Ultrasonic evidence of low bulk modulus and large vibrational anharmonicity in the bismuth cuprate high Tcsuperconductors

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Abstract
The velocities of longitudinal and shear ultrasonic waves propagated in ceramic specimens of single phase Bi(Pb)2223, Bi(Pb)2212 and lead-free Bi2212 have been measured as a function of hydrostatic pressure. The elastic stiffnesses of these bismuth cuprates are unusually small and their hydrostatic pressure derivatives ( delta CL/ delta P)P=0 and ( delta B/ delta P)P=0 at room temperature are large. The ceramic microstructure comprises loosely stacked, thin platelets; the substantial effects of porosity on the elastic properties have been approximated using wave scattering theory in a porous medium. The bismuth cuprates investigated show the common characteristic of high Tc mixed oxides based on copper that the bulk modulus B0 measured ultrasonically is much smaller than the BT(P) determined at very high pressures from X-ray measurements of lattice parameters in a diamond cell. This can be resolved by taking the contribution to the high pressure bulk modulus BT(P) of the pressure derivative ( delta B/ delta P)P=0 into account. In these materials the anharmonicity of the longitudinal acoustic modes in the long wavelength limit is large, probably as a result of the combination of (i) weak interlayer binding forces due to the lone pairs sited between the pairs of widely spaced BiO layers and (ii) intermediate valence effects.