Crystallographic thermal expansion and elasticity across the superconducting transition inYBa2Cu3O7−δ

A thermodynamic treatment for a second-order superconducting phase transformation has been developed which incorporates crystallographic effects. The temperature dependence of x-ray-measured lattice constants in polycrystalline $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ has been used to determine the orthorhombic, crystallographic thermal-expansion coefficient matrix. The principal thermal strains were curvefit above and below the superconducting transition temperature to deduce the thermal-expansion jumps at the phase boundary. The thermodynamic arguments show that the three elastic shear stiffness elements do not contribute to the superconducting specific-heat jump. Also, the three independent shear stresses at the superconducting transition point are zero. The specific-heat jump is, however, related to the three normal stresses at the phase boundary. The experimental thermal-expansion data suggest that a compressive stress aligned with the oxygen-deficient crystallographic â axis changes the transition temperature by 0.3 K/kbar; the $\hat{\mathrm{b}}$ axis stress is 0.07 K/kbar, while the ĉ is 0.1 K/kbar, and all stresses are in compression. The isothermal elastic compliance jumps can be predicted by assuming zero jumps in the adiabatic elastic compliances. The specific-heat jump is calculated from this assumption and crystallographic thermodynamics.