Chemistry: Solid state
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Solid State - (Part 1)
Topics Covered:
- Introduction
- Types of Solids
- Isomorphism & Polymorphism
- Classification of Crystalline Solids
- Crystal Structure
- Unit Cell
- Cubic Crystal System
1.1 Introduction
A solid is a state of matter in which particles are held together by strong intermolecular forces. Therefore, solids have:
- ✔ Definite shape
- ✔ Definite volume
- ✔ Very little compressibility
- ✔ Very small effect of temperature and pressure
The constituent particles of solids may be:
- Atoms
- Ions
- Molecules
Strong interparticle forces are responsible for the definite shape and volume of solids.
1.2 Types of Solids
Solids are classified into two types:
- Crystalline Solids
- Amorphous Solids
A. Crystalline Solids
Definition:
A crystalline solid is a solid in which particles are arranged in a regular, repeating and orderly pattern.
Properties
- Regular arrangement of particles (Long-range order)
- Sharp melting point
- Anisotropic (Properties vary with direction)
- Well-defined crystal shape
Examples
- NaCl
- Ice
- Diamond
- Graphite
- Gold
- Copper
- Ceramics
Crystalline = Crystal = Perfect Order
B. Amorphous Solids
Definition:
Amorphous solids are solids in which particles are arranged randomly. They are also called supercooled liquids.
Properties
- Random arrangement
- No long-range order
- Melt over a range of temperatures
- Isotropic (Same properties in all directions)
Examples
- Glass
- Plastic
- Rubber
- Tar
- Metallic Glass
Amorphous = A Mess (Random Arrangement)
Difference Between Crystalline and Amorphous Solids
| Crystalline | Amorphous |
|---|---|
| Regular arrangement | Random arrangement |
| Sharp melting point | Melt over a range |
| Anisotropic | Isotropic |
| Long-range order | Short-range order |
| Example: NaCl | Example: Glass |
1.2.3 Isomorphism and Polymorphism
Isomorphism
Different substances having the same crystal structure are called isomorphous substances.
Examples- NaF and MgO
- NaNO₃ and CaCO₃
Polymorphism
The existence of the same substance in different crystal structures is called polymorphism.
- Calcite
- Aragonite
Both are forms of CaCO₃.
Allotropy
Polymorphism shown by an element is called allotropy.
- Diamond
- Graphite
- Fullerene
One-Line Revision
- ✔ Crystalline → Regular arrangement
- ✔ Amorphous → Random arrangement
- ✔ Isomorphism → Different substances, same crystal structure
- ✔ Polymorphism → Same substance, different crystal structures
- ✔ Allotropy → Polymorphism in elements
- ✔ Crystal = Lattice + Basis
- ✔ Smallest repeating unit = Unit Cell
- ✔ SC = 1 Atom
- ✔ BCC = 2 Atoms
- ✔ FCC = 4 Atoms
Solid State - (Part 2)
- Density of Unit Cell
- Packing of Particles
- Close Packing
- Coordination Number
- Tetrahedral & Octahedral Voids
- Packing Efficiency
- Important Formula Sheet
1.5.2 Density of a Unit Cell
The density of a crystal is calculated using the following formula:
Where,
| Symbol | Meaning |
|---|---|
| ρ | Density |
| n | Number of atoms per unit cell |
| M | Molar mass |
| a | Edge length of unit cell |
| NA | Avogadro Number (6.022 × 10²³) |
- Find Density
- Find Edge Length
- Find Molar Mass
- Find Number of Atoms
Number of Atoms in Cubic Unit Cells
| Unit Cell | Number of Atoms |
|---|---|
| Simple Cubic (SC) | 1 |
| Body-Centred Cubic (BCC) | 2 |
| Face-Centred Cubic (FCC) | 4 |
1.6 Packing of Particles
Packing refers to the arrangement of atoms in a crystal so that they occupy maximum possible space.
- Better packing → Less empty space
- Better packing → More stability
Coordination Number (CN)
Coordination Number is the number of nearest neighbouring atoms touching a particular atom.
- Better Packing
- Less Empty Space
- Greater Stability
Close Packing in One Dimension
Atoms are arranged in a straight line.
Each atom touches two neighbouring atoms.
A. Square Close Packing
● ● ● ●
● ● ● ●
- Layer Sequence = AAAA....
- Coordination Number = 4
B. Hexagonal Close Packing
● ● ● ●
● ● ●
- Layer Sequence = ABAB....
- Coordination Number = 6
- More Efficient than Square Packing
Three-Dimensional Packing
1. Simple Cubic (SC)
- Layer Sequence = AAAA....
- Coordination Number = 6
- Example: Polonium (Po)
2. Hexagonal Close Packing (HCP)
- Layer Sequence = ABAB....
- Coordination Number = 12
- Examples: Magnesium (Mg), Zinc (Zn)
3. Cubic Close Packing (CCP/FCC)
- Layer Sequence = ABCABC....
- Same as Face-Centred Cubic
- Coordination Number = 12
- Examples: Copper (Cu), Silver (Ag), Gold (Au)
Comparison of Packing
| Structure | Layer Sequence | Coordination Number |
|---|---|---|
| SC | AAAA | 6 |
| HCP | ABAB | 12 |
| FCC / CCP | ABCABC | 12 |
Voids in Crystal
Voids are empty spaces present between atoms.
Tetrahedral Void
- Surrounded by 4 atoms
- Shape = Tetrahedron
Octahedral Void
- Surrounded by 6 atoms
- Shape = Octahedron
Number of Voids
If the number of atoms is N, then:
| Void | Formula |
|---|---|
| Tetrahedral Voids | 2N |
| Octahedral Voids | N |
Tetra = Twice (2N)
Octa = Once (N)
Packing Efficiency
Packing efficiency is the percentage of space occupied by atoms.
(Volume Occupied by Atoms ÷ Volume of Unit Cell) × 100
Packing Efficiency of Different Unit Cells
Simple Cubic (SC)
- Radius Relation → a = 2r
- Packing Efficiency = 52.4%
- Void Space = 47.6%
Body-Centred Cubic (BCC)
- Radius Relation → 4r = √3a
- Packing Efficiency = 68%
- Void Space = 32%
Face-Centred Cubic (FCC)
- Radius Relation → 4r = √2a
- Packing Efficiency = 74%
- Void Space = 26%
Comparison Table
| Crystal | Radius Relation | Coordination Number | Packing Efficiency |
|---|---|---|---|
| SC | a = 2r | 6 | 52.4% |
| BCC | 4r = √3a | 8 | 68% |
| FCC | 4r = √2a | 12 | 74% |
| HCP | Same as FCC | 12 | 74% |
Important Formula Sheet
Density Formula
ρ = nM / (a³NA)
Radius Relations
- SC → a = 2r
- BCC → 4r = √3a
- FCC → 4r = √2a
Packing Efficiency
- SC = 52.4%
- BCC = 68%
- FCC = 74%
- HCP = 74%
Coordination Number
- SC = 6
- BCC = 8
- FCC = 12
- HCP = 12
Number of Atoms
- SC = 1
- BCC = 2
- FCC = 4
Voids
- Tetrahedral = 2N
- Octahedral = N
Quick Revision
- ✔ SC → 1 Atom → CN = 6 → Packing = 52.4%
- ✔ BCC → 2 Atoms → CN = 8 → Packing = 68%
- ✔ FCC → 4 Atoms → CN = 12 → Packing = 74%
- ✔ HCP → CN = 12 → Packing = 74%
- ✔ Tetrahedral Voids = 2N
- ✔ Octahedral Voids = N
- ✔ Density Formula = nM / (a³NA)
Solid State - (Part 3A)
- Number of Particles & Unit Cells
- Crystal Defects
- Point Defects
- Vacancy Defect
- Self Interstitial Defect
- Schottky Defect
- Frenkel Defect
- Impurity Defects
- Non-Stoichiometric Defects
1.7.4 Number of Particles and Unit Cells
The number of particles and unit cells present in a given mass of a crystalline substance can be calculated using density and unit cell parameters.
Number of Particles =
(x × NA) / M
Number of Unit Cells =
x / (ρa³)
Where,
- x = Mass of crystal
- ρ = Density
- a = Edge length
- NA = Avogadro Number
- M = Molar Mass
If density and edge length are given, first calculate the number of unit cells and then calculate the number of atoms.
Solved Concept
In an FCC crystal,
- Corner atom contribution = 1/8
- Face atom contribution = 1/2
Example:
If element C occupies corners and D occupies face centres,
Number of C atoms = 8 × 1/8 = 1
Number of D atoms = 6 × 1/2 = 3
1.8 Crystal Defects
Real crystals are never perfectly arranged. They contain small irregularities called crystal defects.
Crystal defects are irregularities present in the regular arrangement of atoms, ions or molecules in a crystal.
Why do defects occur?
- During crystallization
- Rapid cooling
- Heating
- Addition of impurities
Types of Crystal Defects
| Type | Description |
|---|---|
| Point Defects | Defects involving one or few lattice points |
| Line Defects | Defects along a line |
| Plane Defects | Defects over a plane |
In this chapter, only Point Defects are important.
Point Defects
Point defects are irregularities produced at lattice points.
There are three major classes of point defects.
- Stoichiometric Defects
- Impurity Defects
- Non-Stoichiometric Defects
A. Stoichiometric Defects
In these defects, the chemical formula of the compound remains unchanged. The ratio of cations and anions remains the same.
Types
- Vacancy Defect
- Self Interstitial Defect
- Schottky Defect
- Frenkel Defect
1. Vacancy Defect
A particle is missing from its regular lattice position. The empty position is called a vacancy.
Characteristics
- Particle is absent from lattice.
- Vacancy is created.
- Occurs during crystallization or heating.
Missing Particle → Vacancy Defect
2. Self Interstitial Defect
Some atoms leave their normal lattice positions and occupy interstitial spaces.
Two Cases
- Extra atom occupies an interstitial space.
- An existing atom shifts to an interstitial site.
Effects
- Density may increase if an extra atom enters.
- Density remains unchanged if an existing atom only shifts.
Interstitial = Atom enters empty space.
Solid State - (Part 3B)
- Electrical Properties of Solids
- Band Theory
- Conductors
- Insulators
- Semiconductors
- Intrinsic Semiconductors
1.9 Electrical Properties of Solids
Solids show a wide range of electrical conductivity. Based on their conductivity, solids are classified into three categories.
- Conductors
- Insulators
- Semiconductors
Electrical conductivity tells us how easily electricity passes through a material.
Classification of Solids
| Type | Conductivity | Examples |
|---|---|---|
| Conductors | Very High | Cu, Ag, Al |
| Insulators | Very Low | Rubber, Glass, Plastic |
| Semiconductors | Intermediate | Silicon (Si), Germanium (Ge) |
1.9.1 Band Theory
Band theory explains why some solids conduct electricity while others do not.
When many atoms come together to form a crystal, their atomic orbitals overlap and form energy bands.
- Conduction Band
- Valence Band
- Band Gap
1. Conduction Band
The conduction band is the higher energy band.
- Contains free electrons.
- Electrons move easily.
- Responsible for electrical conduction.
2. Valence Band
The valence band is the lower energy band.
- Contains bound electrons.
- Electrons cannot move freely.
- Normally filled with electrons.
3. Band Gap
Band gap is the energy difference between the valence band and the conduction band.
Importance of Band Gap
- Small band gap → Better conductivity
- Large band gap → Poor conductivity
Band Gap of Some Materials
| Material | Band Gap (eV) |
|---|---|
| Sodium | 0 |
| Germanium | 0.67 |
| Silicon | 1.12 |
| Diamond | 5.47 |
Diamond is an insulator because it has a very large band gap.
1.9.2 Conductors
Conductors allow electricity to pass easily.
Characteristics
- Large number of free electrons.
- Conduction band is partially filled or overlaps with the valence band.
- Very high electrical conductivity.
Examples
- Copper
- Silver
- Gold
- Aluminium
1.9.3 Insulators
Insulators do not allow electricity to pass through them easily.
Characteristics
- Valence band completely filled.
- Conduction band empty.
- Very large band gap.
- Almost no free electrons.
Examples
- Glass
- Plastic
- Rubber
- Diamond
1.9.4 Semiconductors
Semiconductors have conductivity between conductors and insulators.
Examples
- Silicon (Si)
- Germanium (Ge)
Characteristics
- Small band gap.
- Few electrons enter the conduction band at room temperature.
- Conductivity increases with temperature.
Conductivity of metals decreases with temperature, whereas conductivity of semiconductors increases with temperature.
Intrinsic Semiconductors
A pure semiconductor without any impurity is called an Intrinsic Semiconductor.
Properties
- Pure Silicon or Germanium.
- Very low conductivity.
- Conductivity increases on heating.
- Equal number of electrons and holes.
A hole is the empty space left behind when an electron moves from the valence band to the conduction band.
Quick Revision
- ✔ Conductors → High conductivity
- ✔ Insulators → Very low conductivity
- ✔ Semiconductors → Intermediate conductivity
- ✔ Conduction Band → Free electrons
- ✔ Valence Band → Bound electrons
- ✔ Band Gap → Difference between conduction & valence bands
- ✔ Silicon & Germanium → Semiconductors
- ✔ Intrinsic Semiconductor → Pure semiconductor
1.9.5 Extrinsic Semiconductors
The electrical conductivity of a semiconductor can be increased by adding a small amount of impurity.
This process is called Doping, and the impurity added is called a Dopant.
Extrinsic Semiconductor = Pure Semiconductor + Dopant
Doping
Doping is the process of adding a very small amount of impurity to a pure semiconductor to increase its conductivity.
Advantages of Doping
- Increases electrical conductivity.
- Creates more charge carriers.
- Used in electronic devices.
n-Type Semiconductor
An n-type semiconductor is obtained by doping Silicon (Si) or Germanium (Ge) with Group 15 elements.
Dopants Used
- Phosphorus (P)
- Arsenic (As)
- Antimony (Sb)
Working
- Group 15 elements have 5 valence electrons.
- Four electrons form covalent bonds.
- One electron remains free.
- The extra electron becomes a charge carrier.
Electrons
N = Negative = Electrons
p-Type Semiconductor
A p-type semiconductor is obtained by doping Silicon (Si) or Germanium (Ge) with Group 13 elements.
Dopants Used
- Boron (B)
- Gallium (Ga)
- Indium (In)
Working
- Group 13 elements have 3 valence electrons.
- One covalent bond remains incomplete.
- An empty space called a hole is created.
- The hole behaves as a positive charge carrier.
Holes
P = Positive = Holes
Difference Between n-Type and p-Type
| Property | n-Type | p-Type |
|---|---|---|
| Dopant Group | 15 | 13 |
| Examples | P, As, Sb | B, Ga, In |
| Major Charge Carrier | Electrons | Holes |
| Minor Charge Carrier | Holes | Electrons |
1.10 Magnetic Properties of Solids
Magnetic properties arise due to the spinning motion of electrons.
On the basis of magnetic behaviour, solids are classified into three types.
- Diamagnetic
- Paramagnetic
- Ferromagnetic
1. Diamagnetic Substances
Diamagnetic substances contain only paired electrons.
Characteristics
- Weakly repelled by magnetic field.
- No permanent magnetic moment.
- All electrons are paired.
Examples
- NaCl
- H₂O
- N₂
- Benzene
2. Paramagnetic Substances
Paramagnetic substances contain one or more unpaired electrons.
Characteristics
- Weakly attracted by magnetic field.
- Magnetism disappears when the field is removed.
Examples
- O₂
- Cu²⁺
- Fe³⁺
- Cr³⁺
3. Ferromagnetic Substances
Ferromagnetic substances contain a large number of unpaired electrons.
Characteristics
- Strongly attracted by magnetic field.
- Can be permanently magnetized.
- Retain magnetism after removing the magnetic field.
Examples
- Iron (Fe)
- Cobalt (Co)
- Nickel (Ni)
- Gadolinium (Gd)
- CrO₂
Comparison of Magnetic Substances
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| Electrons | Paired | Unpaired | Many Unpaired |
| Behaviour | Repelled | Weakly Attracted | Strongly Attracted |
| Permanent Magnet | No | No | Yes |
Board Exam Quick Revision
- ✔ Doping increases conductivity.
- ✔ n-Type → Group 15 Dopant → Electrons.
- ✔ p-Type → Group 13 Dopant → Holes.
- ✔ Conductors → High conductivity.
- ✔ Insulators → Large band gap.
- ✔ Semiconductors → Small band gap.
- ✔ Diamagnetic → Paired electrons.
- ✔ Paramagnetic → Unpaired electrons.
- ✔ Ferromagnetic → Strongly magnetic.
Memory Tricks
- N-Type = Negative = Electrons
- P-Type = Positive = Holes
- Paired = Diamagnetic
- Unpaired = Paramagnetic
- Many Unpaired = Ferromagnetic
- Small Band Gap = Better Conductivity
- Large Band Gap = Poor Conductivity
End of Chapter - Final Formula Sheet
| Concept | Important Point |
|---|---|
| Conductor | High Conductivity |
| Insulator | Large Band Gap |
| Semiconductor | Small Band Gap |
| Intrinsic | Pure Semiconductor |
| Extrinsic | Doped Semiconductor |
| n-Type | Electrons are Majority Carriers |
| p-Type | Holes are Majority Carriers |
| Diamagnetic | Paired Electrons |
| Paramagnetic | Unpaired Electrons |
| Ferromagnetic | Strong Permanent Magnet |
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