describing the structure of solids 2ww2.chemistry.gatech.edu/class/6182/wilkinson/slide1.pdf ·...
Post on 06-Jul-2018
220 Views
Preview:
TRANSCRIPT
Page 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 C60 have markedly different properties– diamond is hard, insulating and insoluble in
common solvents– graphite is a soft lubricant, semimetallic and
insoluble in common solvents– C60 is soft and soluble in benzene
Page 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 3
Unit cell for hcp material
�Note unit cell is not a hexagon shape
Cubic close packing
Page 4
Atomic positions in FCC structure� Can represent atoms on unit cell projection drawing
with heights marked� 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 5
Structures of the metallic elements
� 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
Cu3Au
�At high temperatures Cu3Au 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 6
Holes in cubic close packed structures
Tetrahedral holes
Page 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 8
Structures based on hole filling in close packed anion arrays
Holes in close packed arraysFormula ca tion:anion
coordina tionhole soccupie d
e xample sccp
e xample shcp
MX 6:6 All octahedra l NaCl, Fe O,MnS, TiC
NiAs , Fe S,NiS
4:4 Halfte trahe dra l
ZnS, CuCl,γ-AgI
ZnS, β-AgI
MX2 8:4 Allte trahe dra l
CaF2, ThO2,ZrO2, Ce O2
None
6:3 Halfoctahe dral
CdCl2 CdI2, TiS2
M2X3 6:4 Two-thirdsoctahe dral
Al2O3, Fe 2O3,V2O3, Ti2O3,Cr2O3
Page 9
Molecular structures
�Many molecular materials pack in a way that can be described by using close packing concepts– Crystalline H2, CH4, and HCl can be described
as close packed as the molecules are orientationally disordered in the solid state
Solid C60
� Buckminster Fullerene (C60) is orientationally disordered at room temperature a forms a FCC structure
� On cooling the orientational disorder is lost at 249K
Page 10
Fullerides�Solid C60 can be doped with varying
amounts of alkali and other reactive metals to make “fulleride” salts such as AC60, A2C60, A3C60, A4C60, A6C60– show interesting properties such as
superconductivity in Tl2RbC60 at 45K– structures of simpler compositions can be
described in terms of filling holes in close packed C60 anion array
Connected polyhedra
� Many structures can be represented as connectedpolyhedra– 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� 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 11
Corner, edge and face sharing
�Going from corner, to edge to face sharing decreases the distance between cations
NaCl, ZnS, Na2O and CaF2 structures� NaCl “Rock Salt”
– All O sites occupied: T+ and T- empty� ZnS “Zinc Blende”
– T+ (or T- ) sites occupied: O and T- (or T+ ) empty� Na2O “Antifluorite structure”
– close packed anions– All T sites occupied: O empty
� CaF2 “Fluorite structure”– close packed cations – cations not in contact so Eutactic– All T sites occupied: O empty
Page 12
The NaCl (rock salt) structure
Compounds with the NaCl structure
� Typically, do not have soft anion and soft cation
Page 13
The ZnS (Zinc Blende) structure
Compounds with the zinc blende structure
� Bonding often more covalent than in materials with NaCl structure
Page 14
Fluorite and antifluorite
Compounds with a fluorite structure
� There is no hcp analogue of the fluorite structure as this would require filling face sharing tetrahedra
Page 15
Wurtzite
Compounds with a Wurtzite structure
Page 16
NiAs
� Made up from face sharing NiAs6 octahedra– Short M-M distance favored by compounds that are not
strongly ionic
Compounds with a NiAs structure
Page 17
CsCl
� CsCl does NOT have a body centered lattice.
Compounds with a CsCl structure�Adopted by salts with large cations and some
intermetallics including CsAu
Page 18
Other AX structures� Most AX compounds adopt either NaCl, NiAs,
CsCl or ZnS structures– there are some exceptions– PbO has Pb2+ 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 (TiO2), CdCl2 and CdI2 structures
� Formed by filling half of octahedral holes in close packed array– CdI2 and CdCl2 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 19
Rutile (TiO2)�Edge sharing chains bring metal centers close
together; possible metal-metal bonding
Compounds with a Rutile structure
Page 20
The CdI2 structure� Layers are held together by Van der Waals forces
Compounds with a CdI2 structure� Note anions tend to be soft or capable of hydrogen
bonding
Page 21
The CdCl2 structure
�Long stacking repeat sequence
Compounds with a CdCl2 structure
Page 22
Polyhedral representation of ReO3
� ReO3 is a redish colored metallic oxide– Parent structure for perovskites and may tungsten bronzes
» e.g. NaxWO3 x < 1
Perovskite (CaTiO3)� There are many technologically important materials
with perovskite related structures
Page 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, MgSiO3
» octahedral silicon under pressure!!
Example Perovskites
Page 24
Distortions of the Perovskite structure
�Many “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� In an ideal cubic perovskite we would predict that
a = 2�rA-O = 2rB-O but there are some deviations from this� A tolerance factor, t = (2�rA-O)/(2rB-O) can be defined� For 0.9< t < 1.0 cubic Perovskite typically forms� For t slightly > 1 a perovskite structure with cation displaced
from the octahedra centers may be formed (BaTiO3 t=1.06)– This can lead to phenomena such as Ferroelectricity
� For t φ 1 another structure with a lower B site coordination number will be formed
� For 0.8 < t < 0.9 a distorted Perovskite typically forms� For t < 0.8 a structure with lower A site coordination forms
Page 25
The GdFeO3 structure
� Many different types of octahedral rotations can occur– These lead to larger unit cells– Perovskites with 2�ap x 2�ap x 2ap
unit cells are common
Crystals with dipole moments� Cation displacements in perovskites can lead to
macroscopic dipole– e.g. BaTiO3
– Displacements lower symmetry in addition to any tilting
1.86Å
2.00Å
2.17Å
Ti O
Ba
Page 26
Glazer’s octahedral tilting scheme�Mike Glazer considered all the possible simple
octahedral tilting schemes– see Acta Cryst. B28, 3384 (1972)– restricted discussion to structures with two layer
repeat (2ap x 2bp x2cp) 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� 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 27
Possible tilt combinations� 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 tiltsa0a0a0
1 tilta0a0c-a0a0c+
2 tiltsa0b-c-a0b+c-a0b+c+
3 tiltsa-b-c-a+b-c-a+b+c-a+b+c+
a0b+c-
no rotation about a-axis
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� Different tilts give rise to different lattice centering
Page 28
Derivation of space group symmetry� 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 29
Examples of tilted perovskites� Tilt system (10) and (14) are dominant in practice
Pyrochlores� Pyrchlores have the generic
formula A2B2X6X’– Example La2Sn2O7
– The structure consists of a framework of corner sharing BX6octahedra
– Anions X’ may be completely missing giving rise to defect pyrochlores such as KTaO3
– Defect pyrochlores are often readily ion exchangeable
– B ions may be mixed and structure may be A deficient e.g. KNbWO6
Page 30
Spinel (MgAl2O4)
�Spinel 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
� General formula is AB2O4 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 31
Compounds with a Spinel Structure � Note occurrence of 2,3 2,4 1,3,4 and 1,2,5 spinels
Garnets (A3B’2B”3O12)� Of interest due to magnetism, optical properties and
abilitiy to function as Laser hosts
Page 32
Al2O3, LiNbO3 and FeTiO3
� The corundum structure consists of a close packed oxide array with 2/3 of the octahedral holes filled by cations
� The LiNbO3 structure is closely related to that of Al2O3 with the Li and Nb ordered in the occupied octahedral holes
� FeTiO3 (Illmenite) has the same basic structure as LiNbO3, but it has a differentcation ordering pattern.
Cation ordering in Al2O3, LiNbO3 and FeTiO3
PolarNon-polar
top related