MSE2001H_3_2

MSE2001H_3_2 - 1 Chapter 3 Crystal Structures Introduction...

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1 • Introduction • Bravais Lattice • Crystals with One Atom per Lattice Point • Miller Indices • Densities and Packing Factors of Crystalline Structures • Interstitial Positions and Sizes • Crystals with Multiple Atoms per Lattice Site • Liquid Crystals • Single Crystals and Polycrystalline Materials • Polymorphism • X-Ray Diffraction Chapter 3 Crystal Structures
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2 FCC lattice Atoms touching along the [110] direction Atoms touching along the [111] direction BCC lattice Linear Density Densities of Crystalline Structures cell unit one within contained line the of Length cell unit one within direction along centered atoms of Number L = ρ Close-packed Direction: 1. The directions with the highest linear density 2. The atoms are in direct contact. FCC [110]: r L 2 1 = BCC [111]: r L 2 1 =
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3 Planar Density FCC lattice Portion of sphere on the plane Densities of Crystalline Structures cell unit one within contained plane the of Area cell unit one within plane a an centered atoms of Number P = ρ FCC (111): Close-packed Plane: 1. The plane with the highest planar density 2. The atoms are in direct contact. 2 3 2 1 r L = FCC (110): 2 2 4 1 r L =
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4 Volumetric Density Densities of Crystalline Structures volume unit per atoms of Number the V = ρ r c r a 3 2 4 2 = = 3 2 4 1 r V = Number of atoms: 6 In a unit cell? 2
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5 Interstitial Positions The APF is less than 1.0 for all crystals. Æ There is still plenty of room inside crystals. The size and position of the holes in crystals Æ interstices Interstitial Positions in FCC
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6 Interstitial Positions Octahedral positions Tetrahedral positions FCC BCC HCP 5 4 a 2 o a 2 o a 2 o a 2 o a 2 o a 3 2 o a 3 2 o a 5 4 o a 3 4 o a 4 8 414 . 0 / = r κ 225 . 0 / = r 6 12 155 . 0 / = r 291 . 0 / = r 6 12 414 . 0 / = r 225 . 0 / = r
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7 Crystals with Multiple Atoms Per Lattice Site Example CsCl Two interwoven SC lattices
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8 FCC unit cell with Na + located at FCC positions
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MSE2001H_3_2 - 1 Chapter 3 Crystal Structures Introduction...

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