Nonlinear acoustic effects in niobium single crystals caused by dislocations

The temperature dependences of logarithmic decrement 8 and dynamic Young's modulus E in high purity niobium single crystals are investigated in a wide low temperature range from 3 K to 300 K. The measurements are carried out using the two-component composite vibrator method with exciting longitudinal oscillations of a frequency about 88 kHz. A relative amplitude of ultrasonic strain co is varied within the limits from 5z10-9 to 7z10-5. A nonlinear effect is registered in the temperature interval from 50 to 200 K: amplitude dependent contributions to the decrement and Young's modulus are observed when of the ultrasound strain amplitude coc becomes as high as 1z10-5. It is found that coc is dependent on temperature and preliminary plastic deformation. The amplitude dependences delta(epsilon0) and E(epsilon0) at epsilon0 > epsilon0c and their transformations with temperature are investigated in details. The analysis shows that the nonlinear effects are caused by the breakaway of ultrasonically excited dislocations from the impurity atoms. The results obtained agree satisfactorily with the predictions of the Granato-Lucke theory of athermic dislocation hysteresis and its generalization to the case of thermally activated dislocation hysteresis proposed by Indenbom and Chernov.