Effects of dilute alloying on the elastic constants and superconducting energy gap in thallium

Velocity of sound and ultrasonic attenuation measurements have been made on two pure and two doped samples of thallium. One of the pure samples was grown from the melt and the other by strain-anneal and called the unmelted sample. All samples were single crystals and all measurements were made using 15 MHz longitudinal sound pulses. The doped samples contained 1/4 At.% and 1/8 At.% tin as an impurity. The elastic constants appropriate for a longitudinal wave travelling in the c axis direction (C[lowered 33]) have been measured as a function of temperature and impurity. The measured elastic constants vary between 4.8 X 10[raised 11] dynes/cm[raised 2] for the pure unmelted sample at 500K to 6.5 X 10[raised 11] dynes/cm[raised 2] for the 1/4 At.% sample at 4.2K. The elastic constants were calculated from velocity of sound data. A simple band structure model based on the two plane wave approximation is presented and the band structure elastic constants calculated. The model gives relative changes in the elastic constants as a function of temperature and/or impurity. A term representing the electrostatic energy of the crystal is subtracted from the measured elastic constants and the result is compared to values predicted by the model. Band structure elastic constants range from -14.6 X10[raised 11] dynes/cm[raised 2] for the pure unmelted sample at 500K to -15.27 X 10[raised 11] dynes/cm[raised 2] for the 1/4 At.% sample at 4.2K. Finally, the limiting superconducting energy gap is measured as a function of sample impurity. The values obtained are 2Delta = 4.6K[lowered B]T[lowered c] 4.6 K[lowered B]T[lowered c], 4.0K[lowered B]T[lowered c], and 3.3-3.6K[lowered B]T[lowered c] for the pure melted sample, pure unmelted sample, 1/8 At.% sample, and 1/4 At.% sample respectively. The value of 2Delta is observed to approach the BCS value of 3.5K[lowered B]T[lowered c] as the doping level is increased.