Mode Gr € uneisen parameters and the low temperature thermal expansion of high-T c superconductor La 1:8 Sr 0:2 CuO 4 K.P. Jayachandran, C.S. Menon * School of Pure and Applied Physics, Mahatma Gandhi University, Priyadarshini Hills, Kottayam, 686 560 Kerala, India Received 2 July 2001; received in revised form 15 February 2002; accepted 6 March 2002 Abstract The anisotropy of low temperature thermal expansion of La 1:8 Sr 0:2 CuO 4 (LSCO) is analysed theoretically using quasiharmonic theory of thermal expansion. Vibrational anharmonicity as determined by the generalised Gr€ uneisen parameters(GPs) c 0 j and c 00 j ofthevariousnormalmodefrequenciesofthelatticehasbeenstudied. c 0 j referstochangein frequencies due to a uniform areal strain perpendicular to the c-axis and c 00 j to the change in frequencies due to a uniformarealstrainalongthe c-axisofLSCOcrystal.ThegeneralisedGPsarecalculatedusingthesecond-andthird- order elastic constants. The second- and third-order elastic constants are calculated using deformation theory. The strainenergydensity / isestimatedbytakingintoaccounttheinteractionsofninenearestneighboursofeachatomin the unit cell of LSCO. The energy density thus obtained is compared with the strain-dependent lattice energy from continuummodelapproximationtoobtainthecompletesetofnon-vanishingsecond-andthird-orderelasticconstants ofLSCO.AllthegeneralisedGPsarepositive.Generally, c 00 j exhibitshighervaluesthan c 0 j exceptforthecaseof c 00 2 .Thus the crystal is more anisotropic along the c-axis than in ab-plane. The longitudinal acoustic mode c 00 3 is the most an- isotropicofallthemodegammas.ThelowtemperaturelimitsoftheGPs c ? ð0Þ and c k (0)arefoundtobealmostequal. This is presumably due to the absence of discrepancies in anharmonicity along the c-axis and along the ab-plane in LSCO at low temperatures. The low temperature limit of the lattice thermal expansion c L is calculated from mode Gr€ uneisen gammas. c L hasbeenobtainedas4.3forLSCO.Thelowtemperaturelimit c L is positive and therefore, we expect the volume lattice thermal expansion to be positive down to absolute zero in LSCO. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 62.20.D; 74.25.L; 74.62.F Keywords: Gr€ uneisen parameters; Thermal expansion; Superconductors 1. Introduction The thermal expansion of a solid arise strictly due to the anharmonicity of the crystal lattice, the nonlinearity of interatomic forces with re- spect to atomic displacements. Usually the an- harmonic properties are described in terms of Gr€ uneisen parameters (GPs) c,whichquantifythe volume or strain dependence of the lattice vibra- tional frequencies. c is important in characterising high-T c oxide superconductors, appearing in the volume dependence of superconducting transition Physica C 383 (2002) 159–168 www.elsevier.com/locate/physc * Corresponding author. Tel.: +91-481-59-7923. E-mail address: spapf@sancharnet.in (C.S. Menon). 0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S0921-4534(02)01316-3