Predicting the superconducting transition temperature for libc
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Predicting the Superconducting Transition Temperature for LiBC. Transition Temperature, T c High Transition Temperature of MgB 2 , 39K Similarity in Structure of MgB 2 and LiBC. Lack of Success in Formulating Superconducting LiBC. Introduction. BCS Theory of Superconductivity.

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Predicting the Superconducting Transition Temperature for LiBC

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Predicting the superconducting transition temperature for libc

Predicting the Superconducting Transition Temperature for LiBC


Introduction

Transition Temperature, Tc

High Transition Temperature of MgB2, 39K

Similarity in Structure of MgB2 and LiBC

Lack of Success in Formulating Superconducting LiBC

Introduction


Bcs theory of superconductivity

BCS Theory of Superconductivity

  • Bardeen, Cooper, and Schrieffer (1972)

  • Effect of Phonon Vibrational Modes on Electrons

    • Electrons as Fermions: Half Spin (1/2, 3/2, etc.)

    • Coupled Electrons as Bosons: Integral Spin

  • Allen-Dynes Equation: Tc  : ωln , 


Electron band structure

Electron Band Structure

  • Hybridization of Atomic Energy Levels from Bonding

  • Picture of Allowed Levels but not Probabilities

    • Multiple Locations with Same Energy Level

    • Slope of Bands

    • Density of States (DOS)


Electron band structure1

Electron Band Structure

  • Hybridization of Atomic Energy Levels from Bonding

  • Picture of Allowed Levels but not Probabilities

    • Multiple Locations with Same Energy Level

    • Slope of Bands

    • Density of States (DOS)


Phonon dispersion

Phonon Dispersion

  • Graphs Similar to Electron Band and DOS Plots

  • Vibrational Frequencies for Energy Levels


Computations

Computations

  • BICON – CEDiT

    • Martin Brändle, Ruedi Rytz, and Gion Calzaferri, Department of Chemistry and Biochemistry, Univeristy of Berne

    • Electron Band Structure

  • Unisoft

    • P. Elter and G. Eckold, Institut for Physical Chemistry, University of Göttingen

    • Phonon Dispersion Curve


Determination of spring constants

Determination of Spring Constants

  • BICON – CEDiT for Total Energy

  • Displacements along Lines between Atom Pairs

  • Equation from Classical Mechanics: E = ½ k x2

  • Inaccuracy

    • Other Atoms in Structure

    • ABINIT a common project of the Université Catholique de Louvain, Corning Incorporated,and other contributors (http://www.abinit.org)


Figures

Figures


Calculations and results

Calculations and Results

  • High and Low Values of  (Doping)

    • The Effect of Doping ( = 0.5 and 1.0)

    • DOS Peak near Fermi Level

  • Logarithmically Averaged Frequency, ln

  • Values of Tc: 16 K and 45.4 K


Calculations and results1

Calculations and Results

  • High and Low Values of  (Doping)

    • The Effect of Doping ( = 0.5 and 1.0)

    • DOS Peak near Fermi Level

  • Logarithmically Averaged Frequency, ln

  • Values of Tc: 16 K and 45.4 K


Conclusions

Conclusions

  • Tc Lower than Expected

    • Effect of Doping on ln

    • Anharmonicity

  • Range Still High


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