Dynamic elastic moduli of niobium at low temperatures: temperature dependences in the normal state, influence of superconducting transition, dislocation effects

Abstract

The low-temperature elastic properties of niobium crystals of different purity and orientations are investigated in normal (N) and superconducting (S) states. The experiments are carried out by the composite vibrator technique at frequencies 90 kHz. Temperature dependences of Young`s modulus E(T) and shear modulus G(T) in the normal and superconducting states are measured in the temperature range 2 K < T< 12 K. It is found that both the temperature dependences of elastic moduli in normal state M_N(T) as well as the dependences DM_NS(T)= M_N(T) - M_S(T) have in some cases features (anomalies) that can not be explained within the theoretical description of direct interaction of crystal lattice acoustic deformations with electron and phonon excitations in metals. In particular, it is established that for rapidly cooled samples there exists a temperature range where an anomalous increase in the elastic moduli is observed at the N–S transition. To interpret these anomalies, a concept of resonant interaction of sound oscillations with low-energy dislocation excitations is suggested. It is shown, that the anomalies may be due to the superposition of the low-temperature dynamic dislocation relaxation and a quasistatic thermodynamic change of the electron contribution to the elastic moduli at temperatures below T_c. The data obtained are compared with the results known from the high-frequency experiments at frequencies 10–30 MHz.