Solids are rigid and possess definite shape and volume. In solids, ions atoms or molecules are held together by strong inter ionic, interatomic, or intermolecular forces. The properties of the solids depend upon the nature of constitutional particles and the binding forces operating between them.

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## Types of solids:

We normally get two types of solids-Crystalline and amorphous. The difference between them are-

## Classification of solids based upon the nature of inter-particle forces:

Depending upon the nature of binding force, solids are classified as ionic, covalent, molecular and metallic solids.

The comparative of the solids are-

## True solid

A true solid may be defined as a matter which possesses rigidity, definite shape, definite volume, and long-range of order.

## Pseudo solid

Pseudo solids have a shape but can be easily distorted. Ex-Glass, pitch.

## Isotropic substances and anisotropic substances

• The substances which have the same physical properties such as electrical conductivities, refractive index, thermal expansion, mechanical strength, etc. identical in all directions in the space are called isotropic substances. This property is known as isotropy. Amorphous substances are isotropic.
• The substances which have different physical properties in all directions in the space are called anisotropic substances and the property is called anisotropy. Crystalline solids are anisotropic.

## Unit cell

Unit cell is the smallest three-dimensional groups of lattice points, which when repeated in three dimensional in space, give the whole lattice of the crystal.

## Seven Crystal system

• To describe a unit cell, six parameters are required. (a, b and c are the three sides and Î±,Î², and Î³ are the three angles
• Based upon certain rotation axes, crystals are classified into seven categories called seven Crystal System.
• Based on these seven crystal systems and the four possible variations, there are 14 possible three-dimensional lattices. These are called Bravais lattices.
• Among the seven crystal systems, cubic is the most symmetric whereas triclinic is the most unsymmetrical system.

## Space lattice and crystal lattice

Space lattice is the regular pattern of points, which describes the three dimensional arrangement of particles in a crystal structure. When the points are replaced with actual atoms or ions, it is called crystal lattice.

## Close packing

Constituent particles of a crystal pack in such a way that the volume is minimum and density become maximum and attain stability. This type of packing is called close packing.

### 1. Close Packing in One dimension

Each sphere touch one another making a line arrangement. C.N= 2

### 2. Square Close Packing in Two Dimensions

Each sphere remains attached with 4 other spheres. C.N=4

### 3.Hexagonal Close Packing in Two Dimensions

The spheres in the second row are placed in the gaps between the spheres of the first row. Each sphere touches 6 neighboring spheres. C.N=6

### 4. Three dimensional close packing from two dimensional square close packed structures

The second layer is placed over the first layer such that the spheres of the upper layer are exactly above those of the first layer.

### 5. Three dimensional packing (hcp)

The third layer may be placed above the second layer such that the tetrahedral voids of the second layer are covered by the spheres of the third layer. The spheres of the third layer are exactly aligned with those of the first layer.

This structure is called a hexagonal close-packed (hcp) structure. Ex: Mg, Be, Zn, Cd, Ti, Zr

### 6.Three dimensional packing (ccp)

The third layer may be placed above the second layer such that the octahedral voids of the second layer are covered by the spheres of the third layer. The spheres of the third layer are not aligned with those of the first or second layer.

This structure is called cubic close packed (ccp) or face centred cubic (fcc) structure.

Ex: Fe, Cu, Ag, Au, Al, Pt, Co

## Crystal structure of common metals

All noble gases have ccp structure, except He which has hcp structure.

## Voids

1. The space which is left in between the particles of a closest packed arrangement.
2. Trigonal voids: voids present in triangular spaces in 2-dimentional packing .
3. In 3-dimention we get tetrahedral and octahedral voids.

### Number of voids filled and formula of the compound

1. The number of octahedral voids = number of particles present in the close packing.
2. The number of tetrahedral voids= 2 x Number of octahedral voids.
3. Usually, in ionic compounds, anions are present in the packing whereas cations occupy the voids.

Coordination number: It is the number of equidistant neighbour atoms that an atom has in its crystal structure.

## The relation between a, r and d of the unit cell

a= Edge length, r= radius of atom, d= nearest neighbour distance or inter ionic distance.

## Packing Fraction

Packing Fraction is equal to the ratio of the volume occupied by the atoms present in a unit cell to the total volume of the unit cell.

Packing fraction shows how closely the atoms are packed together in a unit cell. The packing density decreases in the order: fcc> bcc> Simple cube.

## Derivation of packing efficiency

### Simple cubic unit cell:

• Let â€˜aâ€™ be the edge length of the unit cell and r be the radius of the sphere.
As sphere are touching each other
Therefore a = 2r
No. of spheres per unit cell = 1/8 Ã— 8 = 1
Volume of the sphere = 4/3 Ï€r3
Volume of the cube = a3= (2r)3= 8r3
âˆ´Fraction of the space occupied =1/3Ï€r3/ 8r3= 0.524
âˆ´% occupied = 52.4 %

### Body-centred cubic unit cell:

In Triangle EFD
Let DF= b and we know that ED=EF= a (edge length)
Now, b2= a2+ a2= 2a2
In Triangle AFD
Let, AF = c and we know that FD = b & AD = a (edge length)
Now, c2= a2+ b2=a2+ 2a2= 2a2
or c =âˆš3 a
We know that c is body diagonal.As the sphere at the centre touches the sphere at the corner. Therefore body diagonalc = 4r
i.e.âˆš3 a = 4r
or r = (âˆš3/4)a
or a = 4r /âˆš3
âˆ´Volume of the unit cell = a3= (4r / âˆš3)3= 64r3/ 3âˆš3
No. of spheres in bcc = 2
âˆ´The volume of 2 spheres = 2Ã—4/3Ï€r3

### Face-Centred Cubic (hcp and ccp Structures)

Let â€˜râ€™ be the radius of sphere and â€˜aâ€™ be the edge length of the cube
As there are 4 sphere in fcc unit cell

âˆ´The volume of four spheres = 4 (4/3Ï€r3)
In fcc, the corner spheres are in touch with the face centred sphere. Therefore, face diagonal AD is equal to four times the radius of sphere AC= 4r,

But from the right angled triangle ACD , AC = âˆšAD2+ DC2=âˆša2+a2=âˆš2a
4r = âˆš2a  or a = 4/âˆš2 r
âˆ´volume of cube = (2/âˆš2 r)3

## Defect

Any irregularities of constituent particles from perfectly ordered arrangement in a crystal is called defect.

#### 1.Point Defect

Irregularities from ideal arrangement around a point or an atom in a crystalline substance.

#### 2.Line Defect

Irregularities from ideal arrangement in entire rows of lattice points.

#### 3. Stoichiometric Defect

These are the point defects that do not disturb the stoichiometry of the solid. The ratio of the cations and anions remains same.

#### 4. Vacancy Defect

When some of the lattice sites are vacant, the crystal is said to have a vacancy defect. Density decreases. Seen in non-ionic solids.

#### 5. Interstitial defect

When some constituent particles also occupy an interstitial site, the crystal is said to have interstitial defects. Density increases. Seen in non-ionic solids.

#### 6. Frenkel defect

Cation is dislocated from its normal site to an interstitial site.It creates a vacancy defect at its original site and an interstitial defect at its new location.

Seen in ionic substances which have low coordination no and in which there is a large difference in the size of cation and anion.

Ex: ZnS, AgCl, AgBr, AgI.

The ionic compound remains electrically neutral and stoichiometrically same.This defect increases the temperature.

#### 7. Schottky defect

In an ionic compound if equal no of cations and anions are missing, it is called schottky defect.

#### 8. Impurity Defect

When some foreign particles are present in the crystal.Ex: Molten NaCl containing little amt of SnCl2 .

#### 9. Metal excess defect due to anionic vacancies.

A negative ion is missing from its normal site in the lattice. Thus the metal ion becomes in excess. The hole caused by the absence of negative ion is occupied by an electron to maintain electrical neutrality.

The electrons trapped in anion vacancies are referred to as F-Centre(F-Farbe which means colour)

#### 10.Metal deficiency defect

It is due to missing of a cation of a lower valence and another lattice site occupied by a cation of higher valence.

Ex: FeO, FeS, NiO etc. It is seen in those metals which show variable valencies.

## Characteristics of crystalline solids

### Structure of simple ionic crystals

1. AB type: It is of three types:
1. Rock salt (NaCl) type.Halides of Li, Na , K and CsF, Halides of ammonium, Oxides and sulphides of Mg, Ca, Sr and Ba, AgCl, AgBr, CaCO3, CaC2.
2. CsCl: CsBr, CsI, TlCl, TlBr.
3. ZnS: Chloride , bromide and iodide of Cu, AgI, BeS.
2. AB2 type: CaF2, BaF2, BaCl2, SrF2, SrCl2, CdCl2, PbF2.
3. A2B type: Na2O, Li2O, K2O, Rb2O, Rb2S.

### Effect of pressure and temperature on crystal structure

An increase in temperature decreases the coordination number whereas increase in pressure increases the same. At about 760 K, CsCl (C.N=8:8) changes to NaCl (C.N=6:6) structure. Applying pressure during crystallisation, NaCl changes to CsCl structure.

Nature of bonding in metallic solids is explained by

1. Electron sea or electron gas theory
2. Molecular orbital theory or Band theory

## Band, valence band and conduction band

The atomic orbitals of the metal atoms are close in energy. They overlap to form molecular orbitals which are very close in energy to each other. This set of molecular orbitals is called a band. The band formed from atomic orbitals of lower energy is called valence band. It holds the valence electrons.Conduction band is formed from empty or partially filled atomic orbitals of higher energy.In conductors, the energy difference in the valence band and conduction band is negligible.

In semiconductors, there is a small energy gap and in insulators, there is a large energy gap. As electrons jump from valence band to conduction band, the conductivity of electricity takes place. As the gap between the bands’ increases, the conductivity decreases.

## Types of semiconductors

1. Intrinsic semiconductors: The substances which are insulator at room temperature and become semiconductor when heated or irradiated with light are intrinsic semiconductor.
2. Extrinsic semiconductor: These are formed by adding impurity to the insulator (dopping).They are of two types:
1. n-type semiconductor: The term n-type comes from the negative charge of the electron. In n-type semiconductors, electrons are the majority carriers and holes are the minority carriersn-type semiconductors are created by doping an intrinsic semiconductor with donor impurities.
2. p-type semiconductor: The term p-type refers to a positive charge of the hole. As opposed to n-type semiconductors, p-type semiconductors have a larger hole concentration than electron concentration. In p-type semiconductors, holes are the majority carriers and electrons are the minority carriers. p-type semiconductors are created by doping an intrinsic semiconductor with acceptor impurities.

### Electrical property of metals

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