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.
Key equation
N=8(18)+6(12)+Nbody
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.
1
Given
8 corner atoms
6 face atoms
2
Working
Corners: 8 × 18 = 1
3
Step 2
Faces: 6 × 12 = 3
4
Step 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.
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Exam preparation
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 mistakes
Base classification on atomic arrangement.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Unit Cell and Crystal Lattice
Sticky Notes · Quick Revision
1.
Key Point 1
Unit cell is the smallest repeating crystal portion.
2.
Key Point 2
Crystal lattice is generated by repeating the unit cell in three dimensions.
3.
Key Point 3
Basis means the particles placed at lattice points.
4.
Key Point 4
SC, BCC and FCC contain 1, 2 and 4 effective atoms per unit cell.
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6 concept questions
Easy → Medium → Hard
Explanation after each answer
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?
