Describing the structure of solids 2ww2.chemistry.gatech.edu/class/6182/wilkinson/slide1.pdf ·...

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

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

Unit cell for hcp material

�Note unit cell is not a hexagon shape

Cubic close packing

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

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

Holes in cubic close packed structures

Tetrahedral holes

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

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

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

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

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

The NaCl (rock salt) structure

Compounds with the NaCl structure

� Typically, do not have soft anion and soft cation

The ZnS (Zinc Blende) structure

Compounds with the zinc blende structure

� Bonding often more covalent than in materials with NaCl structure

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

Wurtzite

Compounds with a Wurtzite structure

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

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

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

Rutile (TiO2)�Edge sharing chains bring metal centers close

together; possible metal-metal bonding

Compounds with a Rutile structure

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

The CdCl2 structure

�Long stacking repeat sequence

Compounds with a CdCl2 structure

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

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

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

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

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

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

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

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

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

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

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

Describing the structure of solids 2ww2.chemistry.gatech.edu/class/6182/wilkinson/slide1.pdf ·...

Documents

Transcript of Describing the structure of solids 2ww2.chemistry.gatech.edu/class/6182/wilkinson/slide1.pdf ·...