Topic 7.1.47 min read
Unit Cell and Crystal Lattice
A unit cell is the smallest repeating three-dimensional portion of a crystal. Repetition of the unit cell forms the crystal lattice; the basis consists of atoms, ions or molecules associated with lattice points.
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Beginner Level
A crystal is built by repeating a tiny three-dimensional building block called a unit cell. Repeating it in every direction makes the full crystal lattice.
Recommended for Class 11
Unit Cell and Crystal Lattice
Overview
A unit cell is the smallest repeating three-dimensional portion of a crystal. Repetition of the unit cell forms the crystal lattice; the basis consists of atoms, ions or molecules associated with lattice points.
Learning Outcomes
- Unit cell is the smallest repeating crystal portion.
- Crystal lattice is generated by repeating the unit cell in three dimensions.
- Basis means the particles placed at lattice points.
- SC, BCC and FCC contain 1, 2 and 4 effective atoms per unit cell.
- Unit cells are described by sides a, b, c and angles α, β, γ.
- Seven crystal systems arise from different side and angle relations.
Intermediate Level
Unit Cell, Lattice and Basis
| Term | Meaning |
|---|---|
| Unit cell | smallest repeating three-dimensional portion |
| Lattice | imaginary periodic arrangement of points |
| Basis | atom, ion or molecule attached to each lattice point |
| Crystal structure | lattice plus basis |
Counting Effective Atoms
A corner atom is shared by eight cells and contributes 18. A face atom is shared by two cells and contributes 12. A body-centre atom belongs fully to one cell.
| Cubic cell | Locations | Effective atoms |
|---|---|---|
| Simple cubic (SC) | 8 corners | 1 |
| Body-centred cubic (BCC) | 8 corners + 1 body centre | 2 |
| Face-centred cubic (FCC) | 8 corners + 6 face centres | 4 |
Lattice Parameters
A unit cell has side lengths a, b and c, and interaxial angles α, β and γ.
Seven Crystal Systems
| System | Side relation | Angle relation |
|---|---|---|
| Cubic | a = b = c | α = β = γ = 90° |
| Tetragonal | a = b ≠ c | all 90° |
| Orthorhombic | a ≠ b ≠ c | all 90° |
| Rhombohedral | a = b = c | α = β = γ ≠ 90° |
| Monoclinic | a ≠ b ≠ c | α = γ = 90°, β ≠ 90° |
| Triclinic | a ≠ b ≠ c | α ≠ β ≠ γ ≠ 90° |
| Hexagonal | a = b ≠ c | α = β = 90°, γ = 120° |
Solved Counting Examples
FCC Atom Count
Find the effective number of atoms in an FCC unit cell.
- 8 corner atoms
- 6 face atoms
Corners: 8 × 18 = 1
Faces: 6 × 12 = 3
Total = 1 + 3
Final answer: 4 atoms per unit cell
Common Mistakes
- Classify a solid from particle arrangement, not appearance alone.
- Use crystalline, polycrystalline, polymeric and amorphous precisely.
- Support comparisons with structure and physical properties.
Short-Question Preparation
Q. Define a unit cell.
A. The smallest basic portion that repeats in three dimensions to form a crystal.
Q. Define crystal lattice.
A. The structure obtained by periodic repetition of unit cells or lattice points.
Q. How many effective atoms are in SC, BCC and FCC?
A. SC has 1, BCC has 2 and FCC has 4.
Q. Name the seven crystal systems.
A. Cubic, tetragonal, orthorhombic, rhombohedral, monoclinic, triclinic and hexagonal.
Sticky Notes
- Unit cell is the smallest repeating crystal portion.
- Crystal lattice is generated by repeating the unit cell in three dimensions.
- Basis means the particles placed at lattice points.
- SC, BCC and FCC contain 1, 2 and 4 effective atoms per unit cell.
- Unit cells are described by sides a, b, c and angles α, β, γ.
- Seven crystal systems arise from different side and angle relations.
60-Second Revision
A unit cell is the smallest repeating three-dimensional portion of a crystal. Repetition of the unit cell forms the crystal lattice; the basis consists of atoms, ions or molecules associated with lattice points.
Summary
A unit cell is the smallest repeating three-dimensional portion of a crystal. Repetition of the unit cell forms the crystal lattice; the basis consists of atoms, ions or molecules associated with lattice points.
Ask-the-Tutor Modes
- Explain it simply.
- Compare the structures.
- Give material examples.
- Prepare a board-style answer.
- Test me with an MCQ.
Exam Focus
Exam Focus
Important points
- Unit cell is the smallest repeating crystal portion.
- Crystal lattice is generated by repeating the unit cell in three dimensions.
- Basis means the particles placed at lattice points.
- SC, BCC and FCC contain 1, 2 and 4 effective atoms per unit cell.
- Unit cells are described by sides a, b, c and angles α, β, γ.
- Seven crystal systems arise from different side and angle relations.
Common exam traps
- Confusing structural categories
Long question structure
Definition → particle arrangement → properties → examples → comparison.
Common Mistakes
Common Mistakes
- Mistake
Base classification on atomic arrangement.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Unit cell is the smallest repeating crystal portion.
Crystal lattice is generated by repeating the unit cell in three dimensions.
Basis means the particles placed at lattice points.
SC, BCC and FCC contain 1, 2 and 4 effective atoms per unit cell.
A unit cell is the smallest repeating three-dimensional portion of a crystal. Repetition of the unit cell forms the crystal lattice; the basis consists of atoms, ions or molecules associated with lattice points.
- Definition
- A unit cell is the smallest repeating three-dimensional portion of a crystal. Repetition of the unit cell forms the crystal lattice; the basis consists of atoms, ions or molecules associated with lattice points.
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Exam Practice
Important Question
Q1. Define a unit cell.
Important Question
Q2. Define crystal lattice.
Important Question
Q3. How many effective atoms are in SC, BCC and FCC?
Important Question
Q4. Name the seven crystal systems.