• 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

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

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– Alternate anions and cations

cation

anion

Ionic Compounds

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: tetrahdral 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)– 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

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+