The effect of hydrostatic pressure on the elastic behaviour of GdBa₂Cu₃O_7-x

Abstract

The pressure dependences of ultrasonic longitudinal and shear waves have been measured in the high-Tc superconductor GdBa2Cu3O7-x. The effects of porosity have been taken into account by using wave scattering theory in a porous medium. The pressure dependence ( delta B/ delta P)P=0 of the bulk modulus of the nonporous matrix at room temperature has the considerable value of 55. The adiabatic bulk modulus B0s measured ultrasonically at atmospheric pressure is much smaller than that BT(P) determined by X-ray measurements of lattice parameters at high pressure; this discrepancy is due to the large pressure dependence of the bulk modulus. It is suggested that the rather small bulk modulus and its large pressure dependence could be due to a combination of fluctuating copper valence and to the vacant sites in the crystal structure.

An equation of state of high-temperature superconductor

“…Since high-To copper oxide compounds have three lattice parameters of different values, it is more convenient to express the potential energy as a function of volume as follows [7,8]: (2) where A = amZ 2, the repulsive parameter B and n are evaluated from the equilibrium condition, and the bulk modulus data are obtained from the relations given below: where Kr(O) is the bulk modulus at P=0. In Eq.…”

“…After the discovery of superconductivity around 30 K in the La-Ba-Cu-O system by Bednorz and Muller [ 1], the importance of high-pressure investigation was realized "and several experimental studies were then made to measure the bulk modulus, shear modulus, and young modulus and their pressure derivatives under the effect of high pressure for many high-Tc superconductor [2,3]. For this purpose they considered high-To superconductors and predicted their properties by measuring the velocity of longitudinal and transverse waves propagated in these superconductors.…”

“…To explain the experimental results as achieved by the previous workers [2,3] for high-Tc superconductors we have made an attempt by formulating an expression for the potential energy as a function of volume. Since most of the high-To superconductors are highly ionic in character [4,5], i.e., the individual ~Department of Physics, G. B. Pant University of Agriculture and Technology, Pantnagar 263 145, India.…”

Ultrasonic determination of the elastic moduli and their pressure dependences in very dense YBa{sub 2}Cu{sub 3}O{sub 7{minus}x}

“…x [1][2][3] (and other related cuprates, including GdBa2Cu_OT.xin both its orthorhombic and tetragonal forms [4,5], Bi2Sr_Ca_tCu, O4+2,(with n=2 and 3) [6] and Lal.xSr0.2CuO4 [3]) is much smaller than that B r(p) determined [7][8][9][10][11][12] at very high pressures from x-ray measurements of lattice parameters in a diamond cell. This difference has been ascribed [1][2][3][4][5][6] to the large magnitude of (OB/OP)e--o determined from the effects of hydrostatic pressure on ultrasonic wave velocity.…”

“…x [1][2][3] (and other related cuprates, including GdBa2Cu_OT.xin both its orthorhombic and tetragonal forms [4,5], Bi2Sr_Ca_tCu, O4+2,(with n=2 and 3) [6] and Lal.xSr0.2CuO4 [3]) is much smaller than that B r(p) determined [7][8][9][10][11][12] at very high pressures from x-ray measurements of lattice parameters in a diamond cell. This difference has been ascribed [1][2][3][4][5][6] to the large magnitude of (OB/OP)e--o determined from the effects of hydrostatic pressure on ultrasonic wave velocity. A recent reanalysis [ 13] of the high pressure x-ray [7][8][9][10][11][12] and neutron [14][15][16] diffraction data has led to a substantial reduction of Br(p) and a large increase in the value of its pressure derivative (igB/OP): both trending towards the ultrasonic values and conf'm'rfing the earlier observation [1,2] of the highly pressure dependent nature of the bulk modulus at moderate pressures.…”