{"id":294,"date":"2018-12-05T09:59:35","date_gmt":"2018-12-05T09:59:35","guid":{"rendered":"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=294"},"modified":"2018-12-05T12:04:49","modified_gmt":"2018-12-05T12:04:49","slug":"superconductivity-and-some-introductory-concepts","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/chapter\/superconductivity-and-some-introductory-concepts\/","title":{"rendered":"Superconductivity and some introductory concepts"},"content":{"raw":"<div>\r\n<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/aIMd6xC8WtU\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<strong>Learning Outcomes<\/strong>\r\n\r\n&nbsp;\r\n\r\nAfter studying this module, you shall be able to\r\n<ul>\r\n \t<li style=\"text-align: justify\">Learn about the combined effect of electrical and magnetic properties of superconductors and their importance in the applications of superconductors.<\/li>\r\n \t<li style=\"text-align: justify\">Learn about the physics of superconductors and the basics and principle of superconducting systems.<\/li>\r\n \t<li style=\"text-align: justify\">Know the a) types of superconductors and b) how they are different from each other c) Soft and hard nature of superconductors.<\/li>\r\n \t<li style=\"text-align: justify\">Learn about the thermodynamic variables of prime importance like entropy, specific heat and conductivity etc. which are responsible for the development of the theory of superconductivity.<\/li>\r\n \t<li style=\"text-align: justify\">Learn\u00a0 about\u00a0 that<span style=\"text-align: initial;font-size: 1em\">\u00a0 the\u00a0 critical\u00a0 temperatures\u00a0 of\u00a0 the\u00a0 superconductors\u00a0 vary\u00a0 with\u00a0 the\u00a0<\/span>isotopic masses by relation.<\/li>\r\n \t<li style=\"text-align: justify\">Learn about the fact that energy gap is totally different from that of insulators because in<span style=\"text-align: initial;font-size: 1em\"> the insulators, <\/span>energy<span style=\"text-align: initial;font-size: 1em\"> gap is tied to the lattice, while in the case of superconductors, it is tied to the Fermi gas.<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<div><\/div>\r\n<strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 1 Introduction<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">With the <\/span>liquification<span style=\"text-align: initial;font-size: 1em\"> of helium in 1908 by Heike Kamerlingh lead to the starting steps in the discovery of <\/span>superconductity<span style=\"text-align: initial;font-size: 1em\">. In 1911, when he was studying the variation of the resistance with the temperature for Mercury. He was shocked that at 4.15 K, the dc resistance decreased sharply. With this <\/span>experiment<span style=\"text-align: initial;font-size: 1em\"> superconductivity was discovered. At very-very low temperatures, most of the metals, many alloys <\/span>and<span style=\"text-align: initial;font-size: 1em\"> certain chemicals compounds lose their resistance completely, the phenomenon is regarded as <\/span><strong style=\"text-align: initial;font-size: 1em\">superconductivity<\/strong><span style=\"text-align: initial;font-size: 1em\"> and such type of material is termed as <\/span><strong style=\"text-align: initial;font-size: 1em\">Superconductor<\/strong><span style=\"text-align: initial;font-size: 1em\">. At <\/span>further<span style=\"text-align: initial;font-size: 1em\"> later stage, Meissner and Ochsenfeld that the superconductors are perfectly diamagnetic also. We can clearly differentiate between a normal conductor and superconductor by viewing the graph in <\/span><strong style=\"text-align: initial;font-size: 1em\">Fig.1.<\/strong><\/p>\r\n\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-297\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-100.png\" alt=\"\" width=\"460\" height=\"268\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong>Fig. 1: <\/strong>Variation of resistance with temperature (in K).<\/p>\r\n&nbsp;\r\n\r\n<strong>1.1 Macroscopic Electromagnetic Properties<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">These two macroscopic properties accounts for the basic principles of superconductivity. Let them discuss in some detail:<\/p>\r\n&nbsp;\r\n\r\n<strong>Zero Resistance State (Electrical Effects):<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">In the superconducting transitions, the resistance of the material falls to a very small value. It is quite interesting to check that the resistance actually falls to zero value? Onnes experimented with the superconducting circuit to check the low resistance through the decay of current flowing through the circuit. And the current decays according to the following equation:<\/p>\r\n<img class=\"size-full wp-image-298 alignleft\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-101.png\" alt=\"\" width=\"439\" height=\"49\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Where I(t) is the value of current at any time , R is the resistance and the L is used for coil inductance.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Suppose for a lead coil, L=1.4X10-3 H, where the magnetic field value decayed to nearly 2% in the 7 h only and the resistivity was deduced to less than 4x10\u201425 ohm m. Therefore we can easily understand that why resistance of a superconductor can be taken as zero.<\/p>\r\n&nbsp;\r\n\r\n<strong>Magnetic Field Effects<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Under the application of very weak magnetic field (few hundred Orsteds), the quenching of the superconductivity is observed, which results in the failure in generating the high magnetic field value through Joule dissipation. This result is quite similar to the observed by Silsbee in 1916. According to him, critical value of current (Ic) produces critical magnetic field (Hc) on the surface of superconductor. The temperature dependence of critical field is given by the following relation:<\/p>\r\n<img class=\"size-full wp-image-299 alignleft\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-102.png\" alt=\"\" width=\"498\" height=\"59\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\nThe above equation can understood in the following graph easily.\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-300\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-103.png\" alt=\"\" width=\"269\" height=\"237\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong>Fig. 2<\/strong>: Variation of critical field with Temperature.<\/p>\r\n&nbsp;\r\n\r\nThe above relation shows that the graph will be a parabolic curve. According to the relation:\r\n\r\n&nbsp;\r\n\r\n<strong>At 0K,<\/strong>\u00a0\u00a0 <strong>H<\/strong><strong>C<\/strong><strong> (T)=H<\/strong><strong>C<\/strong><strong> (0)<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>At T=T<\/strong><strong>C<\/strong><strong>, H<\/strong><strong>C<\/strong><strong> (T<\/strong><strong>C<\/strong><strong>) =0<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">These conditions define the boundary of the curve, below which superconductivity is present and outside it normal state is present.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">However the above curve takes the form depending upon the types of superconductors, So it\u2019s better to have a look <\/span>on<span style=\"text-align: initial;font-size: 1em\"> the classification of superconductors.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Magnetization behavior<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Depending upon various phenomenological parameters superconductors have been classified mainly into two types. One of them is soft (Type I) and other one is hard superconductors. Let us study them briefly before studying their thermal properties.<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The superconductors in which magnetization behaves like the curve as given in the following Fig.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">3 are termed as Type-1 superconductors.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-301\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-104.png\" alt=\"\" width=\"693\" height=\"307\" \/>\r\n<p style=\"text-align: justify\"><strong>Fig.3: <\/strong>a) Magnetization versus applied magnetic field for type -1 superconductors and b) for type-II superconductors.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">A abrupt fall in the magnetization can be observed from the with the increasing applied magnetic field. Since the critical magnetic field is too low in this case that this type of superconductors do not have too much useful technical applications. However, hard superconductors have magnetization curve as given in the right hand side of <strong>Fig. 3<\/strong>. These superconductors do not jump abruptly to the normal state like type-1 superconductors. They show superconducting properties upto a field strength HC2 and exhibit perfect diamagnetism for the fields less than HC1. So is is clear that a large amount of magnetic field is needed to destroy the superconducting properties of the material. The in between state is known as mixed state or vortex state. These superconductors\u00a0<span style=\"text-align: initial;font-size: 1em\">have wide application range like high field magnets in particle <\/span>acceleration ,<span style=\"text-align: initial;font-size: 1em\"> experimental magnetic levitation, in fusion reactors, SQUID, <\/span>and<span style=\"text-align: initial;font-size: 1em\"> MRI also.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">2.\u00a0\u00a0 Thermal Properties<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">The thermal properties of superconductors have been extensively studied and compared with those of the same materials in the normal state. There are a number of thermodynamic effects in the normal and the superconducting state of a superconductor which are of great importance in the development of superconductivity theories. Among them Entropy, Specific heat, thermal conductivity and energy gap are of more importance. This section explains these parameters except energy gap which will be covered in the later section.<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">2.1 Entropy<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">It is experimentally proven that entropy for all superconductors\u2019 decreases if we go below <\/span>critical<span style=\"text-align: initial;font-size: 1em\"> temperature. As we know that entropy is a measure of <\/span>disordered<span style=\"text-align: initial;font-size: 1em\"> state of a system so the above statement clearly suggests that the Entropy for <\/span>superconducting<span style=\"text-align: initial;font-size: 1em\"> state is less than that of <\/span>normal<span style=\"text-align: initial;font-size: 1em\"> conductor. For the clear demonstration, Entropy for Aluminum in normal and superconducting <\/span>sate<span style=\"text-align: initial;font-size: 1em\"> is given in the following figure.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-302\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-105.png\" alt=\"\" width=\"364\" height=\"223\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong>Fig.4: <\/strong>Variation of Entropy with Temperature (in K) for Aluminium (for normal as well as for superconducting state.<\/p>\r\n&nbsp;\r\n\r\n<strong>2.2 Specific heat<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The specific heat in a normal conductor consists of two contributions one is electronic and the other one is for lattice. Let us say them C<sub>e<\/sub> and C<sub>l<\/sub> respectively. In the case of electronic contribution, C<sub>e<\/sub> is\u00a0<span style=\"text-align: initial;font-size: 1em\">linearly proportional to the absolute temperature (T) and in the second case; C<sub>l<\/sub> is proportional to the\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">T<sup>3<\/sup>. So the total specific heat takes the form as:<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">C= C<sub>e<\/sub>+ C<sub>l<\/sub>= AT+BT<sup>3<\/sup>---------------------------------------------3<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">where A and B are constants. These relationships can be clearly understood in the form of the following graphs.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-303\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-106.png\" alt=\"\" width=\"619\" height=\"316\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong>Fig.5: <\/strong>Temperature variation of heat capacity in normal and superconductivity sates (left side) and electronic contribution of heat capacity Vs TC\/T.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">However, in the superconducting state lattice contribution will remain same and the only change occurs for the electronic contribution Ce. The electronic contribution of specific heat is non linear in case of superconducting state.<\/p>\r\n&nbsp;\r\n\r\n<strong>3.\u00a0\u00a0 Isotope Effect<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">It is well known fact proved by previous observations that the critical temperatures of the superconductors varies with the isotopic masses. Let us take the example of Mercury; in Mercury critical temperature varies from 4.185 K to 4.146 K for the isotopic masses 199.5 and 203.4 atomic mass units. If we mix different isotopes of same material, the transition temperature varies accordingly. The experimental results reveal the following relation for these two.<\/p>\r\n<img class=\"size-full wp-image-304 alignleft\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-107.png\" alt=\"\" width=\"470\" height=\"36\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\nWhere M is the isotopic mass.\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Since there is a complete dependence of Tc on the isotopic masses, so we can clearly find the direct involvement of lattice vibrations and electron-lattice interactions in superconductivity.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-305\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-108.png\" alt=\"\" width=\"239\" height=\"215\" \/>\r\n<p style=\"text-align: center\"><strong>Fig.6: <\/strong>Variation of isotopic mass with Temperature.<\/p>\r\n&nbsp;\r\n\r\n<strong>4.\u00a0\u00a0Manifestation of Energy Gap<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">In the previous section, it has been observed that the specific heat abruptly changes at the critical temperature i.e Tc. This suggests the existence of energy gap inside the superconductor. However this type of energy gap is totally different from that of insulators because in the insulators, energy gap is tied to the lattice, while in the case of superconductors, it is tied to the Fermi gas. Here the difference lies! Which simply means energy gap exists between the superconducting electron levels i.e. between the lowest excited level and the ground level. The energy gap is given by;<\/p>\r\n&nbsp;\r\n\r\n<sub>Eg=2\u0394<\/sub> ------------------------------------------------------5\r\n\r\n&nbsp;\r\n\r\nwhere\u00a0\u00a0 is termed as energy gap parameter\r\n\r\n&nbsp;\r\n\r\n\u0394= 1.4K<sub>b<\/sub>T<sub>c<\/sub>\u00a0\u00a0\u00a0\u00a0 for Ga\r\n\r\n&nbsp;\r\n\r\nEg \u224810<sup>-4<\/sup> Ev\r\n\r\n&nbsp;\r\n\r\nThe energy is basically a function of temperature and is demonstrated in the following <strong>Fig.7.<\/strong>\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-306\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-109.png\" alt=\"\" width=\"624\" height=\"264\" \/>\r\n<div><\/div>\r\n<p style=\"text-align: center\"><strong style=\"text-align: initial;font-size: 1em\">Fig.7<\/strong><span style=\"text-align: initial;font-size: 1em\">: Variation of <\/span>energy<span style=\"text-align: initial;font-size: 1em\"> gap with temperature in the left, In the right side: <\/span>energy<span style=\"text-align: initial;font-size: 1em\"> gap in the normal and superconducting <\/span>sate<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/p>\r\n\r\n<div>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Ground state electrons are superconducting electrons while electrons in the excited state are normal electrons. With the rise in the temperature a greater number of electrons are excited in the higher band above the energy gap. Therefore at critical temperature all electrons get excited thereby vanishing the energy gap at TC. In the case of superconductors, the existence of energy gap means that the photons with the energy less than the energy gap can\u2019t be absorbed. Therefore, the measurement of energy gap can be done only by directing microwave radiations at the superconductors. Whenever microwave radiations has more energy then the band gap, strong absorption takes place and more number of superconducting electrons are excited to the states above the energy gap.<\/p>\r\n\r\n<\/div>\r\n<div>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Superconductivity and some introductory concepts<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/aIMd6xC8WtU\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<strong>\u00a0 \u00a0 5. SUMMARY<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Superconductors materials are those which have zero dc resistance below a certain temperature <em>Tc<\/em>, called the critical temperature. A second property of a type I superconductor is that it behaves as a perfect diamagnet. Applied magnetic flux is expelled from the interior of a type I superconductor. This phenomenon is known as the<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Meissner effect. The superconductivity of a type I superconductor gets destroyed when an applied magnetic field exceeds certain critical magnetic field (Bc).<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Type- II superconductor consists of two critical fields. When an applied field is quite less than the critical field, <em>B<\/em><em>c<\/em>1, the material behaves as superconductor and no flux penetration\u00a0<span style=\"text-align: initial;font-size: 1em\">is possible. When the applied field becomes greater than critical field, <\/span><em style=\"text-align: initial;font-size: 1em\">B<\/em><em style=\"text-align: initial;font-size: 1em\">c<\/em><span style=\"text-align: initial;font-size: 1em\">2, the superconducting state gets completely destroyed and the flux penetrates takes material. The critical temperatures of the superconductors vary with the isotopic masses by\u00a0<\/span><span style=\"color: inherit;font-size: inherit;text-align: initial\">relation.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The abrupt variation of specific heat with the critical temperature suggests the presence of <\/span>energy<span style=\"text-align: initial;font-size: 1em\"> gap inside superconductors. Under the application of zero applied filed, persistent currents when <\/span>set<span style=\"text-align: initial;font-size: 1em\"> up in a superconducting ring, (also called supercurrents) circulates for several years with no measurable losses.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0 Value Addition:<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>Do You Know?<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Year 2011 has been marked as the 100th anniversary of discovery of Superconductivity which was discovered by a Dutch scientist Heike Kamerlingh Onnes at Leiden University. He discovered superconductivity while he was liquefying Helium. But before the liquification of Helium, the lowest temperature which was available for researchers was 14K and its was for solid hydrogen. Originally Onnes named his discovery \"supra conductivity\" but later it is was called as \"superconductivity,\" that is the term we use today. He first experiment with the gold and platinum and he moved to the Mercury because it is quite earier to work with the pure metal. At that time scientists have a general thinking that pure metals show zero resistance at liquid-helium temperatures. Till date Five Nobel Prizes in Physics have been awarded for research in superconductivity.<\/p>\r\n&nbsp;\r\n\r\n<strong>Suggested Reading<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong>Ginzburg-Landau <\/strong><strong>theory<\/strong>\r\n\r\n&nbsp;\r\n\r\nThis theory is named after Vitaly Lazarevich Ginzburg and Lev Landau. It is mathematical theory used to describe superconductivity. In the initial stage, it was considered as a phenomenological model which describes type-I superconductors without taking their microscopic properties. At a later stage, a new version of Ginzburg\u2013Landau theory came from the three scientists Bardeen, Cooper, Schrieffer microscopic theory which accounts for microscopic interpretation of all its parameters. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work.\r\n\r\n&nbsp;\r\n\r\n<strong>For More Details ( on this topic and other topics discussed in Text Module) See<\/strong>\r\n\r\n&nbsp;\r\n\r\n1.\u00a0 Introduction to Superconductivity by M.Tinkham, Mc-Graw-Hill Inc.\r\n\r\n2.\u00a0\u00a0\u00a0 Superconductivity by C P Poole, H A Farach and R J Creswick, Academic Press Inc.\r\n\r\n&nbsp;\r\n\r\n<strong>For General Study on Origins of Superconductivity<\/strong>\r\n\r\n&nbsp;\r\n\r\n1.Introduction to solid state physics by C.Kittel,\r\n\r\n2.The solid state by H M Roseberg\r\n\r\n3. Superconductivity, superfluids and condensates by J Annet\r\n\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Glossary:<\/strong>\r\n\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Critical Field<\/strong>\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">The filed at which superconductivity is destroyed is known as <\/span>critical<span style=\"text-align: initial;font-size: 1em\"> field.<\/span>\r\n\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Entropy<\/strong>\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">It is the measure of disordered state or randomness of a system.<\/span>\r\n\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Isotope<\/strong>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Isotopes are variant of <\/span>chemical<span style=\"text-align: initial;font-size: 1em\"> element which differs in the number of neutrons, <\/span>however<span style=\"text-align: initial;font-size: 1em\"> all isotopes have <\/span>equal<span style=\"text-align: initial;font-size: 1em\"> number of protons.<\/span><\/p>\r\n&nbsp;\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Penetration depth<\/strong>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">It is the distance from the surface of the specimen <\/span>upto<span style=\"text-align: initial;font-size: 1em\"> where magnetic field reduces 1\/e times the field at the surface.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Specific heat<\/strong><\/p>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The specific heat is defined as <\/span>amount<span style=\"text-align: initial;font-size: 1em\"> of heat per unit mass required to raise the temperature by one degree Celsius.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Superconducting state<\/strong><\/p>\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">When material exhibits infinite conductivity when cooled to a sufficiently low temperature, the phenomenon is known as superconductivity and the corresponding state is known as <\/span>superconducting<span style=\"text-align: initial;font-size: 1em\"> state.<\/span><\/p>\r\n\r\n<\/div>","rendered":"<div>\n<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/aIMd6xC8WtU\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Learning Outcomes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>After studying this module, you shall be able to<\/p>\n<ul>\n<li style=\"text-align: justify\">Learn about the combined effect of electrical and magnetic properties of superconductors and their importance in the applications of superconductors.<\/li>\n<li style=\"text-align: justify\">Learn about the physics of superconductors and the basics and principle of superconducting systems.<\/li>\n<li style=\"text-align: justify\">Know the a) types of superconductors and b) how they are different from each other c) Soft and hard nature of superconductors.<\/li>\n<li style=\"text-align: justify\">Learn about the thermodynamic variables of prime importance like entropy, specific heat and conductivity etc. which are responsible for the development of the theory of superconductivity.<\/li>\n<li style=\"text-align: justify\">Learn\u00a0 about\u00a0 that<span style=\"text-align: initial;font-size: 1em\">\u00a0 the\u00a0 critical\u00a0 temperatures\u00a0 of\u00a0 the\u00a0 superconductors\u00a0 vary\u00a0 with\u00a0 the\u00a0<\/span>isotopic masses by relation.<\/li>\n<li style=\"text-align: justify\">Learn about the fact that energy gap is totally different from that of insulators because in<span style=\"text-align: initial;font-size: 1em\"> the insulators, <\/span>energy<span style=\"text-align: initial;font-size: 1em\"> gap is tied to the lattice, while in the case of superconductors, it is tied to the Fermi gas.<\/span><\/li>\n<\/ul>\n<\/div>\n<div><\/div>\n<p><strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 1 Introduction<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">With the <\/span>liquification<span style=\"text-align: initial;font-size: 1em\"> of helium in 1908 by Heike Kamerlingh lead to the starting steps in the discovery of <\/span>superconductity<span style=\"text-align: initial;font-size: 1em\">. In 1911, when he was studying the variation of the resistance with the temperature for Mercury. He was shocked that at 4.15 K, the dc resistance decreased sharply. With this <\/span>experiment<span style=\"text-align: initial;font-size: 1em\"> superconductivity was discovered. At very-very low temperatures, most of the metals, many alloys <\/span>and<span style=\"text-align: initial;font-size: 1em\"> certain chemicals compounds lose their resistance completely, the phenomenon is regarded as <\/span><strong style=\"text-align: initial;font-size: 1em\">superconductivity<\/strong><span style=\"text-align: initial;font-size: 1em\"> and such type of material is termed as <\/span><strong style=\"text-align: initial;font-size: 1em\">Superconductor<\/strong><span style=\"text-align: initial;font-size: 1em\">. At <\/span>further<span style=\"text-align: initial;font-size: 1em\"> later stage, Meissner and Ochsenfeld that the superconductors are perfectly diamagnetic also. We can clearly differentiate between a normal conductor and superconductor by viewing the graph in <\/span><strong style=\"text-align: initial;font-size: 1em\">Fig.1.<\/strong><\/p>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-297\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-100.png\" alt=\"\" width=\"460\" height=\"268\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-100.png 460w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-100-300x175.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-100-65x38.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-100-225x131.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-100-350x204.png 350w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong>Fig. 1: <\/strong>Variation of resistance with temperature (in K).<\/p>\n<p>&nbsp;<\/p>\n<p><strong>1.1 Macroscopic Electromagnetic Properties<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">These two macroscopic properties accounts for the basic principles of superconductivity. Let them discuss in some detail:<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Zero Resistance State (Electrical Effects):<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">In the superconducting transitions, the resistance of the material falls to a very small value. It is quite interesting to check that the resistance actually falls to zero value? Onnes experimented with the superconducting circuit to check the low resistance through the decay of current flowing through the circuit. And the current decays according to the following equation:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-298 alignleft\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-101.png\" alt=\"\" width=\"439\" height=\"49\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-101.png 439w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-101-300x33.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-101-65x7.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-101-225x25.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-101-350x39.png 350w\" sizes=\"auto, (max-width: 439px) 100vw, 439px\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Where I(t) is the value of current at any time , R is the resistance and the L is used for coil inductance.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Suppose for a lead coil, L=1.4X10-3 H, where the magnetic field value decayed to nearly 2% in the 7 h only and the resistivity was deduced to less than 4&#215;10\u201425 ohm m. Therefore we can easily understand that why resistance of a superconductor can be taken as zero.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Magnetic Field Effects<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Under the application of very weak magnetic field (few hundred Orsteds), the quenching of the superconductivity is observed, which results in the failure in generating the high magnetic field value through Joule dissipation. This result is quite similar to the observed by Silsbee in 1916. According to him, critical value of current (Ic) produces critical magnetic field (Hc) on the surface of superconductor. The temperature dependence of critical field is given by the following relation:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299 alignleft\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-102.png\" alt=\"\" width=\"498\" height=\"59\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-102.png 498w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-102-300x36.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-102-65x8.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-102-225x27.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-102-350x41.png 350w\" sizes=\"auto, (max-width: 498px) 100vw, 498px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>The above equation can understood in the following graph easily.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-300\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-103.png\" alt=\"\" width=\"269\" height=\"237\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-103.png 269w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-103-65x57.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-103-225x198.png 225w\" sizes=\"auto, (max-width: 269px) 100vw, 269px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong>Fig. 2<\/strong>: Variation of critical field with Temperature.<\/p>\n<p>&nbsp;<\/p>\n<p>The above relation shows that the graph will be a parabolic curve. According to the relation:<\/p>\n<p>&nbsp;<\/p>\n<p><strong>At 0K,<\/strong>\u00a0\u00a0 <strong>H<\/strong><strong>C<\/strong><strong> (T)=H<\/strong><strong>C<\/strong><strong> (0)<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>At T=T<\/strong><strong>C<\/strong><strong>, H<\/strong><strong>C<\/strong><strong> (T<\/strong><strong>C<\/strong><strong>) =0<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"font-size: 1em;text-align: initial\">These conditions define the boundary of the curve, below which superconductivity is present and outside it normal state is present.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">However the above curve takes the form depending upon the types of superconductors, So it\u2019s better to have a look <\/span>on<span style=\"text-align: initial;font-size: 1em\"> the classification of superconductors.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Magnetization behavior<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Depending upon various phenomenological parameters superconductors have been classified mainly into two types. One of them is soft (Type I) and other one is hard superconductors. Let us study them briefly before studying their thermal properties.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The superconductors in which magnetization behaves like the curve as given in the following Fig.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">3 are termed as Type-1 superconductors.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-301\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-104.png\" alt=\"\" width=\"693\" height=\"307\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-104.png 693w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-104-300x133.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-104-65x29.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-104-225x100.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-104-350x155.png 350w\" sizes=\"auto, (max-width: 693px) 100vw, 693px\" \/><\/p>\n<p style=\"text-align: justify\"><strong>Fig.3: <\/strong>a) Magnetization versus applied magnetic field for type -1 superconductors and b) for type-II superconductors.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A abrupt fall in the magnetization can be observed from the with the increasing applied magnetic field. Since the critical magnetic field is too low in this case that this type of superconductors do not have too much useful technical applications. However, hard superconductors have magnetization curve as given in the right hand side of <strong>Fig. 3<\/strong>. These superconductors do not jump abruptly to the normal state like type-1 superconductors. They show superconducting properties upto a field strength HC2 and exhibit perfect diamagnetism for the fields less than HC1. So is is clear that a large amount of magnetic field is needed to destroy the superconducting properties of the material. The in between state is known as mixed state or vortex state. These superconductors\u00a0<span style=\"text-align: initial;font-size: 1em\">have wide application range like high field magnets in particle <\/span>acceleration ,<span style=\"text-align: initial;font-size: 1em\"> experimental magnetic levitation, in fusion reactors, SQUID, <\/span>and<span style=\"text-align: initial;font-size: 1em\"> MRI also.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">2.\u00a0\u00a0 Thermal Properties<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">The thermal properties of superconductors have been extensively studied and compared with those of the same materials in the normal state. There are a number of thermodynamic effects in the normal and the superconducting state of a superconductor which are of great importance in the development of superconductivity theories. Among them Entropy, Specific heat, thermal conductivity and energy gap are of more importance. This section explains these parameters except energy gap which will be covered in the later section.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">2.1 Entropy<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">It is experimentally proven that entropy for all superconductors\u2019 decreases if we go below <\/span>critical<span style=\"text-align: initial;font-size: 1em\"> temperature. As we know that entropy is a measure of <\/span>disordered<span style=\"text-align: initial;font-size: 1em\"> state of a system so the above statement clearly suggests that the Entropy for <\/span>superconducting<span style=\"text-align: initial;font-size: 1em\"> state is less than that of <\/span>normal<span style=\"text-align: initial;font-size: 1em\"> conductor. For the clear demonstration, Entropy for Aluminum in normal and superconducting <\/span>sate<span style=\"text-align: initial;font-size: 1em\"> is given in the following figure.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-302\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-105.png\" alt=\"\" width=\"364\" height=\"223\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-105.png 364w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-105-300x184.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-105-65x40.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-105-225x138.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-105-350x214.png 350w\" sizes=\"auto, (max-width: 364px) 100vw, 364px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong>Fig.4: <\/strong>Variation of Entropy with Temperature (in K) for Aluminium (for normal as well as for superconducting state.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>2.2 Specific heat<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The specific heat in a normal conductor consists of two contributions one is electronic and the other one is for lattice. Let us say them C<sub>e<\/sub> and C<sub>l<\/sub> respectively. In the case of electronic contribution, C<sub>e<\/sub> is\u00a0<span style=\"text-align: initial;font-size: 1em\">linearly proportional to the absolute temperature (T) and in the second case; C<sub>l<\/sub> is proportional to the\u00a0<\/span><span style=\"text-align: initial;font-size: 1em\">T<sup>3<\/sup>. So the total specific heat takes the form as:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">C= C<sub>e<\/sub>+ C<sub>l<\/sub>= AT+BT<sup>3<\/sup>&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;3<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">where A and B are constants. These relationships can be clearly understood in the form of the following graphs.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-303\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-106.png\" alt=\"\" width=\"619\" height=\"316\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-106.png 619w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-106-300x153.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-106-65x33.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-106-225x115.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-106-350x179.png 350w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Fig.5: <\/strong>Temperature variation of heat capacity in normal and superconductivity sates (left side) and electronic contribution of heat capacity Vs TC\/T.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">However, in the superconducting state lattice contribution will remain same and the only change occurs for the electronic contribution Ce. The electronic contribution of specific heat is non linear in case of superconducting state.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>3.\u00a0\u00a0 Isotope Effect<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">It is well known fact proved by previous observations that the critical temperatures of the superconductors varies with the isotopic masses. Let us take the example of Mercury; in Mercury critical temperature varies from 4.185 K to 4.146 K for the isotopic masses 199.5 and 203.4 atomic mass units. If we mix different isotopes of same material, the transition temperature varies accordingly. The experimental results reveal the following relation for these two.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-304 alignleft\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-107.png\" alt=\"\" width=\"470\" height=\"36\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-107.png 470w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-107-300x23.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-107-65x5.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-107-225x17.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-107-350x27.png 350w\" sizes=\"auto, (max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Where M is the isotopic mass.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Since there is a complete dependence of Tc on the isotopic masses, so we can clearly find the direct involvement of lattice vibrations and electron-lattice interactions in superconductivity.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-305\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-108.png\" alt=\"\" width=\"239\" height=\"215\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-108.png 239w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-108-65x58.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-108-225x202.png 225w\" sizes=\"auto, (max-width: 239px) 100vw, 239px\" \/><\/p>\n<p style=\"text-align: center\"><strong>Fig.6: <\/strong>Variation of isotopic mass with Temperature.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>4.\u00a0\u00a0Manifestation of Energy Gap<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">In the previous section, it has been observed that the specific heat abruptly changes at the critical temperature i.e Tc. This suggests the existence of energy gap inside the superconductor. However this type of energy gap is totally different from that of insulators because in the insulators, energy gap is tied to the lattice, while in the case of superconductors, it is tied to the Fermi gas. Here the difference lies! Which simply means energy gap exists between the superconducting electron levels i.e. between the lowest excited level and the ground level. The energy gap is given by;<\/p>\n<p>&nbsp;<\/p>\n<p><sub>Eg=2\u0394<\/sub> &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;5<\/p>\n<p>&nbsp;<\/p>\n<p>where\u00a0\u00a0 is termed as energy gap parameter<\/p>\n<p>&nbsp;<\/p>\n<p>\u0394= 1.4K<sub>b<\/sub>T<sub>c<\/sub>\u00a0\u00a0\u00a0\u00a0 for Ga<\/p>\n<p>&nbsp;<\/p>\n<p>Eg \u224810<sup>-4<\/sup> Ev<\/p>\n<p>&nbsp;<\/p>\n<p>The energy is basically a function of temperature and is demonstrated in the following <strong>Fig.7.<\/strong><\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-306\" src=\"http:\/\/msp07.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-109.png\" alt=\"\" width=\"624\" height=\"264\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-109.png 624w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-109-300x127.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-109-65x28.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-109-225x95.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-content\/uploads\/sites\/107\/2018\/12\/Untitled-109-350x148.png 350w\" sizes=\"auto, (max-width: 624px) 100vw, 624px\" \/><\/p>\n<div><\/div>\n<p style=\"text-align: center\"><strong style=\"text-align: initial;font-size: 1em\">Fig.7<\/strong><span style=\"text-align: initial;font-size: 1em\">: Variation of <\/span>energy<span style=\"text-align: initial;font-size: 1em\"> gap with temperature in the left, In the right side: <\/span>energy<span style=\"text-align: initial;font-size: 1em\"> gap in the normal and superconducting <\/span>sate<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/p>\n<div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Ground state electrons are superconducting electrons while electrons in the excited state are normal electrons. With the rise in the temperature a greater number of electrons are excited in the higher band above the energy gap. Therefore at critical temperature all electrons get excited thereby vanishing the energy gap at TC. In the case of superconductors, the existence of energy gap means that the photons with the energy less than the energy gap can\u2019t be absorbed. Therefore, the measurement of energy gap can be done only by directing microwave radiations at the superconductors. Whenever microwave radiations has more energy then the band gap, strong absorption takes place and more number of superconducting electrons are excited to the states above the energy gap.<\/p>\n<\/div>\n<div>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Superconductivity and some introductory concepts<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/aIMd6xC8WtU\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>\u00a0 \u00a0 5. SUMMARY<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Superconductors materials are those which have zero dc resistance below a certain temperature <em>Tc<\/em>, called the critical temperature. A second property of a type I superconductor is that it behaves as a perfect diamagnet. Applied magnetic flux is expelled from the interior of a type I superconductor. This phenomenon is known as the<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Meissner effect. The superconductivity of a type I superconductor gets destroyed when an applied magnetic field exceeds certain critical magnetic field (Bc).<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Type- II superconductor consists of two critical fields. When an applied field is quite less than the critical field, <em>B<\/em><em>c<\/em>1, the material behaves as superconductor and no flux penetration\u00a0<span style=\"text-align: initial;font-size: 1em\">is possible. When the applied field becomes greater than critical field, <\/span><em style=\"text-align: initial;font-size: 1em\">B<\/em><em style=\"text-align: initial;font-size: 1em\">c<\/em><span style=\"text-align: initial;font-size: 1em\">2, the superconducting state gets completely destroyed and the flux penetrates takes material. The critical temperatures of the superconductors vary with the isotopic masses by\u00a0<\/span><span style=\"color: inherit;font-size: inherit;text-align: initial\">relation.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The abrupt variation of specific heat with the critical temperature suggests the presence of <\/span>energy<span style=\"text-align: initial;font-size: 1em\"> gap inside superconductors. Under the application of zero applied filed, persistent currents when <\/span>set<span style=\"text-align: initial;font-size: 1em\"> up in a superconducting ring, (also called supercurrents) circulates for several years with no measurable losses.<\/span><\/p>\n<\/div>\n<div>\n<p><strong>\u00a0 \u00a0 Value Addition:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Do You Know?<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Year 2011 has been marked as the 100th anniversary of discovery of Superconductivity which was discovered by a Dutch scientist Heike Kamerlingh Onnes at Leiden University. He discovered superconductivity while he was liquefying Helium. But before the liquification of Helium, the lowest temperature which was available for researchers was 14K and its was for solid hydrogen. Originally Onnes named his discovery &#8220;supra conductivity&#8221; but later it is was called as &#8220;superconductivity,&#8221; that is the term we use today. He first experiment with the gold and platinum and he moved to the Mercury because it is quite earier to work with the pure metal. At that time scientists have a general thinking that pure metals show zero resistance at liquid-helium temperatures. Till date Five Nobel Prizes in Physics have been awarded for research in superconductivity.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Suggested Reading<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Ginzburg-Landau <\/strong><strong>theory<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>This theory is named after Vitaly Lazarevich Ginzburg and Lev Landau. It is mathematical theory used to describe superconductivity. In the initial stage, it was considered as a phenomenological model which describes type-I superconductors without taking their microscopic properties. At a later stage, a new version of Ginzburg\u2013Landau theory came from the three scientists Bardeen, Cooper, Schrieffer microscopic theory which accounts for microscopic interpretation of all its parameters. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>For More Details ( on this topic and other topics discussed in Text Module) See<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>1.\u00a0 Introduction to Superconductivity by M.Tinkham, Mc-Graw-Hill Inc.<\/p>\n<p>2.\u00a0\u00a0\u00a0 Superconductivity by C P Poole, H A Farach and R J Creswick, Academic Press Inc.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>For General Study on Origins of Superconductivity<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>1.Introduction to solid state physics by C.Kittel,<\/p>\n<p>2.The solid state by H M Roseberg<\/p>\n<p>3. Superconductivity, superfluids and condensates by J Annet<\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Glossary:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Critical Field<\/strong><\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">The filed at which superconductivity is destroyed is known as <\/span>critical<span style=\"text-align: initial;font-size: 1em\"> field.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Entropy<\/strong><\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">It is the measure of disordered state or randomness of a system.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Isotope<\/strong><\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Isotopes are variant of <\/span>chemical<span style=\"text-align: initial;font-size: 1em\"> element which differs in the number of neutrons, <\/span>however<span style=\"text-align: initial;font-size: 1em\"> all isotopes have <\/span>equal<span style=\"text-align: initial;font-size: 1em\"> number of protons.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Penetration depth<\/strong><\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">It is the distance from the surface of the specimen <\/span>upto<span style=\"text-align: initial;font-size: 1em\"> where magnetic field reduces 1\/e times the field at the surface.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Specific heat<\/strong><\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">The specific heat is defined as <\/span>amount<span style=\"text-align: initial;font-size: 1em\"> of heat per unit mass required to raise the temperature by one degree Celsius.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Superconducting state<\/strong><\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">When material exhibits infinite conductivity when cooled to a sufficiently low temperature, the phenomenon is known as superconductivity and the corresponding state is known as <\/span>superconducting<span style=\"text-align: initial;font-size: 1em\"> state.<\/span><\/p>\n<\/div>\n","protected":false},"author":3,"menu_order":19,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-mahavir-singh"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-294","chapter","type-chapter","status-publish","hentry","contributor-prof-mahavir-singh"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/294","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":3,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/294\/revisions"}],"predecessor-version":[{"id":307,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/294\/revisions\/307"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapters\/294\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/media?parent=294"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/pressbooks\/v2\/chapter-type?post=294"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/contributor?post=294"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp07\/wp-json\/wp\/v2\/license?post=294"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}