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Crystal lattice [1] Tran Anh Tuan Materials Engineer MES Team
Lattice = array of points with identical surroundings 3D - lattice
Lattice = array of points with identical surroundings Unit cell
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
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
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 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
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
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
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
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
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
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
..to be continued

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Lattice 1

  • 1. Crystal lattice [1] Tran Anh Tuan Materials Engineer MES Team
  • 2. Lattice = array of points with identical surroundings 3D - lattice
  • 3. Lattice = array of points with identical surroundings Unit cell
  • 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. 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. 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 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. 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. 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. 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. 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. 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. 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