Point Defects and Stoichiometry
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Direct answer
A Schottky defect removes one cation and one anion together from the lattice (stoichiometry preserved, density lowered), while a Frenkel defect demotes an ion — usually the smaller cation — to an interstitial site (density unchanged). Schottky defects favour highly ionic crystals with similar-sized ions and high coordination numbers such as NaCl, CsCl and AgBr; Frenkel defects favour compounds with large size disparity such as ZnS, AgCl and AgBr, and AgBr uniquely shows both. Beyond vacancies, metal-excess and metal-deficiency defects generate non-stoichiometric phases: electrons trapped in anion vacancies (F-centres) colour NaCl yellow when heated in sodium vapour, and mixed-valence iron makes Fe0.95O the textbook cation-deficient case.
What you must remember
- Schottky signature: equal numbers of cation and anion vacancies, crystal composition unchanged, mass per unit cell drops while volume does not — density decreases.
- Frenkel signature: vacancy plus interstitial of the same ion; no mass loss, so density stays exactly as calculated for the perfect crystal.
- The exception to memorise: AgBr displays both Schottky and Frenkel defects — quoted directly as a JEE fact.
- F-centre physics: an anion vacancy occupied by an unpaired electron absorbs visible light, so excess-sodium NaCl turns yellow and excess-potassium KCl turns violet; more F-centres, deeper the colour.
- Metal excess, second route: interstitial cations with nearby electrons, as in ZnO heated to give yellow non-stoichiometric oxide that reverts white on cooling.
- Metal deficiency: cation vacancies balanced by oxidation of neighbours, classic in FeO (Fe2+/Fe3+ mixture) with formula Fe(0.95)O.
- Impurity doping: adding CdCl2 to NaCl forces cation vacancies (Cd2+ replaces two Na+ sites); adding SrCl2 works the same way — vacancy count equals dopant concentration.
- Semiconductor connection: group 15 dopants (As in Si) give n-type conduction, group 13 dopants (B in Si) give p-type — electrons versus holes.
Density consequence of Schottky versus Frenkel
Reason it through rather than recalling: density is mass of the unit cell divided by its volume. A Schottky pair removes one Na+ and one Cl- from each affected cell — the lattice parameter barely budes, but the cell loses roughly 58 amu per pair, so measured density falls below the ideal value; this is precisely how the number of defects per cubic centimetre is estimated experimentally. A Frenkel defect relocates an ion within the same cell: mass and volume are both unchanged, so the density is identical to the perfect crystal. Now extend to colour: when NaCl is heated in sodium vapour, sodium atoms sit on surface sites and release electrons that fall into anion vacancies; these trapped electrons absorb in the visible and the crystal turns yellow — no stoichiometric salt of sodium and chlorine is yellow, which is the elegant proof that the colour belongs to the defect, not the chemistry.
Where this stands in the current syllabus
The solid state chapter was removed from the JEE Main syllabus in the 2023 rationalisation, but JEE Advanced retains solid state in its physical chemistry section, so Advanced candidates must keep point defects exam-ready — colour centres and defect-type identification are precisely the kind of statement questions Advanced sets. NEET-UG also retains the chapter. Within JEE Main's trimmed list, only the semiconductor-doping logic resurfaces (through physics-style questions on materials). Traps to log: assuming every coloured crystal owes colour to F-centres (d-d transitions colour many transition-metal salts), confusing metal excess with metal deficiency in FeO, and forgetting that impurity dopants in NaCl generate cation vacancies, never anion ones.
Frequently asked questions
Which point defect lowers the density of a crystal?
Schottky, because cations and anions leave the lattice in pairs while the cell volume is conserved; Frenkel defects leave density untouched.
Why does ZnS preferentially show Frenkel defects?
Zn2+ is small relative to S2-, so it slips into interstitial spaces easily, and the partly covalent lattice tolerates the distortion without collapsing.
What exactly is an F-centre?
An anion vacancy occupied by a free electron; it absorbs visible light, which is why alkali halide crystals with metal excess show colour.
Why is FeO written as Fe0.95O?
Some Fe2+ sites are vacant and charge balance is restored by oxidising other irons to Fe3+, producing a cation-deficient, non-stoichiometric phase.
What defect does CdCl2 doping introduce into NaCl?
Each Cd2+ replacing two Na+ ions creates one cation vacancy, so the vacancy concentration equals the dopant concentration.