## CHM 501 Lecture

### Solid State Structure

Since ions are basically spherical objects, the structures of ionic compounds arise from packing of spheres. Generally the most effective way to do this is to put objects as close to each other as possible (closest packed structures). There are two common closest packed structures.

Hexagonally closest packed (hcp): an ABAB sequence of spheres

solid circles are the 1st, 3rd, 5th, etc., layers open circles are the 2nd, 4th, 6th, etc. layers

There are two types of vacancies or holes: those with four neighbors (Td holes) and those with six neighbors (Oh holes). ~74% of the volume is empty; each sphere has twelve nearest neighbors adjacent to it

Cubic closest packed: ABCABC sequence of spheres

ccp = face centered cubic, i.e. draw a cube and put spheres at the corners and the center of each of the faces

Ionic compounds nearly always form closest packed structures if the ions are simple and spherical (nonspherical ions change things). Normally, the largest ion (typically the anion) forms the lattice and the smaller ion fills the holes - either Td or Oh holes.

When closest packed structures are not formed (and even when they are), the usual way of thinking about solid state crystalline structures is to find the smallest unit that repeats itself via translational symmetry over the whole macroscopic structure. This smallest repeat unit is called the unit cell. There are 14 types of unit cells called Bravais Lattices. The atoms or ions in the crystal do not determine the unit cell; it is determined by the translational symmetry!

To determine the Bravais lattice, 6 parameters are specified, 3 distances and 3 angles, and the occupation of the cell

Ionic Radii - the effective radius of an ion in a crystal

We assume that ionic radius is constant from compound to compound

How are these found?

Crystal structures only give internuclear distances r0

Assume that r0 = r+ + r (r+ = cation radius; r = anion radius)

Landé assumed that in LiI the iodides "touched" and that the Li+ fit completely in the holes

d = r + r

r0 = r+ + r

So now both radii can be determined.

Note: ionic radii are coordination number (CN) dependent.

Thus, radii are reported with CN, since this is important as well.

Real Crystals:

In real life lattices are not perfect; defects always exist, even at 0 K (this is thermodynamically required: enthalpy prefers perfection but entropy prefers randomness; get a balance with mostly perfect but a few defects).

Schottky defects: equal numbers of cations and anions are missing from the lattice

Frenkel defects: small ion (usually the cation) moves to interstitial site creating a hole that doesn't belong or pushing larger ion off the lattice site

Nonstoichiometric Compounds: many compounds do not follow the freshman chemistry idea that stoichiometry of compounds is in the ratio of small whole numbers.

FeO is more typically is found as FexO where x~0.95-0.99

Charge neutrality must still be maintained so a better description is (Fe2+)3x-2(Fe3+)2-2xO

F centers: e become part of the lattice
NaCl + Na Na1+(Cl)(e)