States of matter and what is inside a material
Everything is made of tiny atoms. How they sit decides the state.
- Solid: atoms are fixed in place and only shiver. A solid keeps its shape.
- Liquid: atoms touch but can slide. A liquid takes the shape of its pot.
- Gas: atoms are far apart and move fast. A gas fills the whole space.
Inside a solid there are two main patterns. In a crystal (iron, copper, salt) atoms repeat in a tidy pattern called a lattice. In an amorphous solid (glass, many plastics) there is no tidy pattern. Plastics are made of long chains of molecules. A metal is really a crowd of tiny crystals called grains.
The atoms are held by bonds: metallic bond in metals (a sea of free electrons), ionic or covalent bonds in ceramics, and covalent chains with weak pulls between chains in polymers. A composite joins two materials so that each does a job.
Deformation and flow
Deformation means a change of shape under a push or pull (a load).
- Elastic: the shape comes back when you let go, like a spring. Atoms only stretch their bonds a little.
- Plastic: the shape stays changed. Layers of atoms have slipped. The load at which this starts is the yield point.
- Brittle: the material cracks with almost no plastic stretch. Glass and ceramics do this.
Stress is the load on each unit of area: stress = force ÷ area. Strain is the stretch compared with the starting length: strain = extra length ÷ original length. In the elastic region, stress ÷ strain stays the same. This number is Young's modulus, a measure of stiffness.
Flow: a liquid flows because its atoms slide. A thick liquid (honey) has high viscosity; a thin one (water) has low viscosity. Heating lowers viscosity. That is why hot glass, hot plastic and molten metal can be shaped or poured. Some solids also flow very slowly under load when hot. This slow flow is called creep.
Why structure sets properties
A property is how a material behaves: strong, hard, bendy, light, hot or cold to carry, good or bad conductor.
- Metals: layers can slip, so they bend (ductile) and can be hammered (malleable). Free electrons carry heat and electricity.
- Ceramics: strong bonds hold atoms firmly, so they are hard and take high heat, but layers cannot slip, so they are brittle.
- Polymers: long chains with weak pulls between them. Light, flexible, poor conductors. Heat makes chains slide (thermoplastics melt).
- Composites: strong fibres inside a soft base give strength with low weight.
Change the structure and you change the property. Small grains make metal stronger. Adding a few other atoms (an alloy) blocks slipping and makes it harder. Heating and cooling steel changes its grains and its hardness.
Try it: bend a paperclip a little (it springs back), then a lot (it stays bent), then bend it back and forth until it snaps.
Key formulas and definitions
- Stress σ = F ÷ A (unit: pascal, Pa; 1 MPa = 1 N/mm²)
- Strain ε = ΔL ÷ L₀ (no unit)
- Young's modulus E = σ ÷ ε (elastic region only)
- Steel E ≈ 200 GPa, aluminium ≈ 70 GPa, nylon ≈ 3 GPa
Worked examples
1. A rod of cross-section 50 mm² carries a pull of 5000 N. Find the stress.
σ = F ÷ A = 5000 ÷ 50 = 100 N/mm² = 100 MPa.
2. A bar 200 mm long stretches by 0.1 mm. Find the strain.
ε = ΔL ÷ L₀ = 0.1 ÷ 200 = 0.0005 (0.05%).
3. The stress is 100 MPa and the strain is 0.0005 (elastic). Find Young's modulus. Which metal is it likely to be?
E = 100 ÷ 0.0005 = 200 000 MPa = 200 GPa. This matches steel.
4. A steel has yield stress 250 MPa. What pull makes a 20 mm² bar start to yield?
F = σ × A = 250 × 20 = 5000 N. Above this the bar will not spring back fully.
Common mistakes
- Thinking elastic means "stretchy like rubber". It only means the shape comes back. Steel is elastic too, for tiny stretches.
- Mixing up stress and strain. Stress has units (Pa); strain is a pure ratio.
- Saying hard = strong. Glass is hard but brittle; it breaks easily.
- Believing a solid has no motion. Its atoms shiver all the time; heat makes them shiver more.