Solids: Class 11 Chemistry

Key points

In a solid the particles are held in fixed positions and can only vibrate. A solid has a definite shape and volume, is almost incompressible and has high density. Solids are of two kinds: crystalline and amorphous.

A crystalline solid has a regular, repeating three dimensional arrangement of particles. It has flat faces, a sharp melting point and a definite heat of fusion. It is anisotropic, which means some physical properties such as refractive index and electrical conductivity differ with direction. Examples are NaCl, sugar, quartz and diamond. Crystals cleave along definite planes when struck.

An amorphous solid has no long range order. It has no sharp melting point, softening over a range of temperature. It is isotropic, meaning properties are the same in all directions, and it breaks into pieces with irregular surfaces. Glass, rubber and plastics are examples. Amorphous solids are sometimes called supercooled liquids.

Crystalline solids are classified by the particles at the lattice points and the forces between them:

• Ionic solids (NaCl, KBr): ions held by strong electrostatic attraction. They are hard and brittle, have high melting points, and conduct electricity only when molten or dissolved.
• Covalent or network solids (diamond, silicon carbide, quartz): atoms joined by a network of covalent bonds. They are very hard with very high melting points and do not conduct, except graphite.
• Metallic solids (Cu, Fe, Na): positive ions in a sea of delocalised electrons. They are malleable, ductile, lustrous and good conductors.
• Molecular solids (ice, iodine, dry ice): molecules held by weak intermolecular forces. They are soft with low melting points and do not conduct.

A space lattice is the regular arrangement of points in space that shows the pattern of a crystal. The unit cell is the smallest repeating part of the lattice which, repeated in three dimensions, builds the whole crystal. It is described by the edge lengths a, b, c and the angles α, β, γ between them.

There are seven crystal systems, based on the edges and angles of the unit cell:

• Cubic: a = b = c, all angles 90° (NaCl, diamond).
• Tetragonal: a = b ≠ c, all angles 90° (white tin).
• Orthorhombic: a ≠ b ≠ c, all angles 90° (rhombic sulfur).
• Monoclinic: a ≠ b ≠ c, α = γ = 90°, β ≠ 90° (monoclinic sulfur).
• Triclinic: a ≠ b ≠ c, no angle 90° (CuSO₄·5H₂O).
• Hexagonal: a = b ≠ c, α = β = 90°, γ = 120° (graphite, zinc).
• Rhombohedral (trigonal): a = b = c, α = β = γ ≠ 90° (calcite).

In a cubic lattice there are three types of unit cell: simple (particles at the 8 corners), body centred (corners plus one at the centre) and face centred (corners plus one at the centre of each of the 6 faces). A corner particle is shared by 8 cells, so it counts 1/8. A face particle is shared by 2 cells, so it counts 1/2. A simple cubic cell has 1 atom, a body centred cell 2 atoms and a face centred cell 4 atoms.

Coordination number is the number of nearest neighbours of a particle. It is 6 in simple cubic, 8 in body centred cubic and 12 in face centred cubic and hexagonal close packing. The fraction of space filled by atoms (packing efficiency) is 52 % for simple cubic, 68 % for body centred cubic and 74 % for close packed structures. In NaCl each ion is surrounded by 6 of the opposite charge (6:6 coordination). In CsCl the coordination is 8:8.

Isomorphism is the property of different substances having the same crystal shape and similar formulas, so they can grow on each other. Examples are NaNO₃ and CaCO₃, and the alums. Polymorphism is the existence of one substance in more than one crystalline form, such as calcite and aragonite for CaCO₃. For an element this is allotropy, as with the rhombic and monoclinic forms of sulfur. The transition temperature is the temperature at which two forms are in equilibrium, which is 95.5 °C for sulfur.

Real crystals have defects. A Schottky defect occurs when equal numbers of cations and anions are missing from their sites, which lowers the density (NaCl). A Frenkel defect occurs when an ion moves from its site to a gap between sites, with no change in density (AgCl, ZnS). Defects affect electrical conductivity and colour.

Metals are explained by the electron sea model: valence electrons are free to move through the lattice of positive ions. This explains conduction of heat and electricity, lustre, and malleability. Band theory describes the energy levels more fully: in a conductor the valence and conduction bands overlap, in a semiconductor (Si, Ge) the gap is small, and in an insulator the gap is large.

X-ray diffraction is used to study the structure of crystals because the spacing between layers of atoms is similar to the wavelength of X-rays. Bragg's equation relates the wavelength λ, the spacing d between planes and the angle of incidence θ for reflection by successive planes: nλ = 2d sin θ, where n is a whole number called the order of reflection.

Study tip: Make a table of the seven crystal systems with their edges and angles and learn it by writing it out from memory. Remember Z = 1, 2, 4 for simple, body centred and face centred cubic cells, and the coordination numbers 6, 8 and 12. In Bragg's equation, check that λ and d use the same unit.

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Common mistakes

• Counting a corner atom as a whole atom instead of one eighth when finding atoms per unit cell.
• Calling glass a crystalline solid. It is an amorphous solid.
• Confusing isomorphism (different substances, same shape) with polymorphism (same substance, different shapes).
• Saying a Schottky defect leaves density unchanged. It lowers density, while a Frenkel defect does not.
• Forgetting to convert a, in pm or nm, to the same length unit as the density formula needs.

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