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MECH 210 080917 - Crystal Structures

# MECH 210 080917 - Crystal Structures - MECH 210 080917...

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MECH 210 080917 Page 1 of 4 MECH 210 080917 Crystal Structures Crystalline : The state of a solid material characterized by a periodic and repeating three-dimensional array of atoms, ions, or molecules. Crystal structure : The manner in which atoms, ions, or molecules are spatially arranged in crystalline solids. Lattice : The regular geometrical arrangement of points (lattice points representing atoms) in crystal space. Unit cell : The smallest basic structural unit that still retains the overall characteristics of a crystal structure. It is generally defined in terms of atom, or ion, positions within a parallelepiped volume. Lattice parameters : Parameters describing the size and shape of the unit cell, including the dimensions of the sides of the unit cell and the angles between the sides. Three sides: a , b , c Three angles: α , β , γ Figure 1 – Lattice parameters. There are fourteen (14) types of unit cells ( Bravais lattices ) grouped in seven (7) crystal structures. Metallic Crystal Structures (a) FCC unit cell (b) BCC unit cell (c) HCP unit cell Figure 2 – Three most commonly encountered crystal structures. Face-Centered Cubic (FCC) Three mutually perpendicular reference axes x, y, and z Lattice parameters: a = b= c , α = β = γ = 90 ° Four (4) whole atoms are assigned to the FCC unit cell. Atoms touch neighbors along face diagonal directions (close-packed directions) 2 a R 4 = R 2 2 2 R 4 a = = Atomic Packing Factor, APF = 3 3 a R 3 4 4 cell unit the of volume total cell unit a in atoms of volume ° ± ² ³ ´ µ = π = 0.74

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MECH 210 080917 - Crystal Structures - MECH 210 080917...

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