Classification of solids for IIT JEE

Solids are divided into two classes on the basis of haphazard and regular arrangement of the building constituents.

(i) Amorphous solids: The term 'amorphous' has been derived from Greek word 'Omorphe' meaning shapeless. In amorphous solids, the arrangement of the building constituents is not regular but haphazard. Although these solids possess some of the mechanical properties such as rigidity, incompressibility, refractive index, etc., they do not have characteristic shapes or geometrical forms. Amorphous solids resemble liquids which flow very slowly at room temperature and are regarded as supercooled liquids in which the cohesive forces holding the molecules together are so great that the material is rigid but there is no regularity of the structure. Example: Glass, rubber, plastics, etc. 

Amorphous solids do not have sharp melting points. For example, when glass is heated, it softens and then starts flowing without undergoing any abrupt change from solid to liquid state. Thus, amorphous substances are not true solids but can be regarded as intermediate between liquids and solids.

(ii) Crystalline solids: In crystalline solids, the building constituents arrange themselves in a regular manner throughout the entire three-dimensional network. The ordered arrangement of building constituents (molecules, atoms or ions) extends over a large distance. Thus, crystalline solids have a long range order. A crystalline solid consists of a large number of units, called crystals. A crystal is, defined as a solid figure which has a definite geometrical shape, with flat faces and sharp edges.
A crystalline substance has a sharp melting point. i. e., it changes abruptly into liquid state. Strictly speaking a solid state refers to crystalline state or only a crystalline substance can be considered to be a true solid.

The substances which show the same properties in all directions are said to be isotropic and the substances exhibiting directional differences in properties are termed anisotropic. . Amorphous solids like liquids and gases are said to be isotropic as arrangement of building constituents is random and disordered. Hence, all directions are, equal and therefore, properties are the same in all the directions. Crystalline solids are anisotropic. Magnitude of some of the physical properties of crystalline solids such as refractive index, coefficient of thermal expansion, electrical and thermalconductivities, etc., is different in different directions, within the crystal. For example, in the crystal of silver iodide (AgI), the coefficient of thermal expansion is positive in one direction and negative in the other direction.

Fig 1: Anisotropic behaviour of crystals
The phenomenon of anisotropy provides a strong evidence for the presence of ordered molecular arrangement in crystals. This can be explained with the help of Fig.1 in which a simple two dimensional arrangement of two different kinds of atoms has been depicted. When a physical property is measured along the slanting line CD, it will be different from that measured in the direction of vertical line AB, as line CD contains alternate types of atoms while line AB contains one type of atomonly.

All crystals are polyhedra consisting of regularly repeating arrays of atoms, molecules or ions which are the structural units. A crystal is primarily a homogeneous part of a solid substance. It consists of regular patterns of structural units which are bonded by plane surfaces that make definite angles with one another. The geometrical form consisting only of a regular array of points in space is called a lattice or space lattice. A space lattice can be subdivided into a number of small cells known as unit cells. It can be defined as the smallest repeating unit in space lattice which when repeated over and over again results in a crystal of the given substance or it is the smallest block or geometrical figure from which the entire crystal can be built up by its translational repetition in three-dimensions.

On the basis of geometrical considerations, theoretically there can are 32 different combinations of elements of symmetry of a crystal. These are called 34 systems. Some of the system have been grouped together. In all, seven types of basic or primitive unit cells have been recognised among crystals. These are cubic, orthorhombic, tetragonal, monoclinic, triclinic, hexagonal, and rhombohedral.

All crystals do not have simple lattices. Some are more complex. Bravais pointed out that there can be 14 different ways in which similar points can be arranged in a three-dimensional space. Thus, the total number of space lattices belonging to all the seven crystal systems are 14. The crystals belonging to cubic system have three kinds of Bravais lattices. These are:

(i) Simple cubic lattice: There are points only at the corners of each unit.

(ii) Face-centred cubic lattice: There are points at the corners as well as at the centre of each of the six faces of the cube.

(iii) Body-centred cubic lattice: There are points at the corners as well as in the body-centre of each cube.

In a crystal, atoms located at the corner and face-centre of a unit cell are shared by other cells and only a portion of such an atom actually lies within a given unit cell.