PHYSICS

Diffraction of X-rays through crystal lattice: (Bragg’s law) X-rays are used to identify the structure of a crystal. The property of diffraction of x-rays  are used in this procedure.  The wave length of ordinary light is very large comparing with  the value of inter planar spacing. Hence ordinary light cannot penetrate trough the lattice  planes.  But X-rays penetrate through the lattice planes and they are scattered by the  atoms of the crystal lattice. Each atom acts as an opaque and the distance between two  atoms acts as narrow slit. Hence the crystal lattice is considered as diffraction grating. When x-rays are scattered by the successive parallel planes they diffract with each other  and produce diffraction pattern.by studying the diffraction pattern we can find different sets  of planes located in the lattice at different directions.  Bragg used X-rays to study the  structure of crystals.  He derived the condition of maxima of  diffraction pattern which is called

Crystal planes : Crystal planes are defined as imaginary planes inside a crystal lattice passing through the atoms  along x, y and Z directions.  These planes are represented as XY, YZ, ZX and XYZ planes. We cannot  find a single plane in a crystal lattice but set of parallel planes are observed. Miller indices: Miller indices are defined as the reciprocals of intercepts of crystal plane. They are used to  represent the direction of crystal planes. Miller indices are denoted as the coordinates ( h, k, l ) . h : k : l = 1/p : 1/q : 1/r Miller indices represent the structure of unit cell. Procedure to find Miller indices: 1. Identify the plane intercepts on the x, y and z-axes. 2. Represent intercepts in fractional coordinates as ( p, q, r) 3. Take the reciprocals of the fractional intercepts h : k : l = 1/p : 1/q : 1/r 4. convert the small fractions into integers by multiplying with their least common factor  LCM. Significance of Miller indices : Mil

Bravias crystals : There are 7 different basic crystal lattices according to the dimensions (a,b,c) and their angles( ⍺ , 𝛽, ℽ )  of unit cell which are called Bravias crystals.  1 Cubic crystal system :                   a=b=c  and α=β=γ=90  example : NaCl available systems are simple cubic, face centered and body centered cubic systems 2 Tetragonal                a=b ≠ c and  α=β=γ=90  example SiSO4 available systems : simple and body centered cubic systems. 3 Orthorhombic                        a ≠ b ≠c and  α=β=γ=90 example: BaSO4 available systems are simple, body centered ,face centered and base centered cubic systems. . 4 Monoclinic (rhombohedral )                    a ≠ b ≠c and  α=β=90γ=120 example:  Na2So4 available systems: siple and bidy centered cubic systems 5 Triclinic                       a ≠ b ≠c and  α≠β≠γ≠90  example: CaSo4 available systems : simple cubic system only. 6 Trigonal                     a=b=c and  α=β=γ≠90 example:  CuSO4,

Unit cell In Crystals the arrangement of particles is described with three dimensional geometrical  parallelepiped structure.  The unit cell is defined as the smallest size of parallelepiped structure with  minimum number of atoms. In a unit cell there are 6 faces and 8 corners. So 8 atoms are required to form a unit cell and all the  8 atoms are located at the 8 corners each. Lattice Lattice is defined as a three dimensional array of atoms. It describes the size and shape of the unit cell. Parameters of a unit cell A unit cell is described by six parameters. These parameters are three dimensions  and the  angles between them . The Dimensions of unit cell  along three axes of a unit cell are represented by (a, b ,c) . The angle between b and c is represented by α, between a and c by β and between a and b by γ. we can identify the structure of crystal by knowing the parameters of unit cell. Properties of unit cell : 1. Unit cell is the minimum structure. 2. We can

Differences between crystal and amorphous substances: All the substances are classified into crystals and amorphous. 1.In crystalline substances the atoms are located in a  regular three dimensional  arrangement, hence the ions or molecules have well defined  geometrical shape. Amorphous substances do not have regular  arrangement of particles,  therefore do not have well  defined shape. 2.crystals have long range order  Amorphous substances have short range order 3.crystals  have sharp melting  point i.e., they melt at a particular temperature. where as amorphous substances do not have sharp melting point i.e., they melt over a range  of temperature. 4.in crystals fusion point is constant  where as amorphous substances do not have constant heat of  fusion. 5) crystals  are anisotropic, i.e., their thermal, electrical and  optical properties have different  values along the three axes Amorphous substances are isotropic, i.e., they have  same values of properties

Type I and type II superconductors Superconductors are classified into two types.  They are Type I and Type 2 superconductors. classification of type 1 and type 2 superconductors 1.  Type I superconductors are soft  superconductors     Type 2 superconductors are hard  superconductors. 2.critical temperature for  .  

Meissner effect.

Superconductivity: Definition: The phenomenon of obtaining the property of zero resistance and infinity of conductivity is defined as  superconductivity. The substances which exhibit the property of superconductivity are called  Superconductors. Explanation: superconductivity was discovered by Kamerlingh in 1911. He observed that when a substance  is cooled to very low temperature, the resistance of the substance vanishes and the current flows through it without any abstraction and variation. The experiment was done with Helium and found that Helium will be a super conductor at the  temperature 4.2 K. Critical temperature ‘Tc’ (or transition temperature): The temperature where an ordinary substance becomes a superconductor is defined as critical  temperature.  It is denoted by Tc.  examples : For Mercury Tc=4.15 K and for Cd, Tc =0.56 K Tungsten     0.01K Aluminum  1.19 K NiBi            4.25 K ZrAl2          0.30 K Characteristics of superconductors: 1.

BCS theory on superconductors. This theory was proposed by three scientists Bardeen, Cooper and Schrieffer in 1957.  This theory  explains about zero resistance of a superconductor. In normal substances the flow of free electrons is opposed by the vibration of ions or atoms in the  lattice due to the collision between them. Hence the normal conductors possess resistance. In the case of superconductors below the critical temperature (Tc), the atom or the ion is distorted  by the free electron during the collision.  The result produces a mechanical wave called phonon. During this collision the free electron exchanges an amount of its momentum with the lattice ion. Hence the momentum of free electron in reduced. It moves with less momentum. If another free electron collides with the distorted lattice ion (phonon), the second electron gains  an amount of momentum from the phonon. Hence the second free electron moves with greater momentum. But the change in momentum for the two

Helium and Neon laser Construction :  Helium-Neon laser is a gas laser. A mixture  of helium and neon gas  in 10 : 1  ratio  at the  pressure of 1 mm Hg is filled in a discharge tube.  The diameter of tube is 1.5cm and the length 80 cm . The two end of the discharge tube are provided by Brewster  glass windows  .  Two mirrors are arranged on either side of the discharge tube. One f the mirrors is perfect reflector where as the second mirror is a partial reflector.  The two electrodes of the discharge tube are connected to a high tension voltage , frequency generator.  Working :  When high tension voltage is applied  the Helium atoms are excited to higher energy level.  These higher energy levels are meta stable states at 20.06 ev  The excited Helium atoms collide with neon atoms which are in the ground state.  The excited neon atoms  will reach to three meta stable excited states. The excited ne atoms have more energy than He atoms  There is a stimulated emission w

  Ruby laser   Ruby laser is a solid state laser. Ruby is a transparent crystal of aluminium oxide and its chemical composition is  Al 2 O 3 . An amount of aluminium atoms are replaced by chromium atoms with 0.5%. Then the crystal (Al 2 O 3 , Cr2O3) will attain a light pink colour.  Construction :   A ruby rod of length 4 cm and diameter 0.5 cm to 1 cm is used . The end faces of the rod are grounded  and polished to be parallel to each other. One face of the rod is silvered and it acts s perfect reflector. The other face is semi silvered. The ruby rod is surrounded by an optical flash helical pipe filled with Xenon gas. The two ends of Xenon pipe are connected to a high tension voltage for pumping the chromium ions to excited state. The whole arrangement is enclosed in an evacuated chamber.  Working  :   Ruby laser works  on 4 level pumping principle.  when the high tension is applied the xenon pipe releases white light.  The cr+ atoms will reach to two excited levels ‘E3

 population inversion It is defined as the condition which is obtained in stimulated emission of radiation , the number of atoms In the metastable state is greater than the number of atoms in the ground state. This condition is necessary for producing a powerful laser , because maximum number of atoms in the metastable state must be stimulated to jump to the ground level. Lasing action: It is a chain process during stimulated emission in which every atom emits two identical photons and finally a powerful narrow beam of laser is released. To start the lasing process the condition of population inversion must be obtained. That is the number of atoms in meta stable state must be greater than that of ground level. In this process an external photon of selected wavelength incidents on an atom in meta stable state. Then the atom is stimulated to jump down to lower energy level by emitting two identical photons. These two photons are exactly equal to the incident photon. The two

  Spontaneous emission of radiation:   This is the phenomenon of emission of energy in the form of radiation when an atom jumps from excited energy state to the lower energy state after completing its life time in the excited state.   Explanation:  The atoms of a substance are excited to higher energy state from ground state by absorbing an amount of energy indenting on it.  But the atom in the excited level is not stable, because the life time of the atom in the excited state is about 10^-9 sec ( nano second).   After 10^-9 seconds the atoms jump down to the lower energy level releasing an amount of radiation.  The amount of energy released is equal to the difference in the two energy states.  Let the atom is excited to a higher energy state E2 and jumps to lower energy state E1 after its life time.  Then the amount of energy release E = hc/λ= E2-E1  Where λ= wavelength of the radiation and c= velocity of light and  h = Planck's constant. In this transition eac