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Structures of Simple Solids

Structures of Simple Solids. 201350873 이현경. Types of Solids. Crystalline periodic arrangement of atoms exhibiting long range(>10nm) order and retention of symmetry Quasicrystals non-periodic arrangement of atoms exhibiting long-range order, retention of symmetry

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Structures of Simple Solids

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  1. Structures of Simple Solids 201350873 이현경

  2. Types of Solids • Crystallineperiodic arrangement of atoms exhibiting long range(>10nm) order and retention of symmetry • Quasicrystalsnon-periodic arrangement of atoms exhibiting long-range order, retention of symmetry • Amorphousno long range order or symmetry in atomic arrangement Quasicrystal

  3. Types of crystalline solid

  4. Definitions Crystal consist of atoms, or, more commonly, group of atoms repeated regularly in 3dimensions • Lattice : an infinite, regular array of points in space, ion which each lattice point resides in an environment identical to that of every other lattice point • Unit cell : Crystalline solids have atoms, ions, or molecules packed in regular geometric arrays, with the structural unit called the unit cell • Primitive cell : the smallest possible choice of unit cell

  5. Bravais Lattices • Several different unit cells are possible for some structures • The one used may be chosen for convenience, depending on the particular application • The atoms on the corners, edges, or faces of the unit cell are shared with other unit cells • 1/8 for corners, ¼ for edges, ½ for faces, 1 for centers

  6. Bravais Lattices Cubic Unit Cell a = b = c α = β = γ = 90°

  7. Bravais Lattices Tetragonal Unit Cell a = b ≠ c α = β = γ = 90°

  8. Bravais Lattices Hexagonal a = b ≠ c α = β = 90° γ = 120° Rhombohedral a = b = c α = β =γ≠ 90°

  9. Bravais Lattices Orthorhombic a ≠ b ≠ c α = β =γ = 90°

  10. Bravais Lattices Monoclinic a ≠ b ≠ c α = γ = 90°, β ≠90°

  11. Bravais Lattices Triclinic a ≠ b ≠ c α ≠β ≠ γ≠ 90°

  12. Packing of SpheresFour modes of spherical packing

  13. Packing of Spheres Simple Cubic(SC) Sphere in one layer are atop spheres in previous layer. All layers identical Total # of atoms on the unit cell =8x1/8=1 CN=6, Occupancy=52.4%

  14. Packing of Spheres Body-centered cubic(BCC) Alternate layer offset : a-b-a-b- spheres in b layer fit into the small depressions in the a layer Total # of atoms in the unit cell =8x1/8+1=2 CN=8, occupancy=68%

  15. Packing of Spheres Cubic Closest Packing(CCP) Three alternating layers : a-b-c-a-b-c- Total # of atoms in the unit cell =8x1/8+1/2x6=4 CN=12, occupancy=74%

  16. Packing of Spheres Hexagonal closest Packing(PCC) two alternating layers : a-b-a-b- CN=12, occupancy=74%

  17. Hole in Lattices The packing of atoms into various lattices produces interstices or “hole”, which may be filled to produce different compounds. There are two different types of holes in close-packed structures. Oh : octahedral hole # of Oh in a unit cell=(1+12x1/4)=4 Td : tetrahedral hole # of Td in a unit cell=8

  18. Metallic crystals NiAs

  19. Metallic crystals Rock Salt (Sodium Chloride) –MX FCC lattice of anions X in which cations M occupy octahedral holes Cubic closed packing(a-b-c-a-b-c-)=CCP Ex )NaCl, LiCl, KBr, MgO, AgCl Na is coordinated by 6 Cl Clis coordinated by 6 Na CN(M, X) =6 or (6,6) coordination

  20. Metallic crystals Cesium Chloride SC lattice of anions X, cubic holes filled with cations Ex) CaS, TlCl, CsCN CN(M, X) =8, or (8,8)coordination

  21. Metallic crystals Nickel arsenide HCP lattice of anions X, octahedral holes filled with M, X atoms surrounded in trigonal prismatic arrangement of M Ex) NiS, FeS, CoS, CoTe CN(M, X) =6, or (6,6)coordination Left : HCP right : CCP

  22. Metallic crystals Zinc Blende (sphalerite) FCC lattice of anions X in which cation M occupy tetrahedral holes CN(Zn, S)= 4 Cubic closed packing(CCP):a-b-c-a-b-c Ex) CuCl, CdS, HgS, GaP

  23. Metallic crystals Wurtzite HCP lattice of anions X in which cation M occupy tetrahedral holes Hexagonal closed packing(HCP):a-b-a-b CN(Zn, S)=4 ZnS in the sphalerite and wurtzite lattices are poylmorph

  24. Metallic crystals Flourite(CaF2) FCC lattice of cation M in which anions X occupy tetrahedral holes Cubic closed packing(CCP) : a-b-c-a-b CN(Ca)=8 CN(F)=4 Cf) antifluorite(X2M) : FCC lattice of cation inverse of the flourite structure CN(X)=4, CN(M)=8

  25. Metallic crystals Rutile(TiO2) Ti ions : Body centered cubic(a-b-a-b-) Ti - surrounded by 6 O atoms O - surrounded by 3 Ti atoms So, (6,3) coordination

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