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

摘要

The low-temperature elastic properties of niobium crystals of different purity and orientation are investigated in the normal (N) and superconducting (S) states. The experiments are done by the composite vibrator technique at frequencies ～90 kHz. The temperature dependence of Young's modulus E(T) and of the shear modulus G(T) are obtained in the temperature range 2-12 K in the N and S states. It is found that both the temperature dependence of the individual components of the elastic moduli in the normal state, M{sub}N(T), and the temperature dependence of the difference △M{sub}(NS)(T)=M{sub}N(T)-M{sub}S(T) can in some cases have anomalies that cannot be satisfactorily explained in a theoretical description of a direct interaction of the acoustic deformations of the crystal lattice of the metal with the electronic and phonon excitations. In particular, it is found that for fast-cooled samples there exists a temperature region in which an anomalous increase of the elastic moduli at the N-S transition is observed. These anomalies are interpreted in terms of a resonant interaction of the acoustic vibrations with low-energy dislocation excitations. It is shown that they are a consequence of a superposition of a low-temperature dynamic dislocation relaxation and quasistatic thermodynamic variation of the electronic contribution to the elastic moduli at temperatures below T{sub}c. The data agree with known results of high-frequency measurements at frequencies of 10-30 MHz.