Physics of Solids

Pick up a salt crystal and a piece of glass. Both are solid, yet inside they are worlds apart. In a crystalline solid the atoms sit in a perfectly repeating pattern, like bricks in a wall. In an amorphous solid they freeze where they happen to land, like grains in a sand pile.

• Crystalline — long-range ordered lattice; sharp melting point; flat faces (NaCl, quartz, metals, diamond).
• Amorphous — short-range order only; softens over a range, no fixed melting point (glass, rubber, plastic, wax).

Zoom into a crystalline solid and you find a lattice: a regular 3-D array of points where atoms sit. The smallest repeating block that, copied in every direction, rebuilds the whole crystal is the unit cell — like one floor tile that tiles a room.

• Lattice point — a position occupied by an atom, ion or molecule.
• Unit cell — the smallest box defined by lengths a, b, c and angles; simple cubic, body-centred and face-centred are the common cubic types.

Hang a weight from a wire and it stretches. Two numbers describe what is happening. Stress is the deforming force shared over the cross-section. Strain is how much longer the wire becomes, as a fraction of its original length.

• Stress — force per unit area; a thin wire feels more stress than a thick one under the same load.
• Strain — fractional change in length; dimensionless because it is a length over a length.

Some materials resist stretching far more than others. Young's modulus E is the stiffness of a material: how much stress it takes to produce a given strain. A big E means stiff, a small E means stretchy.

• Stiff (large E) — steel, diamond; huge stress for a tiny stretch.
• Stretchy (small E) — rubber, copper; a small stress gives a large stretch.

Pull a wire steadily and plot stress against strain. The story unfolds in stages, ending when the wire snaps.

• Elastic limit (proportional region) — the curve is straight; release the load and the wire returns to its exact length.
• Yield point — beyond here the wire stretches permanently; it will not fully recover.
• Plastic region — large strain for little extra stress; the wire is being permanently deformed.
• Breaking / fracture point — the wire reaches its ultimate stress and snaps.

Within the elastic limit, the deeper rule behind the straight part of the curve is Hooke's law: the extension of a spring or wire is directly proportional to the stretching force.

Each equal weight you hang on a spring adds the same extra stretch — that constant step is Hooke's law in action. The slope of the load–extension line is the spring constant k.

Stretching a spring takes work, and that work is stored as elastic potential energy, ready to spring back. Because the force grows from zero to F as you stretch, the energy is the area of the triangle under the load–extension line.

This is the energy in a drawn bow, a wound clock spring, and a stretched catapult — let go, and it converts straight back into kinetic energy.

In a solid, atomic energy levels merge into broad bands. The filled valence band and the empty conduction band are separated by a forbidden energy gap. The size of that gap decides everything about how the solid conducts.

• Conductor — bands overlap (no gap); electrons flow freely (metals).
• Insulator — a very wide gap (> 5 eV); electrons can't cross (glass, diamond).
• Semiconductor — a small gap (≈ 1 eV); a little heat or light lets some electrons jump (silicon, germanium).

Everything ties back to the order of the atoms and how electrons live in the bands.

• Steel — large Young's modulus and high yield stress: stiff and strong for beams, cables and rails.
• Rubber — tiny Young's modulus and huge elastic strain: tyres, shock mounts and elastic bands store energy and bounce back.
• Silicon — a semiconductor with a ≈ 1 eV band gap: the heart of every transistor, solar cell and microchip.

1. Crystalline = ordered lattice; amorphous = jumbled (glass, rubber).
2. The unit cell is the smallest box that tiles into the whole crystal.
3. stress = F / A (Pa); strain = ΔL / L (no units).
4. Young's modulus E = stress / strain — the material's stiffness.
5. Stress–strain curve: elastic limit → yield → plastic → fracture.
6. Hooke's law F = k e holds in the elastic region.
7. Elastic PE = ½ F e = ½ k e² (area under the F–e line).
8. Band gap sets conductor (none) → semiconductor (small) → insulator (wide).