Topics

• Significant figures

• Structural motifs

• Ionic conduction• Fuel cells – PEM and SOFC• Resistivity / conductivity

• Radius ratios

% occupancy of tetrahedral and octahedral voids?

Half tetrahedral

Many stacking variants possible

Many intermediates between CCP and HCP are possible

ZnS

Zn+2

S-2

a

b

c

Zn+2

S-2

Zn+2

S-2

Single (left) and doubled (right) unit cell of ZnS (zinc blend structure)

CuHg

I

Hg

Cu

I

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

Hg

Cu

I

Voids and conduction

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 chargeSmaller charge

Larger sizeSmaller size

Sizes of voids in spherical packings

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

(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.

Resistivity and conductivity

• V = IR

lw

h

• R l R 1/w R 1/h [R 1/Area]

R = V / I ( = V/A)

length

areaR

1

( cm) (S cm-1) Siemens = 1/