What makes a solid a solid?
Matter can be solid, liquid or gas. These are its states of aggregation. In a solid the particles (atoms, ions or molecules) are packed tight. Strong forces hold them. They can only shake (vibrate) in place. So a solid has a fixed shape and a fixed volume, and it is hard to squeeze.
Crystalline and amorphous solids
Crystalline solid: the particles repeat in the same pattern over long distances (long-range order). It melts at one sharp temperature. It breaks along flat faces. Its properties can change with direction (anisotropic). Examples: salt, quartz, ice, metals.
Amorphous solid (amorphous = without form): the particles have order only over very short distances. It softens slowly over a range of temperature. It breaks with curved, uneven edges. It is the same in every direction (isotropic). Examples: glass, rubber, many plastics. Amorphous solids are sometimes called super-cooled liquids.
Four kinds of crystals
| Kind | Particles | Force | Properties | Examples |
|---|---|---|---|---|
| Ionic | + and − ions | ionic attraction | hard, brittle, high melting point; conduct only when melted or dissolved | NaCl, MgO |
| Covalent network | atoms | covalent bonds everywhere | very hard, very high melting point, usually do not conduct (graphite does) | diamond, SiO₂, SiC |
| Molecular | molecules | weak forces between molecules (dispersion, dipole, hydrogen bonds) | soft, low melting point, do not conduct | ice, dry ice, iodine, sugar |
| Metallic | metal ions in a sea of electrons | metallic bond | shiny, bend without breaking, conduct heat and electricity | Cu, Fe, Na |
In an ionic crystal such as NaCl, each Na⁺ is surrounded by 6 Cl⁻ and each Cl⁻ by 6 Na⁺. There are no separate molecules; the formula only gives the ratio 1 : 1.
Unit cells and counting particles
A crystal lattice is the 3D pattern of points where particles sit. The unit cell is the smallest box that, repeated, builds the whole lattice. A cube-shaped cell has edge length a.
- Corner particle: shared by 8 cells → counts ⅛.
- Face particle: shared by 2 cells → counts ½.
- Edge particle: shared by 4 cells → counts ¼.
- Body-centre particle: counts 1.
| Cell | Particles per cell (Z) | Neighbours (coordination number) | Space filled |
|---|---|---|---|
| Simple cubic | 1 | 6 | 52% |
| Body-centred cubic | 2 | 8 | 68% |
| Face-centred cubic (cubic close packing) | 4 | 12 | 74% |
Density of a crystal: ρ = Z × M ÷ (a³ × Nₐ), where M is the molar mass and Nₐ = 6.022 × 10²³ mol⁻¹.
Real crystals have small faults (defects), such as a missing particle (vacancy). These change colour, strength and conductivity.
Liquid crystals
Some substances made of long, rod-like molecules have a state between solid and liquid. They flow like a liquid, but the molecules point in the same direction like a crystal. This is a liquid crystal. A small voltage can turn the molecules, which changes how light passes. That is how LCD screens in watches, calculators and monitors work.
Key formulas and definitions
- Corner = ⅛, edge = ¼, face = ½, body centre = 1
- Z: SC = 1, BCC = 2, FCC = 4
- Coordination number: SC 6, BCC 8, FCC 12
- Packing: SC 52%, BCC 68%, FCC 74%
- Density ρ = Z·M / (a³·Nₐ)
- Radius: SC a = 2r, BCC √3a = 4r, FCC √2a = 4r
Worked examples
1. A cubic cell has particles at the 8 corners and at the centre of every face. How many particles belong to one cell?
8 × ⅛ = 1 from corners; 6 × ½ = 3 from faces. Z = 1 + 3 = 4 (FCC).
2. In a compound, atoms A sit at the corners and atoms B at the face centres of a cube. Find the formula.
A = 8 × ⅛ = 1; B = 6 × ½ = 3. Ratio A : B = 1 : 3, so the formula is AB₃.
3. Sort into ionic, covalent network, molecular or metallic: diamond, ice, copper, KCl.
Diamond: covalent network. Ice: molecular (hydrogen bonds). Copper: metallic. KCl: ionic.
4. Copper is FCC with a = 361 pm. Find the atomic radius.
For FCC, √2 a = 4r, so r = √2 × 361 / 4 = 1.414 × 361 / 4 ≈ 128 pm.
5. Copper (M = 63.5 g/mol) is FCC with a = 3.61 × 10⁻⁸ cm. Find its density.
a³ = 4.70 × 10⁻²³ cm³. ρ = 4 × 63.5 / (4.70 × 10⁻²³ × 6.022 × 10²³) = 254 / 28.3 ≈ 8.97 g/cm³.
6. Why does glass soften over a range of temperature but salt melts at 801 °C sharp?
In salt every bond is the same, so all break at one temperature. In glass the bonds differ in strength because the order is random, so they break one by one over a range.
Common mistakes
- Counting every corner particle as a whole particle. A corner gives only ⅛ to one cell.
- Saying NaCl is made of NaCl molecules. It is a giant lattice of ions; NaCl is only the ratio.
- Thinking amorphous means "not solid". Glass is a real solid; it just has no long-range order.
- Using pm or Å in the density formula without changing a to cm. 1 pm = 10⁻¹⁰ cm.