Sound velocity and elastic constants in oxide superconductors

Studies on sound velocity and attenuation in superconductors are useful from the following points: some superconductors undergo a structural transformation at a temperature, Ts, well above the superconducting transition temperature Tc. A typical examples is Nb3Sn which undergoes a martensitic transformation before becoming superconducting. Changes in sound velocity and a peak in the attenuation at a certain temperature are indicators to a displacive phase transition at that temperature; and the superconducting phase transition at Tc is a second order transition which does not involve a change in density. The thermodynamics of the transition leads to the following result: Kn - Ks = (Kn2/4π) (∂Hc/∂p)2 Tc. Here Kn and Ks are the bulk modulii in the normal and superconducting phases respectively at Tc, Hc is the thermodynamic critical field and p is the pressure. The bulk modulus in the superconducting phase will be less than the bulk modulus in the normal phase. Similar will be the behavior of the other elastic modulii. So one should expect a slight decrease in the sound velocity as the sample becomes superconducting. This change will only amount to a few hundred parts per million