Close Packings of Spheres I.

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close packed layers 3rd layer at position S: h.c.p. 3rd layer at position T: c.

c.c.: face-centered cubic) space filling: 74.05% A. R.

1 Close Packings of Spheres I. close packed layer a non-close packed layer stacking of 2 close packed layers 3rd layer at position S: h.c.p. 3rd layer at position T: c.c.p. h.c.p.: hexagonal close packing c.c.p.: cubic close packing (or f.c.c.: face-centered cubic) space filling: 74.05% A. R. West, Solid State Chemistry and ist Applications, Wiley & Sons, 1984.

2 Close Packings of Spheres II. hexagonal close packing h.c.p. stacking sequence:... A B A B A B... Z = 2; 2 octahedral voids; 4 tetrahedral voids unit cell Graphics: ATOMS V5.1, E. Dowty, Shape Software 1999.

3 Close Packings of Spheres III. cubic close packing c.c.p. or f.c.c. stacking sequence:... A B C A B C A B C... Z = 4; 4 octahedral voids; 8 tetrahedral voids Graphics: ATOMS V5.1, E.Dowty, Shape Software 1999.

4 Symmetry of a Cubic Close Packing Spacegroup: F 4/m 3 2/m (short: F m 3 m) F: lattice centering 4/m: C 4 rotation axis // a m mirror plane a 3: C 3i rotation-inversion axis // [1 1 1] 2/m: C 2 rotation axis // [1 1 0] m mirror plane [1 1 0] A. R. West, Solid State Chemistry and ist Applications, Wiley & Sons, 1984.

5 Symmetry of a Hexagonal Close Packing Spacegroup: P 6 3 /m 2/m 2/c (short: P 6 3 /m m c) P: lattice centeringc 6 3 /m: 6 3 screw axis // c m mirror plane c 2/m: C 2 rotation axis // [2 1 0] m mirror plane [2 1 0] 2/c: C 2 rotation axis // [1 0 0] c glide plane [1 0 0] A. R. West, Solid State Chemistry and ist Applications, Wiley & Sons, 1984.c

Body-centered Cubic Arrangement Spacegroup: I m 3 m 2 Atoms / unit cell 68% space filling Coordination of an atom: 8 + 6 (8x2.

6 Body-centered Cubic Arrangement Spacegroup: I m 3 m 2 Atoms / unit cell 68% space filling Coordination of an atom: (8x2.48Å, 6x2,86Å in iron) C.N. = 12 for h.c.p. and f.c.c Caveat! Spacegroup P m 3 m for CsCl U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

7 Metal Structures I. h c i hexagonal close packed cubic close packed body-centered cubic (68% space filling) others U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

8 Some More Close Packed Structures topological concept! The h.c.p. oxide layers in rutile and γ- Li 3 PO 4 are not planar but are buckled. The oxide ion arrangement in these may alternatively be described as tetragonal packed (t.p.). A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

9 Rocksalt Structure Type I. NaCl, f.c.c. array of Na + all octahedral voids are occupied by Cl Or vice versa! Stacking sequence for cations and anions is identical Space group: F m 3 m U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, M. Almon, Seminar, University of Gießen, 1999.

10 Kristallstrukturen - Gittermodelle Steinsalz (Halit), NaCl, kubisch, a = 5,62 Å Cl Na + Röntgenstrukturanalyse

11 Rock Salt Structure Type II. Members of the rock salt structure family Again! Chemically different compounds adopt the same crystal structure. U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

12 Wurtzite (ZnS) Structure Type ZnS, h.c.p. array of Zn 2+ ½ of tetrahedral voids occupied by S 2 Or vice versa! Stacking sequence for cations and anions is identical Zn 2+ -Ion Space group: P 6 3 m c S 2- -Ion U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, M. Almon, Seminar, University of Gießen, 1999.

13 Structures Related to ZnO (Wurtzite type) β-ligao 2, Pbn2 1 β-li 2 BeGeO 4, Pn β II -Li 3 PO 4, Pmn2 1 β II -Li 2 ZnSiO 4, Pmn2 1 ZnO, P6 3 mc A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

14 Wurtzite and NiAs-Type I. Wurtzite NiAs for both types h.c.p. of anions A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

15 Wurtzite and NiAs-Type II. No cation-cation interaction! A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

16 Wurtzite and NiAs-Type III. Cation-cation interaction! A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

17 Zinc Blende (Sphalerite) and Fluorite ZnS, f.c.c. array of Zn 2+ ½ of tetrahedral voids occupied by S 2 CaF 2, f.c.c. array of Ca 2+ all tetrahedral voids occupied by F alternative representation of the fluorite structure pronouncing the cubic [CaF 8 ] coordination units A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

NiAs-Type Structure Family c/a ratio for members of the NiAs family: 1.39 to 1.68 (ideal: 1.633 for h.c.p.) P 3 metal-metal interaction along c-axis valence electron concentration v.e.c. determines distortion (P ) P 2 4 sophisticated balance between M-M and P-P interactions U.

18 NiAs-Type Structure Family c/a ratio for members of the NiAs family: 1.39 to 1.68 (ideal: for h.c.p.) P 3 metal-metal interaction along c-axis valence electron concentration v.e.c. determines distortion (P ) P 2 4 sophisticated balance between M-M and P-P interactions U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, R. Hoffmann, Solids and Surfaces, VCH Verlagsgesellschaft, Weinheim, 1988.

19 Diamond - Sphalerite Diamond C Sphalerite, Zinc Blende ZnS F 4 1 /d 3 2/m F 4 3 m U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

20 Various AB 2 -Structure Types Major AB 2 -structure types: SiO 2 (Quartz, Cristobalite, 4 : 2); TiO 2 (Rutile, 6 : 3); CaF 2 (Fluorite, 8 : 4) Specialities: CdCl 2 and CdI 2 : layer type structures, various stacking sequences A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

21 Some More Close Packed Structures topological concept! The h.c.p. oxide layers in rutile and γ- Li 3 PO 4 are not planar but are buckled. The oxide ion arrangement in these may alternatively be described as tetragonal packed (t.p.). A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

22 TiO 2 Rutile Structure Type I. O 2- - Ionen Ti 4+ - Ionen Space group: P 42/m n m Lattice [0 0 1], c-axis [1 0 0] [1 1 0] eacho 2- -ion is square-planar coordinated by 3 Ti 4+ (C.N. = 3) eachti 4+ -ion is octahedrally coordinated by 6 O 2- (C.N. = 6) A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, M. Almon, Seminar, University of Gießen, 1999.

23 TiO 2 Rutile Structure Type II. representations of the crystal structure: from the unit cell to a 3-dimensional arrangement characteristic: chains of the edge-sharing octahedra [TiO 6 ] A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, M. Almon, Seminar, University of Gießen, 1999.

24 Rutile Type Structures Oxides as well as fluorides adopt the structure type Many derivatives of the rutile structure type are known A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

25 Cristobalite SiO 2 b a Space group: F d 3 m Lattice [1 0 0], a-axis [1 1 1] [1 1 0] Diamond SiO 2 f. c. c. arrangement of C and Si with C (Si) in ½ of the tetrahedral voids Elektrides Oxides 2e O 2 topological relation! U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

26 Carnegieite An Alumosilicate Na[AlSiO 4 ] [ ][Si 2 O 4 ] U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

27 α-quartz SiO 2 I. Space group: P chiral and polar piezoelectric material U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

28 α-quartz SiO 2 II and 3 1 -screw axis, respectively screw axis: combined rotation & translation chiral (enantiomeric) crystals U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

29 Spinell Mg II Al III 2 O 4 kubisch, a = 8,081 Å; Baueinheiten: [Mg II O 4 ] und [Al III O 6 ] O 2 Al/Cr 3+ Mg 2+ Chromophor [CrO 6 ]

30 Rinmans Grün und Thénards Blau Zn II Co III 2O 4 Co II Al III 2O 4 Chromophor: [Co III O 6 ] Chromophor: [Co II O 4 ] Farbpigmente

31 ReO 3 and derived Structures I. ReO 3 Structure Type P m 3 m, a = 3,734 Å corner-sharing octahedra ReO 6/2

32 ReO 3 and derived Structures II. Introduction of a crystallograpic shear plane CS Reduction [ReO 6/2 ] [ReO 6/2 ] + [ReO 3/2 O 3/3 ] ReO 3 a ReO 3 + b ReO 2.5

33 ReO 3 and derived Structures III. Tungsten tri-oxide WO 3-x O. T. Sørensen Ed., Nonstoichiometric Oxides, Academic Press, 1981.

These metal centres interact through metallic bonding

These metal centres interact through metallic bonding The structures of simple solids The majority of inorganic compounds exist as solids and comprise ordered arrays of atoms, ions, or molecules. Some of the simplest solids are the metals, the structures