin. 

In Ch. 21 Buntkowsky and Limbach review recent NMR work on the dynamics of dihydrogen and dideuterium in the coordination sphere of transition metals. In addition to inelastic neutron scattering and liquid state NMR, the effects of coherent (exchange couplings) and incoherent rotational tunneling of D2 pairs in transi-... 

Experiments have also been started that use the inelastic light scattering and include the methods of coherent anti-Stokes Raman spectroscopy (CARS), as well as electron energy loss spectroscopy (EELS). The methods (see, for instance, (4)(5)) are based on the application of various physical processes, as can be seen from their names. Accordingly they complement one another and enable us to study the elementary excitations of a surface over a wide range of energies and wave vectors. 

P. A, Reynolds,/ Chem. Phys., 59, 2777 (1973). Lattice Dynamics of the Pyrazine Crystal Studied by Coherent Inelastic Neutron Scattering. 

---