Solid State
Solid State covers unit-cell types, packing efficiency, density calculations, defects and electrical behaviour of solids. Numerical density and defect-identification questions are standard.
Unit cells and packing
- Simple cubic: Z = 1, packing efficiency 52.4%.
- Body-centred cubic: Z = 2, packing efficiency 68%.
- Face-centred cubic/ccp: Z = 4, packing efficiency 74%.
- Density d = ZM/(a^3 NA), with a in cm.
Defects and conductivity
- Schottky defect: equal cation and anion vacancies; density decreases; found in NaCl and KCl.
- Frenkel defect: cation leaves its site and occupies an interstitial site; density unchanged; found in AgCl and ZnS.
- Metal excess due to anion vacancies gives F-centres, trapped electrons that colour the crystal.
- n-type semiconductors are doped with a higher-valency element (P in Si); p-type with a lower-valency element (B in Si).
Worked example
NaCl crystallises in an fcc lattice with Z = 4, M = 58.5 g mol-1 and edge length 564 pm. Calculate its density. Reasoning: a = 564 pm = 5.64 x 10-8 cm, so a^3 = 1.79 x 10-22 cm3. d = (4 x 58.5)/[(1.79 x 10-22)(6.022 x 10^23)] = 234/107.8 = 2.17 g cm-3.
Traps
- Use Z = 4 for fcc, not 1 or 2.
- Convert pm to cm before substituting into the density formula.
- Schottky lowers density; Frenkel does not.
- An F-centre is an electron in an anion vacancy, not a cation vacancy.