SOLID STATE | CHEMISTRY — CLASS 12 | CBSE

  

 

 

🔬 CHEMISTRY — CLASS 12

SOLID STATE

CHAPTER — 1

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📌 Topics Covered:

🔹 General Characteristics of Solid State

🔹 Amorphous & Crystalline Solids

🔹 Crystal Lattice & Unit Cell

🔹 Types of Cubic Unit Cells (SC, BCC, FCC)

🔹 Packing Efficiency & Density Calculations

🔹 Voids (Tetrahedral & Octahedral)

🔹 Imperfections in Solids (Point Defects)

🔹 Electrical & Magnetic Properties

 

✅ Simple Language  |  📊 Tables & Charts  |  🎯 Exam-Ready Notes

 

1. Introduction to Solid State

 

The solid state is one of the three fundamental states of matter. In solids, particles (atoms, ions, or molecules) are tightly packed and held together by strong intermolecular forces. Unlike liquids or gases, solids have a definite shape and volume.

 

🌟 Why is Solid State Important?

• Most materials we use daily — metals, glass, ceramics, salt — are solids.

• Understanding solids helps in designing semiconductors, medicines, and new materials.

• Solid-state chemistry is the foundation of electronics and materials science.

 

1.1 General Characteristics of Solids

All solids share some common properties. These characteristics arise due to the strong attractive forces between particles and their fixed positions.

 

Property	Description
Definite Shape	Solids do not change their shape on their own.
Definite Volume	Volume remains fixed regardless of container.
Incompressibility	Cannot be compressed easily (closely packed).
Rigidity	Particles cannot move freely; they vibrate in place.
High Density	Particles are very close to each other.
Low Diffusion	Particles cannot mix easily with other solids.

 

2. Types of Solids

 

Solids are broadly classified into two types based on the arrangement of their constituent particles:

 

2.1 Amorphous Solids (Greek: Amorphos = No Form)

In amorphous solids, particles are arranged in a random, irregular pattern. There is no long-range order. These are also called pseudo-solids or supercooled liquids.

 

📌 Key Features of Amorphous Solids

• No definite melting point — they soften over a range of temperature.

• Not true solids — they behave like liquids over very long time scales.

• Isotropic — same properties in all directions.

• Examples: Glass, Rubber, Plastics, Wax, Tar, Fibre Glass.

• Glass flows slowly over centuries — old cathedral windows are thicker at bottom!

 

2.2 Crystalline Solids (True Solids)

In crystalline solids, particles are arranged in a perfectly ordered, repeating 3D pattern called a crystal lattice. They have long-range order throughout the structure.

 

📌 Key Features of Crystalline Solids

• Sharp melting point — they melt at an exact temperature.

• Anisotropic — properties differ in different directions.

• True solids — rigid and maintain shape permanently.

• Examples: NaCl (Table salt), Diamond, Quartz, Sugar, Ice.

• They have flat faces, sharp edges, and characteristic angles.

 

2.3 Comparison: Amorphous vs Crystalline

Property	Amorphous	Crystalline	Example
Arrangement	Irregular	Regular/Ordered	—
Melting Point	Not sharp	Sharp & fixed	—
Shape	Irregular	Definite geometry	—
Isotropy	Isotropic	Anisotropic	—
Cleavage	Irregular break	Clean, flat cleavage	—
True Solid?	No (pseudo)	Yes	—
Example	Glass, Rubber	NaCl, Diamond	—

 

3. Classification of Crystalline Solids

 

Crystalline solids are classified into four types based on the nature of particles and the forces holding them together:

 

3.1 Ionic Solids

Ions (positive & negative) are arranged alternately in a crystal lattice and held by strong electrostatic forces.

✦  Particles: Cations (+) and Anions (−)

✦  Binding Force: Electrostatic (ionic) force

✦  Melting Point: Very HIGH (e.g., NaCl melts at 801°C)

✦  Hardness: Very hard and brittle

✦  Conductivity: Insulator in solid state; conductor when molten or dissolved

✦  Examples: NaCl, KCl, MgO, ZnS, CaF₂

 

3.2 Covalent / Network Solids

Atoms are connected by a continuous network of covalent bonds throughout the crystal — like a giant molecule.

✦  Particles: Atoms

✦  Binding Force: Covalent bonds

✦  Melting Point: Very HIGH (diamond > 3500°C)

✦  Hardness: Extremely hard (Diamond is hardest natural substance)

✦  Conductivity: Insulators (except Graphite — conductor due to free π electrons)

✦  Examples: Diamond, SiO₂ (Quartz), SiC, AlN

 

💡 Diamond vs Graphite — Same Element, Different Properties!

Diamond: Each carbon bonded to 4 others in tetrahedral arrangement → hardest solid, insulator.

Graphite: Each carbon bonded to 3 others in layers → soft (layers slide), good conductor.

This is called ALLOTROPY — same element, different crystalline forms.

 

3.3 Molecular Solids

Molecules are held together by weak intermolecular forces (van der Waals forces, dipole-dipole, or hydrogen bonds).

 

Sub-type	Details & Examples
Non-polar Molecular	Held by weak London dispersion forces. Very low MP. Examples: H₂, O₂, Cl₂, I₂, CO₂, CH₄, noble gases (Ar, Ne)
Polar Molecular	Held by dipole-dipole forces. Slightly higher MP. Examples: HCl, SO₂, H₂S
Hydrogen-bonded	Held by strong H-bonds. Highest MP among molecular. Examples: H₂O (ice), NH₃, HF

 

3.4 Metallic Solids

Metal atoms are arranged in a lattice and held together by a 'sea of delocalized electrons' — called the metallic bond.

✦  Particles: Positive metal ions (kernels) + free electrons

✦  Binding Force: Metallic bond (delocalized electron cloud)

✦  Melting Point: Variable (Hg = −39°C; W = 3422°C)

✦  Hardness: Variable (soft Na to hard Fe)

✦  Conductivity: Excellent — free electrons carry current

✦  Examples: Fe, Cu, Al, Ag, Au, Zn

 

🔑 Quick Summary — 4 Types of Crystalline Solids

1. Ionic Solids       → Ions         → Electrostatic  → Hard, Brittle, High MP   → NaCl

2. Covalent Solids    → Atoms         → Covalent bonds → Very Hard, Very High MP  → Diamond

3. Molecular Solids   → Molecules     → Weak forces    → Soft, Low MP             → Ice

4. Metallic Solids    → Atoms+e⁻      → Metallic bond  → Variable, Conductor      → Copper

 

4. Crystal Lattice and Unit Cell

 

The three-dimensional arrangement of particles (atoms/ions/molecules) in a crystal is called a Crystal Lattice or Space Lattice. It is a regular, repeating pattern extending in all three dimensions.

 

📖 Important Definitions

🔹 Lattice Point: The position in the lattice where a particle is located.

🔹 Crystal Lattice: The 3D arrangement of all lattice points.

🔹 Unit Cell: The smallest repeating portion of the crystal lattice.

🔹 Bravais Lattices: 14 types of unit cells classified into 7 crystal systems.

 

4.1 The 7 Crystal Systems

Based on the length of axes (a, b, c) and angles (α, β, γ) between them, all crystals fall into 7 systems:

Crystal System	Axial Lengths & Angles | Example
Cubic	a = b = c, α = β = γ = 90° | NaCl, Diamond, KCl
Tetragonal	a = b ≠ c, α = β = γ = 90° | SnO₂, TiO₂
Orthorhombic	a ≠ b ≠ c, α = β = γ = 90° | KNO₃, BaSO₄
Hexagonal	a = b ≠ c, α = β = 90°, γ = 120° | Mg, ZnO, Graphite
Rhombohedral	a = b = c, α = β = γ ≠ 90° | Calcite, Quartz
Monoclinic	a ≠ b ≠ c, α = γ = 90°, β ≠ 90° | Na₂SO₄·10H₂O
Triclinic	a ≠ b ≠ c, α ≠ β ≠ γ ≠ 90° | K₂Cr₂O₇, H₃BO₃

 

5. Types of Cubic Unit Cells

 

The cubic system is the most important and common in chemistry. There are three types of cubic unit cells:

 

5.1 Simple Cubic (SC) / Primitive Cubic

Atoms are present only at the 8 corners of the cube. Each corner atom is shared among 8 unit cells.

✦  Atoms per unit cell = 8 × (1/8) = 1

✦  Coordination Number = 6

✦  Packing Efficiency = 52.4%

✦  Example: Polonium (Po) — only metal with SC structure

 

5.2 Body-Centred Cubic (BCC)

One atom at each corner + one atom at the body centre of the cube.

✦  Atoms per unit cell = 8 × (1/8) + 1 = 1 + 1 = 2

✦  Coordination Number = 8

✦  Packing Efficiency = 68%

✦  Examples: Na, K, Cr, W, Mo, α-Fe, Ba

 

5.3 Face-Centred Cubic (FCC) / Cubic Close-Packing (CCP / ABCABC)

One atom at each corner + one atom at the centre of each face (6 faces). FCC is same as CCP structure.

✦  Atoms per unit cell = 8 × (1/8) + 6 × (1/2) = 1 + 3 = 4

✦  Coordination Number = 12

✦  Packing Efficiency = 74% (Most efficient cubic packing)

✦  Examples: Cu, Ag, Au, Al, Ni, NaCl (ionic), diamond cubic

 

📊 Comparison of Cubic Unit Cells

Property          | Simple Cubic (SC)    | BCC               | FCC/CCP

─────────────────────────────────────────────────────────────────────────

Atoms/Unit Cell   | 1                    | 2                 | 4

Coord. Number     | 6                    | 8                 | 12

Packing Eff.      | 52.4%                | 68%               | 74%

Void Space        | 47.6%                | 32%               | 26%

Example           | Polonium             | Na, Fe, Cr        | Cu, Ag, Au

 

6. Close Packing of Spheres

 

In a crystal, particles pack as closely as possible to minimize empty space. There are two important close-packed structures:

 

6.1 Hexagonal Close Packing (HCP) — ABAB pattern

In HCP, the second layer (B) is placed in the hollows of the first layer (A). The third layer is placed directly above the first layer (A). Pattern: ABABAB...

✦  Coordination Number = 12

✦  Packing Efficiency = 74%

✦  Examples: Mg, Zn, Ti, Be, Cd

 

6.2 Cubic Close Packing (CCP / FCC) — ABCABC pattern

The third layer (C) is placed differently from both A and B. Pattern: ABCABC...

✦  Coordination Number = 12

✦  Packing Efficiency = 74% (same as HCP)

✦  Examples: Cu, Ag, Au, Al, Ni

 

💡 Key Insight: HCP vs CCP

Both HCP and CCP have the SAME packing efficiency (74%) and coordination number (12).

They differ only in the stacking sequence of layers.

HCP: ABABAB...  (hexagonal symmetry)

CCP: ABCABC...  (cubic symmetry = FCC)

 

6.3 Voids in Close-Packed Structures

When spheres pack together, empty spaces (voids/holes) are left. These voids are very important because smaller atoms/ions can fit into them.

 

Type of Void	Description
Tetrahedral Void	Formed when a sphere of second layer is above the triangular void of first layer. Surrounded by 4 spheres. Smaller size — radius ratio = 0.225r.
Octahedral Void	Formed between 3 spheres of layer A and 3 of layer B. Surrounded by 6 spheres. Larger size — radius ratio = 0.414r.

 

📌 Number of Voids Formula

If 'n' = number of close-packed spheres in a unit cell:

🔹 Number of Tetrahedral Voids = 2n

🔹 Number of Octahedral Voids  = n

So: For FCC (n = 4):  Tetrahedral voids = 8,  Octahedral voids = 4

 

7. Density of Unit Cell

 

One of the most important numerical calculations in Solid State Chemistry is finding the density of a crystal using unit cell parameters.

 

🔢 DENSITY FORMULA

Z × M

d  =  ─────────

NA × a³

Where:

d  = density of the crystal (g/cm³)

Z  = number of atoms per unit cell  (SC=1, BCC=2, FCC=4)

M  = molar mass of the element (g/mol)

NA = Avogadro's number = 6.022 × 10²³ mol⁻¹

a  = edge length of the unit cell (in cm)

a³ = volume of the unit cell

 

Solved Example

✏️ Example Problem

Q: An element has BCC structure with edge length a = 287 pm. Molar mass = 56 g/mol.

Calculate the density of the element.

Solution:

Z = 2 (BCC), M = 56 g/mol, a = 287 pm = 287 × 10⁻¹⁰ cm

NA = 6.022 × 10²³ mol⁻¹

d = (Z × M) / (NA × a³)

= (2 × 56) / (6.022 × 10²³ × (287 × 10⁻¹⁰)³)

= 112 / (6.022 × 10²³ × 2.364 × 10⁻²³)

= 112 / 14.23

≈ 7.87 g/cm³

Answer: Density ≈ 7.87 g/cm³  (This element is Iron — Fe!)

 

8. Imperfections / Defects in Solids

 

A perfect crystal would have all particles in their correct positions at 0 K. In reality, all crystals have some imperfections. These are called Crystal Defects.

 

📌 Types of Defects

1. Point Defects — Missing, extra, or misplaced atoms at lattice points.

2. Line Defects — Defects along a row of atoms.

3. Planar Defects — Defects at grain boundaries.

In Class 12, we mainly study POINT DEFECTS.

 

8.1 Stoichiometric Defects (No change in composition)

 

Defect	Description, Occurs In & Effect
Vacancy Defect	Some lattice sites are empty. Occurs in non-ionic solids when heated. Decreases density.
Interstitial Defect	Extra atoms occupy interstitial spaces. Occurs in non-ionic solids. Increases density.
Schottky Defect	Equal number of cations and anions are missing. Occurs in ionic solids with similar sized ions. Decreases density. Example: NaCl, KCl, AgBr.
Frenkel Defect	Smaller ions leave lattice and occupy interstitial spaces. No change in density. Occurs in ionic solids with large size difference. Example: ZnS, AgCl, AgBr, AgI.

 

🔑 Schottky vs Frenkel — Quick Difference

Schottky Defect:  Ions are MISSING → Density DECREASES  → NaCl (equal sized ions)

Frenkel Defect:   Ions DISPLACED  → Density UNCHANGED  → ZnS, AgCl (unequal sized ions)

AgBr shows BOTH Schottky and Frenkel defects — used in photographic films!

 

8.2 Non-Stoichiometric Defects (Change in composition ratio)

Defect	Description & Example
Metal Excess Defect (F-Centre)	Extra cations occupy interstitial spaces, electrons fill anion vacancies. These electrons absorb visible light → crystal appears coloured. Example: NaCl heated in Na vapour turns yellow; KCl turns violet/lilac.
Metal Deficiency Defect	Fewer cations than anions. Some metal ions exist in higher oxidation states. Example: FeO — always Fe₀.₉₅O instead of FeO; some Fe³⁺ present.

 

💡 F-Centre (Farbe = Colour)

When NaCl crystals are heated in Na vapour → Na atoms deposit on surface → extra Na⁺ ions

enter lattice → Cl⁻ vacancies are filled by electrons → these electrons are called F-centres.

F-centres absorb light and make the crystal appear coloured.

NaCl + Na vapour → Yellow crystal

KCl + K vapour → Violet/Lilac crystal

 

8.3 Impurity Defects

When a foreign atom/ion enters the crystal lattice, it creates an impurity defect.

✦  Substitutional Impurity: Foreign ion replaces host ion. Example: SrCl₂ added to NaCl → Sr²⁺ replaces Na⁺. Each Sr²⁺ creates one cation vacancy to maintain electrical neutrality.

✦  Interstitial Impurity: Foreign atom occupies void. Example: Carbon in iron (steel formation).

 

9. Electrical Properties of Solids

 

Solids can be classified based on their ability to conduct electricity. This depends on the band structure — the arrangement of energy levels (bands) in a solid.

 

9.1 Band Theory of Solids

In isolated atoms, electrons occupy discrete energy levels. When atoms come together in a crystal, these levels broaden into energy BANDS.

✦  Valence Band (VB): Filled with valence electrons.

✦  Conduction Band (CB): Empty or partially filled band where electrons can move freely.

✦  Forbidden Gap (Band Gap): Energy gap between VB and CB.

 

Type of Solid	Band Structure & Conductivity
Conductors (Metals)	VB and CB overlap OR CB is partially filled. No band gap. Conductivity: 10⁴ – 10⁷ S/m. Examples: Cu, Ag, Al, Fe
Insulators	Large band gap (> 3 eV). Electrons cannot jump to CB. Conductivity: < 10⁻²⁰ S/m. Examples: Diamond, Wood, Plastic, Glass
Semiconductors	Small band gap (~1 eV). Electrons can jump at room temperature or by heating/doping. Conductivity: 10⁻⁶ to 10⁴ S/m. Examples: Si, Ge, GaAs

 

9.2 Types of Semiconductors

🔬 Intrinsic Semiconductors

Pure semiconductors with small band gap.

Conductivity is due to thermal excitation of electrons.

Examples: Pure Silicon (Si), Pure Germanium (Ge)

At 0 K → insulator. At room temperature → slight conductivity.

 

🔬 Extrinsic Semiconductors (Doped)

Conductivity is increased by adding impurities (doping).

n-type Semiconductor:

• Doped with Group 15 element (P, As, Sb) into Group 14 (Si, Ge)

• Extra electron available → electrons are majority charge carriers

• Example: Si doped with Phosphorus (P)

p-type Semiconductor:

• Doped with Group 13 element (B, Al, Ga) into Group 14 (Si, Ge)

• One electron less → hole is created → holes are majority charge carriers

• Example: Si doped with Boron (B)

 

10. Magnetic Properties of Solids

 

The magnetic behaviour of a substance depends on the number of unpaired electrons in its atoms or ions. Paired electrons create opposing magnetic moments that cancel, while unpaired electrons create net magnetic moments.

 

Type	Description & Examples
Diamagnetic	All electrons are PAIRED. Weakly REPELLED by magnetic field. Very weak effect. Examples: NaCl, TiO₂, Cu, Zn, H₂O, Benzene
Paramagnetic	Has UNPAIRED electrons. Weakly ATTRACTED by magnetic field. Effect lost when field is removed. Examples: O₂, Cu²⁺, Fe³⁺, CuO, TiO
Ferromagnetic	Unpaired electrons spontaneously align parallel in same direction — magnetic domains form. Strongly attracted. Retain magnetism permanently. Examples: Fe, Co, Ni, CrO₂ (used in audio tapes)
Antiferromagnetic	Magnetic moments alternate — cancel each other. Net magnetism = 0. Examples: MnO, MnO₂, Cr₂O₃, V₂O₃
Ferrimagnetic	Unequal number of parallel and anti-parallel magnetic moments. Net magnetism is small but non-zero. Examples: Fe₃O₄ (magnetite), ZnFe₂O₄, MgFe₂O₄

 

💡 Easy Memory Trick for Magnetic Properties

DIA  → Dull, Indifferent, Away from magnet (repelled)  → ALL paired electrons

PARA → Partially attracted (weak)  → Some unpaired electrons

FERRO→ Strongly pulled  → Large domains aligned  → Fe, Co, Ni

FERRI→ FERRIte (mixed oxides)  → Unequal anti-parallel moments  → Fe₃O₄

ANTI → Anti = cancel each other → Equal anti-parallel moments → MnO

 

11. Important Formulae & Quick Revision

 

 

📐 All Important Formulae at a Glance

1. DENSITY:  d = (Z × M) / (NA × a³)

2. PACKING EFFICIENCY = (Volume occupied by atoms in unit cell / Total volume) × 100

SC  = (π/6)  = 52.4%

BCC = (π√3/8) = 68%

FCC = (π/3√2) = 74%

3. NUMBER OF VOIDS (in CCP/HCP, n = number of atoms):

Tetrahedral voids = 2n

Octahedral voids  = n

4. RADIUS RATIOS for Voids:

Tetrahedral void: r/R = 0.225

Octahedral void:  r/R = 0.414

Cubic void:       r/R = 0.732

5. ATOMS PER UNIT CELL:

Corner atom  → shared by 8 cells → contributes 1/8

Edge atom    → shared by 4 cells → contributes 1/4

Face atom    → shared by 2 cells → contributes 1/2

Body centre  → 1 cell only        → contributes 1

 

Quick Revision Table

Structure	Z (Atoms)	CN	Pack. Eff.
SC (Primitive)	1	6	52.4%
BCC	2	8	68%
FCC/CCP	4	12	74%
HCP	6 (full cell)	12	74%

 

⭐ EXAM IMPORTANT POINTS

1. Schottky Defect → DECREASES density (NaCl, KCl, KBr)

2. Frenkel Defect  → NO change in density (ZnS, AgCl, AgBr)

3. AgBr shows BOTH Schottky and Frenkel defects

4. F-Centre → responsible for colour in crystals (NaCl → yellow when heated in Na vapour)

5. CrO₂ is ferromagnetic → used in magnetic audio/video tapes

6. Fe₃O₄ is ferrimagnetic (also called magnetite/lodestone)

7. Graphite is covalent solid but good conductor (due to delocalized π electrons in layers)

8. Diamond is hardest natural substance (each C bonded to 4 C in tetrahedral arrangement)

9. In n-type semiconductor: electrons are majority carriers (doped with Group 15)

10. In p-type semiconductor: holes are majority carriers (doped with Group 13)

 

 

🎯 END OF CHAPTER 1 — SOLID STATE 🎯

Best of luck for your exams! Keep learning and keep growing. ✨