Ultrasonic-attenuation investigation of the mixed state in three vanadium samples of varying purity

Ultrasonic-attenuation measurements were performed in three single-crystal vanadium samples, with resistivity ratios of 7.8, 245, and 450 as a function of magnetic field and temperature. Measurements obtained as a function of applied magnetic field were compared to the theoretical predictions of Houghton and Maki (HM) for the region near $H_{c2\mathrm{}}$. Because of the varying purity of the samples, the HM predictions for the dependence of the normalized attenuation on mean free path were also tested. In all cases, the experimental results were in good qualitative agreement with the HM predictions. Ultrasonic-attenuation measurements as a function of temperature compared well to the BCS theory and yielded critical temperatures of 4.69, 5.26, and 5.27°K with corresponding zero temperature energy gaps of $\frac{2\Delta \mathrm{}\left(0\right)\mathrm{}}{k{T}_c}=3.6, 3.6, \mathrm{and} 3.5$ in order of increasing sample purity.