Physics Project

Synthesis and Characterization of

Cu_0.5Tl_0.5Ba₂Ca₂Cu₃O_10-δ

Superconductor

By

Muhammad Aatif khan

Department of Physics

Islamia College University

Peshawar, Pakistan.

2012

Synthesis and Characterization of

Cu_0.5Tl_0.5Ba₂Ca₂Cu₃O_10-δ

Superconductor

A Project submitted to the department of physics, Islamia college university Peshawar, in the partial fulfillment of the requirement for the degree of

Master of Science

in

Physics

by

Muhammad Aatif khan

Department of Physics

Islamia College University

Peshawar, Pakistan.

2012

Certificate

This is to certify that Mr. Muhammad Aatif khan has carried out the experimental work in this Project under my supervision and is accepted in its present form by the Department of Physics, Islamia college University Peshawar as satisfying the Project requirement for the degree of Master of Science in Physics

Supervisor

Lecturer Sami Ullah

Department of Physics

Islamia College University

Peshawar, Pakistan

Submitted through

Chairperson

Prof. Dr. Shazia Naeem

Department of Physics

Islamia College University

Peshawar, Pakistan

DEDICATED

TO

MY parents,

Loving Brothers and Caring Sisters,

To whom these words may stand a

little adoration.

ACKNOWLEDGEMENTS

It gives me great pleasure and satisfaction to acknowledge the endowment of the creator of the universe, Allah Almighty, the most gracious, compassionate and beneficent to His creature, who enabled me to complete my research work successfully. I offer my humblest and sincere words of thanks to The Holy Prophet Muhammad (P.B.U.H) who is forever a source of guidance and knowledge for humanity.

This work would have not been possible without the invaluable contributions of many individuals. First and foremost, I wish to thank my reverend supervisor Lecturer Sami Ullah for all of his support, advice, and guidance during the whole period of my study.

I am thankful to chairperson, department of physics, for the provision of all possible facilities and full cooperation. I would like to pay lots of appreciations to all my teachers who blessed me with knowledge and guidance.

Thanks to all my friends for their help and support.

Finally, I need to thank some individuals on the personal side of my life. To my loving parents, brothers and sisters, my sincerest gratitude for all they have done. I could not wish for a more supportive, loving family, and for them I am deeply thankful and blessed.

MuhammadAatif khan

1. Introduction

1.1 Superconductivity……...….................................................................. (1)

1.2 Some important terms in superconductivity......................................... (3)

1.2.1 Meissner-Ochsenfeld................................................................ (3)

1.2.2 Zero resistivity....................................................................... .. (3)

1.2.3 BCS Theory…………………………………………………. (3)

1.3 Critical Parameters in super conductivity……………………………. (7)

1.3.1 Critical Temperature (Tc)……………………………………. (7)

1.3.2 Critical Current Density (Jc)………………………………… (7)

1.3.3 Critical Magnetic Field (Hc)………………………………… (8)

1.4 Types of superconductors……………………………………………..... (9)

1.4.1 Type I superconductor ………………………………………….. (9)

1.4.2 Type II superconductor…………………………………………. (10)

1.5 High temperature superconductors…………………………..………..... (10)

1.6 Structure of high temperature superconducto............................................ (12)

1.7 Applications of high temperature superconductors…………………….. (15)

1.7.1 Superconductor transmission lines………………………………... (15)

1.7.2 Power Applications, High Tc.................................................... (16)

1.7.3 Fault-Current Limiters…………………………………………...... (16)

1.7.4 Superconducting Motors………………………………………...... (16)

1.7.5 Superconducting Maglev Trains................................................. (16)

1.7.6 Superconductor in MRI Imaging.................................................. (17)

1.7.7 SQUID Magnetometer…………………………………………..... (17)

1.7.8 Internet…………………………………………………………...... (17)

1.7.9 Plasma Confinement……........………..................................... (18)

References.........................................................................................(18)

2. Experimental Techniques

2.1 Preparation of Samples………………………………………………….....(20)

2.2 Characterization…………………………………………………………....(20)

2.3 Electricity Resistivity........................................................................................(20)

2.3.1 Temperature dependence of electricity resistivity……………............(21)

2.3.2 DC- Electrical Resistivity Measurement……………...........................(22)

2.3.3 Methods of Resistivity Measurement.....................................................(23)

2.3.4 Four Probe Method.................................................................................(23)

2.3.5 Apparatus…………………………………………………………......(24)

2.3.6 The Cryostat...........................................................................................(24)

2.3.7 Resistivity Measurements…………………………………........…....(24)

2.4 X-ray Diffraction………………………………………………………….....(25)

2.4.1 Determination of the crystal structure…………………………….....(25)

2.4.2 X-ray Diffraction and Brag’s Law...................................................... (26)

2.4.3 X-ray Diffraction Methods……………………………………....…. (28)

2.5 AC susceptibility ………………………………………………………..…. (30)

2.5.1 AC susceptibility Measurements…………………………………...(31)

2.5.2 Experimental Arrangement……………………………..…………..(31)

References.................................................................................................................(33)

3. Results and Discussion

3.1 Result and discussion.............................................................................................(34)

References.................................................................................................................(36)

List of Figures

Figure 1.1 Variation of electricity resistivity with temperature………………….(2)

Figure 1.2 Behavior of non -superconducting and superconducting materials…...(2)

Figure 1.3 Superconducting transition in pure and impure specimens…………...(3)

Figure 1.4 Diagram of Meissner effect magnetic field lines, etc…...........................(4)

Figure 1.5 Resistivity verses temperature variation in mercury…………….…....(5)

Figure 1.6 Voltage verses current graph for superconductive wire………...........(8)

Figure 1.7 Relation between the temperature and the magnetic field .................(9)

Figure 1.8 Magnetization versus applied magnetic field for a bulk superconductor exhibiting a complete Meissner effect (perfect diamagnetism). A superconductor with this behavior is called a Type1 superconductor. Abovethe critical field, H_c the specimen is a normal conductor and the magnetization is too small to be seen on this scale….........…………. (10)

Figure 1.9 Superconducting magnetization curve of a Type II superconductor. The

flux starts to penetrate the specimen at a field H_c1 lower than the

thermodynamic critical field H_c. The specimen is a vortex state between H_c1and H_c2, and it has superconducting properties up to H_c2. Above H_c2

the specimen is normal conductor in every respect, except for possible surface effects. For given H_c the area under the magnetization curve is samefor Type II superconductor as for a Type I.....................................(10)

Figure 1.10 Variation of T_C with number of CuO₂ planes .................................... (13) Figure 1.11 Unit Cell of Cu_1-xTl_x-1234......................................................................(15)

Figure 1.12 Diagram of superconducting wire…………………………………...(16)

Figure 1.13 Diagram of maglev train………………………………………...…..(17)

Figure 2.1 Arrangement for resistivity measurements……………………...........(25)

Figure 2.2 Diffraction of x-rays by planes of atoms................................................(27)

Figure 2.3 An x-ray diffractometer........................................................................ (31)

Figure 2.4 Bridge network for ac susceptibility measurements………………........ (33)

Figure 3.1 X-ray diffraction scan of (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10-d superconduct...(34)

Figure 3.2 Resistivity curve of (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10-d superconductor.….....(35)

Figure 3.3: AC-susceptibility measurement of (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10-d superconductor.........................................................................................(35)

Introduction

1.1 Superconductivity

The remarkable subject of superconductivity was discovered over half a century ago in which the electrical resistivity of all metals and alloy vanishes altogether when they are cooled to very low temperatures. To understand it, one must know about the possible source of resistance in a conductor. The current in a conductor is carried by “conduction electrons” which are free to move through the material. Electrons have a wave like-nature, and an electron traveling through a metal can be represented by a plane wave progressing in the direction of motion. A conductor (such as metal) has a crystalline structure with the atoms lying on a regular repetitive lattice sites, and it is a property of a plane wave that it can pass through a perfectly periodic structure without being scattered into other directions. Hence an electron is able to pass through a perfect conductor without any loss of momentum in its original direction. In other words, if a current passed through a perfect crystal it will experience no resistance. However, any fault in periodicity of the crystal will scatter the electron wave and introduce some resistance. There are two effects which can introduce resistance. First is a lattice vibration in which atoms are vibrating about their equilibrium position. Second effect is unintentional introduction of defects in the compound during growth of material. Both the thermal vibrations and imperfections scatter the moving conduction electrons and give rise to electrical resistance. This is why the electrical resistivity decreases when a metal or alloy is cooled. When the temperature is lowered, the thermal vibrations of atoms decrease and the conduction electrons are less scattered, Fig.1.1.

For perfectly pure metal, where the electron motion is impeded only by the thermal vibrations of the lattice, the resistivity should approach zero as the temperature is reduced towards zero K. Any real specimen of metal cannot be perfectly pure and will contain some impurities. Therefore electrons, in addition to being scattered by thermal vibrations of these lattice atoms, are also scattered by impurities, and this impurity scattering is more or less independent of temperature. As a result there is a certain “residual resistivity” (ρ_о), shown in

Fig.1.1 that remains even at the lowest temperatures. The more impure the metal, the larger be its residual resistivity.

Fig.1.1 Variation of electrical resistivity of metals with temperature.

Certain metals, however, show a very remarkable behavior; when they are cooled, there electrical resistance decrease in the usual way, but on reaching a temperature a few degrees above zero they suddenly lose their electrical resistance, Fig.1.2. They are then said to have passed into superconducting state. The phenomenon is called as superconductivity; the material is called a superconductor.

Fig.1.2 Behavior of non-superconducting and superconducting materials.

The temperature at which a superconductor loses resistance is called its superconducting transition temperature or critical temperature, this temperature is written as T_c, is different for different metallic elements. A large number of alloys are superconductors. It is possible for an alloy to be a superconductor, even if it is composed of two metals.Conductors, which are not metals in ordinary sense, can show superconductivity ;for

example, the semi conducting mixed oxide of barium, lead and bismuth are superconductors.

On cooling, the transition to superconducting state may be extremely sharp if the specimen is pure and physically perfect. However, if the specimen is impure or has disordered crystal structure, the transition may be considerably broadened; Fig.1.3 shows the transition in pure and impure specimens.

Fig.1.3 Superconducting transition in pure and impure specimens.

Early researchers made the somewhat paradoxical observation that the best conducting materials could not be made to exhibit superconductivity. A good conductor is, by definition, a material that will allow electrons to carry current with a minimum resistance. Since the primary cause of resistance is the collisions of electrons with the lattice, a good conductor must have a minimal interaction between the electrons and the lattice. Consequently, the lattice is unable to mediate an attractive force between the electrons and the superconducting phase transition cannot occur. The converse of this observation also holds as the metals exhibiting poor conductivity make excellent superconductors with relatively higher critical temperatures.

1.2 Important phenomena and theories related to superconductivity

1.2.1 Meissner-Ochsenfeld Effect

1.2.2 Zero Resistivity

1.2.3 BCS Theory

1.2.1 Meissner-Ochsenfeld Effect

One of the properties of superconductors most easy to demonstrate is the Meissner Effect. Superconductors are strongly diamagnetic. A specimen in superconducting state never allows a magnetic flux density to exist in its interior. As in a ‘perfect’ conductor, according to Faraday’s Law, applied magnetic field is opposed by the induced magnetic field, here in the case of superconductor, Faraday’s Law of induction alone explains magnetic repulsion by a superconductor. At a temperature below its critical temperature T_c, a superconductor will not allow any magnetic field to freely enter into its volume. This is because microscopic magnetic dipoles are induced in the superconductors that oppose the applied field. This induced field then repels the source of the applied field, and will consequently repel the magnet associated with that field. This implies that if a magnet was placed on top of the superconductor, when the superconductor was above its critical temperature, and then it was cooled down to below T_c, the superconductor would then exclude the magnetic field of the magnet. This can be seen quite clearly since magnet itself is repelled, and thus is levitated above the superconductor. For this experiment to be successful, the force of repulsion must exceed the weight of the magnet.

Here, one must keep in mind that this phenomenon will occur only if the strength of the applied field does not exceed the value of the critical field H_c, of that superconductor material. This magnetic repulsion phenomenon is called the Meissner Effect and is named after the person who first discovered it in 1933[1]. It remains today as the most unique and dramatic demonstration of the phenomenon of superconductivity, Fig.1.4.

Fig.1.4 Expulsion of magnetic field from a superconductor sample in an applied external field.

1.2.2 Zero resistivity

When a superconductor is cooled to its critical temperature T_c(R=0), its resistance decreases to zero. Classically, the electrical conductivity is defined as

(1.1)

Where , , and are mass of electron, number of electrons, charge on electron and mean free time, respectively. As the temperature decreases, the lattice vibrations begin to freeze, therefore, the scattering of electrons from lattice vibrations diminishes. This results in enhancement of (the mean free time of the carriers between collisions) and decreases resistivity. For infinite t at sufficiently low temperature the resistivity vanishes entirely which is observed in superconductors [2].

If the phonon scattering were the only mechanism contributing to resistivity, then the resistivity is expected to vanish at absolute zero. But besides phonon scattering, the electrons are also scattered by impurity atoms and lattice imperfections. Due to these additional mechanisms, even at zero K a small residual resistivity is observed [3]. The variation of resistivity with temperature for pure Mercury (Hg) at low temperatures, was studied by Kammerlingh Onnes in 1911 and surprisingly, he observed that the resistivity vanished altogether, i.e. became zero at 4.15 K as shown in the Fig. 1.5

Fig 1.5 Variation of resistivity with temperature in Hg.

1.2.3 BCS Theory

Superconductivity was not sufficiently explained until 1957 when John Bardeen and his graduate assistants Leon Cooper and John Schrieffer proposed a microscopic explanation [6] that would later be named as the BCS Theory. This theoretical explanation later awarding them the Nobel Prize, making John Bardeen the only man in history to be awarded this honor twice.

In BCS theory of superconductivity they attributed superconductivity to an attractive interaction between two electrons through electron-phonon interaction. The attractive interaction between electrons can be understood in the following way: one electron interacts with a positive ion in the lattice and deforms the lattice: a second electron of compatible momentum value interact with the ion in the distorted lattice so as to minimize the energy. The interacting electrons are said to form a pair. The electrons of a pair have equal and opposite momentum (i.e. one with +k and other with –k), with the one in spin up state and the other in spin down state, so that the total spin of a pair is zero. The electron pairs are called Cooper pairs. The important feature of Cooper pair is that excitation can take place in only pairs of electrons; i.e., if the state with +k and spin up (↑) is occupied, the corresponding state with –k and spin down (↓ ) is also occupied and if the state of +k is vacant, the state of –k is also vacant.

The cooper pair have net zero spin and are able to condense into quantum mechanical ground state with long range order. One consequence of this is the existence of small energy gap near E_F. The formation of cooper pairs results in the minimization of the total energy of the system and leads to a small energy gap ∆ near the Fermi energy E_F. Most of the special characteristics of a superconductor can be understood as a consequence of the existence of small energy gap [3].

This BCS theory prediction of Cooper pair interaction with the crystal lattice has been verified experimentally by the isotope effect; the critical temperature of a material depends on the mass of the nucleus of the atoms.

(1.7) If an isotope could be induced in a material by adding neutrons to the element under consideration causing isotope to make it more massive and as a result we see the decrease/increase of the critical temperature. Another prediction of the BCS theory is the existence of energy gap 2∆ at the Fermi level.

The BCS theory went on to predict many other physical properties of the superconducting state. For most of the metallic superconductors such as Al , Hg , etc. these agreed very well with the experimental facts, providing strong evidence in support of the theory. For example , two key predictions where the behavior of nuclear magnetic resonance (NMR) relaxation rate, 1/T₁ below the critical temperature T_c and the temperature dependence of the attenuation coefficient for ultra sound [7].

1.3 Critical Parameters in Superconductivity

To understand the phenomenon of superconductivity some of the critical parameters should be taken into account, which are of utmost importance and could be categorized as follows;

1.3.1 Critical Temperature (T_c)

1.3.2 Critical Current Density (J_c)

1.3.3 Critical Magnetic field (H_c)

1.3.1 Critical Temperature (T_c)

According to BCS theory, as long as the superconductor is cooled to very low temperatures, the formation of cooper pair takes place, due to the reduced atomic motion (vibrations). As the superconductor gains heat energy, the vibrations in the lattice become more violent and break the cooper pairs. As they break, superconductivity is destroyed. Superconducting alloys and metals have characteristic transition temperatures at which they are transformed from normal conductors to superconductors called critical temperatures (T_c). The resistivity of a material becomes zero below the superconducting critical transition temperature. Superconductors made from different materials have different T_c values, YBa₂Cu₃O₇ have T_c about 92K [8], while for HgBa₂Ca₂Cu₃, it is up to 133K [9].

1.3.2 Critical Current Density (J_c)

Since there is no loss in electrical energy when superconductors carry electrical currents, relatively narrow wires made of superconducting materials can be used to carry huge currents. But there is a certain maximum current limit that these materials can carry, above which they become normal conductors. If too much current is pushed through a superconductor, it will revert to a normal state even though it may be below its transition temperature. The value of the critical current density (J_c) as a function of the temperature is

shown in Fig.1.6. During J_c measurements it is observed that the colder you keep the superconductor the more current it can carry. For practical applications, J_c values in excess of 1000 A/mm² are preferred.

Fig.1.6 I-V Characteristic of a superconductor showing critical current flowing through it.

Magnetic 1.3.3 Critical field (H_c)

An electrical current in a wire creates a magnetic field around the wire. The strength of the magnetic field increases as the current in the wire is increased. Because superconductors are able to carry large currents without any loss of electrical energy, so they are all well suitable for making strong electromagnets. When a superconductor is cooled below its transition temperature (T_c) and a magnetic field is increased around it, the magnetic field (H) remains around the superconductor. If we increase magnetic field to a certain point, the superconductor will go to the normal resistive state. This maximum value of the magnetic field (at a given temperature) is known as the critical magnetic field (H_c). For all superconductors there exists regions of temperatures and magnetic fields within which a material is in the superconducting state. Outside this region, the material is in the normal state as shown in, Fig.1.7.

Fig.1.7 Dependence of critical magnetic field of a superconductor on the temperature.

1.4 Types of Superconductors

According to their magnetic properties, superconductors are divided in to two following types,

1.4.1 Type 1 superconductors

1.4.2 Type II superconductors

1.4.1 Type 1 superconductors

Type I superconductors are very pure metals. For example very pure samples of lead, mercury, and tin are examples of Type I superconductors. Complete Meissner effect (i.e. B=0 inside a superconductor) is observed in type I superconductors. Fig.1.8. is a graph of induced magnetic field of a Type I superconductor versus applied field. It shows that when an external magnetic field (horizontal abscissa) is applied to a Type I superconductor the induced magnetic field (vertical ordinate) exactly cancels that applied field until there is an abrupt change from the superconducting state to the normal state. The values of H_c are always too low for type I superconductors to have any useful technical application in coils for superconducting magnets

Fig.1.8. Magnetization versus applied magnetic field for a type 1 superconductor.

1.4.2 Type II Superconductors

High temperature ceramic superconductors such as YBa₂Cu₃O₇(YBCO) and Bi₂CaSr₂Cu₂O₉ are examples of Type II superconductors. Fig.1.9. is a graph of induced magnetic field of a Type II superconductor versus applied field. Type II superconductor have superconducting electrical properties up to a field denoted by H_c2. Between the lower critical field H_c1 and the upper critical field H_c2 the flux density B≠0 and the Meissner effect is said to be incomplete. The value of H_c2 may be 100 times or more high than the value of the critical field H_c calculated from the thermodynamics of the transition. In the region between H_c1 and H_c2 the superconductor is threaded by the flux lines and said to be in vortex state [2].

Fig.1.9. Superconducting magnetization curve of a Type II superconductor.

The flux starts to penetrate the specimen at a field H_c1 lower than the thermodynamic critical field Hc. The specimen is a vortex state between H_c1 and H_c2, and it has superconducting properties up to H_c2. above H_c2 the specimen is normal conductor in every respect, except for possible surface effects. For given H_c the area under the magnetization curve is same for Type II superconductor as for a Type I.

1.5 High temperature superconductors

In 1911 Kammerling Onnes, after the liquification of helium observed that the electrical resistance of various metals such as mercury, lead and tin disappeared completely at a critical temperature T_c. Later on, this phenomenon was found in many metals and alloys [1]. But until quite recently it was strictly a low temperature phenomenon as the highest critical temperature of 23.3K was achieved in Nb₃Ge superconductor which was still a very low temperature. But the revolution in the field of superconductivity came in 1986, when Bednorz and Muller discovered superconductivity in oxides of ceramic materials, i.e. La-Ba-Cu-O, with a critical temperature of 30K. The existence of high temperature superconductivity in this system was confirmed by magnetic studies. The T_c(0) was found to increase by the replacement of Ba with Sr at normal pressure. The application of external pressure was also found to increase the T_c(0) of the final compound. The possible source of increase of critical temperature is the reduction of lattice parameters when external pressure is applied [10].

The second phase in the progress of high T_c superconductor came with the discovery of superconductivity in Y-Ba-Cu-O with a critical temperature above the boiling point of the liquid nitrogen. In this system T_c(0) ranges from 80 to 92K. By the structural analysis it was found that the lattice parameters of this compound follow orthorhombic structure. From the detail characterization it was later found that the mixed valance ratio of Cu, the density of carrier in the conducting CuO₂ planes controlled by O₂ content play a crucial role in achieving the superconductivity above 77K in this compound [10-11].

Discoveries of La-based and Y-based superconductors have stimulated a worldwide race towards superconductor with higher critical temperature. In spite of much effort, the reproducible superconductivity has remained at 90K for RE-Ba-Ca-O-based (RE = rare earth element) high temperature superconductors. Two important breakthroughs were made by Maeda, Sheng and Hermman by their discoveries of superconductivity in Bi and Tl-based superconductors [12]. Maeda et.el synthesized the Bi-Sr-Ca-Cu-O oxide, with transition temperature around 110K. These series of superconductors are more ductile and stable than La and Y-based superconductor because it consists of several superconductive phases which are not trivial to be separated [13]. Another characteristic CuO based high temperature superconductor is the Tl-Ba-Ca-Cu-O, which was discovered by Sheng and Hermann. This superconducting system has two superconducting phases one with single Tl-O layer and the other with double Tl-O layer in their charge reservoir block These two compounds have critical temperature of 130K and 127K respectively. These compounds due to their higher critical current, irreversibility field H_irr and lower surface resistance R_s were found promising for their use in device applications. The Tl-based materials have also got multiphase character, which is controlled by amount of Tl and fabrication temperature [12]. Thee their use in applications.ity field Hirr30K and 127K respectivily.ocksred and Muller discovered artificial superconductor I superconductor with even higher critical temperature belongs to Hg-Ba-Ca-Cu-O family has also been discovered. In Hg-based high temperature superconductors, the HgBa₂Ca₂Cu₃O_8+d has highest critical temperature around 135K which is prepared at normal pressure. Hg-based superconductors were also prepared under high pressure which provided crucial clues to the existence of superconductivity at higher temperatures. The critical temperature of optimally doped phases HgBa₂Ca_m-1Cu_mO_2m+2+d with m=1, 2, 3 have been investigated. The critical temperature of HgBa₂Cu₁O_4+d is 94K, HgBa₂Ca₁Cu₂O_6+d and HgBa₂Ca₂Cu₃O_8+d phase have shown T_c around 135K. The T_c of later two phases have shown dependence on oxygen content in HgBa₂O_4-d charge reservoir layer. For Hg-based superconductor the highest T_c attained up till now is 138K of Hg₀.₈Tl_0.2Ba₂Ca₂Cu₃O₈ sample. The resistivity of these compounds when measured under pressure have shown T_c(0) around 160K [13-14].

Another class of high temperature superconductor is CuBa₂Ca_n-1Cu_nO_2n+4-d, which has CuBa₂O_4-d charge reservoir layer. These materials have Cu in the charge reservoir layer and have shown lowest anisotropy (g=1.6) among all cuprates high temperature superconductors. The highest T_c(0) in this family is credited to Cu-1223, with T_c(0) =120K. These compounds are prepared under high pressure (~ 4GPa) [15-16]. But the partial replacement of Cu by Tl in the charge reservoir made it possible, to synthesis these compound at normal pressure. The resulting Cu_1-xTl_xBa₂Ca_n-1Cu_nO_2n+4-d compound still have low anisotropy and have shown higher critical temperature too. The (Cu_1-xTl_x-1223) compound of this family has T_c(0) around 132K, which is highest in this family Cu_1-xTl_xBa₂Ca₂Cu₃O_10-d [17].

1.6 Structure of High Temperature Superconductor

Multi layered cuprates have common structural characteristic described by the formula MCa_n-1Cu_nO_2n, where M is the Charge reservoir layer and Ca_n-1Cu_nO_2n are superconductor blocks. The charge reservoir layer is generally represented by ABa₂O_4-d; where A: Tl, Bi, Cu, Hg. The type of atom ‘A’ in the charge reservoir layer forms a new homologous series of superconductor compounds. Whereas superconductor block consist of CuO₂ planes and are separated by Ca atoms. In each homologous series the number of CuO₂ planes varies from n=1 to n=5. The function of charge reservoir layer is to supply the carriers to the conducting CuO₂ planes and the optimum number of carriers in these planes determines the critical temperature of a particular compound. In multilayered cuprates outer planes have pyramidal five-fold oxygen coordination whereas the inner planes have square four-fold oxygen coordination. The outer planes are found to be over doped with carriers, whereas the inner planes are in under doped region of carrier dopings [18].

The superconducting transition temperature in homologous series depends upon the ‘n’ number of CuO₂ planes. The T_c(0) increases upto n=3 and then decreases with further increase in n. The decrease in the T_c(0) for n>3 is suggested to be due to the inhomogeneous distribution of carriers in inner and outer CuO₂ planes and the Tc(0) is determined from the intrinsic T_c’s of the two types of the CuO₂ planes. Fig.1.10. shows the variation of critical temperature as a function of ‘n’ for typical multilayered cuprates of MBa₂Ca_n-1Cu_nO_2n (M=Hg, Tl). [18-19]. The charge distribution among the CuO₂ planes well correlates with the electrostatic potential associated with apical oxygen at each CuO₂ plane, which has more attraction for holes in the outer plane (OP) than in the inner plane (IP). The difference in the doping level increases with ‘n’ which increase the density of carriers. This difference between the carrier concentrations N_h(OP) and N_h(IP) is smallest for n=3 and the inner plane can achieve an optimally doped state, that is the reason due to which most of the multilayered cuprates have the highest T_c at n=3.

Fig. 1.10. Variation of TC with number of CuO₂ planes.

It has been pointed out that the decrease in T_c for n³4 is due to the large inhomogeneity of the carrier distribution. The outer plane (OP) can have enough charge carriers for superconductivity, whereas the inner plane (IP) carriers become too small to induce superconductivity. Systematic investigation of the multilayered high-T_c superconductor by nuclear magnetic resonance (NMR) experiments have revealed that the carrier concentration of OP(Nh (OP)) adjacent to the charge reservoir layer (CRL) is always greater than that of IP(Nh (IP)) [20-21].

Since the discovery of superconductivity in both CuBa₂Ca_nCu_n+1 and TlBa₂Ca_nCu_n+1 systems (designated as Cu-12n(n+1) and Tl-12n(n+1) respectively), these compounds have been extensively characterized. Both of these systems are isostructural except the position of oxygen in the charge reservoir layer. The superconducting properties of these compounds could be enhanced by optimizing the carrier concentration. The carrier concentration could be modified by cation substitution, by varying oxygen contents and by applying external pressure [22-23]. The as-prepared samples of CuTl-12n(n+1) superconductor are in the over doped region of carriers and the effective density of state near the Fermi level D(E_F) is greater than optimum value. The carrier concentration in CuTl-1223 superconductor could be optimized by carrying out post-annealing in nitrogen atmosphere. The critical temperature of this compound could be increased by carrying out post-annealing experiments. Through these experiments we can optimize the charge state of Tl atoms from Tl⁺³ to Tl⁺¹. Thallium with Tl⁺¹ has lower quantity of oxygen with it whereas Tl⁺³ has more oxygen. The more oxygen in the charge reservoir layer hinders the flow of electron to the conducting CuO₂ planes; oxygen controls this through its higher electro negativity. The lower oxygen concentration associated with Tl⁺¹ can efficiently allow the electron flow to the conducting CuO₂ planes. Therefore the change of oxidation state of Thallium from Tl⁺³ to Tl⁺¹ brings the carrier concentration in CuO₂ planes to optimize level [24].

On the other hand the doping of various cations especially the alkali metals and transition metals at the planner site and at charge reservoir layer has a strong influence on the properties of high temperature superconductors. The substitution of magnetic ions such as Ni⁺², Co⁺³, Fe⁺³ etc. causes a drastic change in the structural and superconducting properties due to the magnetic ordering inside the plane and at the charge reservoir layer. Fig.1.11 Unit Cell of Cu_1-xTl_x-1234

1.7 Applications of High Temperature Superconductors

1.7.1 Superconducting Transmission Lines

Since 10% to 15 % of generated electricity is dissipated in resistive losses in transmission lines, the prospect of zero loss superconducting transmission lines is appealing. In prototype superconducting transmission lines at Brookhaven National laboratory, 1000 MW of power can be transported within an enclosure of diameter 40 cm.

This amounts to transporting the entire output of a large power plant on one enclosed transmission line. This could be a low voltage AC transmission lines on towers in the conventional systems. The superconductor used in these protype applications is usually niobium-titanium, and liquid helium cooling is required. Current experiments with power applications of high-temperature superconductors focus on uses of BSCCO in tape forms and YBCO in thin film forms. Current densities above 10,000 amperes per square centimeter are considered necessary for practical power applications, and this threshold has been exceeded in several configurations.

Fig.1.12 Superconducting wire.

1.7.2 Power Applications, High T_c

Power applications of high temperature superconductors would have the major advantage of being able to operate at liquid nitrogen temperature. The biggest barrier to their application has been the difficulty to fabricating the materials into wires and coils. Current development focuses on BSCCO and YBCO materials.

1.7.3 Fault-Current Limiters High fault-currents caused by lighting strikes are a troublesome and expensive nuisance in electric power grids. One of the near-term applications for high temperature superconductors may be the construction of fault-current limiters, which operate at 77K. The need is to reduce the fault current to a fraction of its peak value in less than a cycle (1/60sec). A recently tested fault-current limiter can operate at 2.4 kV and carry a current of 2200 amperes. It was constructed from BSCCO material.

1.7.4 Superconducting Motors

Superconducting motors and generators could be made with a weight of about one tenth that of conventional devices for the same output. This is the appeal of making such devices for specialized applications. Motors and generators are already very efficient, so it may be possible to build very large capacity generators for power plants where structural strength considerations place limits on conventional generators. In 1995, the Navel Research Laboratory demonstrated a 167 hp motor with high-T_c superconducting coils made from Bi-2223. It was tested at 4.2K and at liquid neon temperature, 28K with 112 hp produced at the higher temperature.

1.7.5 Superconducting Maglev Trains

While it is not practical to lay down superconducting rails, it is possible to construct a superconducting system onboard a train to repel conventional rails below it. The train would have to be moving to create the repulsion, but once moving would be supported with very little friction. There would be resistive loss of energy in currents in the rails. Ohanian reports an engineering assessment that such superconducting trains would be much safer than conventional rail system at 200 km/h. A Japanese magnetically levitated train set a speed record of 321 mile/h in 1997 using superconducting magnets on board the train. The magnets induced currents in the rails below them, causing a repulsion, which suspends the train above the track.

Fig.1.13 The Yamanashi MLX01 MagLev test vehicle achieved a speed of 361 miles per hour on December 2003.

1.7.6 Superconductors in MRI Imaging

Superconducting magnets find application in magnetic resonance imaging (MRI) of the human body. Besides requiring strong magnetic fields of the order of a Tesla, magnetic resonance imaging requires uniform fields and stability of extreme type over the time across the subject. Maintaining the magnet coils in the superconducting helps to achieve parts-per-million spatial uniformity over a space large enough to hold a person, and ppm/hour stability with time.

1.7.7 SQUID Magnetometer

The superconducting quantum interference device (SQUID) consists of two superconductors separated by thin insulating layers to form two parallel Josephson junctions. The device may be configured as a magnetometer to detect incredibly small magnetic fields small enough to measure the magnetic fields in living organisms. SQUID’S have been used to measure the magnetic fields in mouse brains to test whether there might be enough magnetism to attribute their navigational ability to an internal compass. The great sensitivity of the SQUID devices is associated with measuring changes in magnetic field associated with one flux quantum [3]. One-flux quanta can be expressed as

Φ_o = 2πһ/2e ≈ 2.0678×10^-15 tesla.m²

1.7.8 Internet

Superconductors may even play a role in Internet communications soon. For high-speed data

communications up to 160 GHz. Since Internet traffic is increasing exponentially, superconductor technology is being called upon to meet this super need.

1.7.9 Plasma Confinement

A Tokamak is a type of device in which dense high temperature plasma is confined by a large external magnetic field. The magnetic field is generated by a superconducting magnetic system consisting of large number of different winding. In different countries different plants are constructed to confine the plasma with superconducting magnets.

References

[1] Engineer Guide to High Temperature Superconductivity, James D. Doss, John Wiley

& Sons New York (1989).

[2] Introduction to Solid State Physics, Charles Kittle, Seventh Edition.

[3] Materials Science, M. S. Vijaya.

[4] V.L. Ginzburg and L.D. Landau, Eksp.Teor. 20 (1950).

[5] The Physics of Superconductors, An Introduction to Fundamental and Application,

P.Muller, A.V Ustinov (Eds.) and V.V Schmidt.

[6] Solid State Physics, An Introduction to Theory and Experiment, Harald Ibach, Hans

Luth, Springer-Verlog, Berlin New York. (1995).

[7] Superconductivity, Superfluids and condensates, James F. Annett.

[8] M.K. Wu, J.R.Ashburn, C.J.Torng, P.H.Hor, R.L.Meng, L.Gao, Z.J.Huong,

Y.Q.Wang and C.W.Chu, Phys.Rev.Lett. 58, (1987) 315.

[9] A. Schilling, M.Contoni, J.D.Guo and H.R.Ott, Nature, 363, (1993) 56.

[10] C. W. Chu, P. H. Hor, R. L. Meng, Phys. Rev. Lett. 58, (1987) 9.

[11] A. G. Mamalis, D. E. Manolakos, A. Szalay, G. Pantazopoulos, Processing of High

Temperature Superconductor, Penney lvenia U.S.A, (2000) 315.

[12] Z. Z. Sheng, W. Kiehl, J. Bennett, Phys. Rev. Lett. 52, (1988) 20.

[13] L. Gao, Y. Y. Xue, F. Chen, Q. Xiong, Phys. Rev B. 50, (1994) 6.

[14] www. “A decade after the discovery of High T_c Superconductivity”.

[15] H. Ihara, K. Tanaka, A. Iyo, N. Terada, Physica B 1085, (2000).

[16] K. Tokiwa, H. Aota, A. Iyo, Phys B. 284-288 (2000) 1077

[17] T. Watanabe, S. Miyashita, N. Ichioka, Phys B. 284-288 (2000) 1075.

[18] A. Iyo, Y. Tanaka, Y. Kodama, H. Kito, Physica C 445-448 (2006) 17.

[19] Xiaojia Chem, Changde Gong, Phys. Rev. B, 59, (1999) 6.

[20] Robert V. kasowski, Phys. Rev B vol. 38, (1998) 10.

[21] M. Di Stasio, K. A. Muller, Phys Rev Lett. Vol 64, (1990) 23.

[22] K. Tokiwa, C. Kunugi, H. Aota, J. of Low Temp. Phys. Vol 117, N0. 3 (1999).

[23] A. Iyo, Y. Aizawa, Y. Tanaka, Physica C 357-360 (2001) 324.

[24] K. Tanaka, A. Iyo, N. Terada, Phys Rev B. Vol. 63, (2001) 315.

Experimental Techniques

2.1 Preparation of Samples:

The sample of and Cu0.5Tl0.5Ba2Ca3Cu4O12-d was prepared by simple solid state reaction method using Ba(NO3)2, CaCO3 and Cu2(CN)2.H2O as starting compounds. These materials were mixed according to the formula unit Cu0.5Tl0.5Ba2Ca3Cu4O12-d and ground for about an hour in a quartz mortar and pestle. The mixed material was put in a quartz tube and loaded in a preheated furnace at 880oC. The heating was carried out for 24hrs in air and then furnace is cooled to room temperature. The material was then ground for an hour and put again in the preheated furnace for second firing at 880oC for 24hrs. A specific amount of the Tl2O3 was added following the formula unit Cu0.5Tl0.5Ba2Ca3Cu4O12-d and was mixed about an hour. The thallium mixed material was pelletized under 6 tons pressure. The pallets were wrapped in the thin aluminum foil to preserve any possible loss of volatile Tl at high temperature and to develop the equilibrium vapour pressure of Tl; three layers of aluminum foil were applied to the pallet before annealing. The wrapped pallets were then put in a preheated furnace at 880oC for heat treatment for 7 minutes. After the heat treatment the pellets were quenched to room temperature.

2.2 Characterization:

The superconductor samples were characterized by resistivity measurements using four-probe method and structure was determined by XRD (X-ray diffraction). Diamagnetic characteristics of superconducting samples were measured ac-susceptibility measurements using Lock-in amplifier.

2.3 Electrical Resistivity:

When current flows through a conductor, some resistance is offered to the flow of this current. This resistance arises due to the collisions of electrons to the atoms in the conductor. The resistivity due to the collisions of these electrons is given by

(2.1)

Where r is the resistivity, ‘e’ is the charge on the carrier, ‘m’ is the mass of the charge carrier, ‘n’ is the concentration of the charge carriers and t is the average time between two collisions of the free charge carrier. The probability of an electron to suffer a scattering per unit time will be 1/t. For example if t = 10^-14 sec, then it means that there will be 10¹⁴ collisions suffered by the electron in a second. The reason of these collisions is that the lattice is not perfect. Imperfections in the lattice may arise due to many reasons like vibrations of the atoms about their mean positions and the addition of external impurity atoms at the lattice sites. So the electrons are scattered by phonons and the impurities at the lattice sites. So the total probability of an electron being scattered will be partly by phonons and partly by impurities. i.e.

(2.2)

So the resistivity is due to lattice imperfections and by phonons.

r = r_ph + r_i (2.3)

Here ri is the resistivity due to the lattice imperfections and is independent of temperature. The rph, the ideal resistivity is due to vibrations of atoms about their mean positions and it temperature is dependent[1,2].

2.3.1 Temperature dependence of electrical resistivity:

The resistivity of the substance also depends upon the temperature. As we know that the resistance of a conductor to the flow of electrons arises due to the collisions of the electrons with the atoms at the lattice sites.

As we increase the temperature of the conductor, the amplitude of vibrations of the lattice atoms increases, causes the lattice atoms to offer more scattering cross section to the flow of free electrons. This makes the collisions between free electrons and the atoms in the lattice more frequent and consequently the resistance of the conductor increases. At high temperatures the scattering probability depends upon the mean square amplitude of vibrations of the lattice atoms. This, indeed, is one of the basic experimental facts about the simple metals such as copper, sodium, potassium etc. Any decrease in the temperature will result in lowering the amplitude of thermally excited vibrations. At any temperature ‘T’, the resistivity dependence on temperature is of the order of T5 at low temperatures for normal scattering process. Experimental results for alkali metals have confirmed this T5 dependence.

2.3.2 DC-Electrical Resistivity Measurements:

According to Ohm’s Law

V = IR (2.4)

(2.5)

Where V is the applied voltage and ‘I’ is the current flowing in the circuit and R is the resistance offered by the conductor to the moving electrons that constitute the current. Experiments have shown that the resistance of the conductor also depends upon the geometry of the conductor along with the temperature. It has been found that the resistance of the conductor is directly proportional to its length and inversely proportional to its area of cross section. If ‘L’ is the length of a certain conductor and ‘A’ is the area of cross section, then we can write that

(2.6)

Where r is the proportionality constant and is called the resistivity of the conductor. The resistivity of a material depends upon the temperature as discussed earlier. So the resistivity in terms of temperature can be written as

(2.7)

The SI unit of the resistivity is -cm.

If length L, area of cross section A and the current I through the material are constant, then the resistivity variation is proportional to the voltage drop and are calculated by using Eq. 2.7.

2.3.3 Methods of Resistivity Measurement:

The factors affecting the suitability of the methods and precision attainable include the contact resistance and form of a sample usually in our case it was the bulk superconducting material. The samples in our case was superconductors of Cu_1-xTl_x -1223. The simplest method of measuring resistivity is to measure voltage drop V across the sample, the current through the sample I and calculating the length L between voltage contacts and area of cross section A and using equation.

r (T) = (2.8)

2.3.4 Four Probe Method:

We measured resistivity of the superconducting materials using the four-probe method. This method is widely used for measurements of resistivity in metals, semiconductors and superconductors. Fig.2.1 shows the experimental arrangement for four-probe method.

Fig.2.1 Arrangement for resistivity measurements.

The contacts were made by silver paste on the surface of the superconducting bulk material and copper wires. The distance between the middle contacts is ‘L’ and the cross sectional area A (width × thickness) was measured and the voltage drop across the voltage contacts was also measured. By using formula given below, we can calculate the resistivity of the samples as [3].

r (T) = (2.9)

2.3.5 Apparatus:

The resistivity measurement employing four-probe method consists of following apparatus:

1. The constant current source was constructed by connecting a resistance in series with the MW2122A regulated DC power supply.
2. A micro-ammeter was connected in series, which can measure current up to 1000μA with an accuracy of 1.0μA.
3. The P-2000/E KEITHLEY MULTIMETER was used to measure voltage drops across the samples corresponding to the variations in the temperature.
4. Temperature measurements were carried out by using a copper constant thermo couple.

2.3.6 The cryostat:

A simple cryostat consists of

1. Liquid Nitrogen Dewar.

2. A brass pipe with sample holder at one end and connecting wires at the other end.

2.3.7 Resistivity Measurements:

Resistivity measurements were carried out in a systematic way by using following steps.

1. The sample was washed with acetone and fixed with blue stick to the sample holder; at the other end of the blue stick is the hot junction of the thermocouple.
2. Electrical leads were attached to the sample using silver paste, which makes Ohmic contacts of the leads with the sample.
3. The electrical leads were connected to the voltmeter, ammeter and multimeter. The other end of the thermocouple was attached with copper wire to produce a colder junction. This junction point of the thermocouple was dipped in the liquid nitrogen and kept at 77K during measurement.
4. The sample holder was covered with a metallic cap. The lowering or raising of the sample holder in the liquid nitrogen container controlles the temperature of the sample.
5. The changes in the voltage drop across the sample with the temperature were recorded.
6. The data was measured during heating cycle.
7. The dimensions of the sample were measured by using Vernier Caliper and Screw Gauge.

These measured dimensions were used to calculate the resistivity of the sample. The resistivity behavior of the sample was observed by plotting a graph between resistivity and temperature.

2.4 X-Ray Diffraction:

2.4.1 Determination of the crystal structure:

Historically, much of our understanding regarding the atomic and molecular arrangements in solids has resulted from x-ray investigation; furthermore, x-rays are still very important tool in determining the structure of new materials. We will now give a brief overview of the diffraction phenomenon to see how we can determine the atomic interplaner distances and crystal structures by using x-rays.

2.4.2 X-Ray diffraction and Bragg’s Law:

When a wave encounters a series of regularly spaced obstacles, the wave is then scattered, this scattering of the wave with the obstacles is called diffraction. Scattering can occur from obstacles only when the spacing between two obstacles is comparable to the wavelength of the wave. Furthermore, diffraction is a consequence of specific phase relationships between two or more waves that have been scattered from obstacles. X-rays are electromagnetic waves that have high energies and short wavelengths (wavelengths of the order of the atomic spacing for solids). When a beam of x-rays is incident on a solid-state material, a portion of this beam is scattered in all directions by the electrons associated with each atom or ion that lies on the path of the beam.

We can examine the necessary conditions for the diffraction of x-rays from a periodic arrangement of atoms by considering three parallel planes of atoms X-X/, Y-Y/ and Z-Z/ in the Fig.2.3. These planes have same Miller indices i.e. h, k and l. These planes are separated by the interplaner spacing “d_hkl”. Now if we make incident a parallel, monochromatic and coherent (in phase) beam of x-rays of wavelength λ on these three planes at an angle θ, then the three rays in the beam will be scattered by the three atoms located at the positions A, C and E.

Fig.2.2 Diffraction of x-rays by planes of atoms.

The scattered waves will constitute constructive interference if the spacing between two planes is comparable to the integral multiple ‘n` of the wavelength of the x-rays. i.e.

n _λ = 2 d_hklSinθ (2.10)

Where ‘n’ is the order of reflection, which may be any integer. i.e. n=1,2,3…

This relation was developed by W.L.Bragg and is known as the Bragg’s Law. For a fixed value of ‘λ’ and ‘d_hkl’ there may be several values of angles of incidence θ₁, θ₂, θ₃ etc. from which the diffraction may occur for the corresponding ‘n’ values.

For the constructive interference of the waves, Bragg’s law should be satisfied and we get a high intensity diffracted beam and if it is not satisfied, then there will be destructive interference so in this case we yield a very low intensity of the diffracted beam. Bragg’s law states the essential condition, which must be met if diffraction is to occur.

Since Sinθ cannot exceed unity, we may write equation (2.8) as,

n_l / 2d_hkl=Sinθ <1 (2.11)

Therefore, nl must be less than 2dhkl. For diffraction the smallest value of ‘n’ is 1. The n=0 corresponds to the beam diffracted in the same direction as the transmitted beam, so it cannot be observed. Therefore, the condition for diffraction at any observable angle is

l<2d_hkl (2.12)

For most set of crystal planes ‘d_hkl’ is of the order of 3Å less, which means that λ can not exceed about 6Å. The commonly used target materials in x-ray tubes are Cu and Mo. These two target material produce x-rays with wavelengths 1.54Å and 0.8Å respectively

[4-6].

The magnitude of the distance between two adjacent and parallel planes of atoms (i.e. the interplaner spacing d_hkl) is a function of Miller indices (h, k and l) as well as the lattice parameters. The crystal structures with cubic symmetry have the following relation between the dhkl and lattice parameters

(2.13)

Where ‘a’ is the lattice parameter (unit cell edge length)

Similar relationship for crystal structure like tetragonal and hexagonal are given by

For tetragonal structure,

or

(2.12)

For hexagonal crystal structures

(2.13)

Where ‘a’ and ‘c’ are the lattice parameters

Bragg’s law is necessary condition but not sufficient for diffraction by real crystals. It specifies that the diffraction will occur for unit cells having atoms positioned only at cell corners. However, atoms situated at other sites (e.g. face and interior unit cell positions as with FCC and BCC) act as extra scattering centers, which can produce out of phase scattering at certain Bragg angles. The net result is the absence of some diffracted beams that according to equation 2.8 should be present.

2.4.3 X-Ray Diffraction Technique:

X-Ray diffraction can occur whenever the Brag’s law, nl=2dSinθ, is satisfied. This equation puts very stringent conditions on l and θ for any given crystal. With monochromatic radiation, an arbitrary setting of a single crystal in a beam of x-ray will not in general produce any diffracted beams. Some ways of satisfying the Bragg’s law must be devised and this can be done by continuously varying either l or θ during the experiment. The scheme in which these quantities varied given in three main diffraction methods is given by

l θ

1) Lau Method Variable Fixed

2) Rotating Crystal Method Fixed Variable

3) Powder Method Fixed Variable

One common diffraction technique employs a powder polycrystalline specimen consisting of many fine and randomly oriented particles that are exposed to monochromatic x-rays.

Each powder particle (or grain) is a crystal and having a large number of them with random orientation ensures that some particles are properly oriented such that every possible set of crystallographic planes will be available for x-rays diffraction.

The diffractometer is an apparatus used to determine angle at which diffraction occurs for powdered specimen, its features are represented schematically in Fig 2.4. A powder specimen in the form of a flat plate is supported so that rotation about the axis is possible; this axis is perpendicular to the plane of paper. The monochromatic x-ray is generated at in x-ray tube then it is passed through a divergent slit to produce a well-defined and focused beam. The beam then hit the powder specimen and the intensities of the diffracted beams after passing through the receiving slit are detected with a counter. The specimen, x-ray source and counter are all coplanar. The counter is mounted on moveable carriage that may also be rotated about its axis; its angular position in the term of 2θ is calculated on a marked scale. The carriage and the specimen are mechanically coupled in such a way that a rotation of the specimen through θ is accompanied by a 2θ rotation of the counter, this assure that the incident and reflection angle are maintained equal to one another. Utilization of a filter provides a near monochromatic beam. As the counter moves at constant angular velocity, a recorder automatically plots the diffracted beam intensity (monitored by the counter) as function of 2θ.

Fig.2.3 An x-ray diffractometer.

One of the primary uses of the x-ray diffractometry is for the determination of a crystal structure. The unit cell size and geometry may be resolved from the angular positions of the diffraction peaks, whereas arrangement of the atoms with in the unit cell is associated with relative intensities of these peaks[4, 5]. Other uses of x-ray include qualitative and quantitative chemical identification and determination of residual stress and crystal size.

2.5 Ac Susceptibility:

Suppose a magnetic field of flux density B_a is applied to a superconductor. We may neglect demagnetizing effects; we consider a long superconducting rod with the field applied parallel to its length. An applied magnetic field of flux density B_a produces a flux density in material equal to μ_rB_a where μ_r is the relative permeability of the material. Metals, other than ferromagnetic have relative permeability, which is very close to the unity, flux density within material due to the applied magnetic field is equal to B_a. But we have seen the total flux density inside the superconducting body is zero. This perfect diamagnetism arises because surface screening current circulate so as to produce a flux density B_i which everywhere inside material exactly cancels the flux density due to the applied field; B_i= -B_a. A rod shaped superconducting specimen behaves like a long solenoid with circulating current that create a flux density exactly equal in magnitude but opposite in direction, the flux density due to the applied magnetic field. We can, however, describe the perfect diamagnetisms in another way. Because we cannot actually observe the screening current which arises when a magnetic field is applied. We could suppose that perfect diamagnetism arises from some special bulk magnetic property of the superconducting material. We can describe the perfect diamagnetism simply by saying that for superconducting material μ_r=0, so that the flux density inside is zero using relation B=μ_rB_a. Here we don not consider the mechanism by which the diamagnetism arises; the effect of screening current is included in the statement μ_r=0. The strength H_a of the applied magnetic field is given by

H_a= (2.14)

and the flux density in a magnetic material is related to the strength of the applied field by

B=μ_o (H_a+M) (2.15)

where M, is the magnetization of the material. The magnetization of a superconductor, in which B=0, given by

M= -H_a (2.16)

and the magnetic susceptibility (ratio of the magnetism to the magnetic field strength) given by

χ=-1 (2.17)

2.5.1 Ac Susceptibility Measurements:

AC susceptibility is a simple method of probing both the static and dynamic magnetic and superconducting properties of materials. It is used for determining superconducting transition temperatures and critical current densities since the 1960's[7].. The AC susceptometer is an indispensable tool for the study of high TC's cuprates in the late 1980's. In the 1990's, AC susceptibility measurements have been progressively used by SQUID and torque measurements with which better sensitivities can be achieved allowing the study of smaller samples or samples with weaker magnetic signals. Ac susceptibility is the only technique where the actual susceptibility (dM/dH) is measured directly instead of measuring the gradient of the initial magnetization curve. At last, the magnitude of the applied field is usually smaller with ac susceptometer than with dc techniques and the state probed by ac susceptibility is much closer to the ground state.

2.5.2 Experimental Arrangement:

A simplified diagram of ac susceptibility apparatus is shown in Fig.2.5

Fig. 2.4 Harshorn bridge network for ac susceptibility measurements.

The measurements of the ac susceptibility relies on the change of the mutual inductance of a set of two coils or the self-inductance of a single coil if a magnetic sample is inserted. Experimentally, the ac susceptometer operates as a modified Harshorn bridge network (shown in Fig. 2.5): a primary coil produces a small ac field and the resulting emf, directly proportional to the derivative of the magnetization of the sample, induced in the secondary (pick-up) coil wound around the sample is analyzed. The in-phase and out-of-phase components (w.r.t. the driving current of the primary coil) of the out-of-balance voltage are proportional to the real χ' and imaginary χ'' components of the susceptibility. It should be noted that the harmonics of the signal can also be detected for looking at non-linear effects such as those induced by inter-grain couplings in high temperature superconductors.

References:

[1]. Charles Kittle, Introduction to Solid State Physics, Sixth Edition, Jhon Wiley and Sons New York 1974.

[2]. Blackmore

[3]. A. G. Mamalis, D. E. Manolakos, A. Szalay, G. Pantazopoulos, Processing of High Temperature Superconductor, Penney lvenia 17604 U. S. A. 2000.

[4]. B. e. Warren, X-ray diffraction, (General publishing company, 1969)

[5]. P.Harold, X-ray diffraction procedures for polycrystalline and amorphous materials, second edition, Jhon-Wiley, 1977.

[6]. B. D. Cullity, Element of X-ray Diffraction, second edition, (Addision-Wesely Publishing company, Inc. London 1977.

[4]. M. Ali Omer, Elementary Solid State Physics, First Edition, Edition Wesely Publishing Company (1974)

[7]. Martin Nikolo, Am. J. Phys. Vol. 63, No. 1, 1995

Results of (Cu_0.5Tl_0.5)Ba₂Ca₃Cu₄O_12-d Superconductors

The structure of the material was analyzed by X-ray diffraction. The resistivity measurements were carried out by four-probe method. The Diamagnetic characteristics of superconductor samples were measured by AC-susceptibility measurements using Lock-in amplifier. The Results and discussions using the above experimental techniques are given in the following.

X-ray diffraction scans of (Cu_0.5Tl_0.5)Ba₂Ca₃Cu₄O_12-d sample is shown in Fig.3.1. Most of the diffraction lines could be indexed according to tetragonal structure following P4/mmm symmetry. A sharp (001) line in the diffraction scans of (Cu_0.5Tl_0.5)Ba₂Ca₃Cu₄O_12-d sample is a finger print of presence of predominant Cu_1-xTl_x-1234 phase, along with inclusion of (Cu_0.5Tl_0.5)Ba₂Ca₃Cu₄O_12-d phase. The lengths of a & c-axes are found to be a=3.88Ǻ, b=18Ǻ[35].

Figure 3.1: X-ray diffraction scan of (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10-d superconductor.

The resistivity measurement of (Cu_0.5Tl_0.5)Ba₂Ca₃Cu₄O_10-d sample is shown in Fig.3.2. The zero resistivity critical temperature T_c(R=0) is observed around 117K. The sample has shown onset of superconductivity around 137K. The normal state resistivity of the sample gradually decreases with the decrease in temperature. This shows metallic variations of resistivity from room temperature down to onset of superconductivity.

Figure 3.2: Resistivity curve of (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_12-d superconductor.

The ac magnetic susceptibility measurement of the sample is shown in Fig.3.3. The onset of diamagnetism as observed from in-phase component of magnetic susceptibility (c') is around 120. The in-phase component of magnetic susceptibility (c') showing the magnitude of the diamagnetism. The out-of-phase component of magnetic susceptibility (c'') has shown a well defined peak showing the enhanced inter-grain connectivity of the sample.

Figure 3.3: AC-susceptibility measurement of (Cu_0.5-xPb_xTl_0.5)Ba₂Ca₃Cu₄O_12-d superconductor.

References

[3] Creation of best performance High-Tc Superconductor based on Cu-1234

H. Ihara, Y. Tanaka, A. Iyo, H. Kito, N. Terada, M. Tokumoto, K. Ishida, Y. Sekita, H. Yamamoto, K. Hayashi, Nawazish A. Khan, A. Sundaresan, J. Nie, T. Kojima, E. Harashima, Y. Ishiura, F. Tateai, M. Kawamura, Bulletin of Electrotechnical Laboratory, 63, 67 (1999).

[4] Raman Active Apical Oxygen Modes in Cu1-xTlxBa2Ca3Cu4O12-y Superconductor Thin Films

Nawazish A. Khan and H. Ihara, World Scientific 2004.

[5] Weak Link behavior of Cu1-xTlxBa2Ca3Cu4O12-y superconductor thin films,

Nawazish A. Khan, P. Kameli, and A. A. Khurram, Supercond. Sci. Technol. 19, 410 (2006).