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Department of Physics

Unit I Semester 6th

Solid materials are classified on the basis of arrangement of atoms within the solid. There are twomain categories: Materials in which atoms are placed randomly(lack regular arrangement) in a longrange are called amorphous. Examples are pitch, plastic. Materials in which atoms are placed in a high ordered structure(regular and regular pattern) in a long range are called crystalline. Examplesare diamond, quartz. Polycrystalline materials are materials with a high degree of short-range order and no long-range order. These materials consist of small crystalline regions with random orientation called grains, separated by grain boundaries. Crystals are categorized by their crystalt sructure and the underlying lattice. While some crystals have a single atom placed at each lattice point, most crystals have a combination of atoms associated with each lattice point. Thiscombination of atoms is also called the basis. OR we can say that basis is an aggregate of atomsoccupying space point’s position. The classification of lattices, the common semi-conductor crystalstructures and the growth of single-crystal semiconductors are discussed in the following sections.

Bravais lattices.

In 1848 A. Bravis, the French Crystallographer proved that there are only 14 space lattices in total,which are required to describe all possible arrangements of points in space. These are the distinct lattice types, which when repeated can fill the whole space. It is subjected to the condition that eachlattice point has exactly identical environment. The lattice can therefore be generated by three unit vectors, and a set of integers k, l and m so that each lattice , point, identified by a vector can be obtained from:

The construction of the lattice points based on a set of unit vectors is illustrated by Figure

Figure: The construction of lattice points using unit vectors.In two dimensions, there are five distinct Bravais lattices, while in three dimensions

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