Solid State
Solid State examines how particles pack into crystals and how that packing controls density, defects and physical properties. The board tests unit-cell types, packing efficiency, density calculations, point defects and band theory.
Core rules
- Simple cubic: Z = 1, packing efficiency 52.4%. Body-centred cubic: Z = 2, 68%. Face-centred cubic/ccp: Z = 4, 74%.
- Density: d = ZM/(a^3 N_A); convert pm to cm (1 pm = 10^-10 cm).
- Schottky defect: missing cation-anion pair, lowers density (NaCl). Frenkel: ion displaced to interstitial site, density unchanged (AgCl).
- Band theory: conductors have overlapping or partly filled bands; insulators a large gap; semiconductors a small gap.
Worked example
An FCC metal has a = 4.00 x 10^-8 cm and M = 64 g/mol. For FCC, Z = 4. a^3 = 64 x 10^-24 cm^3. d = (4 x 64)/(64 x 10^-24 x 6.022 x 10^23) = 256/38.54 = 6.64 g cm^-3. The reasoning is that Z counts atoms per unit cell and a^3 is the cell volume; N_A converts grams per mole to grams per atom.
Traps
Using Z = 2 for FCC, forgetting the cube on a, mixing pm and cm, and confusing Schottky (density falls) with Frenkel (density unchanged). Do not call a semiconductor a conductor because its gap is small, not zero.