Structures of Solids
Structures of 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
- 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 crystal structure of sodium chloride
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.
Close packing of spheres
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