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ELECTRIC POTENTIAL

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  Electric potential :-         C url of electrical field is zero therefore, electric field is conservative field. Scalar potential is defined only for conservative field.        In the following we first show that curl of electric field is zero . We know field of a point charge at the origin.      If we take the integral along a closed path Then, . Apply Stoke theorm   Here,  This result can be generalised for any charge distribution using the principal of superposition. The general result is 
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Lattice vibration

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  LATTICE VIBRATION:-      E very atom has a tendency to vibrate about their mean position at temperature above zero Kelvin. The mean position is referred as the Bravais lattice site . These vibrations occur due to interatomic interactions. As the atoms in the solids are present at lattice sites , so these vibrations are called lattice vibrations. Fig.1            Lattice vibration are the results of absorption of heat energy. A lattice is an array of atoms connected with each other by elastic springs or strings .      Here all the atoms present at lattice sites are coupled and the motion of one single atom is shared by the neighbouring atoms. Thus the crystal vibrates on a whole . The dynamic external forces which are responsible for the vibrations obey Hooke's law. It is assumed that the amplitude of the vibrations are small as compared to the interatomic spacing. Harmonic approximation is valid for lattice vibrations. T...
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X-ray diffraction

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Diffraction of x-rays by crystals:      X -rays can be diffracted by crystals in the same way as the visible light is diffracted by a diffraction grating. So crystal can act like diffraction gratings. The idea that crystals can diffraction x-rays was given by  Von laue .    X-rays form part of the electromagnetic spectrum which were discovered by Roentgen. From the optical properties of x-rays , Sommerfeld estimated that the wavelength of x-rays is about 10^-10m. Crystalographers has estimated from a knowledge of density and molecular mass that spacings between two lattice points in a crystal is also about 10^-10m. From these two physical facts it occurred to max Von laue that crystals serve as diffraction gratings for x-rays and show the phenomena of diffraction. He took the help of his colleagues Friedrich and knipping. X-rays were used for demonstration of diffraction in crystal due to the fact that the wavelength of x-rays is comparable to the interatom...
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