Solid State: The Complete NEET Picture

The solid state is one of the three states of matter in which constituent particles occupy fixed positions and vibrate in place rather than translating freely. Solids are broadly classified into crystalline and amorphous types. Crystalline solids exhibit long-range ordered arrangements of their constituent particles, resulting in a sharp melting point, anisotropic properties (direction-dependent), and clean cleavage along specific planes. Common examples are quartz, NaCl, diamond, and metals. Amorphous solids, by contrast, possess only short-range order, melt over a range of temperatures, are isotropic, and fracture irregularly. Glass, rubber, and polythene are typical amorphous solids; glass is sometimes called a supercooled liquid because it flows imperceptibly over geological time.

Crystal Lattice and Unit Cells

A crystal lattice is a regular, three-dimensional array of points, each representing the average position of a particle. The smallest repeating structural unit is the unit cell. There are seven crystal systems and fourteen Bravais lattices in total, but NEET examinations focus exclusively on the three cubic unit cells and hexagonal close packing.

In the Simple Cubic (SC) cell, atoms reside only at the eight corners, each shared by eight adjacent cells, giving Z = 8 × (1/8) = 1 atom per cell. The coordination number is 6, and atoms touch along the cube edge so that a = 2r. The packing efficiency is π/6 ≈ 52.4% — the lowest of any cubic structure.

The Body-Centered Cubic (BCC) cell has atoms at all eight corners plus one at the body centre, giving Z = 2. The body-centre atom contacts all corner atoms along the body diagonal, so a√3 = 4r and r = a√3/4. The coordination number is 8 and packing efficiency is π√3/8 ≈ 68%. Examples include Na, K, Fe(α), Cr, and W.

The Face-Centered Cubic (FCC) cell has atoms at all eight corners and at the centre of each of the six faces, giving Z = 8 × (1/8) + 6 × (1/2) = 4. Atoms touch along the face diagonal, so a√2 = 4r and r = a√2/4. The coordination number is 12 — the highest of the three cubic types. Packing efficiency is π/(3√2) ≈ 74.0%. Examples: Cu, Ag, Au, Al, Pt. Both FCC (ABCABC stacking = cubic close packing, CCP) and HCP (ABAB stacking) achieve this maximum 74% packing efficiency with CN = 12.

Density Formula

The density of any crystal unit cell is derived from the mass and volume of that cell:

$\rho = \frac{Z \cdot M}{a^3 \cdot N_A}$

where Z = atoms per cell, M = molar mass in g/mol, a = edge length in cm, and N_A = $6.022 \times 10^{23}$ $mol^{-1}$. A critical NEET skill is converting edge length units: 1 Å = 10^{-8} cm; 1 pm = 10^{-1}^{0} cm. For silver (FCC, M = 108 g/mol, a = 4.077 Å), this formula yields ρ ≈ 10.59 g/$cm^{3}$, closely matching the experimental value.

Voids and Ionic Structures

In close-packed structures with n atoms, there are n octahedral voids (radius ratio 0.414) and 2n tetrahedral voids (radius ratio 0.225). The size and occupancy of these voids determine the stoichiometry and structure of ionic crystals.

In the NaCl structure, $Cl^{-}$ forms FCC (n = 4); $Na^{+}$ fills all n = 4 octahedral voids, giving 4 formula units per cell and 6:6 coordination. The radius ratio $r^{+}$/$r^{-}$ lies between 0.414 and 0.732. Similar structures: KCl, MgO, CaO, FeO.

In the CsCl structure, $Cl^{-}$ forms a simple cube with $Cs^{+}$ at the body centre; CN = 8:8 and $r^{+}$/$r^{-}$ > 0.732. Z = 1 formula unit per cell. Examples: CsBr, CsI.

In the ZnS (zinc blende) structure, $S^{2-}$ forms FCC (n = 4); $Zn^{2+}$ fills only half (4 of 8) the tetrahedral voids, giving CN = 4:4 and $r^{+}$/$r^{-}$ between 0.225 and 0.414. Examples: CuCl, SiC.

In fluorite ($CaF_{2}$), $Ca^{2+}$ is in FCC; all 8 tetrahedral voids are filled by $F^{-}$, giving CN = 8:4. Antifluorite ($Na_{2}O$) reverses the roles: $O^{2-}$ in FCC, $Na^{+}$ in all tetrahedral voids, CN = 4:8.

Crystal Defects

Point defects occur at specific lattice sites. Schottky defects involve equal numbers of cation and anion vacancies; ion pairs migrate to the surface, reducing crystal mass and decreasing density. Found in NaCl, KCl, CsCl, AgBr. Frenkel defects involve cation displacement to interstitial sites within the crystal; since no atoms leave, density is unchanged. Found in ZnS, AgCl, AgBr, AgI. The critical NEET exception is AgBr, which shows both Schottky and Frenkel defects.

Non-stoichiometric defects alter the ion ratio. Metal excess (F-centres) traps electrons in anion vacancies, causing crystal colouration (NaCl → yellow, KCl → violet) and n-type semiconductor behaviour. Metal deficiency creates cation vacancies compensated by higher-oxidation cations (e.g., $Fe_{1}$₋ₓO), giving p-type behaviour.

Semiconductors and Magnetic Properties

In band theory, conductors have zero band gap, semiconductors have small gaps (~1 eV), and insulators have large gaps (>3 eV). Doping Si with Group 15 elements (P, As) gives n-type semiconductors (excess electrons); doping with Group 13 (B, Ga) gives p-type (holes). Semiconductor conductivity increases with temperature; metal conductivity decreases.

Magnetic behaviour: diamagnetic (all paired, weakly repelled — NaCl, $C_{6}H_{6}$), paramagnetic (unpaired, weakly attracted — $O_{2}$, $Cu^{2+}$), ferromagnetic (domains aligned — Fe, Co, Ni, strongly attracted), antiferromagnetic (antiparallel equal domains, cancel — MnO), ferrimagnetic (antiparallel unequal, net moment — $Fe_{3}O_{4}$, ferrites).

The two most heavily tested NEET concepts in solid state are the density formula ρ = ZM/($a^{3}$Nₐ) and the Schottky/Frenkel defect distinction (Schottky decreases density; Frenkel does not).