Chemistry chp no: 1. Solid State

 

Chapter 1 – Solid State

Class 11 Chemistry | Maharashtra State Board

1.1 Introduction

In the solid state, the particles are held together by strong interparticle forces of attraction.

Because of these strong forces, solids have a definite shape and a definite volume.

When temperature or pressure changes, the shape and volume of a solid change only slightly.

The smallest particles present in solids may be atoms, ions or molecules.

In this chapter, all these smallest particles are called constituent particles or simply particles.

Key Points

• Strong attraction exists between the particles of a solid.
• Solids have a fixed shape.
• Solids have a fixed volume.
• Changes in temperature and pressure produce only small changes in solids.
• The particles of solids may be atoms, ions or molecules.

1.2 Types of Solids

Solids are divided into two main types.

Type of Solid	Description
Crystalline Solid	Particles are arranged in a regular and repeating pattern.
Amorphous Solid	Particles are arranged randomly.

1.2.1 Crystalline Solids

In crystalline solids, the particles are arranged in a regular and periodic pattern.

This regular arrangement continues throughout the crystal over a long distance.

Characteristics of Crystalline Solids

1. Particles are arranged in a regular and repeating pattern throughout the crystal.
2. Crystalline solids have a sharp melting point. They melt at a definite temperature.
3. Most crystalline solids are anisotropic. Their physical properties, such as refractive index, thermal conductivity and electrical conductivity, may be different in different directions.

Examples

• Ice
• Sodium chloride (NaCl)
• Sodium
• Gold
• Copper
• Diamond
• Graphite
• Ceramics

Quick Revision

• Solids have strong interparticle forces.
• They have fixed shape and fixed volume.
• The constituent particles may be atoms, ions or molecules.
• There are two types of solids: crystalline and amorphous.
• Crystalline solids have a regular arrangement of particles.
• Crystalline solids melt at a definite temperature.
• Most crystalline solids are anisotropic.

1.2.2 Amorphous Solids

Amorphous solids do not have a regular arrangement of particles.

The particles are arranged randomly. They do not show a long-range ordered structure, but a short-range order is present.

Characteristics of Amorphous Solids

1. Random Arrangement of Particles

The particles are arranged irregularly.

The arrangement is not repeated throughout the solid.

2. No Sharp Melting Point

Amorphous solids do not melt at one fixed temperature.

They soften gradually over a range of temperatures and then start to flow.

3. Isotropic Nature

The physical properties of amorphous solids are the same in every direction.

Properties such as refractive index and electrical conductivity do not change with direction.

Examples of Amorphous Solids

• Glass
• Plastic
• Rubber
• Tar
• Metallic Glass

Quick Revision

• Particles are arranged randomly.
• No long-range order is present.
• Short-range order is present.
• They do not have a fixed melting point.
• They soften gradually on heating.
• They are isotropic.
• Examples: Glass, Plastic, Rubber, Tar and Metallic Glass.

Difference Between Crystalline and Amorphous Solids

Crystalline Solids	Amorphous Solids
Regular arrangement of particles.	Random arrangement of particles.
Long-range order is present.	Only short-range order is present.
Sharp melting point.	No sharp melting point.
Anisotropic.	Isotropic.

1.2.3 Isomorphism and Polymorphism

The similarity or difference in the crystal structure of substances is explained by Isomorphism and Polymorphism.

Isomorphism

When two or more different substances have the same crystal structure, they are called isomorphous substances.

These substances also have the same atomic ratio of their constituent atoms.

Examples

• NaF and MgO (Atomic ratio = 1 : 1)
• NaNO₃ and CaCO₃ (Atomic ratio = 1 : 1 : 3)

Polymorphism

When a single substance exists in two or more different crystalline forms, the property is called Polymorphism.

These different crystal forms are called Polymorphs.

Different polymorphs are formed under different conditions.

Examples

• Calcite and Aragonite are two crystalline forms of Calcium Carbonate (CaCO₃).
• α-Quartz, β-Quartz and Cristobalite are different crystalline forms of Silica (SiO₂).

Allotropy

When polymorphism occurs in elements, it is called Allotropy.

The different forms of an element are called Allotropes.

Example

• Diamond
• Graphite
• Fullerene

These are the allotropic forms of Carbon.

Quick Revision

• Isomorphism → Different substances with the same crystal structure.
• Isomorphous substances have the same atomic ratio.
• Polymorphism → One substance having different crystal structures.
• Different forms are called polymorphs.
• Polymorphism in elements is called allotropy.
• Diamond, Graphite and Fullerene are allotropes of Carbon.

1.3 Classification of Crystalline Solids

Crystalline solids are divided into four types according to the type of particles present and the force that holds them together.

• Ionic Crystals
• Covalent Network Crystals
• Molecular Crystals
• Metallic Crystals

1.3.1 Ionic Crystals

The particles present in ionic crystals are positively charged ions (cations) and negatively charged ions (anions).

These ions are held together by electrostatic force of attraction between opposite charges.

Characteristics

• Constituent particles are ions.
• Cations and anions may have different sizes.
• Particles are held together by electrostatic force.
• Ionic crystals are hard and brittle.
• They have high melting points.
• They do not conduct electricity in the solid state.
• They conduct electricity when melted or dissolved in water.

Examples

• NaCl
• KCl
• CaF₂
• K₂SO₄

1.3.2 Covalent Network Crystals

The constituent particles are atoms.

The atoms are connected to each other by a continuous network of covalent bonds.

The entire crystal behaves as one giant molecule.

Characteristics

• Constituent particles are atoms.
• Atoms are joined by covalent bonds.
• They form a rigid three-dimensional network.
• They are very hard.
• They have high melting and boiling points.
• They are poor conductors of heat and electricity because electrons are localised in covalent bonds.

Examples

• Diamond
• Quartz (SiO₂)
• Boron Nitride
• Carborundum

1.3.3 Molecular Crystals

The constituent particles are molecules or unbonded atoms of the same substance.

The atoms inside each molecule are joined by covalent bonds.

Different molecules are held together by intermolecular forces.

Characteristics

• Constituent particles are molecules.
• Intermolecular forces hold the molecules together.
• They are usually soft.
• They have low melting points.
• They are poor conductors of electricity.
• They are good insulators.

Examples

• Cl₂
• CH₄
• H₂
• CO₂
• O₂

1.3.4 Metallic Crystals

Metallic crystals are formed by atoms of the same metal.

These atoms are held together by metallic bonds.

The valence electrons are free to move throughout the crystal.

The positively charged metal ions remain surrounded by these mobile electrons.

Characteristics

• Held together by metallic bonds.
• Metals are malleable.
• Metals are ductile.
• Good conductors of electricity.
• Good conductors of heat.

Examples

• Sodium (Na)
• Potassium (K)
• Calcium (Ca)
• Iron (Fe)
• Gold (Au)
• Silver (Ag)

Quick Revision

Type	Particles	Force
Ionic	Ions	Electrostatic Force
Covalent	Atoms	Covalent Bond
Molecular	Molecules	Intermolecular Force
Metallic	Metal Atoms	Metallic Bond

1.4 Crystal Structure

The particles in a crystal are arranged in a regular three-dimensional pattern.

This arrangement is explained using two terms:

• Lattice
• Basis

Crystal Lattice

A lattice is a regular three-dimensional arrangement of points.

Each point in the lattice represents the position where a particle is present.

Basis

The particle attached to each lattice point is called the basis.

The basis may be an atom, an ion or a molecule.

Lattice + Basis = Crystal

1.4.2 Unit Cell

The smallest repeating unit of a crystal is called the Unit Cell.

Many unit cells join together in all directions to form the complete crystal.

The shape of the unit cell is the same as the shape of the crystal.

The dimensions of a unit cell are represented by a, b and c.

The angles between the axes are represented by α, β and γ.

Unit Cell Parameters

Parameter	Meaning
a	Length of first edge
b	Length of second edge
c	Length of third edge
α	Angle between b and c
β	Angle between a and c
γ	Angle between a and b

1.4.3 Types of Unit Cell

There are four types of unit cells.

1. Primitive (Simple) Unit Cell – Particles are present only at the corners.
2. Body-Centred Unit Cell – One particle is present at the centre of the cube in addition to the corner particles.
3. Face-Centred Unit Cell – One particle is present at the centre of each face in addition to the corner particles.
4. Base-Centred Unit Cell – One particle is present at the centre of two opposite faces in addition to the corner particles.

Quick Revision

• Crystal structure is a three-dimensional arrangement of particles.
• A lattice is a regular arrangement of points.
• A basis is the particle attached to each lattice point.
• Crystal = Lattice + Basis.
• The smallest repeating unit is called the unit cell.
• Unit cell dimensions are represented by a, b, c, α, β and γ.
• There are four types of unit cells.

1.4.4 Crystal Systems

Mathematical analysis shows that only 14 different space lattices are possible.

These 14 space lattices are called Bravais Lattices.

The 14 Bravais lattices are grouped into 7 crystal systems.

Seven Crystal Systems

No.	Crystal System
1	Cubic
2	Tetragonal
3	Orthorhombic
4	Rhombohedral
5	Monoclinic
6	Triclinic
7	Hexagonal

In this chapter, only the Cubic Crystal System is discussed in detail.

1.5 Cubic System

The cubic system has three types of unit cells.

1. Simple Cubic (SC)
2. Body-Centred Cubic (BCC)
3. Face-Centred Cubic (FCC)

Simple Cubic (SC)

In a Simple Cubic unit cell, particles are present only at the eight corners of the cube.

Number of Particles

Each corner particle is shared by 8 neighbouring unit cells.

Therefore, only 1/8 of each corner particle belongs to one unit cell.

Total particles = 8 × 1/8 = 1 particle

Body-Centred Cubic (BCC)

A Body-Centred Cubic unit cell has particles at all eight corners and one particle at the centre of the cube.

Number of Particles

Corner particles = 8 × 1/8 = 1 particle

Body-centre particle = 1 particle

Total particles = 2 particles

Face-Centred Cubic (FCC)

A Face-Centred Cubic unit cell has particles at all eight corners and one particle at the centre of each face.

Number of Particles

Corner particles = 8 × 1/8 = 1 particle

Each face-centre particle is shared by 2 unit cells.

Therefore, contribution of one face particle = 1/2

Six faces = 6 × 1/2 = 3 particles

Total particles = 1 + 3 = 4 particles

Particles in Different Cubic Unit Cells

Unit Cell	Particles per Unit Cell
Simple Cubic (SC)	1
Body-Centred Cubic (BCC)	2
Face-Centred Cubic (FCC)	4

Quick Revision

• Only 14 Bravais lattices are possible.
• They are grouped into 7 crystal systems.
• The cubic system has three unit cells.
• SC contains 1 particle.
• BCC contains 2 particles.
• FCC contains 4 particles.

1.5.2 Relationship between Molar Mass, Density and Unit Cell Edge Length

The density of a crystalline substance depends on:

• Molar Mass (M)
• Number of particles in one unit cell (n)
• Edge length of the unit cell (a)
• Avogadro Constant (NA)

ρ = nM / a³NA

Meaning of Symbols

Symbol	Meaning
ρ	Density
M	Molar Mass
n	Number of particles in one unit cell
a	Edge length of the unit cell
NA	Avogadro Constant

Important Formula

ρ = nM / a³NA

1.6 Packing of Particles in Crystal Lattice

In a crystal, the particles are packed very closely.

For understanding packing, each particle is considered as a hard sphere.

Closer packing increases the force of attraction between particles.

Coordination Number

The number of nearest neighbouring particles touching a particle is called its Coordination Number.

A higher coordination number means closer packing of particles.

1.6.1 Close Packing in One Dimension

Particles are arranged in a single straight row.

Each particle touches the particles on either side.

Close Packing in Two Dimensions

There are two types of close packing in two dimensions.

1. Square Close Packing
2. Hexagonal Close Packing

Square Close Packing

The rows are placed exactly one above another.

The arrangement is represented as AAAA....

Each particle touches 4 neighbouring particles.

Coordination Number = 4

Hexagonal Close Packing

The second row fits into the gaps of the first row.

The arrangement is represented as ABAB....

Each particle touches 6 neighbouring particles.

Coordination Number = 6

Hexagonal packing has less empty space than square packing.

Quick Revision

• Density depends on M, n, a and NA.
• Formula: ρ = nM / a³NA.
• Packing means arranging particles closely.
• Coordination Number is the number of nearest neighbouring particles.
• One-dimensional packing forms a straight row.
• Square packing has Coordination Number = 4.
• Hexagonal packing has Coordination Number = 6.
• Hexagonal packing is more efficient than square packing.

Close Packing in Three Dimensions

When two-dimensional layers are stacked one above another, a three-dimensional crystal structure is formed.

There are two methods of stacking close-packed layers.

• Stacking of square close-packed layers
• Stacking of hexagonal close-packed layers

Stacking of Square Close-Packed Layers

The second layer is placed exactly above the first layer.

Every layer has the same arrangement.

The stacking pattern is represented as AAAA....

This arrangement forms a Simple Cubic (SC) structure.

Each particle touches 6 neighbouring particles.

Coordination Number = 6

Hexagonal Close-Packed Structure (HCP)

In this arrangement, the second layer is placed in the depressions of the first layer.

The third layer is placed exactly above the first layer.

The stacking sequence is ABAB....

This arrangement forms the Hexagonal Close-Packed (HCP) structure.

Examples: Magnesium (Mg) and Zinc (Zn).

Cubic Close-Packed Structure (CCP/FCC)

The third layer is placed over the octahedral voids of the second layer.

The third layer does not match the first or the second layer.

The stacking sequence is ABCABC....

This arrangement forms the Cubic Close-Packed (CCP) structure.

CCP and Face-Centred Cubic (FCC) structures are the same.

Examples: Copper (Cu) and Silver (Ag).

Voids in Close Packing

Empty spaces present between closely packed particles are called Voids.

There are two types of voids.

• Tetrahedral Void
• Octahedral Void

Tetrahedral Void

A tetrahedral void is formed when one triangular void is covered by a particle from the next layer.

It is surrounded by 4 particles.

Octahedral Void

An octahedral void is formed when two triangular voids from different layers overlap.

It is surrounded by 6 particles.

Coordination Number

Structure	Coordination Number
Simple Cubic (SC)	6
HCP	12
CCP / FCC	12

Number of Voids

If the number of particles is represented by N,

Type of Void	Number
Tetrahedral Voids	2N
Octahedral Voids	N

Quick Revision

• AAAA → Simple Cubic (SC)
• ABAB → HCP
• ABCABC → CCP / FCC
• SC Coordination Number = 6
• HCP Coordination Number = 12
• CCP/FCC Coordination Number = 12
• Tetrahedral Void → Surrounded by 4 particles
• Octahedral Void → Surrounded by 6 particles
• Tetrahedral Voids = 2N
• Octahedral Voids = N

1.7 Packing Efficiency

Packing efficiency is the percentage of space occupied by particles in a unit cell.

It tells us how closely the particles are packed in a crystal.

Packing Efficiency =

(Volume occupied by particles ÷ Total volume of unit cell) × 100

Packing Efficiency of Simple Cubic (SC)

In a Simple Cubic unit cell, particles touch each other along the edges.

Packing Efficiency = 52.36%

Empty Space (Void Space) = 47.64%

Packing Efficiency of Body-Centred Cubic (BCC)

In a Body-Centred Cubic unit cell, particles touch each other along the body diagonal.

Packing Efficiency = 68%

Empty Space (Void Space) = 32%

Packing Efficiency of Face-Centred Cubic (FCC/CCP)

In a Face-Centred Cubic unit cell, particles touch each other along the face diagonal.

Packing Efficiency = 74%

Empty Space (Void Space) = 26%

Hexagonal Close-Packed (HCP) structure also has the same packing efficiency of 74%.

Comparison of Packing Efficiency

Structure	Packing Efficiency	Void Space
Simple Cubic (SC)	52.36%	47.64%
Body-Centred Cubic (BCC)	68%	32%
Face-Centred Cubic (FCC)	74%	26%
Hexagonal Close-Packed (HCP)	74%	26%

Quick Revision

• Packing efficiency is the percentage of space occupied by particles.
• SC Packing Efficiency = 52.36%
• BCC Packing Efficiency = 68%
• FCC Packing Efficiency = 74%
• HCP Packing Efficiency = 74%
• FCC and HCP have the highest packing efficiency.
• SC has the lowest packing efficiency.

1.7.1 Packing Efficiency of Simple Cubic (SC)

1.7.1 Packing Efficiency of Simple Cubic (SC)

What is Packing Efficiency?

Packing efficiency tells us how much space inside a unit cell is actually occupied by atoms (or particles).

Even though atoms are packed closely, they cannot fill the entire space. Some empty spaces called voids always remain between them.

Packing efficiency is expressed as a percentage.

Formula

Packing Efficiency =
(Volume occupied by particles ÷ Volume of Unit Cell) × 100

Simple Cubic (SC) Structure

In a Simple Cubic unit cell, atoms are present only at the eight corners of the cube.

Neighbouring atoms touch each other along the edges of the cube.

Important Point

Since atoms touch each other along the edge, the edge length (a) is equal to twice the atomic radius (r).

a = 2r

Result

After calculating the volume occupied by atoms and comparing it with the total volume of the unit cell, the packing efficiency of a Simple Cubic structure is obtained.

Packing Efficiency = 52.36%

Void (Empty) Space = 47.64%

Meaning of this Result

• Out of the total space inside a Simple Cubic unit cell, only 52.36% is occupied by atoms.
• The remaining 47.64% is empty space called void space.
• Because a large amount of space remains empty, the Simple Cubic structure is not an efficient packing arrangement.

Quick Revision

Property	Value
Atoms touch along	Edge
Relation	a = 2r
Packing Efficiency	52.36%
Void Space	47.64%

1.7.2 Packing Efficiency of Body-Centred Cubic (BCC)

Body-Centred Cubic Structure

In a Body-Centred Cubic (BCC) unit cell, atoms are present at all eight corners and one atom is present at the centre of the cube.

The corner atoms and the body-centre atom touch each other along the body diagonal of the cube.

Important Relation

In a BCC unit cell, the body diagonal is equal to four atomic radii.

√3 a = 4r

Packing Efficiency

Using this relationship, the packing efficiency of a BCC structure is calculated.

Packing Efficiency = 68%

Void Space = 32%

Meaning

• 68% of the space inside the unit cell is occupied by atoms.
• 32% of the space remains empty.
• BCC has a higher packing efficiency than Simple Cubic.

1.7.3 Packing Efficiency of Face-Centred Cubic (FCC / CCP)

Face-Centred Cubic Structure

In a Face-Centred Cubic (FCC) unit cell, atoms are present at all eight corners and at the centre of each face.

Neighbouring atoms touch each other along the face diagonal of the cube.

Important Relation

In an FCC unit cell, the face diagonal is equal to four atomic radii.

√2 a = 4r

Packing Efficiency

The FCC arrangement gives the maximum packing efficiency among cubic crystal structures.

Packing Efficiency = 74%

Void Space = 26%

Hexagonal Close Packing (HCP)

The Hexagonal Close-Packed (HCP) structure also has the same packing efficiency of 74%.

Although the arrangement of layers is different, both FCC and HCP pack atoms equally efficiently.

Comparison of Packing Efficiency

Structure	Atoms Touch Along	Packing Efficiency	Void Space
Simple Cubic (SC)	Edge	52.36%	47.64%
Body-Centred Cubic (BCC)	Body Diagonal	68%	32%
Face-Centred Cubic (FCC)	Face Diagonal	74%	26%
Hexagonal Close Packing (HCP)	Close-Packed Layers	74%	26%

Quick Revision

• SC atoms touch along the edge.
• BCC atoms touch along the body diagonal.
• FCC atoms touch along the face diagonal.
• SC Packing Efficiency = 52.36%
• BCC Packing Efficiency = 68%
• FCC Packing Efficiency = 74%
• HCP Packing Efficiency = 74%
• FCC and HCP have the highest packing efficiency.

1.7.4 Number of Particles and Number of Unit Cells in x g of Metal

Introduction

Sometimes we know the mass of a metal sample, but we need to find how many atoms or how many unit cells are present in it.

These values can be calculated using the molar mass of the metal and Avogadro's constant.

This method is useful because a crystal contains a very large number of atoms arranged in repeating unit cells.

Step 1 : Calculate Number of Moles

The number of moles present in the given sample is calculated using the formula:

Number of Moles = x / M

Here,

Symbol	Meaning
x	Mass of metal sample (g)
M	Molar mass of the metal (g mol⁻¹)

Step 2 : Calculate Number of Particles (Atoms)

One mole contains Avogadro's number of particles.

Therefore, the total number of particles is:

Number of Particles = (x × NA) / M

Here,

Symbol	Meaning
NA	Avogadro Constant = 6.022 × 10²³ mol⁻¹

Step 3 : Calculate Number of Unit Cells

Each unit cell contains a fixed number of particles.

This number depends on the type of crystal structure.

Structure	Particles in One Unit Cell (n)
Simple Cubic (SC)	1
Body-Centred Cubic (BCC)	2
Face-Centred Cubic (FCC)	4

The number of unit cells is calculated by dividing the total number of particles by the number of particles present in one unit cell.

Number of Unit Cells = Number of Particles / n

Formula Summary

Quantity	Formula
Number of Moles	x / M
Number of Particles	(x × NA) / M
Number of Unit Cells	Number of Particles ÷ n

Quick Revision

• Find moles first using x / M.
• Multiply moles by Avogadro Constant to get particles.
• Divide total particles by n to get the number of unit cells.
• SC → n = 1
• BCC → n = 2
• FCC → n = 4

1.8 Crystal Defects

What are Crystal Defects?

An ideal crystal has all its particles arranged in a perfect and regular pattern.

However, in real crystals, this perfect arrangement is usually disturbed.

These irregularities or imperfections in the crystal arrangement are called Crystal Defects.

Crystal defects may be formed during the formation of crystals or due to external conditions such as heating, cooling or pressure.

Why do Crystal Defects Occur?

• No crystal can be completely perfect.
• Some particles may be missing.
• Some particles may move from their original positions.
• Some foreign particles (impurities) may enter the crystal.
• Heating and cooling can also produce defects.

Types of Crystal Defects

Main Type	Examples
Point Defects	Vacancy Defect, Self-Interstitial Defect, Schottky Defect, Frenkel Defect, Impurity Defect
Non-Stoichiometric Defects	Metal Excess Defect, Metal Deficiency Defect

1.8.1 Point Defects

Definition

A point defect is a defect that affects only one lattice point or a very small region of the crystal.

Most point defects involve one or a few particles only.

Vacancy Defect

A vacancy defect is produced when one or more particles are missing from their normal lattice positions.

The vacant position is called a vacancy.

Because of the missing particles, the density of the crystal decreases.

Important Point

Missing particle → Vacancy is formed → Density decreases.

Self-Interstitial Defect

In this defect, an atom leaves its normal position and occupies an empty space between the lattice points.

This extra atom is called an interstitial atom.

Since additional atoms occupy the empty spaces, the density of the crystal increases slightly.

Important Point

Extra atom enters an empty space → Density increases slightly.

Difference Between Vacancy Defect and Self-Interstitial Defect

Vacancy Defect	Self-Interstitial Defect
Particles are missing.	Extra particles occupy interstitial spaces.
Density decreases.	Density increases slightly.
Vacancies are formed.	Interstitial atoms are formed.

Quick Revision

• Crystal defects are imperfections in a crystal.
• Point defects affect only one or a few lattice points.
• Vacancy defect is caused by missing particles.
• Vacancy defect decreases density.
• Self-interstitial defect is caused by extra atoms entering empty spaces.
• Self-interstitial defect increases density slightly.

Schottky Defect

Definition

A Schottky defect is a type of point defect found mainly in ionic crystals.

In this defect, an equal number of positive ions (cations) and negative ions (anions) are missing from their normal lattice positions.

Since both types of ions are missing in equal numbers, the electrical neutrality of the crystal is maintained.

Because some ions are missing, the mass of the crystal decreases while the volume remains almost the same.

Therefore, the density of the crystal decreases.

Important Points

• Occurs in ionic crystals.
• Equal number of cations and anions are missing.
• Electrical neutrality is maintained.
• Density decreases.

Examples

• NaCl
• KCl
• KBr
• CsCl

Frenkel Defect

Definition

A Frenkel defect is another type of point defect found in ionic crystals.

In this defect, a smaller positive ion leaves its normal lattice position and occupies an interstitial space.

The original lattice position becomes vacant, while the ion occupies a new position between the lattice points.

Since no ion leaves the crystal, the total number of ions remains the same.

Therefore, the density of the crystal does not change.

Important Points

• Small cation moves to an interstitial position.
• A vacancy and an interstitial ion are produced together.
• Electrical neutrality is maintained.
• Density remains unchanged.

Examples

• AgCl
• AgBr
• AgI
• ZnS

Difference Between Schottky Defect and Frenkel Defect

Schottky Defect	Frenkel Defect
Equal number of cations and anions are missing.	A small cation moves to an interstitial position.
Density decreases.	Density remains unchanged.
Vacancies are formed.	Both vacancy and interstitial ion are formed.
Occurs in ionic crystals with ions of similar size.	Occurs when cation is much smaller than anion.

Impurity Defect

Definition

An impurity defect is produced when a small amount of a different substance is added to a crystal.

The added substance is called an impurity.

The impurity particles occupy normal lattice positions or interstitial spaces.

The presence of impurities changes some physical properties of the crystal.

Important Points

• Produced by adding a different substance.
• Impurity particles enter the crystal.
• Electrical and physical properties may change.

Quick Revision

• Schottky defect → Equal number of cations and anions are missing.
• Schottky defect decreases density.
• Frenkel defect → Small cation moves to an interstitial position.
• Frenkel defect does not change density.
• Both Schottky and Frenkel defects maintain electrical neutrality.
• Impurity defect is produced by adding a different substance to the crystal.

Metal Excess Defect

Definition

A metal excess defect is a non-stoichiometric defect in which the crystal contains more metal ions than required by its chemical formula.

One common reason for this defect is the absence of some negative ions (anions) from their normal lattice positions.

The electrons left behind occupy these vacant positions to maintain electrical neutrality.

These trapped electrons are called F-centres or Colour Centres.

The presence of F-centres gives colour to crystals that are normally colourless.

Important Points

• Crystal contains excess metal.
• Some anions are missing.
• Electrons occupy the vacant positions.
• F-centres are formed.
• Crystal becomes coloured.

Example

Sodium chloride (NaCl) becomes yellow when heated in sodium vapour because F-centres are formed.

Metal Deficiency Defect

Definition

A metal deficiency defect is a non-stoichiometric defect in which the crystal contains fewer metal ions than required by its chemical formula.

This defect is produced when some metal ions are missing from their normal lattice positions.

To maintain electrical neutrality, nearby metal ions may change to a higher oxidation state.

Important Points

• Crystal contains fewer metal ions.
• Some metal ions are absent.
• Other metal ions change their oxidation state.
• Electrical neutrality is maintained.

Example

Iron(II) oxide (FeO) commonly shows metal deficiency defect.

F-Centres (Colour Centres)

Definition

An F-centre is an electron trapped in the vacant position of a missing negative ion.

These trapped electrons absorb certain wavelengths of light.

Because of this absorption, the crystal appears coloured.

Important Points

• F-centres are trapped electrons.
• They occupy anion vacancies.
• They produce colour in crystals.
• They are also called Colour Centres.

Examples

• NaCl becomes yellow.
• KCl becomes violet.
• LiCl becomes pink.

Summary of Crystal Defects

Defect	Main Feature	Density
Vacancy Defect	Particles are missing.	Decreases
Self-Interstitial Defect	Extra particle occupies interstitial space.	Increases slightly
Schottky Defect	Equal cations and anions are missing.	Decreases
Frenkel Defect	Small cation moves to interstitial position.	No Change
Impurity Defect	Foreign particles enter crystal.	May Change
Metal Excess Defect	Extra metal due to missing anions.	Depends on defect
Metal Deficiency Defect	Some metal ions are absent.	Depends on defect

Quick Revision

• Metal excess defect is caused by missing anions.
• Electrons trapped in anion vacancies form F-centres.
• F-centres produce colour in crystals.
• Metal deficiency defect is caused by missing metal ions.
• Iron(II) oxide (FeO) shows metal deficiency defect.
• NaCl becomes yellow due to F-centres.
• KCl becomes violet due to F-centres.
• LiCl becomes pink due to F-centres.

1.9 Electrical Properties of Solids

Introduction

Different solids conduct electricity in different ways.

Some solids allow electric current to pass through them easily, while others do not.

Based on their ability to conduct electricity, solids are divided into three groups.

• Conductors
• Insulators
• Semiconductors

Conductors

Conductors are substances that allow electric current to pass through them easily.

They contain a large number of free electrons.

These free electrons move easily when an electric field is applied.

Because of the movement of electrons, conductors show high electrical conductivity.

Examples

• Copper (Cu)
• Silver (Ag)
• Aluminium (Al)
• Iron (Fe)

Insulators

Insulators are substances that do not allow electric current to pass through them.

Their electrons are tightly bound to the atoms.

Since electrons cannot move freely, electricity cannot flow through the material.

Examples

• Glass
• Rubber
• Plastic
• Wood

Semiconductors

Semiconductors are substances whose electrical conductivity lies between conductors and insulators.

At low temperature, they conduct very little electricity.

As the temperature increases, their conductivity also increases.

Examples

• Silicon (Si)
• Germanium (Ge)

Band Theory

Band Theory explains why some solids conduct electricity while others do not.

When many atoms come together to form a solid, their atomic orbitals combine.

As a result, a large number of very closely spaced energy levels are formed.

These closely spaced energy levels together form an Energy Band.

Valence Band

The energy band occupied by valence electrons is called the Valence Band.

Normally, this band is completely filled with electrons.

Conduction Band

The higher energy band in which electrons are free to move is called the Conduction Band.

Electrons present in this band can move easily and conduct electricity.

Band Gap

The empty space between the valence band and the conduction band is called the Band Gap.

The size of the band gap determines whether a substance behaves as a conductor, insulator or semiconductor.

Comparison

Property	Conductors	Semiconductors	Insulators
Electrical Conductivity	High	Moderate	Very Low
Free Electrons	Many	Few	Almost None
Examples	Cu, Ag, Al	Si, Ge	Glass, Rubber

Quick Revision

• Conductors contain many free electrons.
• Insulators do not have free-moving electrons.
• Semiconductors have conductivity between conductors and insulators.
• Band Theory explains electrical conductivity.
• Valence Band contains valence electrons.
• Conduction Band contains free-moving electrons.
• Band Gap is the energy difference between the two bands.

Electrical Properties According to Band Theory

Conductors

In conductors, the valence band and conduction band overlap each other.

Because there is no energy gap, electrons move easily from one band to another.

Therefore, conductors allow electric current to pass very easily.

Key Point

Band Gap = Zero

Insulators

In insulators, the valence band is completely filled.

The conduction band is empty.

A very large band gap separates the two bands.

Electrons cannot cross this large energy gap.

Therefore, insulators do not conduct electricity.

Key Point

Large Band Gap

Semiconductors

Semiconductors have a small band gap.

At room temperature, some electrons gain enough energy to move into the conduction band.

These electrons conduct electricity.

Therefore, semiconductors conduct electricity better than insulators but not as well as conductors.

Key Point

Small Band Gap

Intrinsic Semiconductor

An intrinsic semiconductor is a pure semiconductor.

It does not contain any impurity atoms.

Its electrical conductivity depends only on temperature.

Examples

• Pure Silicon (Si)
• Pure Germanium (Ge)

Extrinsic Semiconductor

An extrinsic semiconductor is obtained by adding a very small amount of impurity to a pure semiconductor.

The process of adding impurity is called Doping.

Doping increases the electrical conductivity of the semiconductor.

n-Type Semiconductor

An n-type semiconductor is prepared by adding a pentavalent impurity.

Examples of pentavalent impurities are Phosphorus (P), Arsenic (As) and Antimony (Sb).

These atoms provide one extra electron.

Therefore, electrons become the majority charge carriers.

Majority Charge Carrier

Electrons

p-Type Semiconductor

A p-type semiconductor is prepared by adding a trivalent impurity.

Examples of trivalent impurities are Boron (B), Aluminium (Al) and Gallium (Ga).

These atoms create holes in the crystal.

Therefore, holes become the majority charge carriers.

Majority Charge Carrier

Holes

Difference Between n-Type and p-Type Semiconductors

n-Type	p-Type
Pentavalent impurity	Trivalent impurity
Majority carriers are electrons	Majority carriers are holes
Examples: P, As, Sb	Examples: B, Al, Ga

Chapter Formula Sheet

• Density = nM / a³NA
• SC : a = 2r
• BCC : √3a = 4r
• FCC : √2a = 4r
• Packing Efficiency = (Volume occupied / Volume of Unit Cell) × 100
• SC Packing Efficiency = 52.36%
• BCC Packing Efficiency = 68%
• FCC/HCP Packing Efficiency = 74%
• Moles = x / M
• Particles = (x × NA) / M
• Unit Cells = Number of Particles / n

Final Chapter Revision

• Crystalline solids have regular arrangement of particles.
• Amorphous solids have irregular arrangement.
• There are four types of crystalline solids.
• Crystal = Lattice + Basis.
• SC contains 1 particle, BCC contains 2 particles and FCC contains 4 particles.
• HCP and FCC have the highest packing efficiency (74%).
• Crystal defects change the arrangement of particles.
• Schottky defect decreases density.
• Frenkel defect does not change density.
• F-centres produce colour in crystals.
• Conductors have no band gap.
• Insulators have a large band gap.
• Semiconductors have a small band gap.
• Intrinsic semiconductors are pure.
• Extrinsic semiconductors are produced by doping.
• n-Type → Majority carriers are electrons.
• p-Type → Majority carriers are holes.

Electrical Properties According to Band Theory

Conductors

In conductors, the valence band and conduction band overlap each other.

Because there is no energy gap, electrons move easily from one band to another.

Therefore, conductors allow electric current to pass very easily.

Key Point

Band Gap = Zero

Insulators

In insulators, the valence band is completely filled.

The conduction band is empty.

A very large band gap separates the two bands.

Electrons cannot cross this large energy gap.

Therefore, insulators do not conduct electricity.

Key Point

Large Band Gap

Semiconductors

Semiconductors have a small band gap.

At room temperature, some electrons gain enough energy to move into the conduction band.

These electrons conduct electricity.

Therefore, semiconductors conduct electricity better than insulators but not as well as conductors.

Key Point

Small Band Gap

Intrinsic Semiconductor

An intrinsic semiconductor is a pure semiconductor.

It does not contain any impurity atoms.

Its electrical conductivity depends only on temperature.

Examples

• Pure Silicon (Si)
• Pure Germanium (Ge)

Extrinsic Semiconductor

An extrinsic semiconductor is obtained by adding a very small amount of impurity to a pure semiconductor.

The process of adding impurity is called Doping.

Doping increases the electrical conductivity of the semiconductor.

n-Type Semiconductor

An n-type semiconductor is prepared by adding a pentavalent impurity.

Examples of pentavalent impurities are Phosphorus (P), Arsenic (As) and Antimony (Sb).

These atoms provide one extra electron.

Therefore, electrons become the majority charge carriers.

Majority Charge Carrier

Electrons

p-Type Semiconductor

A p-type semiconductor is prepared by adding a trivalent impurity.

Examples of trivalent impurities are Boron (B), Aluminium (Al) and Gallium (Ga).

These atoms create holes in the crystal.

Therefore, holes become the majority charge carriers.

Majority Charge Carrier

Holes

Difference Between n-Type and p-Type Semiconductors

n-Type	p-Type
Pentavalent impurity	Trivalent impurity
Majority carriers are electrons	Majority carriers are holes
Examples: P, As, Sb	Examples: B, Al, Ga

Chapter Formula Sheet

• Density = nM / a³NA
• SC : a = 2r
• BCC : √3a = 4r
• FCC : √2a = 4r
• Packing Efficiency = (Volume occupied / Volume of Unit Cell) × 100
• SC Packing Efficiency = 52.36%
• BCC Packing Efficiency = 68%
• FCC/HCP Packing Efficiency = 74%
• Moles = x / M
• Particles = (x × NA) / M
• Unit Cells = Number of Particles / n

Final Chapter Revision

• Crystalline solids have regular arrangement of particles.
• Amorphous solids have irregular arrangement.
• There are four types of crystalline solids.
• Crystal = Lattice + Basis.
• SC contains 1 particle, BCC contains 2 particles and FCC contains 4 particles.
• HCP and FCC have the highest packing efficiency (74%).
• Crystal defects change the arrangement of particles.
• Schottky defect decreases density.
• Frenkel defect does not change density.
• F-centres produce colour in crystals.
• Conductors have no band gap.
• Insulators have a large band gap.
• Semiconductors have a small band gap.
• Intrinsic semiconductors are pure.
• Extrinsic semiconductors are produced by doping.
• n-Type → Majority carriers are electrons.
• p-Type → Majority carriers are holes.

Electrical Properties According to Band Theory

Conductors

In conductors, the valence band and conduction band overlap each other.

Because there is no energy gap, electrons move easily from one band to another.

Therefore, conductors allow electric current to pass very easily.

Key Point

Band Gap = Zero

Insulators

In insulators, the valence band is completely filled.

The conduction band is empty.

A very large band gap separates the two bands.

Electrons cannot cross this large energy gap.

Therefore, insulators do not conduct electricity.

Key Point

Large Band Gap

Semiconductors

Semiconductors have a small band gap.

At room temperature, some electrons gain enough energy to move into the conduction band.

These electrons conduct electricity.

Therefore, semiconductors conduct electricity better than insulators but not as well as conductors.

Key Point

Small Band Gap

Intrinsic Semiconductor

An intrinsic semiconductor is a pure semiconductor.

It does not contain any impurity atoms.

Its electrical conductivity depends only on temperature.

Examples

• Pure Silicon (Si)
• Pure Germanium (Ge)

Extrinsic Semiconductor

An extrinsic semiconductor is obtained by adding a very small amount of impurity to a pure semiconductor.

The process of adding impurity is called Doping.

Doping increases the electrical conductivity of the semiconductor.

n-Type Semiconductor

An n-type semiconductor is prepared by adding a pentavalent impurity.

Examples of pentavalent impurities are Phosphorus (P), Arsenic (As) and Antimony (Sb).

These atoms provide one extra electron.

Therefore, electrons become the majority charge carriers.

Majority Charge Carrier

Electrons

p-Type Semiconductor

A p-type semiconductor is prepared by adding a trivalent impurity.

Examples of trivalent impurities are Boron (B), Aluminium (Al) and Gallium (Ga).

These atoms create holes in the crystal.

Therefore, holes become the majority charge carriers.

Majority Charge Carrier

Holes

Difference Between n-Type and p-Type Semiconductors

n-Type	p-Type
Pentavalent impurity	Trivalent impurity
Majority carriers are electrons	Majority carriers are holes
Examples: P, As, Sb	Examples: B, Al, Ga

Chapter Formula Sheet

• Density = nM / a³NA
• SC : a = 2r
• BCC : √3a = 4r
• FCC : √2a = 4r
• Packing Efficiency = (Volume occupied / Volume of Unit Cell) × 100
• SC Packing Efficiency = 52.36%
• BCC Packing Efficiency = 68%
• FCC/HCP Packing Efficiency = 74%
• Moles = x / M
• Particles = (x × NA) / M
• Unit Cells = Number of Particles / n

Final Chapter Revision

• Crystalline solids have regular arrangement of particles.
• Amorphous solids have irregular arrangement.
• There are four types of crystalline solids.
• Crystal = Lattice + Basis.
• SC contains 1 particle, BCC contains 2 particles and FCC contains 4 particles.
• HCP and FCC have the highest packing efficiency (74%).
• Crystal defects change the arrangement of particles.
• Schottky defect decreases density.
• Frenkel defect does not change density.
• F-centres produce colour in crystals.
• Conductors have no band gap.
• Insulators have a large band gap.
• Semiconductors have a small band gap.
• Intrinsic semiconductors are pure.
• Extrinsic semiconductors are produced by doping.
• n-Type → Majority carriers are electrons.
• p-Type → Majority carriers are holes.