Unit cell -defination, types and lattice translation vectors

  In previous post we know about crystalline and amorphous structure .Before we go into the unit cell we have to understand some term. So let's start.

Space lattice 


  The group of points in three dimension is arranged in various pattern and in regular manner, so that environment around every point remains identical. Such group of points are called space lattice and points are called as lattice points.
Space lattice

Basis 

     The crystal lattice has no any significant without any atom or molecules fill that points. 
 So,  the atom or molecules those fill position of lattice point in three dimensions are called basis
   The crystal and basis together gives crystal structure
 Lattice + basis = crystal structure 

Bravais lattice 

     If the lattice point in a space lattice represent the location of basis of same type, then the lattice called as Bravais lattice. 
    Bravais lattice have same type of atoms in lattice. 
    If a lattice contain, the basis of different crystals then the lattice is known as non-bravais lattice. 
 Non-bravais lattice have different type of atoms in lattice. 

Unit cell 

    Unit cell is a smallest group of lattice point or basis arranged in three dimension, so that reputation of which gives the actual crystal lattice.
   The basic unit of crystal structure is unit cell.
Unit cell

There are four type of unit cell depending upon the structure of molecules. 
a.  If each corner of unit cell contain a molecule or atom, this type of unit cell is known as primitive cell or simple cubic cell. 
     It has one atom per unit cell. 
b.  If a unit cell contain one atom at its centre and atoms at each corner then unit cell is called as body centred cubic(BCC).
     It has two atom per unit cell. 
c.  If the unit cell contains atom at the centre of each face of cube along with the atoms at the corner then unit cell is known as face centred cubic cell. 
     It has four atoms per unit cell. 
d.  If a unit cell has two atoms one at upper face and another at lower face along with the atoms at the corner then unit cell is called as base centred cubic. 
      It has two atom per unit cell. 

Lattice translation vectors 

    In geometry and crystallography, a Bravais lattice, is an infinite number of distinct points can be represented in the form of discrete translation operations in three dimensional space 
   R=n1a+n2b+n3c
a, b and c are  called as crystallographic axes. 
Crystal translational vector or basis vector are the vector along the lattice constant a, b and c. 
   The dimensions of all lattice constant of unit cell along crystallographic axes remains same throughout the crystal. 
 When n1, n2 and n3 of R are integer then a, b and c are called primitive translational vector. 
    When n1, n2 and n3 are non integer, then a, b and c can called non-primitive translational vector. 


This is all about unit cell and lattice translation vectors. 
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