Determination of the polarization vectors of lattice waves by anomalous neutron scattering

The Argand diagram representation of coherent inelastic scattering (one-phonon process) is presented. This is used to show that |F(H,q)| ≠ |F({\bar \bf H}, {\bar \bf q})| in a non-centrosymmetric two-atom structure when an anomalous scatterer is present and |F(H,q)| ≠ |F(H , {\bar \bf q})| even in a NaCl-type structure when both atoms are normal scatterers. This paper describes how the polarization vectors of lattice waves may be experimentally determined in a crystal containing a nuclide which scatters thermal neutrons anomalously. The procedures for the determination of the polarization vectors in centrosymmetric and non-centrosymmetric structures when they are, in general, complex and for a Bravais lattice when they are always linearly polarized have also been presented. It is shown that the `phase problem' associated with the determination of the initial phase of elliptic motion can, in principle, be solved by using anomalous neutron scattering.