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# Lattice 1

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### Lattice 1

1. 1. Crystal lattice [1] Tran Anh Tuan Materials Engineer MES Team
2. 2. Lattice = array of points with identical surroundings 3D - lattice
3. 3. Lattice = array of points with identical surroundings Unit cell
4. 4. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ
5. 5. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ simple cubic
6. 6. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ body centered
7. 7. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ face centered
8. 8. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ tetragonal
9. 9. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ bc tetragonal
10. 10. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ orthorhombic
11. 11. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ orthorhombic
12. 12. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ orthorhombic
13. 13. 7 crystal systems c a b Crystal system Cell vector Cell angles Cubic Tetragonal Orthorhombic Hexagonal Monoclinic Triclinic Rhombohedral a = b = c a = b ≠ c a ≠ b ≠ c a = b ≠ c a ≠ b ≠ c a ≠ b ≠ c a = b = c α = β = γ = 90 α = β = γ = 90 α = β = γ = 90 α = β = γ = 120 α = β = 90 ≠ γ α ≠ β ≠ γ ≠ 90 α = β = γ ≠ 90 α β γ orthorhombic
14. 14. ..to be continued