Structures and properties
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1 Crystal structures Structure plays an important role in understanding properties Need to be introduced to different ways of describing structures Models play an important role in communicating structural ideas Structures and properties The three polymorphs of carbon, diamond, graphite and C 60 have markedly different properties diamond is hard, insulating and insoluble in common solvents graphite is a soft lubricant, semimetallic and insoluble in common solvents C 60 is soft and soluble in benzene Page 1
2 The description of structures There are two very useful ways of describing solid structures the filling of holes in close packed arrays the linking of coordination polyhedra Both may be applicable to a particular structure, but one may be more revealing than the other Hexagonal close packing Page 2
3 Unit cell for hcp material ❽Note unit cell is not a hexagon shape Cubic close packing Page 3
4 Atomic positions in FCC structure ❽ Can represent atoms on unit cell projection drawing with heights marked ❽ Can also give atomic coordinates 0,0,0 0,,,,0,0, Only need to specify these four atoms as other a produced by unit cell translational symmetry Body centered packing Page 4
5 Structures of the metallic elements ❽ Many elements adopt close packed structures efficient space filling is generally favored both hcp and ccp give ~75% space filling not obvious why hcp/ccp should be prefered over ccp/hcp preference for bcc due to bonding Cu 3 Au ❽At high temperatures Cu 3 Au has a random distribution Cu and Au atoms over the sites available in a simple FCC structure on cooling the the atoms order» Order-disorder phenomena of this type are quite common in alloys and compounds Page 5
6 Holes in cubic close packed structures Tetrahedral holes Page 6
7 Octahedral holes Generalizations about holes in close packed structures There is one octahedral hole per atom in a close packed array There are two tetrahedral holes per atom in a close packed array Page 7
8 Structures based on hole filling in close packed anion arrays Holes in close packed arrays Formula ca tio n:anio n coordination holes occupied example s ccp MX 6:6 All octahedral NaCl, Fe O, MnS, TiC 4:4 Half te trahe dral MX 2 8:4 All te trahe dral 6:3 Half octahedral M 2 X 3 6:4 Two-thirds octahedral ZnS, CuCl, γ-agi CaF 2, ThO 2, ZrO 2, Ce O 2 example s hcp NiAs, FeS, NiS ZnS, β-agi None CdCl 2 CdI 2, TiS 2 Al 2 O 3, Fe 2 O 3, V 2 O 3, Ti 2 O 3, Cr 2 O 3 Page 8
9 Molecular structures ❽Many molecular materials pack in a way that can be described by using close packing concepts Crystalline H 2, CH 4, and HCl can be described as close packed as the molecules are orientationally disordered in the solid state Solid C 60 ❽ Buckminster Fullerene (C 60 ) is orientationally disordered at room temperature a forms a FCC structure ❽ On cooling the orientational disorder is lost at 249K Page 9
10 Fullerides ❽Solid C 60 can be doped with varying amounts of alkali and other reactive metals to make fulleride salts such as AC 60, A 2 C 60, A 3 C 60, A 4 C 60, A 6 C 60 show interesting properties such as superconductivity in Tl 2 RbC 60 at 45K structures of simpler compositions can be described in terms of filling holes in close packed C 60 anion array Connected polyhedra Many structures can be represented as connected polyhedra For example corner, edge or face sharing tetrahedra and octahedra» some connectivities are never found as they would bring the cations at the center of the polyhedra to close together ❽ Do not get face sharing tetrahedra» Connectivities involving close approach of cations are only found for compounds with low cation formal charge or high degree of covalency Page 10
11 Corner, edge and face sharing ❽Going from corner, to edge to face sharing decreases the distance between cations NaCl, ZnS, Na 2 O and CaF 2 structures ❽ NaCl Rock Salt All O sites occupied: T + and T - empty ❽ ZnS Zinc Blende T + (or T - ) sites occupied: O and T - (or T + ) empty ❽ Na 2 O Antifluorite structure close packed anions All T sites occupied: O empty ❽ CaF 2 Fluorite structure close packed cations cations not in contact so Eutactic All T sites occupied: O empty Page 11
12 The NaCl (rock salt) structure Compounds with the NaCl structure ❽ Typically, do not have soft anion and soft cation Page 12
13 The ZnS (Zinc Blende) structure Compounds with the zinc blende structure ❽ Bonding often more covalent than in materials with NaCl structure Page 13
14 Fluorite and antifluorite Compounds with a fluorite structure ❽ There is no hcp analogue of the fluorite structure as this would require filling face sharing tetrahedra Page 14
15 Wurtzite Compounds with a Wurtzite structure Page 15
16 NiAs ❽ Made up from face sharing NiAs 6 octahedra Short M-M distance favored by compounds that are not strongly ionic Compounds with a NiAs structure Page 16
17 CsCl CsCl does NOT have a body centered lattice. Compounds with a CsCl structure ❽Adopted by salts with large cations and some intermetallics including CsAu Page 17
18 Other AX structures ❽ Most AX compounds adopt either NaCl, NiAs, CsCl or ZnS structures there are some exceptions PbO has Pb 2+ in an irregular environment due to the presence of a stereochemically active lone pair FeO at low T is distorted due to magnetic ordering» Ferromagnetism is not compatible with cubic symmetry Rutile (TiO 2 ), CdCl 2 and CdI 2 structures ❽ Formed by filling half of octahedral holes in close packed array CdI 2 and CdCl 2 are formed by filling all the octahedral sites between alternate close packed layers in hcp and ccp lattices respectively» They are layered structures Rutile structure is formed by filling octahedral sites to give a 3D framework» Adopted by smaller ions than those usually found in fluorite structure Page 18
19 Rutile (TiO 2 ) ❽Edge sharing chains bring metal centers close together; possible metal-metal bonding Compounds with a Rutile structure Page 19
20 The CdI 2 structure ❽ Layers are held together by Van der Waals forces Compounds with a CdI 2 structure ❽ Note anions tend to be soft or capable of hydrogen bonding Page 20
21 The CdCl 2 structure ❽Long stacking repeat sequence Compounds with a CdCl 2 structure Page 21
22 Polyhedral representation of ReO 3 ❽ ReO 3 is a redish colored metallic oxide Parent structure for perovskites and may tungsten bronzes» e.g. Na x WO 3 x < 1 Perovskite (CaTiO 3 ) ❽ There are many technologically important materials with perovskite related structures Page 22
23 Perovskites Perovskite is debatably the most important simple structure type. Ferroelectrics, pyroelectrics, piezoelectrics Superconductors, semiconductors, metals Ferromagnets, antiferromagnets Magnetoresistives Redox catalysts Deep earth mineral, MgSiO 3» octahedral silicon under pressure!! Example Perovskites Page 23
24 Distortions of the Perovskite structure ❽Many perovskites do not have the ideal cubic structure Often octahedra are rotated and/or cations displaced from their ideal positions These displacements and rotations can be responsible for important physical properties Tolerance factor ❽ In an ideal cubic perovskite we would predict that a = 2 r A-O = 2r B-O but there are some deviations from this ❽ A tolerance factor, t = (2 r A-O )/(2r B-O ) can be defined ❽ For 0.9< t < 1.0 cubic Perovskite typically forms ❽ For t slightly > 1 a perovskite structure with cation displaced from the octahedra centers may be formed (BaTiO 3 t=1.06) This can lead to phenomena such as Ferroelectricity ❽ For t φ 1 another structure with a lower B site coordination number will be formed ❽ For 0.8 < t < 0.9 a distorted Perovskite typically forms ❽ For t < 0.8 a structure with lower A site coordination forms Page 24
25 The GdFeO 3 structure ❽ Many different types of octahedral rotations can occur These lead to larger unit cells Perovskites with 2 a p x 2 a p x 2a p unit cells are common Crystals with dipole moments Cation displacements in perovskites can lead to macroscopic dipole e.g. BaTiO 3 Displacements lower symmetry in addition to any tilting 1.86Å Ba 2.00Å Ti O 2.17Å Page 25
26 Glazer s octahedral tilting scheme ❽Mike Glazer considered all the possible simple octahedral tilting schemes see Acta Cryst. B28, 3384 (1972) restricted discussion to structures with two layer repeat (2a p x 2b p x2c p ) unit cell» covers most situations that are found in practice» consider each octahedron to be tiltable by some amount around each of cubic perovskite axes a, b and c.» this places restrictions on tilts of neighboring octahedra Effect of tilting on neighboring octahedra ❽ If you rotate an octahedron in a positive sense about the c axis, adjacent octahedra in the a-b plane must rotate in a negative sense has no implications for rotation in next layer down c Page 26
27 Possible tilt combinations ❽ As rotation around an axis does not require the next octahedron along the axis to do anything in particular there are 10 possible tilt combinations compatible with a two layer repeat ignoring special cases where rotation around two or more axes is the same no rotation about a-axis a + b + c + a + b + c - a + b - c - a - b - c - 3 tilts a 0 b + c + a 0 b + c - a 0 b - c - 2 tilts a 0 b + c - a 0 a 0 c + a 0 a 0 c - 1 tilt a 0 a 0 a 0 No tilts Rotation of all octahedra along the b-axis with the same sense Rotation of every second octahedron along the c-axis with opposite sense Lattice centering of different tilts ❽ Different tilts give rise to different lattice centering Page 27
28 Derivation of space group symmetry ❽ After considering possibility of equal magnitude tilts about different directions 23 possible tilt systems can be derived Space group symmetry can be determined by identifying symmetry elements from drawings 23 possible tilt systems Page 28
29 Examples of tilted perovskites ❽ Tilt system (10) and (14) are dominant in practice Pyrochlores ❽ Pyrchlores have the generic formula A 2 B 2 X 6 X Example La 2 Sn 2 O 7 The structure consists of a framework of corner sharing BX 6 octahedra Anions X may be completely missing giving rise to defect pyrochlores such as KTaO 3 Defect pyrochlores are often readily ion exchangeable B ions may be mixed and structure may be A deficient e.g. KNbWO 6 Page 29
30 Spinel (MgAl 2 O 4 ) ❽Spinel structure can be viewed as ccp anions with half of available octahedral holes filled and 1/8 of tetrahedral holes filled Very important structure for magnetic materials Inversion in Spinels ❽ General formula is AB 2 O 4 fraction of A cations on octahedral sites determines degree of inversion all A cations on tetrahedral sites is a normal Spinel all A cations on octahedral sites is an inverse Spinel can have anything between normal and inverse in practice Page 30
31 Compounds with a Spinel Structure ❽ Note occurrence of 2,3 2,4 1,3,4 and 1,2,5 spinels Garnets (A 3 B 2 B 3 O 12 ) ❽ Of interest due to magnetism, optical properties and abilitiy to function as Laser hosts Page 31
32 Al 2 O 3, LiNbO 3 and FeTiO 3 The corundum structure consists of a close packed oxide array with 2/3 of the octahedral holes filled by cations The LiNbO 3 structure is closely related to that of Al 2 O 3 with the Li and Nb ordered in the occupied octahedral holes FeTiO 3 (Illmenite) has the same basic structure as LiNbO 3, but it has a different cation ordering pattern. Cation ordering in Al 2 O 3, LiNbO 3 and FeTiO 3 Non-polar Polar Page 32
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