Solid State
On this page
Direct answer
Solid state chemistry describes crystals through the unit cell, the smallest repeating box of the lattice. The three cubic cells carry Z = 1 (simple), 2 (body-centred) and 4 (face-centred) atoms with packing efficiencies 52.4, 68 and 74 per cent; density follows d = Z × M / (a^3 × N_A). Ionic structures are read as close-packed anions with cations in octahedral or tetrahedral voids, and point defects explain colour, conductivity and semiconducting behaviour.
What you must remember
- Atoms per cell: simple cubic 1 (eight corners × 1/8), bcc 2 (plus one body-centre atom), fcc 4 (plus six faces × 1/2); coordination numbers 6, 8 and 12.
- Packing efficiency: 52.4 per cent (sc), 68 per cent (bcc), 74 per cent (fcc and hcp) — only fcc and hcp are close-packed.
- Edge relations: sc a = 2r; bcc a = 4r/√3 (body diagonal 4r); fcc a = 2√2 r (face diagonal 4r).
- Density: d = Z × M / (a^3 × N_A), edge in cm for d in g cm^-3 — the standard numerical here.
- Voids: N close-packed spheres give N octahedral and 2N tetrahedral voids; radius ratios 0.414 (octahedral) and 0.225 (tetrahedral) place a cation.
- Structures: NaCl 6:6 (Cl- fcc, Na+ in octahedral voids), CsCl 8:8, ZnS zinc blende 4:4, CaF2 8:4, Na2O antifluorite.
- Schottky defect — paired cation-anion vacancies, density falls (NaCl, CsCl); Frenkel — an ion (small cation) shifts to an interstitial site, density unchanged (ZnS, AgCl); interstitial defects raise density.
- F-centres, electrons trapped in anion vacancies, colour alkali halides: excess Li pink, Na yellow, K violet.
- Doping: group 15 (As in Si) gives n-type electrons; group 13 (B, Al, In) gives p-type holes. Magnetic classes: ferromagnetic Fe, antiferromagnetic MnO, ferrimagnetic Fe3O4.
Common confusion
The classic muddle is Schottky versus Frenkel: Schottky is paired vacancy with density loss, Frenkel is dislocation with density unchanged — Frenkel needs an ion small enough for the interstitial site. Students swap the radius-ratio thresholds, count fcc atoms as 14, and mix up n and p doping — remember the rule: group 15 donor gives n-type, group 13 acceptor gives p-type.
Exam-focused takeaway
JEE Main tests the computational core: atoms per cell, density from the edge, packing fractions, void counting, one-line defect identification. JEE Advanced (where this chapter has traditionally carried weight) pushes reasoning — formula units from occupied voids, radius-ratio structure prediction, F-centre colour questions and doping with band ideas. Draw the cell and mark shared contributions before counting; every numerical begins as geometry bookkeeping.
Frequently asked questions
How many atoms belong to one fcc unit cell?
Four: eight corners × 1/8 gives one, six faces × 1/2 gives three.
What is the packing efficiency of bcc?
68 per cent, below fcc's 74 per cent, because the body-centre atom leaves gaps along the cell edges.
How do Schottky and Frenkel defects differ?
Schottky removes a cation-anion pair (density decreases); Frenkel shifts a small ion into an interstitial site (density unchanged, vacancy plus interstitial created).
What is an F-centre?
An electron trapped in an anion vacancy; it absorbs visible light, colouring crystals like NaCl heated in sodium vapour.
Why is NaCl 6:6 coordinated?
Chloride forms an fcc lattice and Na+ fits the octahedral voids by radius ratio; each ion touches six of the other kind.
What distinguishes n-type from p-type silicon?
n-type is doped with a group 15 donor supplying electrons; p-type with a group 13 acceptor creating holes.