1. Ionic Compounds
anion
cation
Ceramics

2. 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
sites occur within close-packed arrays
common in ionic compounds
if rc is smaller than fRA, then the space is too big and the structure is unstable

3. 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

4. Discussed Already CN f 4 0.225 6 0.414 8 0.732 ZnS: Zinc Blende
CaF2: Fluorite
S2-
Ca2+
Zn2+ F-
rCa/RF = 0.77
CN(Ca2+) = 8
rZn/RS = 0.33 – 0.41
CN(Zn2+) = 4
Cations in close-packed array

5. 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
CNA also = 6; RA/rc = 1.85, Cl- is definitely large enough for CNA = 6

6. Rock Salt Structure Cl Na ccp array with sites shown CN(Cl-) also = 6
CNA also = 6; RA/rc = 1.85, Cl- is definitely large enough for CNA = 6
ccp array with sites shown
CN(Cl-) also = 6
RA/rc > 1  Cl- certainly large enough for 6-fold coordination

7. Lattice Constant Evaluation
rock salt
ccp metal a R a R
4R = 2 a
a = 2(RA + rc) > ( 4/2)RA

8. CsCl Cl- ~ 1.8 Å; Cs+ ~ 1.7 Å; Cs+ is big enough for CN = 8
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  clorine ideally also has large CN
Ca:Cl = 1:1  all sites filled

9. Cesium Chloride
Cl-
1 Cs+/unit cell
1 Cl-/unit cell
CN(Cs) = 8
Cs+

10. Unit Cells & Lattice Points
BCC Metal
CsCl Structure
How many lattice points per unit cell?

11. Covalent Compounds
sp3
s2p1
s2p2
s2p3
s2p4 s2
semi-conductors

12. Covalent Structures Recall: zinc blende  both species tetrahedral
ZnS:
GaAs:
or sp3
single element: C or Si or Sn 4 4
diamond
How many lattice points per unit cell?

13. Brief Review Metals Ionic structures Covalent structures
Close-packed structures (CN = 12)
Cubic close-packed, hexagonal close-packed
Subtle reasons for selecting one over the other
Slightly less close-packed
Body centered cubic (CN = 8)
Influence of covalency
Ionic structures
Close-packed with constraints
Covalent structures
Not close-packed, bonding is directional
Any can be strongly or weakly bonded (Tm)

14. Diamond vs. CCP 8 atoms/cell, CN = 4 4 atoms/cell, CN = 12
½ tetrahedral sites filled

15. Computing density Establish unit cell contents Compute unit cell mass
Compute unit cell volume
Unit cell constant, a, given (or a and c, etc.)
Or estimate based on atomic/ionic radii
Compute mass/volume, g/cc
Example: NaCl
Contents = 4 Na + 4 Cl
Mass = 4(atom mass Na + atomic mass Cl)/No
Vol = a3
Units = Cl Na
Avogardo’s #

16. Single Crystal vs. Polycrystalline
Rb3H(SO4)2
Diamond
Quartz (SiO2)
Ba(Zr,Y)O3-d
Regions of uninterrupted periodicity amalgamated into a larger compact
Periodicity extends uninterrupted throughout entirety of the sample
External habit often reflects internal symmetry
= grains
delineated by grain boundaries

17. Polycrystallinity