## CHM 501 Lecture

### Ionic compounds

Properties: hard, brittle, high mp and bp, often water soluble, electrolytes in solution or melt, usually crystalline. All of this suggests large bond energies.

Necessary conditions for an ionic compound: cation (implies neutral species has a low IP) and anion (implies neutral has a high EA)

We develop a theory of ionic bonding using simple electrostatics. Assume that the ions behave as point charges (i.e., the ions have no volume). Then build a lattice from condensation of gas phase ions and use Coulomb's law to calculate the energy.

Ion Pair

q+, q- are the ionic charges in coulombs

r is the distance between ions in meters

0 is the permittivity of free space

Ion square

Since (in this example) q+=-q-

ion cube

Continue this over the entire lattice to give:

Z+, Z- are the ionic charges in units of e (i.e., +1, +2, -1, -2, etc.)

r is the interionic distance

M is called the Madelung constant.

M depends solely on geometry, i.e., the kind of lattice but the internuclear distances are factored out. Madelung constants are tabulated for all the common lattice types.

ECoul is negative (all terms are positive except Z-), i.e., the bonding is favorable. In fact, too favorable: the most stable situation is when r = 0.

Why? Initial point charge assumption does not allow for nuclear-nuclear repulsion at close distances.

Correct this empirically: add a term that is repulsive at small r but negligible at larger distances. This means either an exponential term or a 1/rn term with large n.

Born repulsion:

n is known as the Born exponent, B is an arbitrary constant

The lattice energy becomes

Need to find two new quantities: B and n.

Evaluate B at equilbrium because (r0 is the equilibrium internuclear distance measured experimentally)

So, at r = r0

To find n, we must move away from the equilibrium position. This means compressing the sample, i.e. measure the compressibility, :

 × 1011 (SI units) unit cell distance  (Å) experimental Elat (kJ/mole) AgCl 2.40 5.54 AgBr 2.74 5.77 AgI 4.11 CaF2 1.23 CaCl2 4.36 CaBr2 4.84 LiF 1.53 4.01 1015.9 LiCl 3.50 5.14 843.9 LiBr 4.30 5.49 799.1 LiI 7.2 6.00 746.4 MgO 0.72 4.20 NaCl 4.18 5.628 769.4 NaBr 5.09 5.94 734.3 NaI 7.1 6.46 689.5 KF 3.30 4.62 802.5 KCl 5.65 6.28 704.2 KBr 6.68 6.57 672.4 KI 8.56 7.05 633.9

 Structure Geometric Madelung Constant Sodium chloride (NaCl) 1.74756 Cesium chloride (CsCl) 1.76267 Zinc blende (ZnS) 1.63806 Wurtzite (ZnS) 1.64132 Fluorite (CaF2) 2.51939 Rutile (TiO2) 2.408 Anatase (TiO2) 2.400 Cadmium iodide (CdI2) 2.36 b-Quartz (SiO2) 2.201 Corundum (Al2O3) 4.040

Sample calculation for NaCl:

= 8.854×10-12 SI units

e = 1.602×10–19 coulombs

M = 1.74756 (NaCl structure)

d = 5.628×10-10 m giving r0 = 2.814×10–10 m

= 4.18×10–11 SI

n is found by

This compares to 769.4 kJ/mole experimental (2.4% error)

lattice energies are thermodynamically negative but reported as positive values (like EA)