Solids
Solids are characterised by definite shape and volume, very low compressibility, and constituent particles held in fixed positions by strong cohesive forces. The PMDC MDCAT 2026 syllabus expects you to distinguish crystalline from amorphous solids, classify crystals by bonding type, and reason about lattice energy and the geometry of ionic crystals. This chapter typically yields 1-2 MCQs.
Crystalline Solids
A crystalline solid has a regular, repeating internal arrangement of particles (atoms, ions or molecules) extending in three dimensions. It has a sharp melting point, definite geometric shape, and shows anisotropy — physical properties (refractive index, conductivity, etc.) depend on direction.
An amorphous solid (e.g. glass, rubber, plastics) has only short-range order. It softens over a temperature range rather than melting sharply, and is isotropic — properties are the same in every direction. Amorphous solids are sometimes called "supercooled liquids".
Properties of crystalline solids
- Regular geometric external shape with definite plane faces, edges and angles.
- Sharp, fixed melting point.
- Anisotropy.
- Cleavage along definite planes.
- Definite heat of fusion.
Crystal Lattice
A crystal lattice (space lattice) is a three-dimensional array of points each of which represents the position of a constituent particle in the crystal. The smallest repeating unit that, when stacked in three dimensions, generates the entire crystal is the unit cell.
Seven crystal systems
Based on the relative lengths a, b, c of the unit-cell edges and the angles α, β, γ between them, all crystals fall into one of seven systems:
- Cubic — a = b = c; α = β = γ = 90° (NaCl, diamond).
- Tetragonal — a = b ≠ c; α = β = γ = 90° (SnO2).
- Orthorhombic — a ≠ b ≠ c; α = β = γ = 90° (rhombic sulphur, BaSO4).
- Monoclinic — a ≠ b ≠ c; α = γ = 90°, β ≠ 90° (monoclinic sulphur, gypsum).
- Triclinic — a ≠ b ≠ c; α ≠ β ≠ γ ≠ 90° (CuSO4·5H2O, K2Cr2O7).
- Hexagonal — a = b ≠ c; α = β = 90°, γ = 120° (graphite, ice, ZnO).
- Rhombohedral / trigonal — a = b = c; α = β = γ ≠ 90° (calcite, NaNO3).
Cubic unit cells — packing efficiency & coordination number
- Simple Cubic (SC): atoms at the 8 corners only. CN = 6. Packing efficiency ≈ 52 %. Effective atoms per cell = 1 (8 × ⅛).
- Body-Centred Cubic (BCC): 8 corners + 1 in body centre. CN = 8. Packing efficiency ≈ 68 %. Effective atoms = 2. Examples: Na, K, Fe (α), Cr.
- Face-Centred Cubic (FCC) / Cubic Close-Packed: 8 corners + 6 face centres. CN = 12. Packing efficiency ≈ 74 % (the densest possible packing of equal spheres). Effective atoms = 4. Examples: Cu, Ag, Au, Al, Pb, NaCl (anion sub-lattice).
Factors Affecting Shape of Ionic Crystals
The geometry adopted by an ionic crystal is decided by:
- Radius ratio r+/r−: predicts coordination number.
- 0.225–0.414 → CN 4 (tetrahedral, e.g. ZnS).
- 0.414–0.732 → CN 6 (octahedral, e.g. NaCl).
- 0.732–1.000 → CN 8 (cubic, e.g. CsCl).
- Stoichiometry of the compound: 1:1 (NaCl, CsCl), 1:2 (CaF2 — fluorite), 2:1 (Na2O — antifluorite).
- Polarisation effects (Fajans' rules): small, highly charged cations or large, easily polarised anions introduce covalent character and may distort the lattice.
- Charge balance: overall electrical neutrality must be preserved.
- Temperature and pressure: some salts show polymorphism (e.g. CsCl → NaCl-type structure above 469 °C).
Ionic vs Molecular Crystals
| Property | Ionic | Molecular | Covalent (network) | Metallic |
|---|---|---|---|---|
| Lattice particles | Cations + anions | Neutral molecules | Atoms (whole network) | Cations in sea of e− |
| Bonding force | Strong electrostatic | Weak van der Waals / dipole / H-bond | Strong covalent | Metallic bond |
| Hardness | Hard but brittle | Soft | Very hard (diamond hardest) | Variable; malleable & ductile |
| Melting point | High | Low | Very high | Moderate to high |
| Electrical conduction | Solid: no · molten/aq: yes | No | No (except graphite) | Excellent in all states |
| Solubility | Polar solvents (water) | Non-polar (mostly); H-bonded ones dissolve in water | Insoluble | Insoluble (react with acids) |
| Examples | NaCl, KBr, CsCl, MgO | I2, dry ice CO2, naphthalene, sucrose, ice | Diamond, graphite, SiO2, SiC | Cu, Fe, Ag, Au, Na |
| Type | Atoms / unit cell | Coordination number | Packing efficiency | Example |
|---|---|---|---|---|
| Simple cubic (SC) | 1 | 6 | 52.4% | Po (only example) |
| Body-centred cubic (BCC) | 2 | 8 | 68% | Na, K, Fe, W, Cr |
| Face-centred cubic (FCC) | 4 | 12 | 74% (closest packed) | Cu, Ag, Au, Al, Pb, NaCl |
| Hexagonal close-packed (HCP) | 6 | 12 | 74% | Mg, Zn, Cd, Ti |
Lattice Energy
Lattice energy (ΔHL) is the energy released when one mole of an ionic crystal is formed from its constituent gaseous ions:
M+(g) + X−(g) → MX(s); ΔHL = −ve
Equivalently, it is the energy required to dissociate one mole of the solid into widely separated gaseous ions (taken as positive). It is a measure of the strength of ionic bonding.
Coulomb dependence
Lattice energy is approximately proportional to:
ΔHL ∝ (q1 × q2) / r
where q1, q2 are the ionic charges and r is the inter-ionic distance (sum of ionic radii).
- Higher charges (Mg2+O2− vs Na+F−) → much larger lattice energy. MgO has ΔHL ~ 3800 kJ mol−1, NaCl ~ 787 kJ mol−1.
- Smaller ions → smaller r → larger lattice energy. NaF > NaCl > NaBr > NaI.
Significance of lattice energy
- Determines melting point and hardness of ionic solids.
- Determines solubility in water (compared with hydration energy).
- Cannot be measured directly — calculated using the Born–Haber cycle, which applies Hess's law to the formation of an ionic compound from its elements via a series of measurable steps (sublimation, ionisation, dissociation, electron affinity, lattice formation).
Worked MCQs
Five MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — it's where the deeper concept lives.
Q1. Which of the following is an amorphous solid?
Glass has only short-range order, no sharp melting point (it softens over a range), and is isotropic — the defining features of an amorphous solid. NaCl, diamond and quartz are all crystalline.
Q2. The packing efficiency of a face-centred cubic (FCC) unit cell is approximately:
FCC (cubic close-packed) is the densest possible packing of equal spheres at ~74 %, with coordination number 12. BCC is ~68 % (CN 8), simple cubic ~52 % (CN 6).
Q3. Which compound has the highest lattice energy?
Lattice energy ∝ q1q2/r. MgO has doubly charged ions (Mg2+, O2−) and small inter-ionic distance, giving an enormous lattice energy (~3800 kJ mol−1). All the others have singly charged ions.
Q4. An ionic crystal in which each cation is surrounded by 8 anions and vice versa (CN = 8) is best illustrated by:
CsCl has a body-centred cubic-like structure with Cs+ at the cube centre and Cl− at the 8 corners (or vice versa). Coordination number is 8:8. NaCl is 6:6, ZnS is 4:4, CaF2 is 8:4.
Q5. Which property is characteristic of an ionic crystal but not a molecular crystal?
Ionic solids have very strong electrostatic lattices (high m.p.) and contain mobile ions when molten or dissolved (good conductors). Molecular crystals have weak intermolecular forces, low m.p., and do not conduct.
Quick Recap
- Crystalline = long-range order, sharp m.p., anisotropic; amorphous = short-range order, softens, isotropic.
- 7 crystal systems: cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, rhombohedral.
- Cubic unit cells: SC (CN 6, 52 %), BCC (CN 8, 68 %), FCC (CN 12, 74 %).
- Crystal types: ionic, covalent (network), molecular, metallic.
- Radius ratio rules: 0.225–0.414 → CN 4; 0.414–0.732 → CN 6; 0.732–1.0 → CN 8.
- Lattice energy ∝ q1q2/r; calculated via Born–Haber cycle (Hess's law).