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4 SUPERCONDUCTING MATERIALS 4.1 Introduction the Electrical Resistivity of a Material Decreases with the Decrease of Temperature

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4 SUPERCONDUCTING MATERIALS 4.1 Introduction the Electrical Resistivity of a Material Decreases with the Decrease of Temperature 4 SUPERCONDUCTING MATERIALS 4.1 Introduction The electrical resistivity of a material decreases with the decrease of temperature. According to the classical free electron theory the electrical resistivity is inversely proportional to the relaxation time. The thermal vibration of atoms, molecules and ions decreases and hence the number of collisions between the conduction electrons with other constituent particles such as atom, ion, and molecules decreases. So the relaxation time increases and hence decreases with the decrease of temperatures. Certain materials exhibits zero resistance, when they are cooled into the ultralow temperature and hence they are said to be superconductors. This chapter deals about the properties, theory and applications of superconductors. 4.2 Occurrence of superconductivity Helium gas was liquefied by Heike Kamerlingh Onnes in the year 1908. The boiling point of liquid helium is 4.2 K. He studied the properties of metals by lowering their temperatures using liquid helium. In 1911, he studied the electrical properties of mercury at very low temperatures. He found that the resistivity of mercury suddenly decreases nearly 105 times around 4.2 K as shown in Fig.4.1a. The variation of resistivity of normal conductor and superconductor is shown in Fig.4.1b. This drastic change of the resisttivity of mercury around 4.2 K indicates that the mercury gets transformed from one conducting state to another conducting state. This property is said to be superconducting properties. The materials those are exibiting the superconducing properties are said to be superconductors. The temperatures at which a material gets transformed from one conducting state to another conducting state is said to be transition temperature or critical temperature. It is represented by the letter TC. After the invention of superconducting property in mercury, several materials were tested for superconductivity. Good electrical conductors at room temperatures such as gold, copper and silver are not good superconductors. The materials with high resistivity at room temperatures, generally found to be good superconductors. The maximum transition temperature known to the scientists until the year 1985 is 23 K for Nb3Ge. In January 1986, a copper oxide material (Lanthanum- Barium-Copper oxide) was reported to have transition temperatures of 35 K. Another material yttrium barium copper oxide (YBCO) was reported in February 1987 with a transition temperature of 92 K. After this invention, the materials having the 1 transition temperatures above 77 K were studied. The high temperature superconductivity is mostly observed in Bi, Tl, Y, Hg compounds having CuO2 layers. Recently, in May 2009, a compound (Tl4Ba)Ba4Ca2Cu10Oy is found have a transition temperature of 240 K. There is an increase of the transition temperature of the superconducting materials up to 100 K during the last three years (2006 to 2009). Generally the superconducting transition temperature varies from 0.001 K for Rh to 240 K for (Tl4Ba)Ba4Ca2Cu10Oy. The transition temperatures of some superconductors are listed in Table 4.1. (a) (b) Fig.4.1 Variation of resistivity versus temperature, for (a) Hg and (b) normal conductor and superconductors 4.3 Properties of superconductors (i) Electrical resistivity (ρ) The electrical resistivity of the superconducting material is taken as zero, because the sensitivity of the equipments used to measure the resistivity is low and hence it is not possible to measure the resistivity of the superconducting materials. Gallop was able to predict the resistivity of a superconducting wire is less than 10-26 -m using the lack of decay of a current circulating around a closed loop of superconducting wire. This value is nearly 1018 times less than the resistivity of copper at room temperature. The scientists have studied the current flowing through a superconducting solenoid for a period of nearly three year. They found that there is no change in the current of the material. It represents the resistivity of the material in the superconducting state is zero. In a normal conducting material, if a small amount of current is applied and it will be destroyed within 10-4 s due to resistive loss (loss= i2R). 2 Materials Transition Materials Transition temperature, in K temperature, in K Elements Nb 3 Sn 18.3 Al 1.175 Nb3Al 18.9 Hg α 4.15 Nb3Ge 23.0 Hg β 3.95 Nb3Au 11.5 In 3.41 La3In 10.4 Nb 9.46 Zn 0.85 Ceramics Pb 7.196 Bi2Sr2Ca2Cu3O10 110 Sn 3.72 Bi2Sr2CaCu2O9 110 Ti 0.4 Bi2Sr2CaCu2O8 91-92 La 4.88 (Ca1-XSrX)CuO2 110 Ta 4.47 (Ba,Sr)CuO2 90 Cd 0.517 (La,Sr)CuO2 42 Zr 0.61 YBa2Cu3O7 90 Ga 1.083 Tl2Ba2Ca2Cu3O10 47 Th2 1.38 TlBa2CaCu2O7 80 Compounds TlBa2Ca2Cu3O9 105 V3Ge 6.0 TlBa2Ca3Cu4O11 40 V3Ga 14.2 Hg4Tl3Ba30Ca30Cu45O47 138* V3Si 17.4 (Tl4Ba)Ba4Ca2Cu10Oy 240** NbN 16.0 Table 4.1 Transition temperatures of some superconductors-(* discovered in 2006, ** discovered in 2009) (ii) Persistent current Consider a small amount of current is applied to a superconducting ring. The superconducting current will keeps on flowing through the ring without any changes in its value. This current is said to be persistent current. In a superconductor since there is no resistive hear loss (i2R), the supercurrent will keeps on flowing until the specimen is in the superconducting state. (iii) Diamagnetic property Consider a magnetic field is applied to a normal conducting material. The magnetic lines of forces penetrate through the material. Consider a normal conductor is cooled down to very low temperature for superconducting property. If it is cooled down below the critical temperature, then the magnetic lines of forces are ejected from the material. A diamagnetic material also repels the magnetic lines of forces. So, the ejection of magnetic lines of forces, when the superconducting material is cooled down is said to be the diamagnetic property. This property was first observed by Meissner and hence this property is also called as Meissner effect. 3 (a) (b) Fig.4.2 Diamagnetic property (a) Magnetic filed applied into a normal conductor (b) magnetic filed applied into a superconductor The diamagnetic property is easily explained using the following mathematical treatment: The magnetic flux density is given by, B=μO(M+H) For a superconducting material, B=0. Substituting, B=0, we get, 0=μO(M+H) i.e., M=-H M 1 (4.1) H The negative value of the susceptibility shows the diamagnetic properties of the superconducting material. (iv) Application of magnetic field-Tuyn’s law The superconducting materials exhibit the diamagnetic property only below the critical field. If the magnetic field is increased, beyond a minimum value known as critical field, the superconducting property of the material is destroyed, when the field is equal to or greater than the critical magnetic field. The minimum magnetic field required to destroy the superconducting property is known as the critical field. The field required to destroy the superconducting property is given by T2 H(T)H1 C O 2 (4.2) TC where HC(T) is the critical field required to destroy the superconducting property at T K, TC is the critical temperature, HO is the critical field required to destroy the 4 superconducting property at 0 K. Eq.(4.2) is known as Tuyn’s (a) (b) Fig.4.3 Magnetic field versus temperature (a) Application of magnetic field to a superconductor, (b) magnetic filed versus temperature for Sn, Pb and Nb. (v) Application of current-Silsbee current Consider a current of i ampere is applied to a superconducting coil of wire. The application of the current induces a magnetic field and hence the superconducting property is destroyed. The critical current required to destroy the superconducting property is given by, iC 2RHC (4.3) where R is the radius of the superconducting wire, HC is the critical magnetic field required to destroy the superconducting property. This property was discovered by Silsbee and hence Eq.(4.3) is known as Silsbee law. Fig.4.4 Application of current into a superconductor (vi) Effect of pressure Cesium is a normal conductor at normal pressure. If the pressure of cesium is increased to 110 kbar after several phase transformation, it gets converted into a superconductor. The transition temperature of cesium at this pressure is 1.5 K. Silicon becomes a superconducting material at 165 kbar. Its transition temperature is 8.3 K. (vii) Isotopic effect The transition temperature of the superconducting materials varies with the mass numbers. It means that the presence of isotopes changes the transition 5 temperature of the material. The mass number of mercury varies from 199.5 to 203.4. The transition temperature of mercury varies from 4.146 to 4.185 K α respectively. Maxwell showed that TC M = constant. The value of α is found to be ½. This phenomenon is said to be isotopic effect. (viii) Energy gap The superconducting materials possess an energy gap. The energy gap of a superconductor is of different nature than that of a semiconductor. In semiconductors the energy gap is tied to the lattice and in superconductors the energy gap is tied to the Fermi energy. The energy gap separates the superconducting electrons that lie below the energy gap and the normal conducting electrons that lie above the gap. The energy gap of the superconductor is in the order of ~3.5 kTC at absolute zero temperature and it is zero at the critical temperature. The energy gap is determined from the measurements of specific heat capacity, infrared absorption or tunneling. The BCS theory predicts that the variation of energy gap with temperature as 1 T 2 Eg 1.74Eg (0)1 (4.4) TC The temperature variation of the energy gap is well predicted by the BCS theory.
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