• Metallic– Electropositive: give up electrons

• Ionic– Electronegative/Electropositive

• Colavent– Electronegative: want electrons

– Shared electrons along

bond direction

Types of Primary Chemical BondsIsotropic, filled outer shells

+ - +

- + -

+ - +

+ + +

+ + +

+ + +

e-

e-

e-

Close-packed structures

Review: Common Metal Structureshcp ccp (fcc) bcc

ABABABABCABC not close-packed

Features• Filled outer shells spherical atom cores, isotropic bonding• Maximize number of bonds high coordination number• High density

Metals• single element, fairly electropositive• elements similar in electronegativity

cation

anion

Ionic Compounds• elements differing

in electronegativity

CERAMICS

Ionic Bonding & Structures

• Isotropic bonding• Maximize packing density• Maximize # of bonds, subject to constraints

– Like atoms should not touch– Maintain stoichiometry– Alternate anions and cations

Ionic Bonding & Structures

+ –

–

––

–

–

+ –

–

––

–

–

Isotropic bonding; alternate anions and cations

––

–

– –

–+

Just barely stable

Radius Ratio “Rules”

Cubic Coordination: CN = 8

2RA

2(rc + RA)

2 AR a

3c A

A

r RR

3 1 0.732c

A

rR

a

2( ) 3A cR r a

Cuboctahedral: CN = 12

rc + RA = 2RA

rc = RA rc/RA = 1

2RA

rc + RA

Radius Ratio RulesCN (cation) Geometry min rc/RA

2 none(linear)

3 0.155(trigonal planar)

4 0.225(tetrahedral)

CN Geometry min rc/RA

6 0.414(octahedral)

8 0.732(cubic)

12 1(cuboctahedral)

Ionic Bonding & Structures• Isotropic bonding• Maximize # of bonds, subject to constraints

– Like atoms should not touch• ‘Radius Ratio Rules’ – rather, guidelines• Develop assuming rc < RA

• But inverse considerations also apply• n-fold coordinated atom must be at least some size

– Maintain stoichiometry• Simple AaBb compound: CN(A) = (b/a)*CN(B)

– Alternate anions and cations

Radius Ratio Rules

CN (cation) Geometry min rc/RA (f)2 linear none

3 trigonal planar 0.155

4 tetrahedral 0.225

6 octahedral 0.414

8 cubic 0.732

12 cubo-octahedral 1

if rc is smaller than fRA, then the space is too big and the structure is unstable

common in ionic compounds

sites occur within close-packed arrays

Local Coordination Structures• Build up ionic structures from close-

packed metallic structures• Given range of ionic radii: CN = 4, 6, 8

occur in close-packed structurestetrahedral

octahedral

HCP: tetrahedral sites

4 sites/unit cell2 sites/close-packed atom

HCP: octahedral sites

2 sites/unit cell1 site/close-packed atom

Sites in cubic close-packed

8 tetrahedral sites/unit cell2 tetrahedral sites/close-packed atom

4 octahedral sites/unit cell1 octahedral site/close-packed atom

Summary: Sites in HCP & CCP

2 tetrahedral sites / close-packed atom1 octahedral site / close-packed atom

sites are located between layers: number of sites/atom same for ABAB & ABCABC

Common Ionic Structure Types• Rock salt (NaCl) sometimes also ‘Halite’

– Derive from cubic-close packed array of Cl-

• Zinc blende (ZnS)– Derive from cubic-close packed array of S=

• Fluorite (CaF2)– Derive from cubic-close packed array of Ca2+

• Cesium chloride (CsCl)– Not derived from a close-packed array

• Complex oxides– Multiple cations

Example: NaCl (rock salt)

• Cl- ~ 1.81 Å; Na+ ~ 0.98 Å; rc/RA = 0.54

• Na+ is big enough for CN = 6– also big enough for CN = 4,

but adopts highest CN possible

• Cl- in cubic close-packed array

• Na+ in octahedral sites

• Na:Cl = 1:1 all sites filled

CN f

4 0.225

6 0.414

8 0.732

Rock Salt Structure

Cl

Na

CN(Cl-) also = 6RA/rc > 1 Cl- certainly large enough for 6-fold coordination

ccp array with sites shown

Lattice Constant Evaluationccp metal

4R = 2 a

a

R

a

R

a = 2(RA + rc) > ( 4/2)RA

rock salt

Example: ZnS• S2- ~ 1.84 Å; Zn2+ ~ 0.60 – 0.57 Å;

– rc/RA = 0.326 – 0.408• Zn2+ is big enough for CN = 4 • S2- in close-packed array• Zn2+ in tetrahedral sites• Zn:S = 1:1 ½ tetrahedral sites filled• Which close-packed arrangement?

– Either! “Polytypism”– CCP: Zinc blende or Sphaelerite structure– HCP: Wurtzite structure

CN f

4 0.225

6 0.414

8 0.732

ZnS: Zinc Blende

x

yz = 0 z = ½

x

yz = 1 z = ½

x

S2-

x

x

x

CCPanions as CP atomsfill 4/8 tetr sites

ZnS: Zinc Blende

CN(S2-) also = 4RA/rc > 1 S2- certainly large enough for 4-fold coordination

S2-

Zn2+

Example: CaF2 (Fluorite)• F- ~ 1.3 Å; Ca2+ ~ 1.0 Å;

– rc/RA = 0.77

• Ca2+ is big enough for CN = 8 – But there are no 8-fold sites in close-packed arrays

• Consider structure as CCP cations– F- in tetrahedral sites– RA / rc> 1 fluorine could have higher CN than 4

• Ca:F = 1:2 all tetrahedral sites filled• Places Ca2+ in site of CN = 8• Why CCP not HCP? - same reason as NaCl

CN f

4 0.225

6 0.414

8 0.732

Fluorite

CN(F-) = 4CN(Ca2+) = 8 [target]

F-

Ca2+

CsCl• Cl- ~ 1.8 Å; Cs+ ~ 1.7 Å;

– rc/RA = 0.94• Cs+ is big enough for CN = 8

– But there are no 8-fold sites in close-packed arrays• CsCl unrelated to close-packed structures

– Simple cubic array of anions– Cs+ in cuboctahedral sites– RA / rc> 1 chlorine ideally also has large CN

• Ca:Cl = 1:1 all sites filled

Cesium Chloride

Cl-

Cs+1 Cs+/unit cell1 Cl-/unit cellCN(Cs) = 8

Why do ionic solids stay bonded?2

1 2

4electrostaicpair

o

Z Z eEr

• Solid: repulsion between like charges• Net effect? Compute sum for overall all possible pairs

• Pair: attraction only

2

12 4

i jelectrostaticsolid cluster

i j o ij

Z Z eE

r

Sum over a cluster beyond which energy is unchanged

Madelung Energy

Can show 2

0( )

4electrostaticsolid

o

ZeE Nr

For simple structures Single rij

|Z1| = |Z2| = Madelung constant

Structures of Complex Oxides

• Multiple cations– Perovskite

• Capacitors• Related to high Tc superconductors

– Spinel• Magnetic properties

• Covalency– Zinc blende

• Semiconductors– Diamond

• Semiconductors– Silicates

• Minerals

Perovskite– Perovskite: ABO3 [B boron]

• A2+B4+O3 A3+B3+O3 A1+B5+O3

• CaTiO3 LaAlO3 KNbO3

• Occurs when RA ~ RO and RA > RB

• Coordination numbers– CN(B) = 6; CN(A) =– CN(O) = 2B + 4A

• CN’s make sense? e.g. SrTiO3

– RTi = 0.61 Å

– RSr = 1.44 Å

– RO = 1.36 Å http://abulafia.mt.ic.ac.uk/shannon/ptable.php

12

above/below

RTi/RO = 0.45

RSr/RO = 1.06

A

BO

Tolerance factorclose-packed directions

A

B