Third-order elastic constants of the high temperature superconductor Bi 2Sr 2CaCu 2O 8

Abstract

The complete set of non-vanishing third-order elastic moduli of high temperature superconductor Bi 2Sr 2CaCu 2O 8 (Bi-2:2:1:2) is obtained theoretically. The interactions of nine nearest neighbours of each atom in the unit cell of Bi-2:2:1:2 are taken into account, while estimating the strain energy density. Here the finite strain elasticity theory is used to obtain the strain energy density of the Bi-2:2:1:2 system. The energy density φ is compared with the strain dependent lattice energy from the continuum model approximation. The second-order parameter of the potential function φ is fixed by making use of easily and more accurately measurable principal axis C ij . The third-order potential parameter is estimated by assuming a Mie–Grüneisen type interatomic potential. The interlattice displacements as well as the second-order elastic constants are evaluated along with the 12 third-order elastic constants of Bi 2Sr 2CaCu 2O 8. The second-order elastic constants are in good agreement with the reported experimental data. In the case of third-order elastic moduli no such experimental data are available for comparison. All the 12 third-order elastic constants are negative; and the absolute magnitude of third-order elastic constants are generally one order higher than second-order elastic constants as generally expected of crystalline solids. The third-order elastic moduli of different modes show anisotropy.