Why Solid State Matters
Everything you touch is in the solid state. But why is diamond the hardest natural substance while graphite (same element!) is used as a lubricant? Why does sodium chloride shatter cleanly when hit? Why do metals bend without breaking?
The answers lie in crystal structure — how atoms, ions, or molecules arrange themselves in a solid. Solid state chemistry is not just memorising unit cells; it is understanding why materials behave the way they do.
For JEE Main, this chapter typically yields 2–3 questions. For CBSE Class 12, it’s a 5-mark question almost every year. For NEET, it appears less often but the basics (unit cells, packing efficiency, defects) are testable.
Key Terms & Definitions
Crystalline solid: Atoms/ions/molecules arranged in a definite, repeating three-dimensional pattern (long-range order). Has a sharp melting point. Examples: NaCl, diamond, sucrose, iron.
Amorphous solid: No long-range order — atoms arranged randomly. No sharp melting point; softens over a range. Examples: glass, rubber, plastics. These are also called pseudo-solids or supercooled liquids.
Unit cell: The smallest repeating unit of the crystal lattice. Stacking unit cells in three dimensions gives the entire crystal.
Lattice point: Positions in the crystal where identical structural units (atoms, ions, or molecules) are located.
Coordination number: The number of nearest neighbours surrounding a particle in the crystal. Higher coordination number = denser packing.
Packing efficiency: The fraction of total volume of the unit cell that is occupied by spheres. Always a percentage.
Crystal Systems and Bravais Lattices
There are 7 crystal systems based on the relative lengths of unit cell axes (a, b, c) and angles between them (α, β, γ). JEE tests cubic systems most heavily.
For the cubic system (a = b = c, α = β = γ = 90°), there are three arrangements:
| Type | Atoms per Unit Cell | Coordination Number | Packing Efficiency |
|---|---|---|---|
| Simple Cubic (SC) | 1 | 6 | 52.4% |
| Body-Centred Cubic (BCC) | 2 | 8 | 68% |
| Face-Centred Cubic (FCC/CCP) | 4 | 12 | 74% |
- Corner atom: shared by 8 unit cells → contributes 1/8 per unit cell
- Face-centred atom: shared by 2 unit cells → contributes 1/2 per unit cell
- Edge-centred atom: shared by 4 unit cells → contributes 1/4 per unit cell
- Body-centred atom: entirely inside → contributes 1 per unit cell
BCC total: 8 × (1/8) + 1 = 2 atoms FCC total: 8 × (1/8) + 6 × (1/2) = 1 + 3 = 4 atoms
Close-Packing Arrangements
When we stack layers of spheres, the most efficient arrangements are:
AAAA… (simple cubic stacking): Each layer directly above the previous. Least efficient (52.4%). Rare in nature — only Polonium adopts simple cubic structure.
ABAB… (hexagonal close-packed, HCP): The third layer aligns with the first. Examples: Mg, Zn, Ti. Coordination number = 12.
ABCABC… (cubic close-packed, CCP = FCC): The third layer is different from both. Examples: Cu, Ag, Au, Al, Ni. Coordination number = 12.
Both HCP and CCP have identical packing efficiency of 74% — the maximum for equal spheres.
HCP and CCP both have coordination number 12 and packing efficiency 74%. The difference is in the stacking sequence (ABAB vs ABCABC). JEE often gives the metal and asks which structure — Cu/Ag/Au → CCP; Mg/Zn → HCP.
Void (Hole) Analysis
In close-packed structures, there are gaps between spheres called voids:
Tetrahedral void: Formed when a sphere in one layer rests in the depression between three spheres in the layer below. The void is surrounded by 4 spheres. Size ratio: .
Octahedral void: Formed between 3 spheres above and 3 spheres below. Surrounded by 6 spheres. Size ratio: .
- Number of octahedral voids = N
- Number of tetrahedral voids = 2N
In an FCC unit cell with 4 atoms: 4 octahedral voids, 8 tetrahedral voids.
This is crucial for understanding ionic structures — the smaller ion (often cation) fits into the void created by the larger ions (often anions).
Ionic Crystal Structures
Rock salt (NaCl) structure:
- Cl⁻ forms FCC lattice; Na⁺ fills all octahedral voids
- Coordination number: Na⁺ surrounded by 6 Cl⁻, Cl⁻ surrounded by 6 Na⁺
- So coordination is written 6:6
Zinc blende (ZnS) structure:
- S²⁻ forms FCC; Zn²⁺ fills half the tetrahedral voids
- Coordination number: 4:4
Fluorite (CaF₂) structure:
- Ca²⁺ forms FCC; F⁻ fills all tetrahedral voids
- Coordination number: Ca²⁺ has 8 F⁻ neighbours, F⁻ has 4 Ca²⁺ neighbours
- Written as 8:4
Caesium chloride (CsCl) structure:
- Cl⁻ at corners; Cs⁺ at body centre (or vice versa) — this is NOT FCC
- Coordination number: 8:8
JEE Main 2023 asked about the coordination number in NaCl structure. CBSE 2024 asked students to calculate the number of ions per unit cell of NaCl. These are standard 2–3 mark questions. The key is to correctly count using corner/face/body fractions.
Density Formula for Unit Cells
Where:
- = number of atoms/formula units per unit cell
- = molar mass (g/mol)
- = Avogadro’s number ( mol⁻¹)
- = edge length of unit cell (in cm for CGS)
This formula appears in JEE and CBSE almost every year. Given any three quantities, you can find the fourth.
Crystal Defects
Real crystals are never perfect. Defects affect physical and chemical properties — semiconductors, for instance, depend entirely on controlled defects.
Point Defects (Stoichiometric)
Schottky defect: Equal number of cations and anions are missing from their lattice positions. The crystal remains electrically neutral. Density decreases. Seen in ionic crystals with similar-sized ions: NaCl, KCl, CsCl.
Frenkel defect: A smaller ion (usually cation) leaves its lattice site and moves to an interstitial position. No change in density (ion is not lost, just displaced). Seen when cation is much smaller than anion: ZnS, AgCl, AgBr, AgI.
Mnemonic: Schottky = Shrinks density (ions leave). Frenkel = ion Finds a new place (moves to interstitial). Both are intrinsic/stoichiometric defects.
Impurity Defects (Non-Stoichiometric)
Metal excess defect: Extra cations present with electrons trapped in anion vacancies (F-centres). These absorb visible light → crystal appears coloured. Example: NaCl heated in Na vapour → yellow colour.
Metal deficiency defect: Fewer cations than expected. Common in transition metal compounds where variable oxidation states are possible. Example: FeO (often actually Fe₀.₉₅O).
Doping: Deliberate addition of impurity to change electrical properties. This is the basis of semiconductor technology.
- n-type semiconductor: Silicon doped with P or As (group 15) → extra electrons
- p-type semiconductor: Silicon doped with B or Al (group 13) → holes (positive charge carriers)
Solved Examples
Easy — CBSE Level
Q: Calculate the number of formula units of NaCl in its unit cell.
Solution: NaCl has a rock salt (FCC) structure. Na⁺ ions: 12 edge-centred × (1/4) + 1 body-centred = 3 + 1 = 4. Cl⁻ ions: 8 corner × (1/8) + 6 face-centred × (1/2) = 1 + 3 = 4. So there are 4 NaCl formula units per unit cell.
Medium — JEE Main Level
Q: Iron has BCC structure. Its density is 7.87 g/cm³ and atomic mass is 56 g/mol. Find the edge length of its unit cell.
Solution: For BCC, Z = 2.
Hard — JEE Advanced Level
Q: A compound forms hexagonal close-packed structure. What is the total number of voids in 0.5 mol of it? How many of these are tetrahedral voids?
Solution: 0.5 mol contains atoms (= N).
Total voids = octahedral + tetrahedral = N + 2N = 3N = .
Tetrahedral voids = 2N = .
Exam-Specific Tips
CBSE Class 12: Focus on Schottky vs Frenkel defects (comparison table), NaCl and ZnS structures with coordination numbers, and the density formula. A 5-mark question on solid state is almost guaranteed.
JEE Main: Density formula, packing efficiency, number of atoms per unit cell, and coordination numbers are the core. Expect 1–2 straightforward numerical questions.
JEE Advanced: Voids, radius ratios for determining which void is occupied, and defect-based questions on colour centres and electrical conductivity.
Common Mistakes to Avoid
Mistake 1: Counting atoms in FCC incorrectly. Students often count only corner atoms (×8 × 1/8 = 1) and forget the 6 face-centred atoms (×6 × 1/2 = 3). FCC has 4 atoms, not 1.
Mistake 2: Confusing Schottky and Frenkel defects. Remember: Schottky involves ion pairs being absent (density decreases). Frenkel involves cation displacement (density unchanged). AgBr shows BOTH defects — this is a favourite exam fact.
Mistake 3: Using the wrong Z in the density formula. For ionic compounds, Z is the number of formula units per unit cell (e.g., Z = 4 for NaCl, not 4 Na⁺ separately and 4 Cl⁻ separately — use M for the formula unit NaCl = 58.5 g/mol).
Mistake 4: Saying “HCP and FCC are different packings.” They have identical packing efficiency (74%) and coordination number (12). The only difference is the stacking sequence.
Mistake 5: Forgetting that glass is an amorphous solid (not crystalline), so it has no sharp melting point. When a question asks “why does glass soften gradually,” the answer is: amorphous nature (no long-range order).
Practice Questions
1. What is the coordination number of Cs⁺ in CsCl structure?
- In CsCl, the Cs⁺ ion is surrounded by 8 Cl⁻ ions at the corners of a cube, and each Cl⁻ is surrounded by 8 Cs⁺ ions. The coordination is 8:8.
2. Calculate packing efficiency of BCC.
In BCC, the body diagonal = 4r (two corner atoms + one body atom: r + 2r + r = 4r). Relation to edge: a√3 = 4r → r = a√3/4. Volume of 2 atoms = 2 × (4/3)πr³ = 2 × (4/3)π(a√3/4)³ = 8πa³√3/48 = πa³√3/6. Packing efficiency = (πa³√3/6)/a³ = π√3/6 ≈ 0.6802 ≈ 68%.
3. Why is NaCl yellow when heated in sodium vapour?
When NaCl is heated in Na vapour, excess Na atoms are deposited on the crystal surface. Na loses electrons: Na → Na⁺ + e⁻. The Na⁺ ions occupy Cl⁻ vacancies (Schottky defect sites) and the electrons get trapped in these vacancies — these trapped electrons are called F-centres (from German Farbzentrum = colour centre). F-centres absorb visible light (specifically the complementary of yellow → they absorb blue-violet), making the crystal appear yellow.
4. In which ionic compound is the Frenkel defect NOT possible?
Frenkel defect requires the cation to be much smaller than the anion (so it can fit into an interstitial position). In compounds where ions are similar in size (like NaCl, KCl, CsCl), Frenkel defect is NOT possible. These compounds show Schottky defects instead.
5. How many octahedral voids are there in an FCC unit cell?
In an FCC unit cell with 4 atoms, there are 4 octahedral voids: 1 at the body centre + 12 edge-centred positions × (1/4) = 1 + 3 = 4 octahedral voids. (Tetrahedral voids = 8, all inside the unit cell.)
FAQs
Q: Is glass crystalline or amorphous? Glass is amorphous. It has no long-range order — atoms are arranged randomly like a very viscous liquid. This is why glass has no sharp melting point and why it shows conchoidal (shell-like) fracture when broken.
Q: Why is diamond hard but graphite soft? Both are made of carbon but differ in crystal structure. In diamond, each carbon forms 4 strong covalent bonds in a tetrahedral arrangement (sp³) — creating a rigid 3D network. In graphite, carbon forms layers of hexagonal rings (sp²) with weak van der Waals forces between layers — layers slide easily, making it soft and useful as a lubricant.
Q: What is an interstitial compound? Interstitial compounds are formed when small non-metal atoms (H, C, N) fit into the voids (interstices) of a metal lattice. They are very hard, have high melting points, and conduct electricity. Examples: steel (Fe with C in interstitial positions), TiC, TiN.
Q: Why do metals conduct electricity in solid state but ionic compounds don’t? In metals, valence electrons are delocalised and free to move — they form the “sea of electrons.” In ionic solids, all electrons are localised in ionic bonds. Ions are fixed in the lattice and cannot move. (Ionic compounds conduct when molten or in aqueous solution, where ions are free to move.)