1. Objectives By the end of this section you should:
recognise a range of basic crystal structures
appreciate that a variety of important crystal structures can be described by close-packing
be able to compare and contrast similar structures

2. Why? All crystal structures can be described by:
unit cell + symmetry + atomic positions
symmetry
Unit cell (cubic)

3. Why? All crystal structures can be described by:
unit cell + symmetry + atomic positions
It is also helpful to be descriptive!
Can use concepts of close packing, polyhedra, interstitials to compare structures
Complex structures can be related back to basic ones
Correlate with properties?

4. Example 1 – Diamond Structure
Carbon atoms in all fcc positions
Carbon atoms in half of tetrahedral positions (e.g. T+)
Carbon coordinated to 4 other carbon atoms – all are tetrahedral
Looking at tetrahedra in the structure helps us see the “diamond shape”

5. Diamond Structure
Silicon, germanium and -tin also adopt this structure (all group 4 elements)
Melting Point (ºC)
Conductor?
Carbon
3550
Insulator
Silicon
1410
Semiconductor
Germanium
940
-Tin
230
Conductor
radius

6. Example 2 - Zinc Blende (ZnS: Sphalerite)
Sulphur atoms in all fcc positions
Zinc atoms in half of tetrahedral positions (e.g. T+)
Comparison with Diamond
Very important in semiconductor industry (e.g. GaAs)
Ball and stick model shows us the 4-fold coordination in both structures

7. Example 3 – Fluorite/Antifluorite structure
Antifluorite, Na2O
Oxygen atoms in all fcc positions
Sodium atoms in ALL tetrahedral sites
Fluorite, ZrO2
Zr atoms in all fcc positions
O atoms in ALL tetrahedral sites
Note formulae: blue atoms (fcc) – 4 per unit cell
red atoms (tetrahedral) – 8 per unit cell

8. Example 4 - Nickel Arsenide (NiAs)
h.c.p. analogue of rocksalt structure
h.c.p. arsenic with octahedral Ni
c pointing towards us
c pointing upwards

9. Coordination of As is also 6 but as a trigonal prism:
In the c-direction, the Ni-Ni distance is rather short. Overlap of 3d orbitals gives rise to metallic bonding.
The NiAs structure is a common structure in metallic compounds made from (a) transition metals with (b) heavy p-block elements such as As, Sb, Bi, S, Se.

10. Descriptions of Structures
With ccp anion array:
Rock salt, NaCl O occupied
Zinc Blende, ZnS T+ (or T-) occupied
Antifluorite, Na2O T+ and T- occupied
With hcp anion array:
Wurtzite, ZnS T+ (or T-) occupied
With ccp cation array:
Fluorite, ZrO2 T+ and T- occupied

11. Summary (see web pages)

12. Summary of AX structures
 wurtzite
ZnS  CN = 4
 sphalerite
NaCl, NiAs CN = 6
CsCl CN = 8
General trend is to get higher coordination numbers with larger (heavier) cations. This is seen also with AX2 structures

13. Summary of AX2 structures
SiO2, BeF2 silica structure CN = 4 : 2
TiO2, MgF2 rutile structure CN = 6 : 3
CdCl2, CdI2 layer structure CN = 6 : 3
PbO2, CaF2 fluorite structure CN = 8 : 4
Compare: 1) Be, Mg, Ca fluorides
2) Si, Ti, Pb dioxides

14. Ionic radii and bond distances
Ionic radii cannot be accurately “measured” - estimated from trends in known structures or from “electron density maps” (crystallography)
(reference - Shannon, Acta Cryst. (1976) A32 751)
Oxygen ion: r0 taken as 1.26 Å

15. Compromise
PX3012 will return to this concept later in the course

16. Refs:
Krug et al. Zeit. Phys Chem. Frankfurt 4 36 (1955)
Krebs, Fundamentals of Inorganic Crystal Chemistry, (1968)

17. Summary
Many important structures can be described by close packing with different interstitial sites filled
Similar structures sometimes have similar properties (but see section 7)
Comparison of structures can give important information on ionic radii (and trends).