Effect of superconducting transition on temperature dependence of elastic moduli in niobium: Superposition of quasistatic and dynamic effects

Low-temperature elastic properties of niobium crystals of different purity and orientation are investigated in normal (N) and superconducting (S) states. Experiments are carried out using the composite vibrator technique at frequencies ∼90 kHz. Temperature dependences of the Young's modulus E(T) and the shear modulus G(T) in the N- and S-states are measured in the temperature range 2 K < T < 12 K. Both the temperature dependences of elastic moduli in the N-state M N(T) and the dependences ΔM NS(T) = M N(T) - M S(T) have some features that cannot be explained within the concept of direct interaction of sound with electron and phonon excitations in metals. It is established that for rapidly cooled samples there exists a temperature range where the anomalous increase in the elastic moduli is observed at the N-S transition. An interpretation given is based on the assumption of dynamic interaction of sound oscillations with low-energy excitations in dislocations (geometrical kinks) that is superimposed with the quasistatic thermodynamic change of the direct electronic contribution at temperatures below T c. The data are compared with the results obtained in high-frequency experiments