A solid is defined as the form of matter which exhibits rigidity, a definite shape and a definite volume.
Solids can be classified as crystalline solids and amorphous solids.
Crystalline solids can be classified on the basis of the nature of the constituent particles and the binding force in molecules.
In crystalline solids, the constituent particles are arranged in a regular pattern throughout the crystal lattice. This regular and repeating arrangement of points or particles in space is called as space lattice or crystal lattice structure.
Since crystal lattice is a regular and repeating arrangement of partials, a small part of the lattice will be sufficient to explain all the properties and complete crystal lattice.
This smallest part of the crystal lattice, which when repeated in different directions,
produces a complete crystal lattice, is known as unit cell.
In the crystal lattice, each point represents constituent particles (ion or atom or molecule) and is called as lattice point. These points joined by line to form a whole crystal lattice. The arrangement of lattice points in a crystal lattice gives the geometry to a crystal lattice. Crystal lattice can be of two types,
1. Two dimensional lattices
It is a two dimensional regular arrangement of particles in two dimensions or on the plane of a paper.
A unit cell with a certain number of particles in it's corner is known as a primitive unit cell, while a unit cell with corner as well as interior particles is known as interior unit cell.
The type of crystal lattice depends on the type of unit cell. The complete crystal lattice is produced by repeatedly moving unit cells in the direction of its edge.
||Rhombus with an angle of 60oC
2. Three dimensional lattices
In these type of crystal lattices, the constituent particles are arranged in a three dimensional space.
Each smallest unit of the complete space lattice or crystal lattice, which is repeated in different direction to form a complete crystal lattice structure is called a unit cell. It is just like a thick wall made up of regularly arranged bricks. Here the thick wall is the crystal lattice and each brick is a unit cell.
In other words, unit cell is the building block of crystal lattice or space lattice. A unit cell can be explained by using certain parameters. These parameters are as follows. The edge of the unit cell represented by a, b and c. It is dimensions along the three edges.
The angle between the edges are represented by α, β and γ. The angle between edge b and c is α , the angle between edge a and c is β, while γ is the angle between edges a and b. Thus there are a total of six parameters; a , b , c and α, β and γ.
Unit cell can be classified on two different basis.
1.Based upon th parameters of unit cell
The unit cell can be classified into seven different types on the basis of the different parameters a, b and c edges and Î± ,Î² and Ï’ angles. These seven unit cells are also known as Bravais Unit Cells.
||(a≠ b≠ c)||(a=β>=γ=90o)|
||(a≠ b≠ c)||(a≠β >≠ γ≠ 90o)|
2. Based upon the position of particles in unit cell
Each Bravais unit cell is further classified into two types on the basis of the position of the particles at the corner and center. The unit cells which have lattice points only at the corner are termed as primitive unit cells. While the unit cells in which the lattice points are located at the corner as well as at other positions also are called as non-primitive or centered unit cell.
The non-primitive units cells are further divided into three types on the basis of lattice points at other sites.
All bravis unit celsl do not have all these types of unit cells. Hence there are a total of fourteen types of crystal lattices corresponding to seven bravis unit cells.
|Class of crystals
||Possible types of units
||Primitive body centred face centred
||Copper, KCl, NaCl zinc blende, diamond|
||Primitive body centred
||SnO2, White tin, TiO2|
||Primitive body centred, face centred and centred||Rhombic sulfur, KNO3,
|Hexagonal||Primitive||Graphie, Mg, ZnO|
|Trigonal or rhombohedral
||Primitive||(CaCO3) Calcite, HgS(cinnabar)
|Monoclinic||Primitive and end centred||Monoclinic sulfur, Na2SO4.10H2O|
In crystal lattices all the lattice points or particles are taken as a sphere. All the spheres are arranged in such a way that they occupy the maximum available space and leave minimum empty space between them. The packing of spheres can be of different types.
In this packing, particles can arranged only in one dimension. They are arranged in such a way that they touch each other in a row. The coordination number is two in this arrangement.
The two dimensional arrangement of particles in also known as crystal plane. In this arrangement, the packing of particles can be done in two different ways.
In three dimensional close packing, each two dimensional packing is expanded in three dimensional spaces.
1. Simple primitive cubic unit cell and simple cubic lattice
This type of packing is made by three dimension packing from square close packed layers. In square packed layers, all further layers will be built up such that they are
horizontally as well as vertically aligned with each other. This arrangement is also written as 'AAAA type'. There is a simple primitive cubic unit cell and simple cubic lattice.
2. Three dimension packing from hexagonal close packed layers
In hexagonal closed packed structure in two dimensions, the arrangement is 'ABAB' type. The pattern follows in three dimensions also. The third layer and other layers are arranged in the depressions of previous layer. These depressions are known as voids. Voids can be two types; tetrahedral voids, which are surrounded by four particles and octahedral voids surrounded by six particles.
The third layer can be built in two different ways,
Sodium chloride or rock salt has face centered cubic (fcc) arrangement, in which each chloride ion occupies the corners and face centers of the cube, while sodium ions (Na+) are located at the body and edge corners.
The coordination number for both ions is six and number of particles per unit cell is four.
|8 at corners = 8 x 1/8 = 1||12 at edge centers = 12 x 1/4 = 3|
|6 at face centers = 6 x 1/2 = 3
||1 at body center = 1
|Total = 4
||Total = 4
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