Solid State Class 12 Chemistry Notes

Types of Solids and Crystal Lattice

• $\text{Crystalline:}$
• regular repeating arrangement, sharp melting point, anisotropic (e.g. NaCl, quartz, diamond).
• $\text{Amorphous:}$
• irregular arrangement, no sharp melting point, isotropic (e.g. glass, rubber, plastic).
• Both are also classified as ionic, covalent, molecular, or metallic depending on bonding.

• Primitive (simple cubic) — particles only at corners.
• Body-centred cubic (bcc) — particles at corners + centre.
• Face-centred cubic (fcc/ccp) — particles at corners + face centres.
• End-centred cubic — particles at corners + two opposite faces.

Number of Atoms per Unit Cell

Corner atoms contribute $1/8$, edge atoms $1/4$, face atoms $1/2$, and body atom 1.

• $\text{Simple cubic:}$
• $8\times\frac{1}{8}=1$
• atom per cell.
• $\text{bcc:}$
• $8\times\frac{1}{8}+1=2$
• atoms per cell.
• $\text{fcc:}$
• $8\times\frac{1}{8}+6\times\frac{1}{2}=4$
• atoms per cell.

Radius Ratio and Voids

• Tetrahedral void — smaller, forms when 4 spheres surround a gap.
• Octahedral void — larger, forms when 6 spheres surround a gap.
• In an fcc lattice with N atoms there are N octahedral voids and 2N tetrahedral voids.
• e.g. NaCl — Cl⁻ forms an fcc lattice, Na⁺ occupies octahedral voids.

Packing Efficiency and Density

• $\text{Simple cubic:}$
• $52.4\%$
• .
• $\text{bcc:}$
• $68\%$
• .
• $\text{fcc/ccp:}$
• $74\%$
• — the most closely packed.

Defects in Solids (Imperfections)

• $\text{Vacancy:}$
• a missing atom/ion from a lattice site.
• $\text{Interstitial:}$
• an extra particle occupying an interstitial gap.
• $\text{Schottky defect:}$
• equal number of cations and anions missing — decreases density (e.g. NaCl).
• $\text{Frenkel defect:}$
• a cation displaced into an interstitial void — no change in density (e.g. AgCl, ZnS).
• $\text{Impurity defect:}$
• foreign ions introduced, e.g. doping in solids.

Electrical and Magnetic Properties

• Conductors — free electrons; band gap zero.
• Semiconductors — small band gap (Si, Ge); conductivity rises with temperature.
• Insulators — large band gap.
• n-type semiconductor — doped with electron-rich (group 15) impurity.
• p-type semiconductor — doped with electron-deficient (group 13) impurity.
• Magnetic types: diamagnetic (unpaired-free), paramagnetic, ferromagnetic, antiferromagnetic, ferrimagnetic.

Solved Examples

Example: An element crystallises in an fcc lattice with an edge length of $400\,\text{pm}$ and molar mass $60\,\text{g mol}^{-1}$. Find its density.

Solution: For fcc, $Z=4$. Using $\rho = \frac{ZM}{N_A a^3}$ with $a=400\times10^{-10}\,\text{cm}$: $\rho = \frac{4\times60}{6.022\times10^{23}\times(4\times10^{-8})^3} \approx 6.2\,\text{g cm}^{-3}$.