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Crystal Structure

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Maharashtra State Board: Class 12

Definition: Crystal Lattice

The three-dimensional arrangement of constituent particles of a crystalline solid in space, in which each particle is depicted as a point, is known as a crystal lattice.

Maharashtra State Board: Class 12

Definition: Unit cell

A unit cell is the smallest group of lattice points that, when repeated in all directions, will develop the entire lattice.

Maharashtra State Board: Class 12

Key Points: Crystal Structure

Types of Unit Cells:

Type Location of Particles Atoms per Unit Cell

Simple / Primitive

Corners only (1/8 × 8) = 1

Body-centred (bcc)

Corners + 1 at body centre (1/8 × 8) + 1 = 2

Face-centred (fcc)

Corners + 1 at each face centre (1/8 × 8) + (1/2 × 6) = 4
Base-centred Corners + centres of two opposite faces (1/8 × 8) + (1/2 × 2) = 2

Seven Crystal Systems:

System Intercepts Angles Bravais Lattices
Cubic a = b = c α = β = γ = 90° Primitive, FCC, BCC (3)
Tetragonal a = b ≠ c α = β = γ = 90° Primitive, BCC (2)
Orthorhombic a ≠ b ≠ c α = β = γ = 90° Primitive, FCC, BCC, End-centred (4)
Monoclinic a ≠ b ≠ c α = γ = 90°, β ≠ 90° Primitive, End-centred (2)
Triclinic a ≠ b ≠ c α ≠ β ≠ γ ≠ 90° Primitive (1)
Hexagonal a = b ≠ c α = β = 90°, γ = 120° Primitive (1)
Rhombohedral a = b = c α = β = γ ≠ 90° Primitive (1)
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