Q.1 Write short note on the following
(a) Space lattice, (b) basis, (c) unit cell and crystal.
Ans. (a) Space Lattice: -
A space lattice is defined as an infinite array of points in three-dimensional space in which each point is identically located with respect to the other. A two-dimensional lattice may be two types
(1) square array, or (2) rectangular array
In above figures, a and b are the fundamental translation vectors, and c is generated vector. If points are located such that a = b the arrangement will be known as square lattice. If location of the points is such that the arrangement will be called rectangular lattice. Repeated translation of three noncoplaner vectors results into a three-dimensional space lattice. A three- dimensional space lattice may then have either a (1) cubic array when a = b = c, or (2) non-cubic array.
The smallest unit formed by joining these identically spaced points referred to as a unit cell. One such unit cell, shown in above figure, may be cubical or non-cubical depending on the dimensions of translation vectors.
Basis: -
The way of filling-up of points in a space lattice by the atoms is known as Basis. Each point may be occupied by one, two or many atoms in different solids. The space lattice when combines with the basis generates a unit cell. Thus
space lattice + basis = unit cell
The unit cell will be called monoatomic if one atom occupies a lattice point. When two atoms occupy a lattice point, it will make a diatomic unit cell. Similarly the unit cell will be known as multiatomic when too many atoms occupy a lattice point. These types of unit cells are shown in Figs. a-b-c.
In manganese, there are 29 atoms at each corner and 29 atoms at centre of the cube. Thus its unit cell contains 58 atoms.
Unit Cell And Crystal: -
