Nonlinear acoustic effects arising from dislocations in niobium single crystals

The temperature dependence of the logarithmic decrement δ and dynamic Young’s modulus $E$ in niobium single crystals of high purity is investigated in a wide interval of low temperatures $3 K⩽T⩽300 K.$ Measurements are made by means of a two-component composite vibrator method under excitation of longitudinal vibrations with a frequency of 88 kHz and a relative amplitude of the acoustic strain varying in the range $5×10−9<ε0<7×10−5.$ In the temperature interval 50–200 K a nonlinear effect is registered: an amplitude-dependent contribution to the decrement and Young’s modulus is observed when the amplitude of the ultrasound reaches a threshold value $ε0c≳10−5.$ The dependence of the threshold value $ε0c$ on temperature and on preliminary plastic deformation of the sample is established. The amplitude dependences $δ(ε0)$ and $E(ε0)$ at $ε0>ε0c$ and their transformation with temperature are investigated in detail. Analysis shows that the nonlinear effects are due to the breakaway of ultrasonically excited dislocations from impurity atoms. The experimental results are in satisfactory agreement with the conclusions of the Granato–Lücke theory of athermal dislocation hysteresis and its generalization to the case of thermally activated hysteresis proposed by Indenbom and Chernov.