Biripali

  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 

  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. Thus every atom present at lattice sites is considered to be

  HYSTERESIS (B-H CURVE) :           C onsider a ferromagnetic substance (iron bar) is placed in a magnetizing field. As magnetizing field H is slowly increased, the intensity of magnetization also increases. The graphical representation of the extent of magnetization at different value of H. To start with H = 0 and magnetization B is also zero. As H increases B also increases along the curve OA. State of saturation is reached at A  and further increases of H will not increase B.           Now if we decrease H , the demagnetization of the sample does not take place along the curve AO. Thus  as H is decreased and becomes zero then it is seen that B does not become zero but has the value OG called retentivity. Hence demagnetisation lags behind the magnetizing field H. This phenomena in which B lags behind the magnetizing field H is called Hysteresis. The residual magnetism left behind in the magnetic substance when magnetic field is reduced to zero is called retentivity. It gives magneti

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 interatomic spacing in actual crystal.

  RECIPROCAL LATTICE:-   M any properties of crystalline substance are different in different directions. W.H.Miller explain the concept of miller indices to represent the planes and directions of a crystal. In real practice there are many set of planes with different orientations and spacings and it becomes difficult to visualise the slope of the planes. Since all parallel planes have a common normal and simillar indices , so the miller indices of a plane can not be uniquely defined. Therefore to understand many crystallographic problem we consider the normal to be set of planes rather than the planes themselves. The orientation of plane is understood by the direction of normal. DEFINITION OF RECIPROCAL LATTICE:-       T he reciprocal lattice in Fourier space is an infinite periodic three dimensional array of points whose spacings are inversely proportional to the distance between planes in the direct lattice.     The need for devising the concept of the reciprocal lattice was to tabu

                            Solids:-    Sol ids : The solids are the forms of matter in which atoms ands molecules are strongly bound and maintain definite volume and sharp unless changes by applying external forces. Solid state physics: - The solid state physics is the study of the physical properties of the atomic/molecular matter in the solids state. These physical properties include crystal structure, bonding,thermal, electric and magnetic properties. Classification of solids:         Solids are classified into two categories; (1) crystalline solids (2) Amorphous solids. (1) crystalline solid :-        The crystalline solids are defined as an ordered periodic arrangements of atoms, molecules or ions . Properties of crystalline solids:- • The internal arrangements of atoms,ions or molecules of crystalline solids is in a definite order. • The crystalline solids have a sharp melting point. • Below the temperature of crystallization, the crystalline material are in a stable state. As t

Post ulates of kinetics theory :-        Suppose a container with volume v contain a very large numbers N of identical molecules,each with mass m. Then, the kinetics theory postulates the following- (1) The molecules behave a point particles that are small compared to the size of the container and to the average distance between molecules. (2) The molecules are in constant motion. Each molecules collides occasionally with a wall of the container. These collisions are perfectly elastic. (3) There is no force of attraction among the gas molecules and between the gas molecules and walls of the container. (4) The container walls are right and infinitely massive and do not move. (5) The molecules obey Newton's law of motion. (6) The time of collision is much less than the averaged time between two successive collision. Meaning of elastic collisions:- If a molecule with velocity u strikes a wall align along y-axis, then the collision is elastic if • velocity component parallel to w