Introduction - Crystal Structure - Civil Engineering (CE) PDF Download

Introduction
A crystal is a solid composed of atoms or other microscopic particles arranged in an orderly repetitive array. The study of crystal physics aims to interpret the macroscopic properties in terms of properties of the microscopic particles of which the solid is composed. The arrangement of atoms in a Crystal is called Crystal Structure.

Lattice points and Space Lattice:
Points can be imagined in space about which atoms or molecules are located. Such points are called Lattice Points. The totality of such points is called Space Lattice or Crystal Lattice.The Three-Dimensional space lattice (3-D Space lattice) may be defined as a finite array of lattice points in three-dimension in which each and every lattice point has identical surrounding in the array.

Basis and Crystal structure:
Every lattice point can be associated with one or unit assembly of atoms or molecules identical in composition called Basis or Pattern. The regular periodic three-dimensional arrangement of Basic is called Crystal Structure. Space lattice is imaginary. Crystal structure is real.

Bravais and Non-Bravais lattice:
A Bravais lattice is one in which all lattice points are identical in composition. If the lattice points are not identical then lattice is called NonBravais lattice.

The set of lattice points ⊗⁰ s together constitutes a Bravais lattice. Similarly the set of lattice

points  together constitutes a Bravais lattice. But set of all lattice points  and  together constitutes a Non-Bravais lattice. Hence a Non-Bravais lattice could be considered as the superposed pattern of two or more interpenetrating Bravais lattices.

Unit cell and Lattice parameters:
In every crystal some fundamental grouping of particles is repeated. Such fundamental grouping of particles is called unit cell. A unit cell is chosen to represent the symmetry of the crystal. Hence the unit cell with maximum symmetry is chosen. They are the basic building blocks of the crystal. When these unit cells are transferred in three dimension that will generate the crystal.

Each crystal lattice is described by type of unit cell.But each unit cell is described three vectors   when the length of the vectors and the angles (α, β, γ) between them are specified. They are nothing but the intercepts of the faces and the interfacial angles. All together they constitute lattice parameters.

Primitive Cell: Some times reference is made to a primitive cells. Primitive cell may be 

defined as a geometric shape which, when repeated indefinitely in three dimensions, will fill all space and it consists of lattice points only at corners. It consists of only one atom per cell. Therefore unit cells may be primitive (simple) or Non-primitive.

 Crystal system and Bravais space lattice 
Based on lattice parameters crystals are classified into seven basic systems. If atoms are placed only at corners seven crystal system yield seven lattices. But few more lattice could be constructed by placing atoms at face center, body center and base centred., Bravais showed that there are 14 such lattices that exits in nature. Hence the name of the Bravais space lattice. Each crystal system differes from the other in lattice parameters.

(1) Cubic Crystal System(Isometric) a = b = c and α = β = γ = 90⁰ . (Simple or primitive, Face centered (FCC)and Body centered (BCC)).
(2) Tetragonal Crystal System a = b 6= c and α = β = γ = 90⁰ (Simple and body centered).
(3) Orthorhombic Crystal System a 6= b 6= c and α = β = γ = 90⁰ (Simple, Face centered (FCC), Body centered(BCC) and Base centered.
(4)Monoclinic Crystal System a 6= b 6= c and α = β = 90⁰ 6= γ (Simple and Base centered).

(5)Triclinic Crystal System a 6= b 6= c and α 6= β 6= γ 6= 90⁰ (Simple).
(6)Trigonal Crystal System(Rhombohedral) a = b = c and α = β = γ 6= 90⁰ (Simple)
(7)Hexagonal Crystal System a = b 6= c and α = β = 90⁰ , γ = 120⁰