Neutron incoherent elastic scattering study of the temperature dependence of the Debye-Waller exponent in vanadium

Incoherent elastic neutron scattering from vanadium has been employed to determine the mean-squared displacement "${〈u^2〉}_T$" through the Debye-Waller exponent for the temperature range between 4.2 and 296 K. Significant corrections to the scattering data arise from (i) primary scattering due to the cylindrical shape of the vanadium sample and (ii) inelastic scattering. Calculations for ${〈u^2〉}_T$ employed our own experimental values of $g\left(\epsilon \right)$ at room temperature. Experimental values of ${〈u^2〉}_T$ disagree with calculations if one assumes $g\left(\epsilon \right)$ to be independent of temperature. Substantial hardening of the phonon spectrum is required to account for the low-temperature experimental values of $〈u^2〉$. The results suggest that additional work on the temperature dependence of $g\left(\epsilon \right)$, especially for the low-energy phonons, is needed.