Unit 6
Crystals and solids
Why are salt grains little cubes? Why can copper be drawn into wire while diamond is so hard? Why is cadmium sulfide yellow? How much surface does a gram of powder have? This unit starts from unit cells and close packing, uses X-ray diffraction to “see” how atoms are arranged, explains metals, semiconductors and insulators with energy bands, and ends by counting the nitrogen molecules it takes to cover a solid.
- 1 Lattices and unit cells: bookkeeping for atoms Crystal = lattice + basis. Learn to count the atoms in a cell by their shares, meet the seven crystal systems and the three cubic lattices, and get atomic sizes and densities from lattice parameters. 25 min
- 2 Close packing: ABAB and ABCABC Stack equal spheres layer by layer like oranges: the two choices for the third layer give hexagonal and cubic close packing, both 74 % full, with tetrahedral and octahedral holes between the layers. 20 min
- 3 Ionic crystals: polyhedra and radius ratios NaCl, CsCl, ZnS, CaF₂, TiO₂ and perovskite: read structures as coordination polyhedra, predict coordination with the radius-ratio rule, and check a density computed from the cell against measurement. 25 min
- 4 X-ray diffraction: measuring atoms with waves Bragg’s law, the structure factor and systematic absences: recognise simple, body-centred, face-centred and diamond lattices from powder patterns, and see why NaCl and KCl look different. 30 min
- 5 Metals and bands: conductors, semiconductors and colour Add atoms one by one to a chain of molecular orbitals until the levels merge into a band; use the band gap to explain metals, semiconductors and insulators — and why cadmium sulfide is yellow. 30 min
- 6 Surfaces and adsorption: counting the molecules that cover a solid From Langmuir’s balance on sites to BET multilayers: measure the surface areas of a titania, a mesoporous silica and a zeolite from nitrogen isotherms at 77 K, and learn to tell whether a fitting range can be trusted. 35 min