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.