PHONON SPECTRA OF CRYSTALS

Phonon Spectra of crystals: inelastic neutron scattering



Introduction3

Inelastic Neutron scaterring3

Experiments and Equipments4

Neutron triple axis spectrometer4

Time-of-flight6

Back-scattering spectrometry7

References9

Phonon Spectra of crystals: inelastic neutron scattering

Introduction

The experiments of inelastic neutron experiments can provide adequate information about the thermal motion properties of liquids and solids. Inelastic neutron scattering (INS) is an experiment carried out to study the molecular and atomic motion in a condensed matter. It is also used to study the crystal and magnetic field excitations. The inelastic neutron differentiates itself form the elastic collision by the resolving the kinetic energy at the time of the collision between the sample (inelastic one) and the neutrons (Gao et al., 2012, pp. 74-78).

After the collision the result, is communicated by inelastic scattering law (dynamic structure factor or dynamic susceptibility). The formula for inelastic scattering law is S(Q, ?), where Q is the differnece between incoming and outgoing wave vector, and ? is the energy chnged faced by the sample or the medium. If we plot a graph as result of ?, the results can be interpreted in same way the results of the spectra which are obtained from traditional spectroscopic techniques. The inelastic neutron scattering (INS) is seen as a special spectroscopy so far (Shapiro and Shirane et al., 1975, p. 4899).

Inelastic Neutron scaterring

In an inelastic neutron scattering after the neutron is scattered by solid, it can either absorb or emit an amount of energy which is equal to a quantum of phonon energy, hv. The difference of energy is the main cause of the inelastic scattering. The neutrons that are used in the experiment have energy in meV range, the energy change of neutron is although very small in nature but it allows accurate measurement of phonon frequencies. As the neutrons coming in have different velocities and wavelengths before and after they interact with the samples. To measure the phonon energy and the scattering vector, Q, the neutron wave vector before (ki) and after (kf) has to be determined.

Figure 1

Figure 1 shows the scattering pattern of inelastic neutron. The figure shows the triangles in which neutron either lose ( kf < ki) or gain (kf > ki) energy. One thing that is common in both the elastic and inelastic collision is the angle of scattering 2O, the scattering vector is Q = ki - kf (Månsson et.al, 2013,p.8).

Experiments and Equipments

The inelastic scattering of neutron experiments usually requires a monochormatization of incident ...