Solid State: Organised by Concept

A. Classification of Solids

Crystalline solids (long-range order, sharp MP, anisotropic, clean cleavage) vs. amorphous solids (short-range order, melting range, isotropic, irregular fracture). By bonding: ionic (NaCl), covalent network (diamond), molecular (ice), metallic (Cu).

B. Cubic Unit Cells: The NEET Big Three

SC: Z = 1; CN = 6; PE = 52.4%; a = 2r. Only Polonium (Po) adopts SC naturally.

BCC: Z = 2; CN = 8; PE = 68%; a√3 = 4r. Examples: Na, K, Fe(α), Cr, W.

FCC: Z = 4; CN = 12; PE = 74%; a√2 = 4r. Examples: Cu, Ag, Au, Al, Pt.

HCP: Z = 6 (full cell); CN = 12; PE = 74%; c/a = 1.633 (ideal). Examples: Mg, Zn, Ti.

Mnemonic: "S(1)–B(2)–F(4)" and "SC-Edge, BCC-Body, FCC-Face" for contact direction.

C. Density Calculation

$\rho = \frac{ZM}{a^3 N_A}$

Key skill: convert a to cm (1 Å = 10^{-8} cm; 1 pm = 10^{-10} cm). The formula can be rearranged to find a, M, or Z.

Example: Ag (FCC, a = 4.077 Å, M = 108 g/mol) → ρ = 432/40.80 ≈ 10.59 g/$cm^{3}$.

D. Close Packing and Voids

For n close-packed atoms: n octahedral voids (radius ratio 0.414) + 2n tetrahedral voids (radius ratio 0.225) = 3n total.

E. Ionic Crystal Structures

F. Point Defects

Schottky: cation + anion vacancy pair; density decreases; found in NaCl, KCl, CsCl, AgBr. Frenkel: cation to interstitial; density unchanged; found in ZnS, AgCl, AgBr, AgI. AgBr: shows BOTH — the classic NEET exception. Metal excess: F-centres; n-type; NaCl → yellow; KCl → violet. Metal deficiency: cation vacancies; p-type; FeO, FeS.

G. Semiconductors

Band gap: metals = 0; semiconductors ≈ 1 eV; insulators > 3 eV. n-type (Group 15 dopant, extra $e^{-}$); p-type (Group 13 dopant, hole). Semiconductor conductivity increases with T (opposite to metals).

H. Magnetic Properties

Diamagnetic (all paired, repelled: NaCl) → Paramagnetic (random unpaired: $O_{2}$) → Ferromagnetic (aligned domains: Fe, Co, Ni) → Antiferromagnetic (antiparallel equal: MnO) → Ferrimagnetic (antiparallel unequal: $Fe_{3}O_{4}$).