I. Review of Intermolecular Interactions

All intermolecular interactions are electrostatic in nature.

A. Ion-Ion interactions

e.g. NaCl: The ions of opposite charge are attracted to each other.

Equation that approximately describes energy of a single ion-ion attraction:

Coulomb's Law: E = 2.31 x 10^-18 (Q₁Q₂/r)
    where:  Q₁ = charge of the cation
                Q₂ = charge of the anion
                   r = distance between ions (sum of ionic radii)
The approximate energy change for formation of a hypothetically isolated NaCl unit would be:
     E = 2.31 x 10^-18 * [(1 * -1)/(0.95 + 1.81 Å)] = -8.37 x 10^-19 J/mol NaCl:
                (-8.37 x 10^-19 J )(6.02 x 10²³ ion pairs / mol) = -5.04 x 10⁵ J/mol
 
The approximate energy change for the formation of of a hypothetically isolated Li₂S unit would be:
     E = 2.31 x 10^-18 * [(1 * -2)/(0.60 + 1.84 Å)] = -1.89 x 10^-18 J/mol Li₂S:
                          (-1.89 x 10^-18 J)(6.02 x 10²³ ion pairs / mol) = -1.14 x 10⁶ J/mol
 
 

B. Ion-dipole interactions

e.g. NaCl in water: The sodium cations and chloride anions interact preferentially with the negative and positive ends of the water dipoles, respectively.

C. Dipole-dipole interactions

e.g. water: a dipole in a molecule generates permanent partial positive and partial negative centers in one molecule. Opposite partial charges electrostatically attract each other.

D. Dipole-induced dipole

e.g. methane in water: a dipole will induce a temporary dipole in an otherwise non polar molecule, with attraction of opposite partial charges.

E. Induced dipole-induced dipole

(London dispersion forces; Van der Waal's forces)

e.g. methane: non polar molecules interact via induction of temporary very weak dipoles and electrostatic attraction of the resultant partial charges.

A. Highly ordered arrangement of atoms, ions or molecules.

B. Determination of spatial arrangement of atoms in solids?

- diffraction of X-rays

1. X-rays have a wavelength on the order of an angstrom; on the atomic scale.
        Mo Ka = 0.71 Å     Cu Ka = 1.54 Å
            Electrons diffract X-rays.
            Core electrons of an atom will indicate the probable position of an atom.

2. Groups of atoms in the ordered arrangement will lie in planes.
        These planes can be approximated as being continuous from the viewpoint of an X-ray.

3. Condition for constructive interference of X-rays:
    nl = 2d sinq (Bragg equation)
        where l = wavelength of X-ray
                  d = distance between planes of atoms
q = angle of the X-ray to the plane of atoms
 

C. Ordered arrangement of atoms: there are many possibilities!
1. The smallest volume that shows the spatial arrangement of the atoms is called the unit cell. The macroscopic crystal can be thought of as built from unit cells as a brick wall is built from bricks.

2. Types of cubic unit cells:

3. Closest packed arrangement: highest % volume occupied by atoms: FCC (cubic closest packed, abc repeat) and HCP (hexagonal closest packed, ab repeat).

4. Unoccupied space in FCC cell: the holes are named for the shape of unoccupied space; atoms bounding the hole form the vertices of the polyhedron for which the hole is named.

a. octahedral holes: one in the center of the cell and 12 in the midpoints of the cell edges. Total = 4

b. tetrahedral holes: two each along the four body diagonals. Total = 8

D. Types of solids
1. metals: ordered arrangement of atoms
    Main interaction is metallic bonding.
        metallic bonding: metal cations exist in ordered arrangement surrounded by a sea of shared valence electrons. Net charge on each metal atom: zero.

2. ionic solids (salts)
Main interaction is ionic bonding.
    a. AB salts:

CsCl: primitive cubic arrangement of chloride anions and one cesium cation in the body center of the unit cell.
NaCl: FCC lattice of chloride anions and sodium cation occupying all of the octahedral holes.

Comparison of Coulomb energy change and lattice energy:

Coulomb: -5.04 x 10⁵ J
L.E. = -787 kJ = -7.87 x 10⁵ J
Discrepancy? Look at number of interactions around each ion.

ZnS: FCC lattice of sulfide anions and zinc cations in alternate tetrahedral holes.

b. AB₂ salts
CaCl₂: FCC lattice of calcium cations and chloride anions in all of the tetrahedral holes.
 

3. Molecular solids
Main interaction are covalent bonds.
a. One dimensional arrangement of covalent bonds.
   e.g. asbestos: fibrous material

b. Two dimensional arrangement of covalent bonds.
   e.g. mica (vermiculite): crystalline plates that easily flake off from each other; can be expanded to a spongy consistency; used in planting and as a packing material.
   e.g. graphite (pencil lead): crystalline plates that easily flake off from each other; good lubricant; soft material.

c. Three dimensional arrangement of covalent bonds.
   e.g. diamond: very hard material.
 

4. Liquids masquerading as solids
   e.g. glass: amorphous structure.