Module 2: Magnetism & Superconductivity PDF

Module-II : Magnetism & Superconductivity (06 Hrs.) 2.1-Origin of Magnetism in Materials. The origin of magnetism in materials lies in the properties and behaviours of their constituent atoms, specifically the electrons. The primary factors contributing to magnetism are: 1. Electron Spin: Electr...

Module-II : Magnetism & Superconductivity (06 Hrs.) 2.1-Origin of Magnetism in Materials. The origin of magnetism in materials lies in the properties and behaviours of their constituent atoms, specifically the electrons. The primary factors contributing to magnetism are: 1. Electron Spin: Electrons have an intrinsic property called spin, which generates a magnetic moment. This is one of the primary sources of magnetism in atoms. 2. Orbital Motion of Electrons: Electrons moving in their orbits around the nucleus create magnetic fields. The combined effect of these orbital motions contributes to the magnetic properties of the material. A current loop formed by electron revolving in circular motion around the nucleus in an atom behave as a magnetic dipole having magnetic dipole moment. 𝑀 =𝐼 ×𝐴 𝑤ℎ𝑒𝑟𝑒, 𝐴 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑙𝑜𝑜𝑝 = 𝜋𝑟 2 & 𝑞 𝑒 𝐼 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 = 𝐼 = = 𝑡 𝑇 𝑇 = 𝑇𝑖𝑚𝑒 𝑝𝑒𝑟𝑖𝑜𝑑 2𝜋𝑟 We know 𝑣 = , 𝑇 2𝜋𝑟 𝑇= 𝑣 Substituting the value of velocity in I 𝑒 𝑒𝑣 𝐼= = 2𝜋𝑟 2𝜋𝑟 𝑣 We know the area of the circular orbit is 𝐴 = 𝜋𝑟 2  Substituting the values of I & A to calculate magnetic moment, 𝑒𝑣 𝑒𝑣𝑟 𝑀= × 𝜋𝑟 2 = 2𝜋𝑟 2 We know the angular momentum of electron due to its orbital motion is given by , 𝐿 = 𝑚𝑣𝑟, Multiply and divide by 𝑚 to above equation. 𝑒𝑣𝑟 𝑚 𝑒 𝑚𝑣𝑟 𝑒 𝑒 ⃗⃗ = 𝑀 × = = ( ) 𝑚𝑣𝑟 = ⃗ 𝐿 2 𝑚 2𝑚 2𝑚 2𝑚 𝑒 ⃗⃗ = − ( 𝑇ℎ𝑢𝑠 𝑀 ⃗ )𝐿 2𝑚 ⃗⃗ and a𝐿 The -ve sign signifies that 𝑀 ⃗ are oppositely directed. 𝑅𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑎𝑡𝑜𝑚 = 𝑆𝑝𝑖𝑛 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡 + 𝑂𝑟𝑏𝑖𝑡𝑎𝑙 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡 Thus, every atom has its own magnetic moment. Magnetic moment is a vector quantity.It can be added or subtracted as per vector rules. If two neighbouring atoms have magnetic moment in the opposite direction they will cancel out.If they are in same direction they get added up. If all the magnetic moments of atoms in the small region are aligned in the same direction, we called it as domain. The typical size of domains is 0.1 to 1 mm. 2.2-Bohr’s Magnetron. In atomic physics, the Bohr magneton (symbol μB) is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by its orbital or spin angular momentum According to Bohr’s theory the angular momentum of electron is given by, 𝑛ℎ 𝐿= 2𝜋 𝑤ℎ𝑒𝑟𝑒 𝑛 = 𝑝𝑟𝑖𝑛𝑖𝑐𝑝𝑙𝑒 𝑞𝑢𝑎𝑛𝑡𝑢𝑚 𝑛𝑜. 𝑛 = 1,2,3. Substituting value of L in above equation. 𝑒 𝑛ℎ 𝑒ℎ ⃗⃗ = − ( 𝑀 ) =𝑛 2𝑚 2𝜋 4𝑚𝜋 Substituting 𝑚𝑒 = 9.1 × 10−31 𝑘𝑔 ℎ = 6.63 × 10−34 𝑗𝑠, 𝑒 = 1.6 × 10−19 𝑐 𝑛=1 We get 𝐵𝑜ℎ𝑟 𝑚𝑎𝑔𝑛𝑒𝑡𝑟𝑜𝑛 = 𝜇𝐵 = 9.27 × 10−24 𝐴𝑚2 This is the least value of angular momentum known as bohr' s magnetron. 2.3-Types of magnetic materials. Magnetic materials can be classified into three types. Property Diamagnetic Paramagnetic Ferromagnetic Response of Weakly repelled by Weakly attracted by Strongly attracted by material in external the field the field the field mag. field Presence of Present but Present and form Permanent Absent randomly oriented domain structure Magnetic Dipoles Mag. Susceptibility Negative Small & positive High & positive 𝝌 Mag. Permeability 1 »1 µ Magnetization Magnetization When temperature decreased and decreased and is increased above No impact converted to converted to curie point diamagnetic. Paramagnetic. Gold , Silver ,copper Oxygen, Magnesium Iron, Cobalt , nickel Examples air etc. etc. etc.  Why do Diamagnetic Materials do not show permanent magnetic behaviour ? 1. Paired Electrons: In diamagnetic materials, all the electrons are paired. Each pair consists of one electron with an upward spin and another with a downward spin. These opposite spins produce magnetic moments that cancel each other out, resulting in no net magnetic moment. 2. Response to External Magnetic Fields: When an external magnetic field is applied to a diamagnetic material, it induces a weak magnetic field in the opposite direction. This is due to Lenz's law, which states that the induced magnetic field will oppose the change in the external magnetic field. This induced field is very weak and causes the material to be repelled by the magnetic field. 3. Lack of Permanent Magnetic Moments: Since the magnetic moments are induced and not permanent, diamagnetic materials do not retain magnetism once the external field is removed. Why do Paramagnetic Materials not show permanent magnetic behaviour ? 1. Unpaired Electrons: Paramagnetic materials have unpaired electrons, which means they have permanent magnetic moments. However, these moments are randomly oriented in the absence of an external magnetic field due to thermal agitation. 2. Alignment in Magnetic Fields: When an external magnetic field is applied, the magnetic moments of the unpaired electrons tend to align with the field. This alignment results in a weak attraction to the magnetic field. However, the thermal motion of the atoms at room temperature constantly disrupts this alignment, so the overall magnetization remains weak. 3. Temporary Magnetism: The magnetic moments align with the external field, but this alignment is not strong enough to maintain a lasting magnetism once the external field is removed. The induced magnetism is temporary and disappears when the field is switched off. Why do ferromagnetic materials show permanent magnetic behaviour ? 1. Strong Interactions in Ferromagnets: In ferromagnetic materials, there is a strong interaction between neighbouring magnetic moments due to the quantum mechanical exchange interaction. This interaction causes the moments to align parallel to each other, resulting in a strong, permanent magnetization.  2. Domains: Ferromagnetic materials have regions called domains, where the magnetic moments are uniformly aligned. Even without an external magnetic field, these domains can align with each other to produce a strong overall magnetic field. 3. Persistence of Magnetism: Once magnetized, ferromagnetic materials can retain their magnetism even after the external field is removed, due to the strong alignment of the magnetic domains. 2.4-Choice of materials for magnetic data storage. Magnetic data storage is a fundamental technology used to record and retrieve digital information using magnetic media. This technology has been crucial in the evolution of data storage solutions, from the earliest computers to modern-day devices. Understanding magnetic data storage is essential for anyone interested in computer engineering, information technology, and data management. When selecting magnetic materials for data storage applications, consider the following criteria: Coercivity (Hc): The material should have appropriate coercivity to ensure data stability. Higher coercivity materials are more resistant to external magnetic fields. Remanence (Mr): The residual magnetization after removing an external magnetic field. Higher remanence indicates better data retention. Thermal Stability: The material should maintain its magnetic properties over a wide temperature range to prevent data loss due to thermal fluctuations.  Source-Internet Data Density: The material should support high areal density to maximize the amount of data stored per unit area. Materials with high coercivity and anisotropy are often better suited for high- density storage. Corrosion Resistance: The material should resist oxidation and corrosion to ensure long-term data retention, especially in environments with varying humidity and temperature. Magnetic Saturation (Ms): The maximum magnetization the material can achieve. Higher magnetic saturation allows for more robust data storage.  Applications of Magnetic materials for data storage-Hard disk. Basics of Magnetic Data Storage Magnetic data storage operates on the principle of magnetism. It uses magnetic fields to store data on a magnetizable medium, typically in the form of disks or tapes. The key components of a magnetic storage system include: 1. Platter: It’s a rigid circular plate made up of aluminium. The platter is coated with magnetic iron oxide because it has high permeability ( 50 ). This is the material that holds the magnetic patterns representing data. Since magnetic iron oxide is ferromagnetic material, it already has magnetic dipole moments/domains. The platter is subdivided into circular tracks. The concentric circular rings are called tracks. The tracks are further divided into sectors. Sectors are the basic unit/location in which data can be stored This Photo by Unknown Author is licensed under CC BY-SA This Photo by Unknown Author is licensed under CC BY-SA-NC  2. Read/Write Heads: These are small electromagnets used to read from and write data to the magnetic medium. When writing data, the head magnetizes small regions of the medium in patterns that represent binary data (0s and 1s). When reading, it senses the magnetic patterns and converts them back into electrical signals. 3. Spindle and Motor: In devices like hard disk drives, a spindle and motor are used to spin the magnetic platters at high speeds, enabling fast data access. Working Principle Writing Data: When a platter is mounted on a spindle motor , the motor rotates the platter. The read /write head moves very closed to platter or at 1-2 nm distance. The electromagnet writes information on a magnetic medium by converting electrical signals into magnetic. These fields magnetize small regions of the medium, creating patterns that represent binary data. Reading Data: To read data, the read head detects the magnetic patterns on the medium and converts them back into electrical signals, which are then processed by the computer to retrieve the stored information. Types of Magnetic Storage 1. Magnetic Tape: One of the earliest forms of magnetic storage, used primarily for backups and archival storage due to its high capacity and low cost. 2. Hard Disk Drive (HDD): A widely used storage device in computers, known for its large storage capacity and relatively fast data access speeds. HDDs consist of multiple spinning platters coated with magnetic material. 3. Floppy Disk: An older and now largely obsolete form of magnetic storage, used primarily in the late 20th century for transferring small amounts of data between computers. Advantages and Disadvantages Advantages: High Capacity: Magnetic storage devices can store large amounts of data. Cost-Effective: Generally cheaper per unit of storage compared to other technologies. Non-Volatile: Data remains stored even when the power is turned off. Disadvantages: Mechanical Wear: Moving parts in devices like HDDs can wear out over time.  Slower Access Times: Compared to modern solid-state drives (SSDs), magnetic storage devices typically have slower data access speeds. Susceptible to Magnetic Fields: Strong external magnetic fields can potentially corrupt stored data. 2.5-Wireless charging : Let’s understand how wireless charging works. 1. Self-Induction Self-Induction is the process where a changing current in a coil induces an electromotive force (EMF) within the same coil. This is how each coil resists changes in its current. In a wireless charger: The charging pad (transmitter) has a coil of wire. When an alternating current (AC) flows through this coil, it creates a changing magnetic field around it due to self-induction. 2. Mutual Induction Mutual Induction occurs when a changing magnetic field from one coil induces an EMF in a nearby coil. In wireless charging: The charging pad's coil generates a magnetic field due to the changing current (AC). When you place your device (which has its own coil) close to the charging pad, the magnetic field from the charging pad (transmitter) passes through the device’s coil (receiver). 3. Faraday’s Law of Induction Faraday’s Law states that a changing magnetic field within a coil induces an EMF (voltage) in the coil. The amount of induced EMF is proportional to the rate of change of the magnetic flux. In wireless charging: Faraday’s Law explains that the alternating magnetic field created by the transmitter coil induces a voltage in the receiver coil. The strength of this induced voltage depends on the rate of change of the magnetic field (alternating current in the transmitter coil) and the number of turns in the coils.  The changing magnetic field induces a voltage in the device’s coil through mutual induction. Summary: 1. Transmitter Coil (Charging Pad): When an AC flows through the transmitter coil, it creates a changing magnetic field around it (self-induction). 2. Receiver Coil (Device): The device’s receiver coil is placed close to the transmitter coil. The changing magnetic field from the transmitter coil induces a voltage in the receiver coil (mutual induction), as described by Faraday’s Law. 3. Charging Process: This induced voltage in the receiver coil is used to charge the battery of the device. In essence, wireless charging relies on the principles of self-induction, mutual induction, and Faraday’s Law to transfer energy from the charging pad to the device without physical connectors.  Superconductivity. 2.6-Introduction to Superconductivity. Superconductivity is a phenomenon where a material, when cooled below a certain critical temperature, exhibits zero electrical resistance. This allows for the unimpeded flow of electric current without any energy loss. The phenomenon was first discovered in mercury by Heike Kamerlingh Onnes in 1911. The fundamental theory that explains superconductivity is the BCS (Bardeen-Cooper-Schrieffer) theory, proposed in 1957 by John Bardeen, Leon Cooper, and Robert Schrieffer. Superconductors have a wide range of applications, including MRI machines, particle accelerators, and potentially lossless power transmission. Fig. Graphical representation of super conductivity. Critical Temperature (Tc) The temperature below which a material becomes superconducting and exhibits zero electrical resistance is called the critical temperature (Tc). Above this temperature, the material behaves as a normal conductor with finite resistance. As an example, it may be mentioned that electrical resistivity of pure mercury dropped abruptly to zero at around 4.2 K. Different materials have different critical temperatures. 2.7-Zero Electrical resistivity- Zero electrical resistance is a defining characteristic of superconductivity. When a material becomes superconductive, it loses all electrical resistance, allowing electric current to flow without any energy loss. This unique property has profound implications and numerous practical applications. Here’s a detailed explanation: Phenomenon of Zero Electrical Resistance Resistance in Normal Conductors: In normal conductors like copper or aluminium, electrical resistance arises due to collisions between conduction electrons and atoms or impurities in the material. These collisions convert some of the electrical energy into heat, resulting in energy loss. Superconducting State: In the superconducting state, resistance drops to zero. This means that if a current is started in a superconducting loop, it will continue to flow indefinitely without any decrease in current or energy loss, provided the material remains below its critical temperature (Tc). 2.8- Measurement of Zero electrical resistivity- Four-Probe Method. The four-probe method involves using four separate electrical contacts (probes) placed along the material sample. The outer two probes are used to inject a current into the sample, while the inner two probes measure the voltage drop. The separation of current and voltage measurements helps eliminate the effects of contact resistance. Setup 1. Probes: Four metal probes are placed in a line on the surface of the sample. The spacing between the probes should be uniform and small compared to the sample dimensions to ensure accurate measurements. 2. Current Source: A current source is connected to the outer two probes (probes 1 and 4). A constant current (I) is passed through the sample via these probes. 3. Voltmeter: A high-impedance voltmeter is connected to the inner two probes (probes 2 and 3) to measure the voltage drop (V) across a known distance. Measurement Procedure 1. Current Injection: The current source injects a known current through the outer probes (1 and 4). 2. Voltage Measurement: The voltmeter measures the voltage drop (V) between the inner probes (2 and 3). 3. Resistivity Calculation: The resistivity (ρ) of the material is calculated using the measured voltage (V), the injected current (I), and the geometry of the probe arrangement. For a thin film or a sample of uniform thickness (t), the resistivity can be calculated using the following formula: The geometric factor depends on the arrangement of the probes and the sample dimensions. Advantages of the Four-Probe Method 1. Eliminates Contact Resistance: By using separate pairs of probes for current and voltage measurements, the method eliminates the contribution of contact resistance and lead resistance, leading to more accurate results. 2. Accurate for Low Resistivity Materials: This method is particularly useful for measuring materials with very low resistivity, such as superconductors, where the influence of contact resistance can be significant. 3. Versatility: The four-probe method can be used on a variety of sample shapes and sizes, including thin films, bulk materials, and even irregularly shaped samples. 2.9-The Meissner effect. The Meissner effect is a fundamental characteristic of superconductors, discovered by Walther Meissner and Robert Ochsenfeld in 1933. It refers to the expulsion of magnetic fields from the interior of a material when it normal metal is converted into superconducting state. This effect is essential for distinguishing superconductors from perfect conductors and plays a crucial role in the behaviour and applications of superconducting materials. Description of the Meissner Effect 1. Expulsion of Magnetic Fields: When a material transitions from the normal state to the superconducting state (below its critical temperature.it expels magnetic fields from its interior. This means that any magnetic field lines that were present inside the material before it became superconducting are pushed out of the material. 2. Perfect Diamagnetism: Superconductors exhibit perfect diamagnetism due to the Meissner -effect. This means they have a magnetic susceptibility of χ=−1\chi = -1χ=−1, completely canceling out any applied magnetic field within the superconductor. 3. Mechanism Behind the Meissner Effect 4. Formation of Surface Currents: To expel the magnetic field, surface currents are generated in the superconductor. These currents create a magnetic field that exactly cancels the applied magnetic field inside the superconductor, resulting in zero internal magnetic field.  Experimental Observation Meissner-Ochsenfeld Experiment: In their original experiment, Meissner and Ochsenfeld placed a tin cylinder in a magnetic field and cooled it below its critical temperature. They observed that the magnetic field inside the cylinder was expelled as it became superconducting, providing direct evidence for the Meissner effect. perfect diamagnetic behavior of superconductors We know that when the superconducting material is in superconducting state , 𝐵 = 𝜇0 (𝐻 + 𝑀) Inside the superconductor B=0 So 0 = 𝜇0 (𝐻 + 𝑀) (𝐻 + 𝑀) = 0 𝐻 = −𝑀 𝑀 As 𝜒 = = −1, 𝑤ℎ𝑒𝑟𝑒 𝜒 = 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑠𝑢𝑠𝑐𝑒𝑝𝑡𝑖𝑏𝑖𝑙𝑖𝑡𝑦 𝐻 Thus, magnetic susceptibility is negative. We know that for diamagnetic material magnetic susceptibility is negative.Thus from above equation we can say that materials in superconducting state exhibit perfect diamagnetism. 2.10-Types of Superconductors.- Superconductors can be broadly classified into two types. Sr. Property Type I Type II No. 1 Also known as Soft Superconductors Hard Superconductors 2 They are made of Pure Metals Alloys Transition from Normal Sharp. Takes place over a range of 3 state to superconducting temperature state 4 Critical field Only 1 Critical field 2 Critical field 5 Vortex state (State in Since transition is sharp ,no Vortex state present which material present in vortex state is absent between 𝐻𝑐1& 𝐻𝑐2 cohesion of normal & superconducting state. 6 Critical Temperature Ver low Highter than type I 7 Industry applications Critical temperature is difficult to Critical temperature is higher attend therefore less applications therefore the applications in industry are more. 8 Graphs. Magnetic field is applied externally and increased Magnetic field is applied continuously. externally and increased H < Hc → perfectly continuously diamagnetic For H < Hc1 H is increased → superconducting state magnetization of the M  with  in H material increases Hc1 > H < Hc2 proportionally Magnetic flux penetrates H = Hc material Magnetic field penetrates Hc2 > 100 times Hc completelySC was perfectly H > Hc2 diamagnetic Magnetization vanishes  9 Examples with critical temperature. 2.11-The Superconducting Magnetic Energy Storage (SMES)- The Superconducting Magnetic Energy Storage system operates based on several fundamental physics principles: 1.Superconductivity: Zero Electrical Resistance: When certain materials are cooled below a critical temperature, they exhibit zero electrical resistance. This phenomenon, known as superconductivity, allows for the lossless flow of electric current. The primary materials used are often niobium-titanium (NbTi) or niobium-tin (Nb3Sn). Meissner Effect: Superconductors expel magnetic fields from their interior, a phenomenon known as the Meissner effect. This allows them to maintain a stable magnetic field configuration when used in a coil. 2. Electromagnetic Induction (Faraday’s Law of Induction): When a current flows through a conductor (in this case, a superconducting coil), it generates a magnetic field around the conductor. The relationship between the electric current and the magnetic field is governed by Maxwell's equations, specifically Ampere's Law. 3. Energy Storage in Magnetic Fields: Magnetic Energy Storage: The energy EEE stored in the magnetic field of a superconducting coil is given by the equation: E=12LI2E = \frac{1}{2} L I^2E=21LI2 where LLL is the inductance of the coil, and III is the current flowing through it. Since superconductors can carry large currents without resistance, they can store significant amounts of energy in their magnetic fields. 4. Cryogenics: Low Temperature Physics: Superconductors require cooling to cryogenic temperatures (using liquid helium or advanced cryocoolers) to reach and maintain their superconducting state. The behaviour of materials at these low temperatures is governed by principles of cryogenics and low-temperature physics. 5. Electrodynamics: Lorentz Force: The interaction of the magnetic field with electric currents and other magnetic fields is described by the Lorentz force. This force plays a crucial role in the dynamics of the current-carrying superconducting coil within the magnetic field. 6. Quantum Mechanics: Cooper Pairs: In superconductors, electrons form Cooper pairs, which move through the lattice structure without scattering, thus leading to zero electrical resistance. This pairing and movement are described by quantum mechanical principles. Working : Superconducting Coil and Magnetic Field: The superconducting coil, once charged with direct current (DC), maintains the current with negligible losses due to the absence of electrical resistance. The generated magnetic field stores energy that can be tapped into when needed. Cooling System:  The cooling system ensures the coil remains below its critical temperature, thus maintaining its superconducting properties. This involves principles of thermodynamics and heat transfer. Power Conversion System: This system involves converting alternating current (AC) from the power grid to direct current (DC) for storage in the superconducting coil and back from DC to AC for releasing the stored energy. Control System: Ensures the superconducting coil operates within safe limits, managing the charging and discharging processes effectively. In summary, the SMES system leverages the principles of superconductivity, electromagnetic induction, energy storage in magnetic fields, cryogenics, electrodynamics, and quantum mechanics to store and release electrical energy efficiently. 2.12-Superconducting electromagnets Superconducting electromagnets are a type of electromagnet made from coils of superconducting wire. Unlike traditional electromagnets, which are made from copper or aluminum wire, superconducting electromagnets have no electrical resistance when cooled below their critical temperature, allowing them to carry much larger currents without energy loss. This makes them extremely powerful and efficient. Applications 1. Magnetic Resonance Imaging (MRI) Machines: The strong magnetic fields needed in MRI machines are generated by superconducting electromagnets, providing high-quality images for medical diagnostics. The superconducting magnet is typically made from niobium-titanium (NbTi) wire. The magnet is cooled to 4 K (-269°C) using liquid helium, causing the NbTi to become superconducting. A strong, stable magnetic field is then generated, which interacts with the hydrogen nuclei in the body to produce detailed images of internal tissues. 2. Particle Accelerators: Large particle accelerators, like the Large Hadron Collider (LHC), use superconducting magnets to steer and focus particle beams at near-light speeds. The LHC’s superconducting magnets operate at temperatures close to 1.9 K (-271.25°C).  3. Magnetic Levitation (Maglev) Trains: Superconducting electromagnets are used in some maglev trains to achieve frictionless, high-speed travel by levitating the train above the tracks using powerful magnetic fields. 4. Fusion Reactors: Superconducting magnets are used to contain and control the plasma in experimental fusion reactors like the ITER (International Thermonuclear Experimental Reactor). These magnets are crucial for maintaining the extremely high temperatures needed for fusion reactions. ------------------------------------------------------****---------------------------------------------------------