Study of Thermal Diffuse X-Ray Scattering from Lead Single Crystals

Thermal diffuse x-ray scattering (TDS) from lead single crystals has been measured in the longitudinal and transverse branches along the [100] and [111] directions. In order to determine if one can use x rays to obtain reliable dispersion curves from a metal such as lead, the measured TDS was compared with that calculated from lead dispersion curves obtained by means of slow-neutron scattering. The one-phonon intensity was calculated directly from the [100] and [111] neutron data, and the two-phonon intensity was calculated by a method which expresses the cross section in terms of the atomic force constants determined by a fit to the neutron data. The intensity of the higher-order scattering was calculated by a method in which the Debye-Jauncey relation for TDS is expanded in powers of the Debye-Waller factor and the first two terms are subtracted. In addition, a very small Compton-scattering contribution was calculated. It is observed that in all cases, except for some points along the [111] transverse branch, the measured intensity is greater. The differences range from 10 to 60% or higher, and have a periodic dependence on reciprocal-lattice position. The source of this extra scattering has not yet been conclusively identified.