ABSTRACT
This research investigated the effect
of magnetic field on the thermal conductivity of high temperature type II
superconductors. The result suggested that the thermal conductivity of high
temperature type II superconductor YBa2Cu3O7- decreases as the applied magnetic
field increases at a given temperature. We also found out that the
superconducting energy gap of YBa2Cu3O7- decreases in response to increasing
temperature and applied magnetic field. At a critical temperature of about 100K,
we noted a sharp decrease in the energy gap of the substance. This implies
that, the superconducting energy gap decreases in response to increase in
temperature until at a critical temperature of about 100K,the material transits
to normal state, thus resulting to increase in superconducting energy gap
again. Our finding also revealed that specific heat of YBa2Cu3O7- is proportional to electron density.
CONTENTS
Title Page i
Certification ii
Dedication iii
Acknowledgement iv
Abstract v
Table of contents vi
List of Tables viii
List figure ix
- General Introduction 1
- Introduction and Discovery of Superconductivity 1
- Structure of single crystal of YBa2Cu3O7- 3
- Basic properties of Superconductors 5
1.3.1 Electromagnetic properties 6
1.3.2 Thermal properties 9
1.3.3 Isotope effect 11
1.3.4 Tunneling 11
1.4 Type-I and Type-II 12
1.5 Applications of High-Tc Superconductors 13
1.5.1 High magnetic field, High direct current 13
1.5.2 Alternating current devices 13
1.5.3 Bolometer 14
1.5.4 Josephson tunneling 14
1.5.5 Medicine 15
1.6 Theoretical Basis of Superconductivity 15
1.6.1 Phenomenological theories 15
1.6.2 The Ginzburg-Landau theory 16
1.6.3 Microscopic Theory 16
1.7 Purpose of the study 17
2 .0 Review of Literature 18
2.1 Superconductivity in YBa2Cu3O7- 18
2.2 Thermal Conductivity of High-Tc Superconductors 19
2.3 Magneto-thermal conductivity of high-Tc superconductors 21
3.0 Magneto- thermal conductivity of high-Tc type II superconductors (single crystal of YBa2Cu3O7-) 26
3.1 Introduction 26
3.1.1London Equation 26
3.2 Magneto-Temperature Dependence of Superconducting Energy Gap of YBa2Cu3O7- 28
3.3 Calculation of Thermal Conductivity of YBa2Cu3O7- 29
3.4 Superconducting Energy Gap 31
3.5 Critical Temperature 34
3.6 Specific Heat of YBa2Cu3O7- 35
4. 0 Discussions and Conclusion 38
4.1 Discussion 38
4.2 Conclusion 39 References 40
Appendix A: Program for Calculating Thermal Conductivity of YBa2Cu3O7- 44
Appendix B: Program for Calculating Superconducting Energy Gap of YBa2Cu3O7- 45
Appendix C: Program for Calculating Specific Heat of YBa2Cu3O7- 46
LIST OF TABLES
1.1 High temperature superconductors, Tc and year of discovery 3
3.1 Thermal conductivity at different values of applied magnetic field at T = 60K 45
3.2 Temperature dependence of superconducting energy gap of YBa2Cu3O7- 46
3.3 Specific heat (in arbitrary unit) of YBa2Cu3O7- at different temperature 47
LIST OF FIGURES
- The structure of the parent compound of high –Tc superconductor YBa2Cu3O7- 4
- The structure of (a)YBa2Cu3O7 (b)YBa2Cu3O6.5 (c)YBa2Cu3O65
- A phase diagram of Type-II superconductor 14
3.1 Magnetic induction dependence of the thermal conductivity of a single crystal of YBa2Cu3O7- at temperature (T) = 60K 33
3.2. Temperature dependence of superconducting energy gap of YBa2Cu3O7- 35
3.7 Specific heat curve (in arbitrary unit) of YBa2Cu3O7- at different temperatures 37
CHAPTER ONE
General Introduction
- Introduction and Discovery of Superconductivity
The phenomenon of superconductivity was first observed by Kamerlingh Onnes in Leiden in 1911[1], three years after he liquefied helium gas. He then measured the electrical resistivity of metals such as gold, platinium and mercury. He found that the electrical resistivity of mercury vanished almost completely below 4.2K. The phenomenon by which a material loses all its electrical resistivity below a certain temperature is called superconductivity [2]. The temperature at which this occurs is known as the critical or transition temperature and it is normally denoted by Tc. At temperatures below the critical temperature, the superconducting electrons are ordered and therefore, do not carry heat. Thus, the ordered nature of superconducting electrons reduce the thermal conductivity of superconductors since there is no exchange of heat energy due to non- interactive nature of the super- conducting electrons with the lattice [3].
Superconductivity occurs in many metallic elements of the periodic alloys, and inter-metallic compounds at either low or high temperature. The search for new superconductors is an ongoing process by material scientists with superconducting transition temperature (Tc) above 30K in a mixture of lanthanum and barium-copper oxide [4] La2-xBaxCuOx . High temperature superconductors, otherwise known as high-Tc superconductors were first discovered by Bednorz and Müller in 1986 [4]. Attempts to substitute yittrium (Y) for lanthanum (La) resulted in a polyphase mixture containing a new superconductor with Tc ≈ 90K [5]. Several other copper oxide superconductors were discovered, some with Tc above 120K [6]. Magnesium dibromide MgB2 was found to be superconducting with Tc of 39K. [7]
Anderson identified three essential features of the new superconductors [8]. First the materials are quasi–two dimension (2D); the key structural units seem to be the presence of CuO2 plane and the interplane coupling is very weak. Second, high–Tc superconductivity is created by doping a “Mott” insulator. A Mott insulator is a material in which the conductivity vanishes as temperature tends to zero, even though band theory would predict it to be metallic [9]. Third, Anderson proposed that the combination of proximity to a Mott insulating phase and low dimensionality would cause the doped material to exhibit fundamentally new behaviour, not explicable in terms of conventional metal physics.
Generally, superconductors can be categorised into type I and type II superconductors. In type I superconductors, the transition from superconducting state to normal state in the presence of applied magnetic field is very sharp while in type II superconductors, the transition from super-conducting state to normal state in the presence of applied magnetic field takes place after going through a mixed state region. Table 1.1 gives the transition temperature ( Tc ) and the year of the discovery of some novel superconductors.
