Measurement of Lattice Vibrations in Vanadium by Neutron Scattering

Abstract

The energy spectrum of slow neutrons inelastically scattered by vanadium metal has been measured by the time-of-flight technique. The neutrons gain energy by absorbing quanta of lattice vibration energy (phonons). As the nuclear scattering amplitude of vanadium is incoherent, the energy distribution of scattered neutrons is directly related to the frequency distribution of lattice vibrations. The measured neutron energy spectrum, as well as the derived frequency distribution, shows a clearly resolved double peak. This structure, which is distinctly different from the simple Debye distribution, but expected on the basis of detailed calculations, has heretofore not been amenable to direct measurement. The measured frequency distribution is compared with calculations for a body-centered cubic lattice by the Born-von K\'arm\'an theory and qualitative agreement is obtained. A more exact comparison awaits measurement of the elastic constants of vanadium.