Types of Primary Chemical Bonds Isotropic, filled outer shells • Metallic – Electropositive: give up electrons • Ionic – Electronegative/Electropositive • Colavent – Electronegative: want electrons – Shared electrons along bond direction + + e e + + + + e + + + + + + + + Close-packed structures

Ionic Bonding & Structures

Isotropic bonding; alternate anions and cations – – – – – – + – – – – + – – + – – – – – Just barely stable –  Radius Ratio “Rules” 

a

Cubic Coordination: CN = 8

2(r c + R A ) 2

R A



a

2(

R A



r c

)  

r c



R A

 

R A r c R A

 3 3

a

0.732

2R A

CN (cation) 2 Radius Ratio Rules Geometry min r c /R A none (linear) 3 0.155

(trigonal planar) 4 0.225

(tetrahedral)

CN 6 8 12 Geometry min r c /R A 0.414

(octahedral) 0.732

(cubic) 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 r c < R A • But inverse considerations also apply • n-fold coordinated atom must be at least some size – Maintain stoichiometry – Alternate anions and cations

cation Ionic Compounds anion

Radius Ratio Rules CN (cation) 2 3 4 6 8 12 Geometry linear min r c /R A (

f

) none trigonal planar tetrahedral octahedral cubic 0.155

sites occur within 0.225

close-packed arrays 0.414

common in ionic compounds 0.732

cubo-octahedral 1 if r c is smaller than

f

R A , then the space is too big and the structure is unstable

Local Coordination  Structures • Build up ionic structures from close packed metallic structures • Given range of ionic radii: CN = 4, 6, 8 tetrahedral occur in close packed structures octahedral

HCP: tetrahdral sites

4 sites/unit cell 2 sites/close-packed atom

HCP: octahedral sites

2 sites/unit cell 1 site/close-packed atom

Sites in cubic close-packed

8 tetrahedral sites/unit cell 2 tetrahedral sites/close-packed atom 4 octahedral sites/unit cell 1 octahedral site/close-packed atom

Summary: Sites in HCP & CCP

2 tetrahedral sites / close-packed atom 1 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 (CaF 2 ) – Derive from cubic-close packed array of Ca 2+ • Cesium chloride (CsCl) –

Not

derived from a close-packed array

Example: NaCl (rock salt)

• Cl ~ 1.81 Å; Na + ~ 0.98 Å; r c /R A = 0.54

• Na + is big enough for CN = 6 – also big enough for CN = 4, but adopts highest CN possible

CN

4 6 8 • Cl in cubic close-packed array • Na + in octahedral sites • Na:Cl = 1:1  all sites filled

f

0.225

0.414

0.732

Rock Salt Structure

ccp array with sites shown

R A /r c CN(Cl ) also = 6 > 1  Cl certainly large enough for 6-fold coordination

Cl Na

Lattice Constant Evaluation

rock salt ccp metal

a

R 4R =  2

a a

R

a

= 2(R A + r c ) > ( 4/  2)R A

Example: ZnS

• S 2 ~ 1.84 Å; Zn 2+ ~ 0.60 – 0.57 Å; – r c /R A • Zn 2+ = 0.326 – 0.408

is big enough for CN = 4

CN

4 • S 2 in close-packed array 6 • Zn 2+ in tetrahedral sites • Zn:S = 1:1  8 ½ tetrahedral sites filled • Which close-packed arrangement?

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

f

0.225

0.414

0.732

x

ZnS: Zinc Blende S 2-

y z

= 0

z

= ½

z

= 1 x

z

 CCP anions as CP atoms fill 4/8 tetr sites = ½

y

x x x

x

ZnS: Zinc Blende

S 2 Zn 2+ CN(S 2 ) also = 4 R A /r c > 1  S 2 certainly large enough for 4-fold coordination