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structure_nets - Framework Nets and Topologies of...

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Unformatted text preview: Framework Nets and Topologies of Structures Chemistry 754 Solid State Chemistry Dr. Patrick Woodward Lecture #8 Framework Nets Consider the nomenclature used by O'Keeffe, et al. [1] O'Keeffe, Vertex = Linking point (in our discussion the vertex will be generally be an atom, though in some cases it will be a cluster of atoms) Linker (or edge) = Connects vertices, in the simplest form this will be a bond between two vertices (N,M)-connected net = The coordination number (# of linkers) about (N,M)one set of vertices is N, while the coordination number about the the other set of vertices is M. For example ZnS is a (4,4) net, while TiO2 is a (3,6) net. Decoration = A vertex is replaced by a group of vertices (an atom is replaced by a cluster). Expansion = The bonds that link vertices are replaced by a series of bonds. Examples include the oxygen atom in silicates and zeolites or longer molecules like cyanide or the dicarboxylic acids in Yaghi's open frameworks Chem. 152, 3-20 (2000). 152, 3[1] M. O'Keeffe, M. Eddauodi, H. Li, T. Reinke & O.M. Yaghi, J. Solid State O'Keeffe, Eddauodi, Yaghi, 1 Coordination and Stoichiometry If all ions of a given type have the same coordination environment (a environment situation that we will later see is favored) the coordination number number and stoichiometry of a MaXb composition are related by the following formula: Example 1 In SiO2 the Si is tetrahedrally coordinated. What is the coordination number of oxygen? Example 2 In SrTiO3 the Ti is octahedrally coordinated and the Sr is surrounded by 12 oxygens (in a cuboctahedron) What is the coord. number of cuboctahedron) coord. oxygen? (Coordination # M) a = (Coordination # X) b 4 1 = (Coord. # O) 2 Coord. # Oxygen = 4/2 = 2 (Coord. Coord. 6 1 = (Coord. # OTi) 3 (Coord. Coord. # OTi = 2 Coord. 12 1 = (Coord. # OSr) 3 (Coord. Coord. # OSr = 4 Coord. Bond Graphs The relationship between stoichiometry and coordination number presented in the previous slide can also be represented graphically graphically using a bond graph. SiO2 Bond Graph O Si O Ti SrTiO3 Perovskite Bond Graph O O O Al O Sr Al O O Mg MgAl2O4 Spinel Bond Graph O 2 Coordination and Stoichiometry The implications of the formula on the previous slide limit the number of simple stoichiometries and basic coordination numbers that permit all ions of a given type to have the same environment Coordination Numbers Anion Cation 8 8 4 8 6 6 4 6 3 6 2 6 1 6 4 4 3 4 2 4 1 4 Stoichiometry (Example) MX (CsCl) (CsCl) MX2 (Fluorite - CaF2) MX (NaCl, NiAs) (NaCl, NiAs) M2X3 (Corundum - Al2O3) MX2 (Rutile - TiO2) MX3 (ReO3 & Perovskite*) MX6 (K2NiF6)* MX (Sphalerite, Wurtzite) (Sphalerite, Wurtzite) M3X4 (Si3N4, Pt3O4) MX2 (Cristobalite - SiO2) MX4 (CaWO4, ZrSiO4)* *In these examples we are ignoring the large cations. Coordination and Stoichiometry We can also sort this list by stoichiometry Coordination Numbers Anion Cation 8 8 6 6 4 4 4 3 2 4 3 2 1 8 6 4 6 4 6 4 Stoichiometry (Example) MX (CsCl) (CsCl) MX (NaCl, NiAs) (NaCl, NiAs) MX (Sphalerite, Wurtzite) (Sphalerite, Wurtzite) MX2 (Fluorite - CaF2) MX2 (Rutile - TiO2) MX2 (Cristobalite - SiO2) M2X3 (Corundum - Al2O3) M3X4 (Si3N4, Pt3O4) MX3 (ReO3 & Perovskite*) MX4 (CaWO4, ZrSiO4)* *In these examples we are ignoring the large cations. 3 Nets with 1 or 2 Kinds of Vertices Now let's consider some of the more important entries in Table 5 from O'Keeffe et al.: (N,M)-Net Coordination Figures Net (Example) (N,M)3,3 Triangle Triangle SrSi2 3,4 Triangle Square Pt3O4 3,4 Triangle Tetrahedron Boracite (B7O12) 3,4 Pyramid Tetrahedron Si3N4 3,6 Triangle Octahedron Rutile (TiO2) 4,4 Square Square NbO 4,4 Tetrahedron Tetrahedron Diamond 4,4 Square Tetrahedron Coooperite (PtS) PtS) 4,6 Tetrahedron Octahedron Corundum (Al2O3) 4,8 Tetrahedron Cube Fluorite (CaF2) 6,6 Octahedron Octahedron Primitive Cubic (Po) 8,8 Cube Cube Body-centered cubic (Fe) Body- Cooperite (PtS) (4,4)-connected net (4,4)- (3,6)-connected net (3,6)- Rutile (TiO2) Space Group = P42/mmc P4 a = 3.48 c = 6.11 Atom Site x y z Pt 2c 0 0 S 2f Space Group = P42/mnm a = 4.5937 c = 2.9587 Atom Site x y z Ti 2a 0 0 0 O 4f x x 0 x=0.3048 4 Corundum (Al2O3) (hcp, 67% Oct. Holes Filled) hcp, Fluorite (CaF2) (ccp, 100% Tetr. Holes Filled) ccp, Tetr. 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 (4,4) Diamond Net: AB Derivative Diamond Space Group = Fd3m a = 3.563 Atom C Site 8a x 0 y 0 z 0 Sphalerite (ZnS) ZnS) Space Group = F-43m Fa = 5.345 Atom Zn S Site 4a 4c x 0 y 0 z 0 The sphalerite structure is obtained by ordering the vertices of the diamond structure. structure. 5 (4,4) Diamond Net: ABC2 Derivative Chalcopyrite (CuFeS2) Space Group = I-42d Ia = 5.24 c = 10.30 Atom Cu Fe S Site 4a 4b 8d x 0 0 y 0 0 InGaAs2 Space Group = F-43m Fa = 5.345 z 0 Atom Zn S Site 4a 4c x 0 y 0 z 0 0.270 0.125 See Rohrer 4-I (page 183) for more examples and discussion. 4- (6,6) P-Cubic Net: AB Derivative Primitive Cubic (Po) Space Group = Pm3m a = 3.345 Atom Po Site 1a x 0 y 0 z 0 Rock Salt (NaCl) (NaCl) Space Group = Fm3m a = 5.640 Atom Na Cl Site 4a 4b x 0 y 0 z 0 The rock salt structure is obtained by ordering the vertices of the primitive cubic structure. 6 Expanded (6,6) P-Cubic Nets Space Group = Pm3m a = 3.90 Atom Ti Sr O Site 1a 1b 3d x 0 Perovskite (SrTiO3) y 0 0 z 0 0 Space Group = Fm3m a = 8.19 Atom Sc Ta Ba O Site 4a 4b 8c 24e x 0 Ba2ScTaO6 y 0 0 0.257 z 0 0 These structures are analogous to Po and NaCl, with the addition of an oxygen linker and by NaCl, inserting a large cation at the center of each (cation) cube. Interpenetrating Nets Space Group = Pm3m Atom Site Cl 1a Cs 1b x 0 y 0 z 0 CsCl Space Group = Fd3m Atom Zn S Site 8a 8b x 0 y 0 z 0 NaTl The CsCl structure can be obtained from two interpenetrating primitive cubic or P-lattices. P- Interestingly both of these structures reduce to Im3m when all atoms are equivalent. The NaTl structure can be obtained from two interpenetrating diamond or D-lattices. D- 7 Sodalite Na8Al6Si6O24Cl2 We get a simpler representation if we omit oxygen and connect Al & Si with a line. The mineral sodalite consists of a framework of alternating SiO4 and AlO4 tetrahedra. The openings to the cages are small (6 tetrahedra around the ring, openings of ~2.6 ) that sodalite is not considered microporous. The space group is P-43n. The Sodalite cage has 6 square faces (4-rings) pointing toward the vertices of an octahedron. If we connect the square faces a simple cubic pattern occurs, to get the mineral sodalite we add an interpenetrating network cages (the two networks share hexagonal faces). Faujisite If the sodalite cages are connected through intervening hexagonal prisms (each prism is a double hexagonal ring of tetrahedra) The space group of the ideal structure is Fd3m. This SG is the same as diamond, illustrating the tetrahedral connectivity of the sodalite cages. Unlike Sodalite, Faujisite has large openings (12 tetrahedra around the ring, opening of 7.4 ) and is highly porous. It has many commercial uses in catalysis, ion exchange and gas sorption. The Si:Al ratio is variable depending upon the concentration of sodium ions. When the Si/Al ratio is 1-1.5 it is called zeolite X, when the ratio is 1.5-3 it is called zeolite Y. 8 ...
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