Introduction
A solid is that form of matter that possesses rigidity and hence possesses a definite shape and a definite volume.
Classification of Crystalline Solids
Crystalline solids can be further classified depending on the nature of the bonding as:
* Ionic
* Molecular
* Covalent
* Metallic
Space Lattice and Unit Cell
The constituent particles of a crystalline solid are arranged in a definite fashion in the three dimensional space.
The Seven Crystal System
Types of Unit Cells
Face centred cubic
The particles are present not only at the corners but also at the centre of each face of the unit cell.
Calculation of Number of Particles per Unit Cell of a Cubic Crystal System
Keeping the following points in mind we can calculate the number of atoms in a unit cell.
* An atom at the corner is shared by eight unit cells. Hence an atom at the corner contributes 1/8 to the unit cell
* An atom at the face is a shared by two unit cells Contribution of each atom on the face is 1/2 to the unit cell.
Packing of Constituent Particles in Crystals
It is assumed that the atoms are hard spheres of identical size. Packing is done in such a way that they occupy maximum available space. This type of packing is called close packing.
Types of Voids
Radius Ratio
If R = Radius of the sphere in the closed packed arrangement.
r = Radius of the void.
Derivation of the Relationship Between Radius r of the Tetrahedral Void and the Radius R of the Atoms in the Close Packing
A tetrahedral void may be represented in a cube.
Derivation of the Relationship Between Radius r of the Octahedral Void and the Radius R of the Atoms in the Close Packing
A sphere fitting into the octahedral void is shown by shaded circle. A sphere above and a sphere below this small (shaded) sphere have not been shown in the figure.
Examples of Some Substances Having Close Packed Structures
All noble gases crystallize in ccp structure except helium which has hcp structure.
Structures of Oxides of Iron
Iron forms three different types of oxides, which are FeO, Fe2O3 and Fe3O4. These are non-stoichiometric (the ratio of cations and anions may vary from that given in the formula) and are easily oxidized or reduced into each other. These aspects can be explained on the basis of their crystal structure.
Radius Ratio Rules
For the stability of an ionic compound, each cation should be surrounded by maximum number of anions and vice versa. The number of oppositely charged ions surrounding each ion is called its co-ordination number.
Some Important Relations
Relation between nearest neighbor distance (d) and edge length (a) of a unit cell in a cubic crystal.
Efficiency of packing in hcp and ccp structures
We have discussed earlier that in both type of close packing (hcp and ccp) approximately amount of the available volume is occupied by spheres (atoms).
Calculation of Density of a Cubic Crystal from its Edge Length
The edge length of a cubic crystal can be obtained from X-ray studies and knowing the crystal structure possessed by it so that the number of particles per unit cell are known, the density of the crystal can be calculated.
Ionic Radius
It is defined as the distance from the centre of the nucleus upto the last shell containing the electrons.
X-Ray Study of Crystals
In a crystalline solid, the constituent particles (atoms, ions or molecules) are arranged in a regular order. An interaction of a particular crystalline solid with X-rays helps in investigating its actual structure.
Structures of Simple Ionic Compounds
It has a face centred arrangement (or CCP). Cl- ions occupy the corners and face centers, Na+ occupy body centre and edge centers.
Defects in Crystals
According to third law of thermodynamic it is only at OK that true crystals passes perfect order of arrangement of atoms in pure crystals. But with rise in temperature some derivations from complete order takes place. Presence of impurities also adds to disorder.
Types of defects in Crystals
The defect, which arises due to the irregularity in the arrangement of atoms or ions are called point defects.
Stoichiometric Defects
If imperfections in the crystal are such that the ratio between the anions and cations remain same as represented by the molecular formula, the defect is called a stoichiometric defect.
Non-stoichiometric Defects
If an imperfection causes the ratio of cations to anions to become different from that indicated by the ideal chemical formula, the defect is called non-stoichiometric.
Properties of Solids - Electrical Properties
Properties of solids have been exploited for various new innovations in electronic and magnetic devices like transistors, computers, telephones etc.
Magnetic Properties of Solids
The magnetic properties of materials are a consequences of magnetic moments associated will individual electrons. The magnetic moment of an electron is due to its orbital motion and also due to its spin around its own axis.
Dielectric Properties of Solids
Insulators do not conduct electricity because the electrons present in them are held tightly to the individual atoms or ions and are not free to move. However when electric field is applied polarization takes place because the nucleus is attracted towards cathode and electron cloud towards anode.
Piezoelectricity
When these crystals are subjected to mechanical stress, electricity is produced due to displacement of ions. The electricity thus produced is called piezoelectricity. But if an electric field is applied to these crystal there will be atomic displacement causing mechanical strain.
Superconductivity
When the electrical resistance of materials becomes almost zero, the material becomes superconductor. The temperature at which the material shows superconductivity is called transition temperature.
Amorphous Solids
Substances whose particles do not posses a regular orderly arrangement but have short range order. When amorphous solids are heated they become crystalline at some temperature.
Numericals
Chromium has mono atomic body-centred cubic structure. Its cell edge is 300 pm, what is its density? (Molar mass of Cr = 52 g mol-1, Avogadro number N = 6.023 x 1023 mol).
Conclusion
Anything that we look around us has mass and occupies space. Most of the things we use are in solid state. Solids have always attracted considerable interest because of their symmetry, beauty and simplicity of form.
