Intermolecular Forces

Structures of Solids

Crystalline solids

• The atoms, molecules or ions pack together in an ordered arrangement
• Such solids typically have flat surfaces, with unique angles between faces and unique 3-dimensional shape
• Examples of crystalline solids include diamonds, and quartz crystals

Amorphous solids

• No ordered structure to the particles of the solid
• No well defined faces, angles or shapes
• Often are mixtures of molecules which do not stack together well, or large flexible molecules
• Examples would include glass and rubber

The ordered arrangement of atoms, molecules or ions in a crystalline solid means that we can describe a crystal as being constructed by the repetition of a simple stuctural unit.

• Since the crystal is made up of an arrangement of identical unit cells, then an identical point on each unit cell represents an identical environment within the crystal
• The array of these identical points is termed the crystal lattice

• The unit cells shown are cubic
• All sides are equal length
• All angles are 90°
• The unit cell need not be cubic
• The unit cell lengths along the x,y, and z coordinate axes are termed the a, b and c unit cell dimensions
• The unit cell angles are defined as:
• a, the angle formed by the b and c cell edges
• b, the angle formed by the a and c cell edges
• g, the angle formed by the a and b cell edges

The unit cell of sodium chloride is cubic, and this is reflected in the shape of NaCl crystals

The unit cell can be drawn with either the Na⁺ ions at the corners, or with the Cl^- ions at the corners.

• If the unit cell is drawn with the Na⁺ ions at the corners, then Na⁺ ions are are also present in the center of each face of the unit cell
• If the unit cell is drawn with the Cl^- ions at the corners, then Cl^- ions are are also present in the center of each face of the unit cell

Within the unit cell there must be an equal number of Na⁺ and Cl^- ions.

For example, for the unit cell with the Cl^- ions at the center of the faces

• The top layer has (1/8+1/8+1/8+1/8+1/2)=1 Cl^- ion, and (1/4+1/4+1/4+1/4)=1 Na⁺ ion
• The middle layer has (1/2+1/2+1/2+1/2)=2 Cl^- ions and (1/4+1/4+1/4+1/4+1)=2 Na⁺ ions
• The bottom layer will contain the same as the top or 1 each Cl^- and Na⁺ ions
• The unit cell has a total of 4 Cl^- and 4 Na⁺ ions in it. This equals the empirical formula NaCl.

Many ions are spherical and many small molecules pack in a crystal lattice as essentially spherical entities.

Spheres can pack in three-dimensions in two general arrangements:

• Hexagonal close packing
• Cubic close packing

The coordination number is the number of particles surrounding a particle in the crystal structure.

• In each packing arrangement above (hexagonal close pack, cubic close pack), a particle in the crystal has a coordination number of 12
• The NaCl (face centered cubic) has a coordination number of 6

1996 Michael Blaber