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de-Broglie matter waves: After Einstein's photoelectric theory and Compton's X-ray experiment, light had to be viewed as having both particle and wave properties, but massive particles such as electrons were still widely considered completely distinct from waves. However, puzzling questions about the particle interpretation of electrons were already developing as early as 1913 with Niels Bohr's model of the Hydrogen atom. Bohr had succeeded in theoretically explaining the Rydberg formula for the emission specturm of Hydrogen by assuming that the angular momentum of the orbiting electron was restricted to integer multiples of Planck's constant h. Despite its impressive results, Bohr's model had many shortcomings. It was inconsistent with several other observations, and theoretically provided no justi cation for the quantization assumption. This inspired Louis de Broglie to propose the idea that all particles possess an associated matter wave. ...the determination of the stable motions of the electrons in the atom involves whole numbers, and so far the only phenomena in which whole numbers were involved in physics were those of interference and of eigenvibrations. That suggested the idea to me that electrons He may have also been encouraged to take this leap by Einstein's work on the photoelectric effect.

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introduction to wave mechanics: At the turn of the 20th century, physics was starting to look rather mature and polished. At about this time Albert Michelson wrote, The more important fundamental laws and facts of physical science have all been discovered, and these are so rmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i.e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions." [1] However, there were already some indications that big changes were on the horizon. One was the problem that the version of ether theory in existence at the time could not easily be reconciled with the results of the experiment that Michelson had carried out with Morley. Another was the so-called ultraviolet catastrophe that came about with Lord Rayleigh's 1900 version of the Rayleigh-Jeans law of blackbody radiation. THE PLANCK-EINSTEIN EQUATION On December 14th 1900, Max Planck presented a derivation of the blackbody radiation law that was based on the assumption that electromagnetic radiation could only be emitted in particle-like packets with a xed ratio of energy to frequency. This assumption can be written as E = h where  is the frequency and h is a universal constant. This equation came to be known as Planck's equation, though Planck did not initially consider it to be a real physical law. In a letter to a colleague, he wrote

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The wave functions and the probability density at different allowed energy states are shown pictorially as follows:

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Note that here Schriodinger introduces complex numbers without justi cation or comment. This was perhaps a seemingly harmless assumption because electromagnetic theory taught physicists that waves are more conveniently written in complex notation. The fi rst two time derivatives of Ψ are

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Phase and group velocity: To understand the difference between phase and group velocity of waves, consider the following analogy. A group of people, say city marathon runners, start from the starting at the same time. Initially it would appear that all of them are running at the same speed. As time passes, group spreads out (disperses) simply because each runner in the group is running with different speed. If you think of phase velocity to be like the speed of individual runner, then the group velocity is the speed of the entire group as a whole. Obviously and most often, individual runners can run faster than the group as a whole. To stretch this analogy, we note that the phase velocity of waves are typically larger than the group velocity of waves. However, this really depends on the properties of the medium. Briefly, phase velocity refers to a monochromatic wave, let’s say, the velocity of one of the peaks of the wave. For example, a monochromatic wave with angular frequency ω = 2πν (ν is the frequency) travelling in ve x-direction is given by,

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Wave-Particle Duality: Introduction: The Bohr model of the atom involved two puzzling features - the electron was treated as a wave, and light was treated as a particle (a photon).

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Bragg’s spectrometer: X-rays of wavelength ‘λ’ be incident upon the crystal at an angle ‘θ’. The crystal acts as a series of parallel reflecting planes. The intensity of the reflected beam at certain angles will be maximum when the path difference between the two reflected waves from two different planes is nλ. Lattice planes are separated by a distance ‘d’. From figure Path difference = PE EQ = BE sinθ BE sinθ = d sinθ d sinθ = 2d sinθ

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Physical significance of wave function: In 1923 Louis de Broglie, then a graduate student, introduced the conjecture that particlelike objects (say electrons) should display wave properties. “It would seem” he wrote, ... that the basic idea of the quantum theory is the impossibility of imagining an 'isolated quantity of energy 'without associating with it 'a certain frequency'. For now, not only was light to be treated sometimes as a wave and sometimes as a particle,but matter itself- the ultimate, the final repository of atomic, corpuscular properties- the atoms of Democritus, Gassendi, and Newton- now had associated with them in some mysterious way a wave. The physicist of the 1920s had become accustomed to treating light or matter as a wave in diffraction or interference and as a particle in emission, absorption, or transfer of energy. Shortly after de Broglie introduced the idea of the associated wave for an electron, Erwin Schrödinger (in 1926) proposed an answer to the question of what happens to the associated wave if a force acts on it. He introduced now famous equation to study many of the basic problems of the quantum theory. A wave is a disturbance that propagates through space and time, usually with transfer of energy. Wave is distributed in space and the distribution increases with time. Thus the wave energy per unit volume decreases with time about a space point. A particle (micro-particle) is endowed with a mass. It may also have charge, like electron or proton. The mass is concentrated about a space point. Again the energy associated with the particle is concentrated about the particle. Thus wave and particle form two distinctly different physical phenomenon. Schrödinger's equation gives the de Broglie wave associated with an electron, any other particle, or finally any quantum system. Given the mass of the particle, and given the forces to which it is subjected, let us say gravitational, or electromagnetic, then Schrödinger's equation gives the possible waves associated with this particle: the waves (functions of position and time) give a number associated with any position in space at an arbitrary time. And they are designated by the hardest working symbol in twentieth-century physics: the wave function ψ(x,y,z;t) The essence of the Schrödinger equation is that, given a particle, and given the force system that acts, it yields the wave function solutions for all possible energies. The wave function satisfies the most fundamental property of waves-the property of superposition. Just as in classical theory, this means that a trough and a crest can be added to cancel one another. Thus, one can have interference, that most characteristic wave phenomenon. And this now is associated with what were thought of previously as particles: electrons or protons and finally even with entire systems. An idea of Einstein's gave Max Born to propose an interpretation of the wave function whose consequence are possibly as revolutionary as those of any other idea of the twentieth century. Einstein had tried to make the duality of particles-'light quanta or photons'-and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons. This concept could at once be carried over to the ψ-function: |ψ|2 ought to represent the probability density for micro-particles. The probability interpretation, as developed by Born, now is the standard interpretation of the associated wave with any moving micro-particle. The square of the wave function, ψ2 , represents a possibility (probability) density. Thus the particle is likely to be found at the place where the wave function is large and not at the place where the wave function is small. Again, ψ2 is chosen rather than ψ, because ψ itself can be negative and an interpretation for a negative probability is hard to find. With this interpretation, one arrives at the requirement that the total area under the curve ψ2 as a function of x (in one dimensional case) must be equal to 1, because that represents the probability that the electron be in some place-which is to be certain. As a general rule, for bound systems, not all energy levels are possible. The reason is related closely to that proposed initially by de Broglie: an integral number of waves must fit into a closed orbit in order that the orbit be stable. Thus, from the point of view of the Schrödinger equation for a particle that is in a bound state (confined to a finite region of space), not all energies, not all momenta, and not all wavelengths are allowed. Only a discrete set, a small portion of the energies that would have been allowed in Newtonian mechanics, occurs. One gets analogous results, although differing in quantitative detail, for particles contained in three dimensions, for particles contained by walls that are not rigid, and for particles contained by a potential such as that which produces the hydrogen atom. This, then, from Schrödinger's point of view, is the origin of discrete levels of the Bohr atom, and the discrete levels characteristic of all bound quantum mechanical system. Metals can be thought of as three dimensional boxes with the surfaces as boundaries and the valence electrons as relatively free particles. As the dimesion of the box increases the energy levels are very close to each other forming some sort of quasi-continuous states.

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Principles of X-ray Diffraction: Diffraction effects are observed when electromagnetic radiation impinges on periodic structures with geometrical variations on the length scale of the wavelength of the radiation. The interatomic distances in crystals and molecules amount to 0.15–0.4 nm which correspond in the electromagnetic spectrum with the wavelength of x-rays having photon energies between 3 and 8 keV. Accordingly, phenomena like constructive and destructive interference should become observable when crystalline and molecular structures are exposed to x-rays. In the following sections, firstly, the geometrical constraints that have to be obeyed for x-ray interference to be observed are introduced. Secondly, the results are exemplified by introducing the θ/2θ scan, which is a major x-ray scattering technique in thin-film analysis. Thirdly, the θ/2θ diffraction pattern is used to outline the factors that determine the intensity of x-ray ref lections. We will thereby rely on numerous analogies to classical optics and frequently use will be made of the fact that the scattering of radiation has to proceed coherently, i.e. the phase information has to be sustained for an interference to be observed. In addition, the three coordinate systems as related to the crystal {ci}, to the sample or specimen {s} and to the laboratory {li} that have to be considered in diffraction are introduced. Two instrumental sections (Instrumental Boxes 1 and 2) related to the θ/2θ diffractometer and the generation of x-rays by x-ray tubes supplement the chapter. One-elemental metals and thin films composed of them will serve as the material systems for which the derived principles are demonstrated. A brief presentation of one-elemental structures is given in Structure Box1. The Basic Phenomenon:Before the geometrical constraints for x-ray interference are derived the interactions between x-rays and matter have to be considered. There are three different types of interaction in the relevant energy range. In the first, electrons may be liberated from their bound atomic states in the process of photoionization. Since energy and momentum are transferred from the incoming radiation to the excited electron, photoionization falls into the group of inelastic scattering processes. In addition, there exists a second kind of inelastic scattering that the incoming x-ray beams may undergo, which is termed Compton scattering. Also in this process energy is transferred to an electron, which proceeds, however, without releasing the electron from the atom. Finally, x-rays may be scattered elastically by electrons, which is named Thomson scattering. In this latter process the electron oscillates like a Hertz dipole at the frequency of the incoming beam and becomes a source of dipole radiation. The wavelength λ of x-rays is conserved for Thomson scattering in contrast to the two inelastic scattering processes mentioned above. It is the Thomson component in the scattering of x-rays that is made use of in structural investigations by x-ray diffraction. Figure 1 illustrates the process of elastic scattering for a single free electron of charge e, mass mand at position R₀. The incoming beam is accounted for by a plane wave E₀exp(–iK₀R₀), where E₀ is the electrical field vector and K₀ the wave vector. The dependence of the field on time will be neglected throughout. The wave vectors K₀ and K describe the direction of the incoming and exiting beam and both are of magnitude 2π/λ. They play an important role in the geometry of the scattering process and the plane defined by them is denoted as the scattering plane. The angle between K and the prolonged direction of K₀ is the scattering angle that will be abbreviated by 2θ as is general use in x-ray diffraction. We may also define it by the two wave vectors according to ............................eq..(1)

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Compton Effect: Compton (1923) measured intensity of scattered X-rays from solid target, as function of wavelength for different angles. He got Nobel prize for that in 1927. When a beam of monochromatic radiation such as X-rays,
-ray, etc., of high frequency is allowed to fall on a fine scatterer, the beam is scattered into two components namely Let us consider the collision which occurs between the photon (having initially the energy hv =hc/λ) and electron. The electron is free and is at rest before collision with the incident photon. During collision, a part of energy is given to the electron, which in turn increases the K.E. of the electron and hence it recoils at an angle of 9 as shown in figure. The scattered photon moves with an energy hv' = hc/λ' (< hn ) at an angle : with respect to the original direction. Obviously, one can use law of conservation of energy and momentum for such a system. For that, we have to know the momentum and energy values before and after collision.

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Davisson-Germer Experiment: In order to test de Broglie’s hypothesis that matter behaved like waves, Davisson and Germer set up an experiment very similar to what might be used to look at the interference pattern from x-rays scattering from a crystal surface. The basic idea is that the planar nature of crystal structure provides scattering surfaces at regular intervals, thus waves that scatter from one surface can constructively or destructively interfere from waves that scatter from the next crystal plane deeper into the crystal. Their experimental apparatus is shown below. This simple apparatus send an electron beam with an adjustable energy to a crystal surface, and then measures the current of electrons detected at a particular scattering angle theta. The results of an energy scan at a particular angle and an angle scan at a fixed energy are shown below. Both show a characteristic shape indicative of an interference pattern and consistent with the planar separation in the crystal. This was dramatic proof of the wave nature of matter.

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If, on the other hand, the current in the inner solenoid is varied, the field due to it which is non-zero only within the inner solenoid. The flux enclosed by the outer solenoid is, therefore, If is varied, the emf in the outer solenoid is giving

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Magnetism in Matter: we have seen that in the presence of an electric field, a dielectric gets polarized, leading to bound charges. The polarization vector is, in general, in the direction of the applied electric field. A similar phenomenon occurs when a material medium is subjected to an external magnetic field. However, unlike the behaviour of dielectrics in electric field, different types of material behave in different ways when an external magnetic field is applied. We have seen that the source of magnetic field is electric current. The circulating electrons in an atom, being tiny current loops, constitute a magnetic dipole with a magnetic moment whose direction depends on the direction in which the electron is moving. An atom as a whole, may or may not have a net magnetic moment depending on the way the moments due to different elecronic orbits add up. (The situation gets further complicated because of electron spin, which is a purely quantum concept, that provides an intrinsic magnetic moment to an electron.)

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Experimental verification:Compton Effect: Consider the experimental set up shown in the following figure. The monochromatic X-rays from a molybdenum target of an X-rays tube are made to fall on a carbon scatterer (graphite) and the corresponding λ values are calculated using Bragg’s law. The scattered X-ray is observed at the ionization chamber or X-ray detector to to measure its intensity. Compton found that the spectrum recorded after scattering had Ka λ’ line (corresponding toλ’) which is on the longer wavelength side of primary Ka line (corresponding to λ) as shown in figure. He also observed that the change in wavelength Δλ increased rapidly as the scattering angle : increased;  the change in wavelength Δλ was independent of λ.

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Generation of Electromagnetic Waves: We have looked for solutions to Maxwell's equations in free space which does not have any charge or current source. In the presence of sources, the solutions become complicated. If = constant, i.e. if , we only have a steady electric field. If varies uniformly with time, we have steady currents which gives us both a steady electric field as well as a magnetic field. Clearly, time varying electric and magnetic fields may be generated if the current varies with time, i.e., if the charges accelerate. Hertz confirmed the existence of electromagnetic waves in 1888 using these principles. A schematic diagram of Hertz's set up is shown in the figure. The radiation will be appreciable only if the amplitude of oscillation of charge is comparable to the wavelength of radiation that it emits. This rules out mechanical vibration, for assuming a vibrational frequency of 1000 cycles per second, the wavelength work out to be 300 km. Hertz, therefore, made the oscillating charges vibrate with a very high frequency. The apparatus consists of two brass plates connected to the terminals of a secondary of a transformer. The primary consists of an LC oscillator circuit, which establishes charge oscillations at a frequency of . As the primary circuit oscillates, oscillations are set up in the secondary circuit. As a result, rapidly varying alternating potential difference is developed across the gap and electromagnetic waves are generated. Hertz was able to produce waves having wavelength of 6m. It was soon realized that irrespective of their wavelength, all electromagnetic waves travel through empty space with the same speed, viz., the speed of light.

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Self Inductance: Even when there is a single circuit carrying a current, the magnetic field of the circuit links with the circuit itself. If the current happens to be time varying, an emf will be generated in the circuit to oppose the change in the flux linked with the circuit. The opposing voltage acts like a second voltage source connected to the circuit. This implies that the primary source in the circuit has to do additional work to overcome this back emf to establish the same current. The induced current has a direction determined by Lenz's law. If no ferromagnetic materials are present, the flux is proportional to the current. If the circuit contains N turns, Faraday's law gives

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Time Varying Field: Even where there is no relative motion between an observer and a conductor, an emf (and consequently an induced current for a closed conducting loop) may be induced if the magnetic field itself is varying with time as flux change may be effected by change in magnetic field with time. In effect it implies that a changing magnetic field is equivalent to an electric field in which an electric charge at rest experiences a force. Consider, for example, a magnetic field whose direction is out of the page but whose magnitude varies with time. The magnetic field fills a cylindrical region of space of radius . Let the magnetic field be time varying and be given by R \end{array}\right. \end{displaymath}" height="55" src="http://www.cdeep.iitb.ac.in/nptel/Core Science/Engineering Physics 2/Slides/Module-3/main3_clip_image003_0023.gif" width="215" /> Since does not depend on the axial coordinate as well as the azimuthal angle , the electric field is also independent of these quantities. Consider a coaxial circular path of radius which encloses a time varying flux. By symmetry of the problem, the electric field at every point of the cicular path must have the same magnitude and must be tangential to the circle.

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The Lorentz Force: We know that an electric field exerts a force on a charge . In the presence of a magnetic field , a charge q experiences an additional force where is the velocity of the charge. Note that • , which shows that the magnetic force does not do any work. In the case where both are present, the force on the charge q is given by

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Magnetic Field: Electric charges are source of electric fields. An electric field exerts force on an electric charge, whether the charge happens to be moving or at rest. One could similarly think of a magnetic charge as being the source of a magnetic field. However, isolated magnetic charge ( or magnetic monopoles) have never been found to exist. Magnetic poles always occur in pairs ( dipoles) - a north pole and a south pole. Thus, the region around a bar magnet is a magnetic field. What characterizes a magnetic field is the qualitative nature of the force that it exerts on an electric charge. The field does not exert any force on a static charge. However, if the charge happens to be moving (excepting in a direction parallel to the direction of the field) it experiences a force in the magnetic field. It is not necessary to invoke the presence of magnetic poles to discuss the source of magnetic field. Experiments by Oersted showed that a magnetic needle gets deflected in the region around a current carrying conductor. The direction of deflection is shown in the figure below. Thus a current carrying conductor is the source of a magnetic field. In fact, a magnetic dipole can be considered as a closed current loop.

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Amperes Law: Biot-Savart's law for magnetic field due to a current element is difficult to visualize physically as such elements cannot be isolated from the circuit which they are part of. Andre Ampere formulated a law based on Oersted's as well as his own experimental studies. Ampere's law states that `` the line integral of magnetic field around any closed path equals times the current which threads the surface bounded by such closed path. . Mathematically,

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Biot- Savarts' Law: Biot-Savarts' law provides an expression for the magnetic field due to a current segment. The field at a position due to a current segment is experimentally found to be perpendicular to and . The magnitude of the field is

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Potential Energy of a Magnetic Dipole: A current loop does not experience a net force in a magnetic field. It however, experiences a torque. This is very similar to the behaviour of an electric dipole in an electric field. A current loop, therefore, behaves like a magnetic dipole. We define the magnetic dipole moment of a current loop to be a vector of magnitude and direction perpendicular to the plane of the loop (as determined by right hand rule). If the loop has . In a magnetic field, the dipole experiences a torque

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Poynting Vector: Electromagnetic waves, like any other wave, can transport energy. The power through a unit area in a direction normal to the area is given by Poynting vector , given by As and form a right handed triad, the direction of is along the direction of propagation. In SI units ismeasured in watt/m ² The magnitude of for the electromagnetic wave travelling in vacuum is given by

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Diamagnetism: Diamagnetism, being a consequence of Lenz's law is present in all substance though its effect may be masked because of other strong magnetic effects. However, certain substances like Bismuth are strongly diamagnetic. The effect arises because when an atom is placed in a magnetic field, the flux through the atomic orbit changes. This results in an induced current being generated which opposes the changing flux. The effect is equivalent to the atom developing an induced magnetic moment opposite to the direction of the applied field. Displacement Current: We have seen that the magnetic field due to a current is given by Ampere's law

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Torque on a Current Loop in a Uniform Magnetic Field : Though the net force on a closed current loop in a uniform magnetic field is zero, it experiences a torque. Consider a rectangular current loop PQRS of length and width . The loop is in a uniform magnetic field which acts parallel to the x-axis. The loop, which is pivoted about an axis OO', carries a current along the direction shown in the figure. The plane of the loop (i.e. the normal the loop) makes an angle to the direction of the field. We take the shorter sides PQ and RS (as well as the pivot axis OO') to be perpendicular to the field direction, OO' being taken as the y-axis. The longer sides QR and QS make an angle with the field direction. Since the force on a current segment is , the force is directed perpendicular to both and to the direction of the current in these segments. The force has a magnitude and is directed oppositely on the two sides. These forces are labelled and in the figure. (The forces are actually distributed along the lengths and the cancellation occurs for the forces acting on symmetrically placed elements on these two arms.) Further, since the lines of action of the forces acting on corresponding elements on these two sides are the same, there is no torque. The forces acting on the sides PQ and RS (labelled and respectively) are also equal and opposite and have magnitude . However, these forces do not act along the same line. The force on PQ acts parallel to axis while that on RS acts parallel to axis. Note that axis is not in the plane of the loop. The situation can be better visualized by redrawing the figure in the plane containing one of the longer sides and .

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Ferromagnets: In certain substances like Fe, Co, Ni etc. magnetization not only depends on the applied magnetic field but it also depends on the history of the material. In a phenomenon known as hysteresis , a sample of a ferromagnet may exhibit magnetization even when no magnetic field is present exhibiting a memory effect. When a sample of such a material which has no initial magnetic moment is subjected to a magnetic field, the magnetization increases with increasing strength of magnetic field and soon saturates when all the atomic moments have got aligned in the direction of the magnetic field. If field strength is now decreased gradually, the magnetization decreases. However, the magnetization curve does not retrace its path. When the field strength has been reduced to zero, the sample still has some magnetization left. In order to bring the sample to a state of zero magnetization, a coercive field must be applied in the reverse direction.

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Motion in a crossed electric and magnetic fields: The force on the charged particle in the presence of both electric and magnetic fields is given by Let the electric and magnetic fields be at right angle to each other, so that,

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Maxwell's Equations: We are now in a position to collect together all the laws governing the dynamic of electromagnetic field. These equations are collectively known as Maxwell's equations. Gauss's Law of Electrostatics : Gauss's Law of Magnetism :

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Electromagnetic Induction: We have seen that studies made by Oersted, Biot-Savart and Ampere showed that an electric current produces a magnetic field. Michael Faraday wanted to explore if this phenomenon is reversible in the sense whether a magnetic field could be source for a current in a conductor. However, no current was found when a conductor was placed in a magnetic field. Faraday and (Joseph) Henry, however, found that if a current loop was placed in a time varying magnetic field or if there was a relative motion between a magnet and the loop a transient current was established in the conducting loop. They concluded that the source of the electromotive force driving the current in the conductor is not the magnetic field but the changing magnetic flux associated with the loop. The change in flux could be effected by (i) a time varying magnetic field or by (ii) motion of the conductor in a magnetic field or (iii) by a combined action of both of these. The discovery is a spectacular milestone in the sense that it led to important developments in Electrical engineering like invention of transformer, alternator and generator. Shortly after Faraday's discovery, Heinrich Lenz found that the direction of the induced current is such that it opposes the very cause that produced the induced current (i.e. the magnetic field associated with the induced current opposes the change in the magnetic flux which caused the induced current in the first place). Lenz's law is illustrated in the following In the figures the loops are perpendicular to the plane of the page. The direction of induced current is as seen towards the loop from the right. Note that the magnetic field set up by the induced current tends to increase the flux in the case where the magnet is moving away from the loop and tends to decrease it in the case where it is moving towards the loop, Mathematically, Faraday's law is stated thus : the electromotive force is proportional to the rate of change of magnetic flux. In SI units, the constant of proportionality is unity.

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Electromagnetic Induction: We have seen that studies made by Oersted, Biot-Savart and Ampere showed that an electric current produces a magnetic field. Michael Faraday wanted to explore if this phenomenon is reversible in the sense whether a magnetic field could be source for a current in a conductor. However, no current was found when a conductor was placed in a magnetic field. Faraday and (Joseph) Henry, however, found that if a current loop was placed in a time varying magnetic field or if there was a relative motion between a magnet and the loop a transient current was established in the conducting loop. They concluded that the source of the electromotive force driving the current in the conductor is not the magnetic field but the changing magnetic flux associated with the loop. The change in flux could be effected by (i) a time varying magnetic field or by (ii) motion of the conductor in a magnetic field or (iii) by a combined action of both of these. The discovery is a spectacular milestone in the sense that it led to important developments in Electrical engineering like invention of transformer, alternator and generator. Shortly after Faraday's discovery, Heinrich Lenz found that the direction of the induced current is such that it opposes the very cause that produced the induced current (i.e. the magnetic field associated with the induced current opposes the change in the magnetic flux which caused the induced current in the first place). Lenz's law is illustrated in the following In the figures the loops are perpendicular to the plane of the page. The direction of induced current is as seen towards the loop from the right. Note that the magnetic field set up by the induced current tends to increase the flux in the case where the magnet is moving away from the loop and tends to decrease it in the case where it is moving towards the loop, Mathematically, Faraday's law is stated thus : the electromotive force is proportional to the rate of change of magnetic flux. In SI units, the constant of proportionality is unity.

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The Importance of Nanoscale: The Greek word "nano" (meaning dwarf) refers to a reduction of size, or time, by 10-9, which is one thousand times smaller than a micron. One nanometer (nm) is one billionth of a meter and it is also equivalent to ten Angstroms. As such a nanometer is 10-9 meter and it is 10,000 times smaller than the diameter of a human hair. A human hair diameter is about 50 micron (i.e., 50x 10-6 meter) in size, meaning that a 50 nanometer object is about 1/1000th of the thickness of a hair. One cubic nanometer (nm3) is roughly 20 times the volume of an individual atom. A nanoelement compares to a basketball, like a basketball to the size of the earth. Figure 1 shows various size ranges for different nanoscale objects starting with such small entities like ions, atoms and molecules. Size ranges of a few nanotechnology related objects (like nanotube, single-electron transistor and quantum dot diameters) are also shown in this figure. It is obvious that nanoscience, nanoengineering and nanotechnology, all deal with very small sized objects and systems. Officially, the United States National Science Foundation [6] defines nanoscience / nanotechnology as studies that deal with materials and systems having the following key properties.

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Meissner effect: expulsion of magnetic field from the interior of the superconductor Thought experiment Consider a sphere made out of superconductive material. At T>Tc the material is in normal state. When external magnetic field is turned on, the external magnetic field penetrates through the material. On the basis of Faraday’s law,

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Type I and Type II Superconductors: exhibit different magnetic response to external magnetic field. In Type I superconductor the magnetic field iscompletely expelled from the interior for B<BC.

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Applications of nanotechnology: After more than 20 years of basic nanoscience research and 10 years of focused R&D under the NNI, applications of nanotechnology are delivering in both expected and unexpected ways on nanotechnology’s promise to benefit society. Nanotechnology is helping to considerably improve, even revolutionize, many technology and industry sectors: information technology, energy, environmental science, medicine, homeland security, food safety, and transportation, among many others. Described below is a sampling of the rapidly growing list of benefits and applications of nanotechnology. Most benefits of nanotechnology depend on the fact that it is possible to tailor the essential structures of materials at the nanoscale to achieve specific properties, thus greatly extending the well-used toolkits of materials science. Using nanotechnology, materials can effectively be made to be stronger, lighter, more durable, more reactive, more sieve-like, or better electrical conductors, among many other traits. There already exist over 800 everyday commercial products that rely on nanoscale materials and processes:

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BCS theory and Cooper pairs: According to classical physics, part of the resistance of a metal is due to collisions between free electrons and the crystal lattice’s vibrations, known as phonons. In addition, part of the resistance is due to scattering of electrons from impurities or defects in the conductor. As a result, the question arose as to why this does not happen in superconductors? A microscopic theory of superconductivity was developed in 1957 by John Bardeen, Leon Cooper and J. Robert Schrieffer, which is known as the BCS theory. The central feature of the BCS theory is that two electrons in the superconductor are able to form a bound pair called a Cooper pair if they somehow experience an attractive interaction between them. This notion at first sight seems counterintuitive since electrons normally repel one another because of their like charges. This may be thought of in the following way and is illustrated in Figure 1. Figure 1. Classical description of the coupling of a Cooper pair.

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Introduction: From what we have learned about transport, we know that there is no such thing as an ideal (ρ = 0) conventional conductor. All materials have defects and phonons (and to a lessor degree of importance, electron-electron interactions). As a result, from our basic understanding of metallic conduction ρ must be finite, even at T = 0. Nevertheless many superconductors, for which ρ = 0, exist. The first one Hg was discovered by Onnes in 1911. It becomes superconducting for T < 4.2^o K. Clearly this superconducting state must be fundamentally different than the "normal" metallic state. Ie., the superconducting state must be a different phase, separated by a phase transition, from the normal state. Evidence of a Phase Transition: Evidence of the phase transition can be seen in the specific heat (See Fig. 1). The jump in the superconducting specific heat Cs indicates that there is a phase transition without a latent heat

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Applications of superconductors: The first large scale commercial application of superconductivity was in magnetic resonance imaging (MRI). This is a non-intrusive medical imaging technique that creates a two-dimensional picture of say tumors and other abnormalities within the body or brain. This requires a person to be placed inside a large and uniform electromagnet with a high magnetic field. Although normal electromagnets can be used for this purpose, because of resistance they would dissipate a great deal of heat and have large power requirements. Superconducting magnets on the other hand have almost no power requirements apart from operating the cooling. Once electrical current flows in the superconducting wire, the power supply can be switched off because the wires can be formed into a loop and the current will persist indefinitely as long as the temperature is kept below the transition temperature of the superconductor. Superconductors can also be used to make a device known as a superconducting quantum interference device (SQUID). This is incredibly sensitive to small magnetic fields so that it can detect the magnetic fields from the heart (10_-10 Tesla) and even the brain (10_-13 Tesla). For comparison, the Earth’s magnetic field is about 10-4 Tesla. As a result, SQUIDs are used in non-intrusive medical diagnostics on the brain. The traditional use of superconductors has been in scientific research where high magnetic field electromagnets are required. The cost of keeping the superconductor cool are much smaller than the cost of operating normal electromagnets, which dissipate heat and have high power requirements. One such application of powerful electromagnets is in high energy physics where beams of protons and other particles are accelerated to almost light speeds and collided with each other so that more fundamental particles are produced. It is expected that this research will answer fundamental questions such as those about the origin of the mass of particles that make up the Universe. Levitating trains have been built that use powerful electromagnets made from superconductors. The superconducting electromagnets are mounted on the train. Normal electromagnets, on a guideway beneath the train, repel (or attract) the superconducting electromagnets to levitate the train while pulling it forwards. A use of large and powerful superconducting electromagnets is in a possible future energy source known as nuclear fusion. When two light nuclei combine to form a heavier nucleus, the process is called nuclear fusion. This results in the release of large amounts of energy without any harmful waste. Two isotopes of hydrogen, deuterium and tritium, will fuse to release energy and helium. Deuterium is available in ordinary water and tritium can be made during the nuclear fusion reactions from another abundantly available element – lithium. For this reason it is called clean nuclear energy. For this reaction to occur, the deuterium and tritium gases must be heated to millions of degrees so that they become fully ionized. As a result, they must be confined in space so that they do not escape while being heated. Powerful and large electromagnets made from superconductors are capable of confining these energetic ions. An international fusion energy project, known as the International Thermonuclear Experimental Reactor (ITER) is currently being built in the south of France that will use large superconducting magnets and is due for completion in 2017. It is expected that this will demonstrate energy production using nuclear fusion.

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High – Tc superconductors: becomes a superconductor at room temperature. A discovery of this type will revolutionize every aspect of modern day technology such as power transmission and storage, communication, transport and even the type of computers we make. All of these advances will be faster, cheaper and more energy efficient. This has not been achieved to date. However, in 1986 a class of materials was discovered by Bednorz and Müller that led to superconductors that we use today on a bench-top with liquid nitrogen to cool them. Not surprisingly, Bednorz and Müller received the Nobel Prize in 1987 (the fastest-ever recognition by the Nobel committee). The material we mostly use on bench-tops is Yttrium – Barium – Copper Oxide, or YBa2Cu3O7, otherwise known as the 1-2-3 superconductor, and are classified as high temperature (T_c) superconductors. The critical temperature of some high-Tc superconductors is given in Figure 1. Critical temperatures as high as 135 K have been achieved. Whilst this is not room temperature, it has made experiments on superconductivity accessible to more people since these need only be cooled by liquid nitrogen (with a boiling point of liquid nitrogen is 77 K), which is cheap and readily available. This is in contrast to the expensive and bulky equipment that used liquid helium for cooling the traditional types of superconductors. Moreover, the superconductors are calculated to have an upper critical magnetic field, B_c2, of about 200 Tesla – huge! The crystal lattice structure of YBa₂Cu₃O₇ is shown in Figure 1. Unlike traditional superconductors, conduction mostly occurs in the planes containing the copper oxide. It has been found that the critical temperature is very sensitive to the average number of oxygen atoms present, which can vary. For this reason the formula for 1-2-3 superconductor is sometimes given as YBa₂Cu3O_7-δ where δ is a number between 0 and 1. The nominal distance between cooper pairs (coherence length) in these superconductors can be as short as one or two atomic spacings. As a result, the coulomb repulsion force will generally dominate at these distances causing electrons to be repelled rather than coupled. For this reason, it is widely accepted that Cooper pairs, in these materials, are not caused by a lattice deformation, but may be associated with the type of magnetism present (known as antiferromagnetism) in the copper oxide layers. So high–T_c superconductors cannot be explained by the BCS theory since that mainly deals with a lattice deformation mediating the coupling of electron pairs. The research continues into the actual mechanism responsible for superconductivity in these materials.

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Mechanism of superconductivity: Isotope effect, T_c depends on the mass of atoms Interaction between electrons and lattice atoms is critical for the existence of superconductive state. Good conductors (weak scattering from the lattice) are poor superconductors (low TC). Electrons on their flight through the lattice cause lattice deformation (electrons attract the positively charged lattice atoms and slightly displace them) which results in a trail of positively charged region. This positively charged region of lattice atoms attracts another electron and provides for electron-electron coupling.

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The magnetic properties of superconductors: In addition to the loss of resistance, superconductors prevent external magnetic field from penetrating the interior of the superconductor. This expulsion of external magnetic fields takes place for magnetic fields that are less than the critical field. Magnetic field greater than BC destroys the superconductive state.

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Ongoing Research and Development Activities: The atomic-scale and cutting-edge field of nanotechnology which is considered to lead us to the next industrial revolution is likely to have a revolutionary impact on the way things will be done, designed and manufactured in the future. Nanotechnology is entering into all aspects of science and technology including, but not limited to, aerospace, agriculture, bioengineering, biology, energy, the environment, materials, manufacturing, medicine, military science and technology. It is truly an atomic and molecular manufacturing approach for building chemically and physically stable structures one atom or one molecule at a time. Presently some of the active nanotechnology research areas include nanolithography, nanodevices, nanorobotics, nanocomputers, nanopowders, nanostructured catalysts and nanoporous materials, molecular manufacturing, diamondoids, carbon nanotube and fullerene products, nanolayers, molecular nanotechnology, nanomedicine, nanobiology, organic nanostructures to name a few. We have known for many years that several existing technologies depend crucially on processes that take place on the nanoscale. Adsorption, lithography, ion-exchange, catalysis, drug design, plastics and composites are some examples of such technologies. The "nano" aspect of these technologies was not known and, for the most part, they were initiated accidentally by mere luck. They were further developed using tedious trial-and-error laboratory techniques due to the limited ability of the times to probe and control matter on nanoscale. Investigations at nanoscale were left behind as compared to micro and macro length scales because significant developments of the nanoscale investigative tools have been made only recently. The above mentioned technologies, and more, stand to be improved vastly as the methods of nanotechnology develop. Such methods include the possibility to control the arrangement of atoms inside a particular molecule and, as a result, the ability to organize and control matter simultaneously on several length scales. The developing concepts of nanotechnology seem pervasive and broad. It is expected to influence every area of science and technology, in ways that are clearly unpredictable. Nanotechnology will also help solve other technology and science problems. For example, we are just now starting to realize the benefits that nanostructuring can bring to, The following selected observations regarding the expected future advances are also worth mentioning at this juncture.

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Buckyballs: By far the most popular discovery in nanotechnology is the Buckminsterfullerene molecules. Buckminsterfullerene (or fullerene), C60, as is shown in Figure 6 is another allotrope of carbon (after graphite and diamond), which was discovered in 1985 by Kroto and collaborators. These investigators used laser evaporation of graphite and they found Cn clusters (with n>20 and even-numbers) of which the most common were found to be C60 and C70. For this discovery by Curl, Kroto and Smalley were awarded the 1996 Nobel Prize in Chemistry. Later fullerenes with larger number of carbon atoms (C76, C80, C240, etc.) were also discovered. Since the time of discovery of fullerenes over a decade and a half ago, a great deal of investigation has gone into these interesting and unique nanostructures. They have found tremendous applications in nanotechnology. In 1990 a more efficient and less expensive method to produce fullerenes was developed by Krätchmer and collaborators [25]. Further research on this subject to produce less expensive fullerene is in progress. Availability of low cost fullerene will pave the way forfurther research into practical applications of fullerene and its role in nanotechnology. Figure 1. The four allotropes of carbon.

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which is the sum of the electronic, ionic, and dipolar polarizabilities, respectively. The electronic contribution is present in any type of substance, but the presence of the other two terms depends on the material under consideration. The relative magnitudes of the various contributions in are such that in nondipolar, ionic substances the electronic part is often of the same order as the ionic. In dipolar substances, however, the greatest contribution comes from the dipolar part. This is the case for water, as we shall see. Another important distinction between the various polarizabilities emerges when one examines the behavior of the ac polarizability that is induced by an alternating field. Figure 4 shows a typical dependence of this polarizability on frequency over a wide range, extending from the static all the way up to the ultraviolet region. It can be seen that in the range from ω = 0 to ω = ω_d, where ω_d (d for dipolar) is some frequency usually in the microwave region, the polarizability is essentially constant. In the neighborhood ω_d, however, the polarizability decreases by a substantial amount. This amount corresponds precisely, in fact, to the dipolar contribution α_d. The reason for the disappearance of α_d in the frequency range ω > ω_d is that the field now oscillates too rapidly for the dipole to follow, and so the dipoles remain essentially stationary. The polarizability remains similarly unchanged in the frequency range from wd to wi and then drops down at the higher frequency. The frequency wi lies in the infrared region, and corresponds to the frequency of the transverse optical phonon in the crystal. For the frequency range w > wi the ions with their heavy masses are no longer able to follow the very rapidly oscillating field, and consequently the ionic polarizibility α_i, vanishes, as shown in Fig. 4. Thus in the frequency range above the infrared, only the electronic polarizability remains effective, because the electrons, being very light, are still able to follow the field even at the high frequency. This range includes both the visible and ultraviolet regions. At still higher frequencies (above the electronic frequency ω_e, however, the electronic contribution vanishes because even the electrons are too heavy to follow the field with its very rapid oscillations. The frequencies ω_d and wi, characterizing the dipolar and ionic polarizabilities, respectively, depend on the substance considered, and vary from one substance to another. However, their orders of magnitude remain in the regions indicated above, i.e., in the microwave and infrared, respectively. The various polarizabilities may thus be determined by measuring the substance at various appropriate frequencies.

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Dielectric constant and polarizability: The dielectric constant e of an isotropic or cubic medium relative to vacuum is defined in terms of the macroscopic field E: Since the polarization of the medium is produced by the field it is convenient to define the polarizability a of an atom in terms of the local electric field at the atom:

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Eq.(7) shows that X is independent of the field strength and temperature. This is in accordance with Curie’s experimental results.

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Piezoelectricity: The term piezoelectricity refers to the fact that, when a crystal is strained, an electric field is produced within the substance. As a result of this field, a potential difference develops across the sample, and by measuring this potential one may determine the field. The inverse effect - that an applied field produces strain - has also been observed. The piezoelectric effect is very small. A field of 10³ V/cm in quartz (SiO2) produces a strain of only 10_-7. That is, a rod 1 cm long changes its length by 10Å. Conversely, even small strains can produce enormous electric fields. The piezoelectric effect is often used to convert electrical energy into mechanical energy, and vice versa; i.e., the substance is used as a transducer. For instance, an electric signal applied to the end of a quartz rod generates a mechanical strain, which consequently leads to the propagation of a mechanical wave - a sound wave - down the rod. Quartz is the most familiar piezoelectric substance, and the one most frequently used in transducers. The microscopic origin of piezoelectricity lies in the displacement of ionic charges within the crystal. In the absence of strain, the distribution of the charges at their lattice sites is symmetric, so the internal electric field is zero. But when the crystal is strained, the charges are displaced. If the charge distribution is no longer symmetric, then a net polarization, and a concomitant electric field, develops. It is this field which operates in the piezoelectric effect. \ Fig. 1Crystal with center of inversion exhibits no piezoelectric effect, (b) Origin of piezoelectric effect in quartz: crystal lacks a center of inversion.

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Acousing Grating: Principle: When ultrasonic waves are passed through a liquid, the density of the liquid varies layer by layer due to the variation in pressure and hence the liquid will act as a diffraction grating, so called acoustic grating. Under this condition, when a monochromatic source of light is passed through the acoustical grating, the light gets diffracted. Then, by using the condition for diffraction, the velocity of ultrasonic waves can be determined. Construction & Working: The liquid is taken in a glass cell. The Piezo-electric crystal is fixed at one side of the wall inside the cell and ultrasonic waves are generated. The waves travelling from the crystal get reflected by the reflector placed at the opposite wall. The reflected waves get superimposed with the incident waves producing longitudinal standing wave pattern called acoustic grating. If light from a laser source such as He-Ne or diode laser is allowed to pass through the liquid in a direction perpendicular to the grating, diffraction takes place and one can observe the higher order diffraction patterns on the screen. The angle between the direct ray and the diffracted rays of different orders (θ_n) can be calculated easily. According to the theory of diffraction,

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Langevin's Theory of Paramagnetism: Langevin assumes that each atom has a permanent magnetic momentum m. The only force acting on atom is that due to the external field B Let θ be the angle of inclination of the axis of the atomic dipole with the direction of the applied field B Then magnetic potential energy of the atomic dipole is Now, on classical statistics, the number of atoms making an angle between

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Ultrasonic Cleaning applications: Ultrasonic Cleaners in Scientific Labs: Lab Glassware, Test Tubes, Pipettes, Optical & Contact Lenses, Eyeglass Frames, Scientific Instruments, Components Ultrasonic Cleaners in Industrial Manufacturing: Switches, Relays & Motors, Gears, Precision Bearings, Metal & Plastic Parts, Assemblies

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Ultrasonic Production: The term ultrasonics applies to sound waves that vibrate at a frequency higher than the frequency that can be heard by the human ear (or higher than about 20,000 hertz). Sound is transmitted from one place to another by means of waves. The character of any wave can be described by identifying two related properties: its wavelength (lambda,
) or its frequency (f). The unit used to measure the frequency of any wave is hertz. One hertz is defined as the passage of a single wave per second. Ultrasonics, then, deals with sound waves that pass a given point at least 20,000 times per second. Since ultrasonic waves vibrate very rapidly, additional units also are used to indicate their frequency. The kilohertz (kHz), for example, can be used to measure sound waves vibrating at the rate of 1,000 times per second, and the unit megahertz (MHz) stands for a million vibrations per second. Some ultrasonic devices have been constructed that produce waves with frequencies of more than a billion hertz. There are three methods for producing Ultrasonic waves. They are: (i) Mechanical generator or Galton’s whistle. (ii) Magnetostriction generator. (iii) Piezo-electric generator. In this session, you are going to study the method of producing ultrasonic waves using Magnetostriction method. Magnetostriction method: Principle- The general principle involved in generating ultrasonic waves is to cause some dense material to vibrate very rapidly. The vibrations produced by this material than cause air surrounding the material to begin vibrating with the same frequency. These vibrations then spread out in the form of ultrasonic waves. When a magnetic field is applied parallel to the length of a ferromagnetic rod made of material such as iron or nickel, a small elongation or contraction occurs in its length. This is known as magnetostriction. The change in length depends on the intensity of the applied magnetic field and nature of the ferromagnetic material. The change in length is independent of the direction of the field. When the rod is placed inside a magnetic coil carrying alternating current, the rod suffers a change in length for each half cycle of alternating current. That is, the rod vibrates with a frequency twice that of the frequency of A.C. The amplitude of vibration is usually small, but if the frequency of the A.C. coincides with the natural frequency of the rod, the amplitude of vibration increases due to resonance. Construction: The ends of the ferromagnetic rod A and B is wound by the coils L1 and L. The coil L is connected to the collector of the transistor and the coil L1 is connected to the base of the transistor as shown in the figure. The frequency of the oscillatory circuit (LC) can be adjusted by the condenser C and the current can be noted by the milliammeter connected across the coil L. The battery connected between emitter and collector provides necessary biasing i.e., emitter is forward biased and collector is reverse biased for the NPN transistor. Hence, current can be produced by applying necessary biasing to the transistor with the help of the battery.

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Piezoelectric effect: When crystals like quartz or tourmaline are stressed along any pair of opposite faces, electric charges of opposite polarity are induced in the opposite faces perpendicular to the stress. This is known as Piezoelectric effect. Piezoelectric effect- Mechanism: Piezoelectric and inverse piezoelectric effects are only exhibited by certain crystals which lack centre of symmetry. In a piezoelectric crystal, the positive and negative electrical charges are separated, but symmetrically distributed, so that the crystal overall is electrically neutral. Each of these sides forms an electric dipole and dipoles near each other tend to be aligned in regions called Weiss domains. The domains are usually randomly oriented, but can be aligned during poling , a process by which a strong electric field is applied across the material, usually at elevated temperatures. When a mechanical stress is applied, this symmetry is disturbed, and the charge asymmetry generates a voltage across the material. For example, a 1 cm cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage of 12,500 V. Piezoelectric materials also show the opposite effect, called converse (inverse) piezoelectric effect, where the application of an electrical field creates mechanical deformation in the crystal.

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application of ultrasonics: Ultrasonic waves have a wide range of applications in various fields e.g., engineering, medical, metallurgical, physical, chemical, etc. Some of their uses are discussed in below.. Ultrasonic Drilling and Cutting:

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Capacitors used for ac must be unpolarized so they can handle full voltage reversals. They also need to have a lower dissipation factor than capacitors used as dc filter capacitors, for example. One important application of ac capacitors is in tuning electronic equipment. These capacitors must have high stability with time and temperature, so the tuned frequency does not drift beyond some specified amount. Another category of ac capacitor is the motor run or power factor correcting capacitor. These are used on motors and other devices operating at 60 Hz and at voltages up to 480 V or more. They are usually much larger than capacitors used for tuning electronic circuits, and are not sold by electronics supply houses. One has to ask for motor run capacitors at an electrical supply house like Graingers. These also work nicely as dc filter capacitors if voltages higher than allowed by conventional dc filter capacitors are required. The term power factor PF may also be defined for ac capacitors. It is given by the expression

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Ferroelectricity: Ferroelectric crystal exhibits an electric dipole moment even in the absence of an external electric field. In the ferroelectric state the center of positive charge of the crystal does not coincide with the center of negative charge. The plot of polarizations versus electric field for the ferroelectric state shows a hysteresis loop. A crystal in a normal dielectric state usually does not show significant hysteresis when the electric field is increased and then reversed, both slowly. In ferroelectric materials the ionic susceptibility is sensitive to variations in temperature. In these substances, the static dielectric constant changes with temperature according to the relation where C is a constant independent of temperature. This behavior is valid only in the temperature range T > Tc. In the range T < Tc, the material becomes spontaneously polarized, i.e., an electric polarization develops in it without the help of an external field. (This phenomenon is analogous to the spontaneous magnetization which takes place in ferromagnetic materials.)

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Introduction: When the electric hysteresis of a dielectric is ignored and the dielectric properties are regarded as isotropic and linear, the polarization is directly proportional to the electric field strength, and the proportionality constant is independent of the direction of the field.This section mathematically explains the dielectric constant of dielectric in detail. Mathematical Expression:

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Piezoelectric generator: A slab of piezoelectric crystal is taken and using this a parallel plate capacitor is made. Then with other electronic components an electronic oscillator is designed to produce electrical oscillations > 20 kHz. Generally one can generate ultrasonic waves of the order of MHz using piezoelectric generators. Quartz slabs are preferred because it possesses rare physical and chemical properties. A typical circuit diagram is given below. The tank circuit has a variable capacitor 'C' and an inductor 'L' which decides the frequency of the electrical oscillations. When the circuit is closed current rushes through the tank circuit and the capacitor is charged, after fully charged no current passes through the same. Then the capacitor starts discharging through the inductor and hence the electric energy is in the form of electric and magnetic fields associated with the capacitor and the inductor respectively. Thus we get electrical oscillations in the tank circuit and with the help of the other electronic components including a transistor, electrical oscillations are produced continuously. This is fed to the secondary circuit and the piezoelectric crystal (in our case a slab of suitably cut quartz crystal) vibrates, as it is continuously subjected to varying (alternating) electric field, and produces sound waves. When the frequency of electrical oscillations is in the ultrasonic range then ultrasonic waves are generated. When the frequency of oscillation is matched with the natural frequency of the piezoelectric slab then it will vibrate with maximum amplitude. The frequency generated is given as follows:

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Detection of Ultrasonic Waves: Ultrasonic waves propagated through a medium can be detected in a number of ways. Some of the methods employed are as follows: Quartz crystal method: This method is based on the principle of Piezo-electric effect. When one pair of the opposite faces of a quartz crystal is exposed to the ultrasonic waves, the other pairs of opposite faces developed opposite charges. These charges are amplified and detected using an electronic circuit. PROPERTIES OF ULTRASONIC WAVES ACOUSTIC CAVITATION: In general, cavitation is the phenomenon where small and largely empty cavities are generated in a fluid, which expand to large size and then rapidly collapse. When the cavitation bubbles collapse, they focus liquid energy to very small volumes. Thereby, they create spots of high temperature and emit shock waves. The collapse of cavities involves very high energies. Power ultrasound enhances chemical and physical changes in a liquid medium through the generation and subsequent destruction of cavitation bubbles. Like any sound wave ultrasound is propagated via a series of compression and rarefaction waves induced in the molecules of the medium through which it passes. At sufficiently high power the rarefaction cycle may exceed the attractive forces of the molecules of the liquid and cavitation bubbles will form. Such bubbles grow by a process known as rectified diffusion i.e. small amounts of vapour (or gas) from the medium enters the bubble during its expansion phase and is not fully expelled during compression. The bubbles grow over the period of a few cycles to an equilibrium size for the particular frequency applied. It is the fate of these bubbles when they collapse in succeeding compression cycles which generates the energy for chemical and mechanical effects. Cavitation bubble collapse is a remarkable phenomenon induced throughout the liquid by the power of sound. In aqueous systems at an ultrasonic frequency of 20 KHz each cavitation bubble collapse acts as a localised "hotspot" generating temperatures of about 4,000 K and pressures in excess of 1000 atmospheres