1. Topics Significant figures Structural motifs Ionic conduction
Fuel cells – PEM and SOFC
Resistivity / conductivity
Radius ratios

2. % occupancy of tetrahedral and octahedral voids?

3. Half tetrahedral

4. Many stacking variants possible

5. Many intermediates between CCP and HCP are possible

6. ZnS Cu2HgI4 Voids and conduction
Disordered high-T (left) and ordered low-T (right) unit cell of Cu2HgI4. In the disordered phase, there are on average two Cu+ ions and one Hg2+ ion for every four Iˉ anions. However, the positions of these cations are not fixed – in any given unit cell, it is expected that these three cations will occupy a random subset of the four potential tetrahedral Cu/Hg sites, marked in gray.
Cu2HgI4
Single (left) and doubled (right) unit cell of ZnS (zinc blend structure)
Voids and conduction

7. Ionic conduction
For two cations of the same size but different charge, which will be held less tightly by the lattice?
For two cations of the same charge but different sizes, which will move more easily through the lattice?
Larger charge
Smaller charge
Larger size
Smaller size

8. Sizes of voids in spherical packings
(See structure image for BCC structure in Diamond)
A sphere of this size (relative to the lattice of size of its neighbors) is just able to touch all off its neighbors for the void geometries below. CN
Relative radius
Void geometry
Polyhedron name 2
<15.5%
Linear
Line 3
15.5%
Triangular
Triangle 4
25.5%
Tetrahedral
Tetrahedron 6
41.4%
Octahedral
Octahedron 8
73.2%
Cubic (BCC)
Cube 12
100%
Cuboctahedral (HCP, CCP)
Cuboctahedron

9. Resistivity and conductivity
R = V / I (W = V/A)
V = IR h w l
R a l R a 1/w R a 1/h [R a 1/Area]
(W cm)
(S cm-1) Siemens = 1/W