CRYSTAL CHEMISTRY

Wh i l h i ? Reading:

• description and classification of crystals

iti t t l ti hi

What is crystal chemistry? Reading: West 7, 8

• composition-structure relationships

• the conditions in which particular type of crystal structure is observed

• structure property relations• structure-property relations

Common ways to describe crystals:Common ways to describe crystals:

• unit cell approach (specify size, shape and atomic positions)

• close-packing approach (good for metals alloys ionic structures covalent• close-packing approach (good for metals, alloys, ionic structures, covalent

networks, molecular and supermolecular solids)

• space-filling polyhedron approachspace g po y ed o app oac

63

CLOSE-PACKED CRYSTAL STRUCTURESConsider the close-packing of incompressible (hard) spheres:Consider the close-packing of incompressible (hard) spheres:

In 2D, regular close-packing requires an hexagonal array (HCP)

Most efficient wayto pack spheres of single size

• 6 nearest neighbors

Coordination number (CN): 6

In 3D, regular close-packing involves stacking 2D HCP arrays

CCP

Regular(crystalline)

ki

Irregularpacking

packing

64

HEXAGONAL CLOSE-PACKED STRUCTUREAn HCP crystal is a close-packed structure with the stacking sequence ABABABAn HCP crystal is a close-packed structure with the stacking sequence ...ABABAB...

To construct:1st layer: 2D HCP array (layer A)2 d l HCP l i h h h l d i l i i i 1 t l (B)2nd layer: HCP layer with each sphere placed in alternate interstices in 1st layer (B)3rd layer: HCP layer positioned directly above 1st layer (repeat of layer A)

…ABABABAB…

AA

B

A B A AHCP is two interpenetrating simple hexagonal lattices displaced by a1/3 + a2/3 + a3/2

65

HCP STRUCTURE• not a Bravais latticenot a avais lattice

Orientation alternateswith each layerwith each layer

• each sphere touches 12 equidistant nearest neighbors (CN = 12)

Six in plane, six out-of-plane

• structure has maximum packing fraction possible for single-sized spheres (0.74)p g f p f g p ( )

66

HCP STRUCTURE

• unit cell is a simple hexagonal lattice with a two-point basis

(0 0 0)a

• ideal ratio c/a of 8 / 3 1.633(0,0,0)

(2/3,1/3,1/2)a• {0002} planes are close packed

Plan view• ranks in importance with FCC and BCCBravais lattices

67

HCP STRUCTURE

• about 30 elements crystallize in the HCP form

68

CUBIC CLOSE-PACKED STRUCTUREA CCP crystal is a close-packed structure with the stacking sequence ABCABCA CCP crystal is a close-packed structure with the stacking sequence ...ABCABC...

To construct:1st layer: 2D HCP array (layer A)2 d l HCP l i h h h l d i l i i i 1 t l (B)2nd layer: HCP layer with each sphere placed in alternate interstices in 1st layer (B)3rd layer: HCP layer placed in the other set of interstitial depressions (squares, C)4th layer: repeats the 1st layer (A)

ABCABCABC…ABCABCABC…

stacking gof HCP layers

along body diagonals

A B CIt t t th t th CCP t t i j tIt turns out that the CCP structure is just

the FCC Bravais lattice!69

CCP STRUCTURE• CN = 12 packing fraction 0 74• CN = 12, packing fraction 0.74

• {111} planes are close packed

• 4 atoms in unit cell

Plan viewPlan view

70

• most common are HCP and CCP

CLOSE-PACKED STRUCTURESmost common a e C and CC

• an infinite # of alternative stacking sequences exist

Example: silicon carbide has over 250 polytypese.g., 6H-SiC

stacking sequence …ABCACB…

71

STACKING FAULTSStacking faults are one or two layer interruptions in the stacking sequence that

destroy lattice periodicity

e.g., an <110> projection of an FCC lattice:

ABCA

ABC

B

[111]-

missing lA

BCAB

BCABC

[001]-[110]-

[110] planeof atoms

perfect FCCABCABCABC

faulted FCCABCBCABC

C C[110]

The stacking fault is an example of a planar defect2• stacking fault energy γ ~100 mJ m-2

• results also in perpendicular linear defects called dislocations72

EXAMPLE InAs nanowires - <110> projection

Caroff, P. et al. Nature Nanotechnology 4, 50 - 55 (2009) 73

• CCP and HCP have very similar lattice energiesy g• no clear cut trends

74

Nature 353, 147 - 149 (12 Sep 1991)

G A (CC )Rare Gases: Ne, He, Ar, Kr, Xe (CCP)75

gold nanocrystalsX. M. Lin

76

ANOTHER VIEW OF CLOSE PACKING

77

. It was reviewed by a panel of 12 referees; the panel reported in 2003 after 4 years ofreviewed by a panel of 12 referees; the panel reported in 2003, after 4 years of work, that it was “99% certain” of the correctness of the proof, but couldn’t verify the correctness of all of the computer calculations. Hales and Ferguson (his student) received the Fulkerson Prize for outstanding papers in the area of(his student) received the Fulkerson Prize for outstanding papers in the area of discrete mathematics in 2009.

http://en.wikipedia.org/wiki/Kepler_conjecture78

PACKING FRACTIONSThe fraction of the total crystal volume that is occupied by spheres

CCP (and HCP)2aradius

The fraction of the total crystal volume that is occupied by spheres

3

3atoms

4 24 ( )3 4 2 0.7405

6VV

a

fractiona

2a

4radius

cell 6V a2a

a 74%

34 ( )a

BCC3

4aradius

SC

3

( )3 2 0.5236fraction

a

34 32 ( )3 4 0 6802

a

fraction

4

52%33 4 0.6802fraction

a

68%52%

79

80

b f / i ll

DENSITY CALCULATION

atomsm nAV V N

n: number of atoms/unit cellA: atomic mass

VC: volume of the unit cellcell C AV V N VC: volume of the unit cell

NA: Avogadro’s number (6.023x1023 atoms/mole)

Calculate the density of copper.

RCu =0.128nm, Crystal structure: FCC, ACu= 63.5 g/mole

n = 4 atoms/cell, 3 3 3(2 2 ) 16 2CV a R R , ( )C

38 3 23

(4)(63.5) 8.89 /[16 2(1.28 10 ) (6.023 10 )]

g cm

[16 2(1.28 10 ) (6.023 10 )]

8.96 g/cm3 in the literature81

INTERSTICIAL SITES IN CP STRUCTURESA large number of ionic structures can be regarded as built of CP layers of anionsA large number of ionic structures can be regarded as built of CP layers of anions

with the cations placed in interstitial sites

for every anion, there is 1 Octahedral site and 2 Tetrahedral sitesy ,

82

Octahedral holesOctahedral holes

di tdi tcoordinates:coordinates:½00½000½00½00½00½000½ 00½ ½½½ ½½½

= O site

cavities have <100>cavities have <100>i t tii t tiorientationorientation

83

Tetrahedral holes in CCPTetrahedral holes in CCP TT++ sites:sites:+ + ¾¼¼ ¾¼¼ ¼¾¼¼¾¼¼¼¾¼¼¾¾¾¾¾¾¾

TT-- sites:sites:¼¼¼¼¼¼¼¼¼¼¼¼¾¾¼¾¾¼¼¾¾¼¾¾¾¼¾¾¼¾

cavities have <111> orientationcavities have <111> orientation84

Holes in HCPHoles in HCP

O sites:O sites:O sites:O sites:2/3,1/3,1/42/3,1/3,1/42/3,1/3,3/4 2/3,1/3,3/4 , ,, ,

TT++ sites:sites:1/3 2/3 1/81/3 2/3 1/8

(1/3,2/3,1/2)

1/3,2/3,1/81/3,2/3,1/80,0,5/8 0,0,5/8

(0,0,0) TT-- sites:sites:0,0,3/80,0,3/8a2

a1

, ,, ,1/3,2/3,7/8 1/3,2/3,7/8

85

LOCATION OF OCTAHEDRAL HOLES

86

LOCATION OF TETRAHEDRAL HOLES

(3/8 of a unit cell directly above/below each anion)

87

SIZE OF OCTAHEDRAL CAVITYOnly cations smaller than the diameter of the cavity can fit y y

without forcing the anion lattice to expand

2 2a r r

from cell edge

M ti

2 2M Xa r r

from face diagonalM = cationX = anion 2 2 Xa r

.The cation radius must be< 41% of the anion radius88

SIZE OF TETRAHEDRAL CAVITYThe tetrahedral holes are twice asThe tetrahedral holes are twice as

numerous but six times smaller in volume

from face diagonal

2 / 2 2 Xa rg

from body diagonalfrom body diagonal

3 / 2 2 2M Xa r r

The cation radius must be< 23% of the anion radius89

EUTACTIC STRUCTURESStructures in which the arrangement of ions is the same as in a close packed arrayStructures in which the arrangement of ions is the same as in a close packed array

but the ions are not necessarily touching

Within certain loose limits (given by the radius ratio rules), cations too large to fit in the interstices can be accommodated by an

expansion of the anion arrayexpansion of the anion array

• anions don’t like to touch anyway

• modern techniques show that, in many cases, anions (cations) are not as large (small) as previously thoughtg ( ) p y g

• we still describe eutactic structures as CCP or HCP lattices with ions in some fraction of the interstitial siteswith ions in some fraction of the interstitial sites

90

CRYSTALS THAT CAN BE DESCRIBED IN TERMS OF INTERSTITIAL FILLING OF ATERMS OF INTERSTITIAL FILLING OF A

CLOSE-PACKED STRUCTURE

91

SOME EUTACTIC CRYSTAL STRUCTURESVariables:Variables:

1) anion layer stacking sequence: CCP or HCP array?2) occupancy of interstitial sites

92

93

NaCl (ROCK SALT, HALITE) STRUCTURE(CCP 100% O t H l Fill d)(CCP, 100% Oct. Holes Filled)

Space Group = Fm3mLattice = FCCBasis = Cl (0,0,0), Na (½,½,½)

Coordination = 6, 6Cation Coord. → OctahedronAnion Coord → OctahedronAnion Coord. → OctahedronConnectivity → Edge sharing octahedra

with faces parallel to {111}4 NaCl in unit cell 94

POLYHEDRAL REPRESENTATION• shows the topology and indicates interstitial sites• shows the topology and indicates interstitial sites• tetrahedra and octahedra are the most common shapes

Rock Salt:

• Array of edge sharing NaCl6 octahedra

h h d h ll d

Rock Salt:

• Each octahedron shares all 12 edges

• Tetrahedral interstices

Galena (PbS) 95

ROCK SALT - OCCURANCE

• Very common (inc. 'ionics', 'covalents' & 'intermetallics' )

lk l h l ( l ) • Most alkali halides (CsCl, CsBr, CsI excepted)

• Most oxides / chalcogenides of alkaline earths

M n nit id s bid s h d id s ( Z N TiC N H)• Many nitrides, carbides, hydrides (e.g. ZrN, TiC, NaH)

96

COMPLEX ION VARIANT OF ROCK SALT

• space group = Pa3

• sulfur dimers oriented along <111>

97

(CCP T H l Fill d)

ZINC BLENDE (ZnS, SPHALERITE)(CCP, T+ Holes Filled)

Space Group = F43mLattice = FCCB i S (0 0 0) Z (¼ ¼ ¼)Basis = S (0,0,0), Zn (¼,¼,¼)

Coordination = 4, 4Cation Coord. → TetrahedronAnion Coord. → TetrahedronConnectivity → Corner sharing Tetra.4 ZnS in unit cell 98

ZINC BLENDE GaAs

• bonding is less ionic than in rock salt

• common for Be, Zn, Cd, Hg chalcogenides (i.e., ZnS, ZnSe, ZnTe)

• common for III-V compounds (B, Al, Ga, In with N, P, As, Sb)

99

DIAMOND STRUCTURES h l it b t ith id ti l t i ll itiSame as sphalerite, but with identical atoms in all positions

Space Group = F43mLattice = FCCB i C (0 0 0) C (¼ ¼ ¼)Basis = C (0,0,0), C (¼,¼,¼)

Coordination = 4Connectivity → Corner sharing Tetra.y g8 C atoms per unit cell

100

FLUORITE (CaF2) & ANTIFLUORITE (Na2O)Fluorite : CCP of Ca2+, 100% Tetra. Holes Filled with F-

Anti-fluorite : cation and anion positions are reversed

Ca2+

Space Group = Fm3m

Lattice = FCCBasis = Ca2+ (0 0 0) F- (¼ ¼ ¼) & (¾ ¾ ¾)Basis = Ca2+ (0,0,0), F (¼,¼,¼) & (¾,¾,¾)

Coordination = 8, 4 (fluorite)Cation Coord. → CubicAnion Coord. → TetrahedralConnectivity → Edge sharing FCa4 tetrahedra or edge sharing CaF8 cubes4 CaF2 in unit cell 101

ALTERNATIVE REPRESENTATIONS

Ca2+

Displacing the unit cell by ¼ of a body diagonal emphasizes the cubic cation coordination:

F-

102

FLUORITE / ANTIFLUORITE

Ca2+

• origin of the term “fluorescence” (1852)

fl it f fl id f l• fluorite common for fluorides of large,divalent cations and oxides of largetetravalent cations (M2+F2 and M4+O2)

• antifluorite common foroxides/chalcogenides of alkali earths (M2O)

CaF2

103

FLUORESCENT MINERALS

http://en.wikipedia.org/wiki/Fluorescence= fluorite 104

COMPARING NaCl, ZnS, Na2O

NaCl ZnS Na2O

105

106

Li3Bi EXAMPLE

107

NiAs STRUCTURE(HCP, 100% Oct. Holes Filled)

2

Space Group = P63/mmcLattice = Primitive hexagonalBasis = As (0,0,0) & (2/3,1/3,1/2)

Ni (1/3,2/3,1/4) & (1/3,2/3,3/4)Coordination = 6, 6Cation Coord. → OctahedronAnion Coord → Trigonal prismAnion Coord. → Trigonal prismConnectivity → Edge/face sharing Oct.

or edge-sharing trigonal prisms2 NiAs in unit cell 108

Alternative unit cell with Ni at the origin:

109

•Transition metals withNiAs

Transition metals withchalcogens, As, Sb, Bi e.g. Ti(S,Se,Te); Cr(S,Se,Te,Sb); ( , , , )Ni(S,Se,Te,As,Sb,Sn)

110

WURTZITE (ZnS) STRUCTURE(HCP T H l Fill d)(HCP, T+ Holes Filled)

Space Group = P63mcLattice = Primitive hexagonalB i S (0 0 0) & (2/3 1/3 1/2)Basis = S (0,0,0) & (2/3,1/3,1/2)

Zn (0,0,5/8) & (2/3,1/3,1/8)Coordination = 4, 4Cation Coord. → TetrahedronAnion Coord. → TetrahedronConnectivity → Corner sharing Tetra.2 ZnS in unit cell 111

ZnO

Projections perpendicular to close-packed planes

112

113

Very different next-nearest neighbor coordinations & beyond

114

HCP VERSION OF CaF2?N t t k ith ll T t it (T d T ) fill d i HCPNo structures are known with all Tetra. sites (T+ and T-) filled in HCP- i.e. there is no HCP analogue of the Fluorite /Anti-Fluorite structure

Why?

The T+ and T- interstitial sites above and below a layer of close-packed spheres in HCP are too close to each HCP are too close to each other (distance = 0.25c) to tolerate the coulombic repulsion generated by filling with like-charged ions.

Face-linking is unfavorable115

RUTILE STRUCTURE (TiO2)(distorted HCP, 50% Oct. Holes Filled)( , )

Ti O

Space Group = P4 /mnm

(0,0,0)

Space Group = P42/mnm

Lattice = Primitive tetragonalBasis = Ti (0,0,0) & (½,½,½)O (0 3 0 3 0) (0 7 0 7 0) (0 8 0 2 0 5) (0 2 0 8 0 5)O (0.3,0.3,0), (0.7,0.7,0), (0.8,0.2,0.5), (0.2,0.8,0.5)Coordination = 6, 3Cation Coord. → OctahedralAnion Coord. → Trigonal planarConnectivity → chains of edge-sharing Oct.

along c axis, linked by vertices2 TiO2 per unit cell 116

ANATASE STRUCTURE (TiO2)(di t t d CCP 50% O t H l Fill d)(distorted CCP, 50% Oct. Holes Filled)

a = 3.776 Åb 3 776 Å

Volume anatase TiO2: 136.25 Å3

b = 3.776 Åc = 9.486 Å

Ti O

2rutile TiO2: 62.07 Å3

Space Group = I41/amd

Lattice = body-centered tetragonal

Coordination = 6, 3Cation Coord. → OctahedralAnion Coord. → Trigonal planarConnectivity chains of edge sharing OctConnectivity → chains of edge-sharing Oct.

along c axis, linked by vertices4 TiO2 per unit cell 117

RUTILE AND ANATASE

chains of edge sharing oct.,linked at corners

greater density of edge sharing→ a bit less stablelinked at corners → a bit less stable

118

CdI2 STRUCTURE(HCP ith Cd i O t H l f lt t l )(HCP, with Cd in Oct. Holes of alternate layers)

A layered crystal

Cd

I

Space Group = P3m1Lattice = Primitive trigonalB i Cd (0 0 0)Basis = Cd (0,0,0)

I (2/3,1/3,1/4) & (1/3,2/3,3/4)Coordination = 6, 3Cation Coord. → OctahedronAnion Coord. → Trigonal pyramidConnectivity → sheets of edge-sharing Oct.1 CdI2 per unit cell 119

Alternative unit cell with Cd at the origin:the origin:

CdI6 units NiAs6 units6 6

120

CdI2 - OCCURANCE

• Iodides of moderately polarizing cations; bromides andchlorides of strongly polarizing cations; f g y p g ;

e.g. PbI2, FeBr2, VCl2

• Hydroxides of many divalent cations e.g. (Mg,Ni)(OH)2

• Di-chalcogenides of many quadrivalent cations TiS Z S C Te.g. TiS2, ZrSe2, CoTe2

121

CdCl2 STRUCTUREThe CCP analogue of CdI2

(CCP, with Cd in Oct. Holes of alternate layers along [111])

Space Group = R32/m

CdCl6 octahedra

Chlorides of moderately polarizing cationse.g. MgCl2, MnCl2

Di-sulfides of quadrivalent cations e.g. TaS2, NbS2 (CdI2 form as well) 122

Formula Type and fraction of sites occupied CCP HCP

AB All octahedral NaClRock Salt

NiAsNickel Arsenide

Half tetrahedral(T+ or T-)

ZnSZinc Blende

ZnSWurtzite

N O A ti Fl itA2B All tetrahedral Na2O Anti-FluoriteCaF2 Fluorite not known

A3BAll octahedral& t t h d l Li3Bi not knownA3B & tetrahedral Li3Bi not known

AB2

Half octahedral (Alternate layers

full/empty)CdCl2 (Cadmium Chloride) CdI2 (Cadmium Iodide)

full/empty)

Half octahedral(Ordered

framework arrangement)

TiO2 (Anatase) CaCl2TiO2 (Rutile)

arrangement)

AB3

Third octahedral Alternate layers

2/3 full/emptyYCl3 BiI3 123

PEROVSKITE STRUCTURE ABO3 (CaTiO3)(CCP of Ca & O , 25% Oct. Holes Filled by Ti)

B C llA-Cell

Space Group = Pm3mLattice = Primitive cubicB i Ti (0 0 0) C (½ ½ ½)

An extremely important class of ABX3compounds:

B-Cell

Basis = Ti (0,0,0), Ca (½,½,½), O (½,0,0), (0,1/2 ,0) & (0,0,½)

Coordination = Ca-12 ; Ti-6; O-6Ca Coord. → Cuboctahedron

compounds:MagnetoresistanceFerroelectricityMultiferroics

dTi Coord. → OctahedronO Coord. → distorted octahedron (4 Ca, 2 Ti)1 CaTiO3 per unit cell

SuperconductivityCatalysis (fuel cells)Spin transport 124

PEROVSKITE CONNECTIVITY

B-Cell

3D network of corner-sharing octahedra

Network of face-sharing cuboctahedraoctahedra cuboctahedra

125

Perovskites: the most widely studied oxide structurePerovskites: the most widely studied oxide structure

• Wide range of chemistries possible- thousands of examples knownthousands of examples known

• Cubic, tetragonal, and orthorhombic symmetries are common

- high Tc cuprate superconductorsColossal Magneto Resistance (La SrMnO )

Unique properties of perovskites

- Colossal Magneto-Resistance (La,SrMnO3)- fast ion conduction (Li+, O2-), batteries, fuel cells- mixed electronic/ionic conduction, fuel cells- oxidation/reduction catalystsoxidation/reduction catalysts- ferroelectric / piezoelectric ceramics (BaTiO3, Pb(ZrTi)O3)- important mineral structure in lower mantle (MgSiO3, pyroxene)- frequency filters for wireless communications : Ba(Zn1/3Ta2/3)O3q y ( 1/3 2/3) 3

126

Perovskite Structure: ABX3AX

Tolerance factor (t):

A Xr r2( )

A X

B X

tr r

B

t Effect Likely structureA-Cell

t Effect Likely structure

> 1 A cation too large to fit in interstices

Hexagonal perovskite

0.9 - 1.0 ideal Cubic perovskite

0.71 - 0.9 A cation too small Orthorhombic perovskiteperovskite

< 0.71 A cation same size as B cation Possible close packed lattice 127

PEROVSKITESMost perovskites contain distorted octahedra and are not cubic These distortions giveMost perovskites contain distorted octahedra and are not cubic. These distortions give

perovskites a rich physics.

symmetry at 25°CBaTiO3: Ba2+ r = 1.56 Å

Ti4+ r = 0.68 ÅO2- r = 1.26 Å

t = 1.03 - tetragonal

symmetry at 25 C

O r 1.26 Å

KNbO3: K+ 1.65 ÅNb5+ 0.78 Å

t = 1.01 - orthorhombic

LiNbO3: Li+ 1.06 ÅNb5+ 0.78 Å

t = 0.81 – trigonal

LiNbO3 : ferroelectricity, Pockels effect, piezoelectricity, photoelasticity, nonlinear optical polarizabilitynonlinear optical polarizability

128

129

Reading: West 15

C m-2

V m-1V m 1

130

DI- , PARA- , AND FERROELECTRICSdipole moment: p = qd = αEresponse of atom to applied E field

P E

dipole moment: p = qd = αEpolarization: P = Σp/V

p pp

P = ε0χeEP : polarization (C/m2)ε0: vacuum permittivity – 8.85 x 10-12 C2 N-1 m-2

l b l ( l )p χe: electric susceptibility (unitless)E : electric field (V/m, or N/C)

p

dielectric polarization paraelectric polarization ferroelectric polarization

• linear: P = ε χ E • nonlinear • residual (zero field) polarization• linear: P = ε0χeE

• no P without E

• nonlinear

• no P without E

• residual (zero-field) polarization• reversible direction of residual P• very large susceptibilities

131

WHY IS BaTiO3 FERROELECTRIC

ferroelectric phase transition~0.1 Å displacement

> 120°C cubic, not FE< 120°C tetragonal, FE

transition occurs at the Curie temperature, Tc

132

con

stan

t εr = χe+ 1

diel

ectr

ic

133

FERROELECTRIC HYSTERESIS LOOPS

saturation polarization, Psremnant polarization, PR

dipoles aligned “up”

coercive field Ecoercive field, EC

dipoles aligned “down”

134

ORDERED ELECTRIC DIPOLE PHASES

ferroelectric (BaTiO3) • parallel ordering below Tc

antiferroelectric (PbZrO3)• antiparallel ordering below T• antiparallel ordering below Tc

• E field can induceferroelectric state

ferrielectric (Bi4Ti3O12)ferrielectric (Bi4Ti3O12)• net spontaneous polarization in only certain direction(s)

135

CURIE TEMPERATUREThermal energy destroys the ordered electric dipole state The temperature aboveThermal energy destroys the ordered electric dipole state. The temperature above

which this order-disorder phase transition occurs is the Curie temperature, Tc.

Above Tc, the material is often paraelectric.

orderedF / AF

randomizedorientation

PNote: These curves Pomit the “spikes” in Pat Tc

136

PHASE DIAGRAMS

137

K2NiF4 STRUCTURE (La2CuO4) Many “complex” structures are composed of simple familiar building blocks

Doped La2CuO4 was the first (1986) High-Tc Superconducting Oxide (Tc ~ 40 K)B d & Müll d d N b l P i

Many complex structures are composed of simple, familiar building blocks. The high-Tc copper oxide superconductors are an example.

Bednorz & Müller were awarded a Nobel PrizeLa2CuO4 may be viewed as if constructed from an ABAB... arrangement of Perovskite cells - known as an AB Perovskite!

B

A

B

2 La2CuO4 per unit cell 138

ALTERNATE VIEWS OF La2CuO4

We may view the structure as based on:y1. Sheets of elongated CuO6 octahedra, sharing only vertices 2. Layered networks of CuO4

6-, connected only by La3+ ions 139

COMMON STRUCTURAL FORM

Cations formFCC with O2-FCC with O2

interstitials

• Common structural motif of vertex-linked CuO4 squares• This motif occurs in all the high-T superconducting copper oxides • This motif occurs in all the high-TC superconducting copper oxides • The structures differ in the structure of the 'filling' in the 'sandwich‘of copper oxide layers - known as Intergrowth Structures 140

YBa2Cu3O7: THE 1,2,3 SUPERCONDUCTOR• the first material to superconduct at LN2 temperature, Tc > 77 K• YBa2Cu3O7 can be viewed as an Oxygen-Deficient Perovskite

141

T t p s f C sit s:

POLYHEDRAL REPRESENTATION OF YBCOTwo types of Cu sites: 1) Layers of CuO5 square pyramids2) Chains of vertex-linked CuO4 squares

CuO2BaOBaOCuOBaOCuOCuO2YCuO2

142

SPINEL STRUCTURE AB2O4 (MgAl2O4) (CCP, Mg in 1/8th of Tetra. Holes and Al in 50% of Oct. Holes)

a = 8.08 Å

Space Group = Fd3m

• extremely flexible structure, adoptedby over 100 compounds

Lattice = FCCCoordination = Mg-4; Al-6; O-4Mg Coord. → TetrahedronAl Coord. → Octahedron

• normal spinel: 8 A in Tetra., 16 B in Oct.

• inverse spinel: 8 A in Oct., 8 B in Oct. and Al Coord. OctahedronConnectivity → chains of Edge-sharing AlO6

octahedra, linked by MgO 4 tetra.8 MgAl2O4 per unit cell (56 atoms)

8 B in Tetra.• intermediate cations distributions also

occur. 143

144

SPINELS - OCCURANCEAluminium spinels: Aluminium spinels:

Spinel – MgAl2O4, after which this class of minerals is namedGahnite - ZnAl2O4H i F Al OHercynite - FeAl2O4

Iron spinels: Magnetite - Fe3O4Franklinite - (Fe,Mn,Zn)(Fe,Mn)2O4Franklinite (Fe,Mn,Zn)(Fe,Mn)2O4Ulvöspinel - TiFe2O4Jacobsite - MnFe2O4Trevorite - NiFe2O4

Ch i s i ls: Chromium spinels: Chromite - FeCr2O4Magnesiochromite - MgCr2O4

Others with the spinel structure: pUlvöspinel - Fe2TiO4Ringwoodite - Mg2SiO4, an abundant olivine polymorph within the Earth's mantle from about 520 to 660 km mantle from about 520 to 660 km depth, and a rare mineral in meteorites 145

CRYSTAL FIELD STABILIZATION ENERGYIn transition metal compounds d electron effects such as crystal field In transition metal compounds, d electron effects such as crystal field stabilization energy (CFSE) can be important in determining structure.

crystal field splitting diagrams

e.g. MF2 compounds (high spin rutile)

crystal field splitting diagrams

Δoct =

Δtetra =

No CFSE

Δtetra = (4/9)Δoct

CFSEoct = (0.4 × #t2g – 0.6 × #eg) Δoct

146

CATION SITE PREFERENCES IN SPINELSThe larger CFSE of metal ions in octahedral sites is sometimes an important

f d l ( l )

Normal - [A]tet[B2]octO4 Inverse - [B]tet[A,B]octO4

factor in determining spinel structures (normal vs inverse).

γ = fraction of A in oct. sitesγ = 0 is normal, γ = 1 is inverse

In the absence of CFSE effects: 2,3 spinels tend to be normal (MgAl2O4)4,2 spinels tend to be inverse (TiMg2O4)

l E f h f ll In 2,3 spinels, CFSE favors the following: 1) Chromium spinels (Cr3+) are normal2) Magnetite (Fe3O4) is inverse b/c 2) Magnetite (Fe3O4) is inverse b/c

Fe3+ has zero CFSE, while Fe2+ prefers oct. 3) Mn3O4 is normal b/c Mn2+ has no CFSE 147

CORUNDUM STRUCTURE (α-Al2O3)(HCP 2/3 f O t H l fill d)(HCP, 2/3 of Oct. Holes filled)

Space Group = R3c

Lattice = Primitive trigonal

Coordination = 6, 4Cation Coord → OctahedronCation Coord. → OctahedronAnion Coord. → distorted tetrahedronConnectivity → edge, face-sharing Oct.6 Al2O3 per unit cell

• Ruby (Cr), sapphire (Fe, Ti, Cr), Fe2O3

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