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  • Heat transport in the high-tem perature superconductor Yttrium Barium Copper Oxide

    Song Pu Centre for the Physics of Materials

    Department of Physics, McGill University Montral, Qubec, Canada

    A Thesis submitted to the Faculty of Graduate Studies and Research

    in partial Mfdment of the reqnirements for the degree of Master of Science

  • National Libr;try Bibliottieque nationale du Canada

    Acquisitions and Acquisitions et Bibliographie Services senrices bibliographiques 395 Weington Street 395. iue Wellington OawaON K 1 A W OttawaON K 1 A W Canada canada

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    The author retains ownership of the L'auteur conserve la proprit du copyright in this thesis. Neither the droit d'auteur qui protge cette thse. thesis nor substantial extracts fiom it Ni la thse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent tre imprims reproduced without the author's ou autrement reproduits sans son pemission. autorisation.

  • iii

  • To my lovely wzfe and my parent

  • xii 1 OUTLINE AND MOTIVATION 1 2 THERMAL CONDUCTMTY: A REVIEW 4

    . . . . . . . . . . . . . . . . . . . . . . 2.1 Themal conductivity of solids 4 2.1.1 Scattering mechanisms . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Mean fiee path and Mattiessen's d e . . . . . . . . . . . . . . 5 2.1.3 Electrons and the Wiedemann-Fr- law . . . . . . . . . . . . 6

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Phonons 9 2.1.5 Electrons and phonons: a cornparison . . . . . . . . . . . . . . 10

    2.2 Thermal conductivity of conventional superconductors . . . . . . . . 11 2.2.1 Electronic thermal conductivity . . . . . . . . . . . . . . . . . 13 2.2.2 Lattice thermal condnctivity . . . . . . . . . . . . . . . . . . . 17

    3 TRANSPORT PROPERTIES IN Y B A ~ C U ~ O ~ . ~ . A BRIEF REVIEW 19 3.1 Crystal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Electrical resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Heat conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Origin of the peak in K ( T ) . . . . . . . . . . . . . . . . . . . . . . . . 23

    3.4.1 Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.4.2 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    4 EXPERIMENTAL ASPECTS 32 4.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    4.1.1 Crystal growth . . . . . . . . . . . . . . . . . . . . . . . . . . 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Oxygenation 34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Detwinning 34

    . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Zn.dopedcrystals 34

    . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Sample characterization 35 4.2.1 Polarized optical microscopy . . . . . . . . . . . . . . . . . . . 35 4.2.2 Electncal resistivity . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2.3 Scanning electron microscopy . . . . . . . . . . . . . . . . . . 37 4.2.4 Magneticsusceptibility . . . . . . . . . . . . . . . . . . . . . . 38

    4.3 'He cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.4 Thermal conductvity set-np . . . . . . . . . . . . . . . . . . . . . . . 41 4.5 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . . 45

    . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Testonagoldsampb 47

  • 5 RESULTS AND DISCUSSION 51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction 51

    . . . . . . . . . . . . . . . . . . 5.2 Peak in tc(T): effect of Zn impmities 52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Results 52

    5.2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Snmmary .. 65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Anisotropy in K(T) 68

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Results 68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Discussion 71 . . . . . . . . . . . . . . . . . . . . 5.3.3 S n m m a r y ... . . .... 77

    APPENDIX 79 A.l Microwave conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . 79 A.2 Thermal Hall effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

  • Schematic view of the relation between temperature gradient and the thermalcurrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrical conductivity t~ and electronic thermal condnctivity K. of a metal as a fnnction of temperature . . . . . . . . . . . . . . . . . . . The Lorenz ratio nr./oT for an ideaIly pedect metal and for specimens with imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal conductivity of a non-metallie crystal . . . . . . . . . . . . . Thermal condnctivity of Pb-10% Bi d o y . . . . . . . . . . . . . . . . Ratio of superconducting to normal thermal condnctivity for aluminum as a function of T/T. . . . . . . . . . . . . . . . . . . . . . . . . . . . Cornparison of theory and experiment for extremely pure metab . . . . Structure of YBCO crystal . . . . . . . . . . . . . . . . . . . . . . . . Resistivity as a fnnction of temperature. for a carrent dong the a ax is (pa ) and the b axis ( p b ) . . . . . . . . . . . . . . . . . . . . . . . . . .

    . . . . . Temperatnre dependence of thermal conductivity by Yu et al Temperature dependence of the ont-of-plane thermal conductivity n . single crystalline of YBCO . . . . . . . . . . . . . . . . . . . . . . . . Low temperature thermal conductivity vs temperature for the un- twinned YBCO crystd measured by Cohn . . . . . . . . . . . . . . . Thermal conductivity of sintered powder YBa2Cn307-s with different oxygen content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    . . . . . . . Experimental data and theoretical curves by Peacor et al Quasipartide scattering rate in YEBL~CU~OT-~ . . . . . . . . . . . . .

    . . . Microwave conductivity of the detwinncd crystal of YE5azCu307-s Temperature dependence of the ne derived fiom rs - nph by YU e t al . SeCematic representation of a twinned crystal . . . . . . . . . . . . . Picture of a s m d area of a twinned sample . . . . . . . . . . . . . . . The transition temperature by resistivity and snsceptibility . . . . . . The SEM image of one of OUT crystals . . . . . . . . . . . . . . . . . . Susceptibity apparatus . . . . . . . . . . . . . . . . . . . . . . . . . Low-temperature portion of the cryostat . . . . . . . . . . . . . . . . A drawing of the thermal conductivity apparatus . . . . . . . . . . . Resistivity vs temperature of three cernox thermometers . . . . . . . The electncal circuit of the experiment . . . . . . . . . . . . . . . . . Demonstration of analysis performed in order to extract the thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal conductivity of Au sample at low temperature . . . . . . .

  • ... vIl1 FIGURES AND TABLES

    rs vs temperature of a pure Au sample up to T = 150 K . . . . . . . .

    rs(T)/n(l80) vs T for YBa2(Cul..ZnJ307.s by Ting et al . . . . . . . . . . . . rc(T) of YBap(Cnl.,Zn=)30 7.s measured by Henning e t al

    Electrical resistivity vs temperature for YBa2(Cul..Zn. )3 O7-& (a-axis) crystals . . . . . . . . . . . . . . . . . . . . . . . o . . . . . . . . . . Electrical resistivity vs temperature for YBCO crystals (twinned) of

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . different Zn-content Tc and p, as a function of Zn content . . . . . . . . . . . . . . . . . . Thermal conductivity of twinned YBa2Cu30.r-s 6 t h Zn-impurities . Thermal conductivity vs T for detwinned YBa2Cu307-s crystals (a- axis) with different Zn content . . . . . . . . . . . . . . . . . . . . . Effect of Zn (upper) on rnicrowave conductivity measured by Zhang . Comparison of tc.s measured by us with that fiom thermal HaJl effect byKrishana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total thermal conductivity K vs temperature for a pure crystal. exper- imental and fitted curve . . . . . . . . . . . . . . . . . . . . . . . . . rc w T(K). with different Zn concentrations fitted by TW theory with

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . diflerent 7 n vs T(K) with difFexent Zn concentrations fitted by TW theory with different gap scaling ratio x . . . . . . . . . . . . . . . . . . . . . . . Normalized electronic thermal conductivity r c , , , / r ~ . , calculated by Hirsfhfeld e t a l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Demonstration of thermal conductivity consisting of phononic part and electronic part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total thermal conductivity n vs T fitted by using ne. calculated by

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hirshfeld The ratio of K,,, to b, for twinned and detwinned Zn-doped YBCO crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    a.. . . . . . . . . . . The ratio of Tm.. to Tc function of Zn content Khn (measured value) vs tempe