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structure_pack - Close Packed and Eutactic Structures...

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Unformatted text preview: Close Packed and Eutactic Structures Chemistry 754 Solid State Chemistry Dr. Patrick Woodward Lecture #7 Close Packed Array of Spheres The gray spheres represent a 2D Close Packed Array. In 3D the next layer of spheres could sit on the depressions marked in red (B) or those marked in blue (C). (C). AB Stacking AC Stacking 1 Cubic and Hexagonal Close Packing Hexagonal Close Packing (ABAB...) Space Group = P63/mmc ABAB Stacking Cubic Close Packing (ABCABC...) Space Group = Fm3m ABCABC Stacking Hexagonal Close Packing Space Group = P63/mmc a = 2r* c = (8/3)1/2 a Atom Site x y M 2c 1/3 2/3 *r = metallic radius z 1/4 63 screw axis Representative Examples Be (a=2.286 , c=3.583 ) Mg (a=3.209 , c=5.211 ) Zn (a=2.665 , c=4.947 ) Cd (a=2.979 , c=5.617 ) Ti (a=2.506 , c=4.679 ) Zr (a=3.312 , c=5.148 ) Ru (a=2.706 , c=4.282 ) Os (a=2.735 , c=4.319 ) Re (a=2.760 , c=4.458 ) 2 Cubic Close Packing 3-fold axis Space Group = Fm3m a = 4r/(2)1/2 Atom Site x y M 4a 0 0 *r = metallic radius z 0 Representative Examples Cu (a=3.6147 ) Layers stack perpendicular to [111] Ag (a=4.0857 ) Au (a=4.0738 ) Al (a=4.0495 ) Ni (a=3.5240 ) Leads to Face Pd (a=3.8907 ) Centered Cubic Pt (a=3.9239 ) structure Pb (a=4.9502 ) Body Centered Cubic Packing Space Group = Im3m a = 4r/(3)1/2 Atom Site x M 2a 0 *r = metallic radius y 0 z 0 Cubic or Hexagonal Close Packing Coordination Number = 12 Packing Efficiency = 74% Body Centered Cubic Packing Coordination Number = 8 Packing Efficiency = 68% Representative Examples Fe (a=2.8664 ) Cr (a=2.8846 ) Mo (a=3.1469 ) W (a=3.1650 ) Ta (a=3.3026 ) Ba (a=5.019 ) 3 Ordered Structures BCC (Im3m) CsCl (Pm3m) FCC (Fm3m) Cu3Au (Pm3m) Space Group = Pm3m a = {2rCs+2rCl}/(3)1/2 Atom Site x y Cs 1a 0 0 Cl 1b z 0 Space Group = Pm3m a = {2rCs+2rCl}/(2)1/2 Atom Site x y Au 1a 0 0 Cu 3c z 0 0 Eutactic Structures Ionic structures have traditionally been described by starting with a close packing of anions and assuming cations fill voids in the structure. Literal acceptance of this doctrine has several flaws, two of which are: 1. The Coulombic interaction between anions is repulsive, so they would prefer to maximize their separation rather than minimize it. 2.This assumes that anions are much larger than cations, but modern techniques have shown that in crystals this is not necessarily true (see Shannon's crystal radii). Mike O'Keeffe paints a more realistic picture that has the same symmetry. Namely that the ions approximate close packing arrangements in order to maximize the volume of the structure, while keeping the cation-anion distance at its optimal value. He calls these structures Eutactic. [M. O'Keeffe, Acta Cryst. A 33, 924-927 (1977)] 4 Octahedral and Tetrahedral Holes Tetrahedral Interstitial Site (Hole) Octahedral Interstitial Site (Hole) Octahedral & Tetrahedral Holes (CCP) Octahedral Holes Tetrahedral Holes Space Group = Fm3m Atom Site x Anion 4a 0 Oct Hole 4b y 0 z 0 Space Group = Fm3m Atom Site x Anion 4a 0 Tetr Hole 8c y 0 z 0 5 Octahedral Holes (HCP) Space Group = P63/mmc Atom Site x y 1/3 2/3 Anion 2c Oct Hole 2a 0 0 1/4 z 0 Tetrahedral Holes (HCP) Space Group = P63/mmc Atom Site x y 1/3 2/3 Anion 2c Tetr Hole 4f 1/3 2/3 z ~ 0.632 1/4 z z 6 Eutactic Structures Structures obtained by filling Octahedral Holes Structure NaCl NiAs CdCl2 CdI2 TiO2 Al2O3 The Structures obtained by filling Tetrahedral Holes Structure Fluorite Sphalerite Wurtzite In Fraction Packing Holes Filled 1 1 1/2 1/2 1/2 2/3 ccp hcp ccp hcp hcp hcp Fraction Packing Holes Filled 1 1/2 1/2 ccp ccp hcp fluorite (i.e. CaF2) the cations are close packed and the anions fill the tetrahedral holes. The opposite is true of the antifluorite structure (Na2O) hcp anion layers are buckled in rutile. rutile. (ccp, 100% Oct. Holes Filled) ccp, Rock Salt (NaCl) (hcp, 100% Oct. Holes Filled) hcp, NiAs Space Group = Fm3m Atom Site x Cl 4a 0 Na 4b y 0 z 0 Space Group = P63/mmc Atom Site x y As 2c 0 0 Ni 2a z 0 Cation Coord. Octahedron Coord. Anion Coord. Octahedron Coord. Connectivity Edge sharing Octahedra Cation Coord. Octahedron Coord. Anion Coord. Trigonal Prism Coord. Connectivity Edge & Face sharing Oct. Connectivity 7 CdI2/Ca(OH)2 (hcp, 50% Oct. Holes Filled) hcp, Rutile (TiO2) (hcp, 50% Oct. Holes Filled) hcp, Space Group = P-3m1 PAtom Site x Ca/Cd 1a 0 Ca/Cd 1/3 O/I 2d 2/3 y 0 0.2341 z 0 Space Group = P42/mnm Atom Site x Ti 2a 0 O 4f x y 0 x z 0 0 Cation Coord. Octahedron Coord. Anion Coord. Trigonal Pyramid Coord. Connectivity Edge sharing Octahedra Cation Coord. Octahedron x=0.3048 Coord. Anion Coord. Trigonal Planar Coord. Connectivity Edge sharing Octahedra Connectivity (hcp, 67% Oct. Holes Filled) hcp, Corundum (Al2O3) (ccp, 100% Tetr. Holes Filled) ccp, Tetr. Fluorite (CaF2) Space Group = R-3c RAtom Site x 0 Al 12c O 18e 0.305 0 0 y 0.3515 1/4 z Space Group = Fm3m Atom Site x Ca 4a 0 F 8c y 0 z 0 Cation Coord. Octahedron Coord. Anion Coord. Distorted Tetrahedron Coord. Connectivity Edge & Face sharing Oct Cation Coord. Cubic Coord. Anion Coord. Tetrahedral Coord. Connectivity Edge sharing Octahedra 8 (ccp, 50% Tetr. Holes Filled) ccp, Tetr. Sphalerite (ZnS) (hcp, 50% Tetr. Holes Filled) hcp, Tetr. Wurtzite (ZnO) Space Group = F-43m FAtom Site x Zn 4a 0 S 4c y 0 z 0 Space Group = P63mc Atom Site x 1/3 Zn 2b 1/3 O 2b 2/3 2/3 y 0 0.38 z Cation Coord. Tetrahedron Coord. Anion Coord. Tetrahedron Coord. Connectivity Corner sharing Oct. Cation Coord. Tetrahedron Coord. Anion Coord. Tetrahedron Coord. Connectivity Corner sharing Oct. (ccp, Oct. & 1/8 Tetr. Holes) ccp, Tetr. Spinel (MgAl2O4) (hcp, Oct. & 1/8 Tetr. Holes) hcp, Tetr. Olivine (Mg2SiO4) Space Group = Fd3m Atom Site x Mg 8a 1/8 Al 16d O 32e x Mg Coord. Tetrahedron Coord. Al Coord. Octahedron Coord. y 1/8 x x ~ 0.25 z 1/8 x Space Group = Pnma Atom Site x y See page 169 of Rohrer Mg Coord. Octahedron Coord. Al Coord. Tetrahedron Coord. z 9 ...
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This note was uploaded on 06/11/2011 for the course CHEM 101 taught by Professor Stegemiller during the Spring '07 term at Ohio State.

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