The full, readable lecture — the solid state and rigidity, crystalline versus amorphous solids, the four crystal types, the lattice and unit cell, the seven crystal systems, cubic packing, isomorphism and polymorphism, and lattice energy. As you scroll, the panel on the right pictures each idea with an everyday object — stacked oranges, a brick wall, a diamond, a melting ice block.
In a solid the particles are packed closely in fixed positions and can only vibrate about those positions — they cannot move past one another. The result is a body with a definite shape and volume.
Picture a greengrocer's crate of oranges. Once they are stacked, each orange sits in its own hollow and stays there; the whole stack holds its shape. A crystal is the same idea on the scale of atoms — particles packed in a tidy, repeating pattern called a lattice. Loosely pack the same oranges (one type of packing) or nest them tightly (another) and you get different stacks: chemists call these simple cubic, body-centred and face-centred packings.
Look at a grain of table salt under a lens: it is a tiny cube with flat faces, because its particles are stacked in perfect long-range order. Now look at a chip of window glass — no faces, no shape, because its particles froze in a jumble. That single difference, order versus disorder, drives the whole table below.
| Property | Crystalline (salt) | Amorphous (glass) |
|---|---|---|
| Arrangement | regular, repeating, long-range order | irregular, short-range order |
| Melting point | sharp, definite | melts over a range (softens) |
| Shape | definite geometric faces & angles | no regular shape |
| Nature (cleavage) | anisotropic; cleaves along planes | isotropic; irregular break |
| Examples | NaCl, diamond, quartz, ice | glass, rubber, plastic, tar |
Think of four neighbourhoods, each held together by a different "glue". In the ionic block, positive and negative ions alternate and pull on each other. In the metallic block, fixed cations float in a shared sea of electrons. In the molecular block, whole molecules cling weakly by van der Waals forces or hydrogen bonds. In the covalent network, every atom is bolted to its neighbours by strong covalent bonds.
| Type | Particles & force | Properties | Example |
|---|---|---|---|
| Ionic | ions; electrostatic | hard, brittle, high m.p.; conduct when molten/aqueous | NaCl |
| Covalent (network) | atoms; covalent bonds | very hard, very high m.p.; non-conductors (except graphite) | diamond, SiO₂ |
| Molecular | molecules; van der Waals / H-bonds | soft, low m.p.; non-conductors | ice, I₂, dry ice |
| Metallic | cations in a "sea" of electrons | malleable, ductile, lustrous; good conductors | Cu, Fe, Na |
A bricklayer never invents a new brick for each row — one brick shape is repeated thousands of times to build a whole wall. A crystal works the same way: there is one tiny repeating block, the unit cell, and copying it in three directions builds the entire solid.
Take that unit-cell box and start stretching or tilting it. Make all sides equal and all angles 90° and you have the perfect cube; stretch one side and it becomes tetragonal; tilt the angles and you slide toward the fully skewed triclinic. Doing this systematically gives exactly seven systems, classified by the edges and angles of the unit cell.
| System | Edges | Angles | Example |
|---|---|---|---|
| Cubic | a = b = c | all 90° | NaCl |
| Tetragonal | a = b ≠ c | all 90° | SnO₂ |
| Orthorhombic | a ≠ b ≠ c | all 90° | rhombic S |
| Monoclinic | a ≠ b ≠ c | two 90°, one ≠ | monoclinic S |
| Triclinic | a ≠ b ≠ c | none 90° | CuSO₄·5H₂O |
| Hexagonal | a = b ≠ c | 90°, 90°, 120° | graphite |
| Rhombohedral | a = b = c | equal, ≠ 90° | calcite |
How you stack the layers decides the cell. Stack identical layers straight on top of each other and you get simple cubic packing; nest each layer into the hollows in an ABAB rhythm and you build the body-centred idea; offset a third layer (ABCABC) and you reach face-centred close packing. Counting the share of each atom in the box gives the atoms per unit cell.
| Cubic type | Atom positions | Atoms / unit cell |
|---|---|---|
| Simple cubic (SC) | 8 corners | 8 × ⅛ = 1 |
| Body-centred (BCC) | 8 corners + 1 centre | (8 × ⅛) + 1 = 2 |
| Face-centred (FCC) | 8 corners + 6 faces | (8 × ⅛) + (6 × ½) = 4 |
Two ideas about crystal form matter for the exam, and the same carbon atom shows them off. Isomorphism is different substances sharing one crystal shape; polymorphism (for an element, allotropy) is one substance in more than one form. Carbon is the star example: bolt each atom to four others in a rigid 3-D network and you get diamond, the hardest natural solid; arrange the very same atoms in flat sliding layers and you get soft, conducting graphite.
| Allotrope | Structure | Property |
|---|---|---|
| Diamond | each C sp³, 3-D covalent net | hardest natural substance; non-conductor |
| Graphite | sp² layers, delocalised electrons | soft, slippery; conducts electricity |
Heat a crystal and its particles vibrate harder and harder until, at one sharp temperature, the whole ordered lattice gives way at once and the solid melts. The stronger the glue holding the lattice — its lattice energy — the higher that temperature. Larger ionic charges and smaller ions mean greater lattice energy, so MgO melts far hotter than NaCl.