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Crystal Structure

A solid is defined as the form of matter which exhibits rigidity, a definite shape and a definite volume.

Solids can be classified as crystalline solids and amorphous solids.

  1. Crystalline solids have a long range arrangement of constituent particles. They have a sharp melting point and are anisotropic in nature. For example; Quartz , all solid elements (metal and non-metal).
  2. In amorphous solids, there is a short range order in the arrangement of particles. They have irregular shape and are isotropic in nature. They are called as pseudo solids or supercooled liquids. For example; glass, silica, plastic, polymers.

Crystalline solids can be classified on the basis of the nature of the constituent particles and the binding force in molecules.

 

Crystal Lattice Structure

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In crystalline solids, the constituent particles are arranged in a regular pattern throughout the crystal lattice. This regular and repeating arrangement of points or particles in space is called as space lattice or crystal lattice structure.

Since crystal lattice is a regular and repeating arrangement of partials, a small part of the lattice will be sufficient to explain all the properties and complete crystal lattice.
This smallest part of the crystal lattice, which when repeated in different directions,
produces a complete crystal lattice, is known as unit cell.

Crystal Unit Cell

Properties of Crystal lattice

In the crystal lattice, each point represents constituent particles (ion or atom or molecule) and is called as lattice point. These points joined by line to form a whole crystal lattice. The arrangement of lattice points in a crystal lattice gives the geometry to a crystal lattice. Crystal lattice can be of two types,

  1. Two dimensional lattices
  2. Three dimensional lattices.

1. Two dimensional lattices

It is a two dimensional regular arrangement of particles in two dimensions or on the plane of a paper.
A unit cell with a certain number of particles in it's corner is known as a primitive unit cell, while a unit cell with corner as well as interior particles is known as interior unit cell.

Two Dimensional Lattices

The type of crystal lattice depends on the type of unit cell. The complete crystal lattice is produced by repeatedly moving unit cells in the direction of its edge.


Lattice
Unit cell
Square lattice Square
Rectangle lattice Rectangle
Parallelogram lattice
Parallelogram
Hexagonal lattice
Rhombus with an angle of 60oC


2. T
hree dimensional lattices

In these type of crystal lattices, the constituent particles are arranged in a three dimensional space.

Unit Cell

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Each smallest unit of the complete space lattice or crystal lattice, which is repeated in different direction to form a complete crystal lattice structure is called a unit cell. It is just like a thick wall made up of regularly arranged bricks. Here the thick wall is the crystal lattice and each brick is a unit cell.

In other words, unit cell is the building block of crystal lattice or space lattice. A unit cell can be explained by using certain parameters. These parameters are as follows. The edge of the unit cell represented by a, b and c. It is dimensions along the three edges.

The angle between the edges are represented by α, β and γ. The angle between edge b and c is α , the angle between edge a and c is β, while γ is the angle between edges a and b. Thus there are a total of six parameters; a , b , c and α, β and γ.

Types of Unit cells

Unit cell can be classified on two different basis.

1.Based upon th parameters of unit cell

The unit cell can be classified into seven different types on the basis of the different parameters a, b and c edges and α ,β and ϒ angles. These seven unit cells are also known as Bravais Unit Cells.

Category
Edge lengths
Internal angles
Cubic (a=b=c) (α=β=γ=90o)
Tetragonal
(a=b≠ c) (a=β=γ=90o)
Monoclinic
(a≠ b≠c)
(a=β>=90o=γ)
Orthorhombic
(a≠ b≠ c) (a=β>=γ=90o)
Rhombohedral
(a=b=c) (a=β>=γ≠ 90o)
Hexagonal (a=b≠ c)
(a=β=90o, γ=120o)
Triclinic
(a≠ b≠ c) (a≠β >≠ γ≠ 90o)


2. Based upon the position of particles in unit cell

Each Bravais unit cell is further classified into two types on the basis of the position of the particles at the corner and center. The unit cells which have lattice points only at the corner are termed as primitive unit cells. While the unit cells in which the lattice points are located at the corner as well as at other positions also are called as non-primitive or centered unit cell.

The non-primitive units cells are further divided into three types on the basis of lattice points at other sites.

  • Face centered unit cell: When particles are located at the corner as well as at the center of each face, it is termed as face centered unit cell.
  • End-centered unit cell: In such type of unit cells , particles located at the corner and at the center of any two opposite faces.
  • Body centered unit cell: When lattice points are located at the corner and one particle at the center of unit cell , it termed as body centered unit cell.


All bravis unit celsl do not have all these types of unit cells. Hence there are a total of fourteen types of crystal lattices corresponding to seven bravis unit cells.

Class of crystals
Possible types of units
Examples
Cubic
Primitive body centred face centred
Copper, KCl, NaCl zinc blende, diamond
Tetragonal
Primitive body centred
SnO2, White tin, TiO2
Orthorhombic
Primitive body centred, face centred and centred Rhombic sulfur, KNO3,
CaCO3
Hexagonal Primitive Graphie, Mg, ZnO
Trigonal or rhombohedral
Primitive (CaCO3) Calcite, HgS(cinnabar)
Monoclinic Primitive and end centred Monoclinic sulfur, Na2SO4.10H2O
Triclinic
Primitive
K2Cr2O7, CuSO4.5H2O


Cubic Closest Packed Structure

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In crystal lattices all the lattice points or particles are taken as a sphere. All the spheres are arranged in such a way that they occupy the maximum available space and leave minimum empty space between them. The packing of spheres can be of different types.

Close packing in one dimensional

In this packing, particles can arranged only in one dimension. They are arranged in such a way that they touch each other in a row. The coordination number is two in this arrangement.

Close packing in two dimensional

The two dimensional arrangement of particles in also known as crystal plane. In this arrangement, the packing of particles can be done in two different ways.

  • The spheres of the second row are arranged in such a way that they are touching the spheres of the first row and are present exactly below them. Such type of arrangement is termed as 'AAAA' type , because all the layers are same. Each sphere touches four other sphere, hence the coordination number is four. This type of arrangement is also known as square close packing in two dimensions.
  • Another type of two dimensional arrangement is known as hexagonal close packing in two dimensions. In this arrangement, the second layer of spheres is arranged in the depressions of first layer. Hence it also represents as 'ABABAB'.

Close packing in three dimensional

In three dimensional close packing, each two dimensional packing is expanded in three dimensional spaces.

1. Simple primitive cubic unit cell and simple cubic lattice

This type of packing is made by three dimension packing from square close packed layers. In square packed layers, all further layers will be built up such that they are
horizontally as well as vertically aligned with each other. This arrangement is also written as 'AAAA type'. There is a simple primitive cubic unit cell and simple cubic lattice.

2. Three dimension packing from hexagonal close packed layers

In hexagonal closed packed structure in two dimensions, the arrangement is 'ABAB' type. The pattern follows in three dimensions also. The third layer and other layers are arranged in the depressions of previous layer. These depressions are known as voids. Voids can be two types; tetrahedral voids, which are surrounded by four particles and octahedral voids surrounded by six particles.

The third layer can be built in two different ways,

  • Hexagonal close packing (hcp) or Hexagonal crystal structure
  • Cubic closest packed structure(ccp) or face cantered cubic (fcc crystal structure)

Hexagonal Close Packing

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If the third layer placed in the tetrahedral voids and spheres of every third layer are vertically aligned, it is called as 'ABAB' pattern or hexagonal close packing (hcp) and the unit cell is a primitive Hexagonal unit cell.


The best examples of hexagonal close packing are molybdenum, magnesium and beryllium crystals. The packing efficiency of this pattern is 74% and coordination number is 12, because each sphere is in contact with six spheres on the same layer, 3 above and 3 below the plane.

FCC Crystal Structure

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If the third layer is placed over the octahedral voids of the second layer, it is called as cubic close packing (ccp) or face cantered cubic (fcc). Here the sphere of every
fourth layer is aligned vertically. The pattern is 'ABC.. type' as the third layer is arranged differently than the first layer.

FCC Crystal Structure
The packing efficiency and coordination of Cubic close packing is same as hexagonal close packing.

Body Centred Cubic

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The third type of three dimensional arrangement is known as body centred cubic (bcc) , in which the space occupied is 68 % and coordination number is eight. It is generally found in metals like lithium , sodium and rubidium.

Body Centred Cubic

The unit associated with this crystal structure is known as Body centered cubic unit cell.

NaCl Crystal Structure

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Sodium chloride or rock salt has face centered cubic (fcc) arrangement, in which each chloride ion occupies the corners and face centers of the cube, while sodium ions (Na+) are located at the body and edge corners.

NaCl Crystal Structure

The coordination number for both ions is six and number of particles per unit cell is four.

Orange(Cl-)
Blue(Na+)
8 at corners = 8 x 1/8 = 1 12 at edge centers = 12 x 1/4 = 3
6 at face centers = 6 x 1/2 = 3
1 at body center = 1
Total = 4
Total = 4

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