Material Science

Solid state


Molecular Solids: The forces of attraction holding the molecules are Van der Waals forces. Examples of molecular crystals are Ice, Solid Carbon dioxide, Sulphur, CH4 , Wax.
Ionic Solids: The forces of attraction holding the ions together is electrostatic in nature. Examples are NaCl, BaCl2 , CsCl, NaNO3 etc.
Covalent Solids: The binding forces are Covalent Bonds eg. Diamond, Silicon Carbide, Quartz.
Metallic Solids: The binding forces are electrostatic attraction eg. Copper, Aluminium, Silver, Gold etc.


In a crystal the constituent units atoms ions or molecules are arranged in such a way that the arrangement has minimum energy and thus maximum stability. For maximum stability the constituent units in the crystal must be surrounded by maximum number of neighbors. High co-ordination number.
Three dimensional packing of spheres
Hexagonal Close Packing hcp:- The spheres are arranged in a way such that the third layer comes vertically above the first layer the sequence may be represented as  ABABABABA……. This type of arrangement is called hexagonal close packing or hcp arrangement e.g. Beryllium, Calcium, Cadmium, Zinc etc.

Cubic Close Packing ccp: The spheres are arranged in a way such that the fourth layer comes vertically above the first layer. The sequence may be represented as ABCABCABC……. This type of arrangement is called cubic close packing or ccp arrangement. The A,B,C represent the different layers of spheres in a three dimensional arrangement where each layer has a hexagonal close packing in 2 – dimension.


When arranging atoms in a 3D pattern there is space still unoccupied and these are regarded as holes or voids or interstices.
Tetrahedral Voids: These are voids formed by 4 closely touching spheres. Or one sphere resting on three touching spheres. It is called a tetrahedral void because the centres of the 4 touching are placed at the corners of a tetrahedron
Octahedral Voids:These are voids formed by six touching spheres. Or Three spheres belonging to one layer and three spheres belonging to the second layer. The centres of these spheres form a regular Octahedron.

  1. Octahedral Voids are bigger than Tetrahedral voids
  2. Number of Octahedral voids are equal to the number of spheres
  3. Number of Tetrahedral voids are equal to twice the number of spheres

Relationship between size of the voids and spheres is

  • a) Radius of atom ‘r’ in a Tetrahedral void = .225 R
  • b) Radius of atom ‘r’ in an Octahedral void = .414 R

Where R is the radius of the sphere in the close packing arrangement.

Co-ordination Number: The total number of nearest neighbours, atoms or ions of a particular atom or ion in a crystal lattice is called co-ordination number.


The smallest portion of a space lattice which generates the whole crystal by repeating its own dimensions in various directions is called unit cell
The smallest repeating unit in space lattice which when repeated over and over again produces the complete space lattice.

Solid state page 2