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 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

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

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

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