Q.Which of the following types of defects causes a decrease in density of a crystal ?
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Schottky Defect: The Missing-Pair Problem
Imagine you are building a perfect wall out of identical red bricks and identical grey bricks, alternating them in a neat checkerboard pattern. Now picture this: you walk away, and when you come back, a few bricks have vanished — but here is the strange thing — whenever a red brick disappears, a grey brick right next to it disappears too. The wall still has the same ratio of red to grey bricks, but it is now slightly less dense, and there are tiny empty holes where pairs used to be.
That is the core intuition behind a Schottky defect.
In an ionic crystal (like NaCl, KCl, or CsCl), the crystal is held together by electrostatic forces between positive cations and negative anions. A Schottky defect occurs when a pair of ions — one cation and one anion — simultaneously leave their lattice sites and migrate to the crystal surface. The result is a pair of vacancies: an empty spot where a positive ion should be, and an empty spot where a negative ion should be, right next to each other.
The key point: the number of missing cations equals the number of missing anions. This preserves the overall electrical neutrality of the crystal — no net charge builds up.
The Precise Statement
A Schottky defect is a stoichiometric point defect in an ionic crystal in which an equal number of cations and anions are missing from their regular lattice positions, creating a pair of vacancies. Because the crystal loses mass (the missing ions) while its volume remains nearly unchanged, the density of the crystal decreases.
For a crystal with N cation sites and N anion sites, if n Schottky defects are present, the number of vacancies is n on each sublattice. The equilibrium number of defects at temperature T is given by:
n≈Ne−Es/2kT
where Es is the energy required to create one Schottky pair (the energy to remove one cation and one anion), k is Boltzmann's constant, and T is the absolute temperature.
Why Does This Happen?
At any temperature above absolute zero, atoms and ions vibrate. Some ions gain enough thermal energy to break free from their lattice sites. In a pure metal, a single atom can leave, creating a vacancy (a Schottky defect in metals is just a single vacancy). But in an ionic crystal, leaving behind a single charged vacancy would create a local imbalance of charge — a huge electrostatic penalty. The crystal "prefers" to remove a cation and an anion together, so that the region remains electrically neutral.
A common mistake: thinking that a Schottky defect is just any missing ion. It is specifically a pair of missing ions of opposite charge. A single missing ion (with its charge uncompensated) is a different defect — a Frenkel defect or a simple vacancy, depending on context.
Key Characteristics at a Glance
| Property | Schottky Defect |
|---|---|
| What is missing | One cation and one anion |
| Stoichiometry | Preserved (equal numbers missing) |
| Effect on density | Decreases (mass lost, volume nearly constant) |
| Effect on electrical neutrality | Preserved |
| Common in | Ionic crystals with high coordination numbers (e.g., NaCl, KCl, CsCl) |
| Not common in | Crystals where cations and anions are very different in size (e.g., ZnS — here Frenkel defects dominate) |
A Concrete Example: NaCl …
A crystal's density depends on its mass divided by its volume, so a defect only lowers density if it actually removes ions from the crystal without changing its overall volume. …
Schottky defect removes equal numbers of cations and anions from the lattice → mass falls, volume constant → density decreases.
Density = mass / volume. A defect lowers density only if it removes ions from the crystal without changing its overall volume.
- Schottky defect: a pair of oppositely charged ions (one cation + one anion) is missing from the lattice. The number of ions decreases while the crystal volume is unchanged, so the mass per unit volume — the density — DECREASES. …
- CBSE 2022Set E1 markMCQQ.Which of the following types of defects causes a decrease in density of a crystal ?(a) Frenkel(b) Schottky(c) Interstitial(d) F-centre
›Reveal solutionSolution
Schottky defect removes equal numbers of cations and anions from the lattice → mass falls, volume constant → density decreases.
Density = mass / volume. A defect lowers density only if it removes ions from the crystal without changing its overall volume.
- Schottky defect: a pair of oppositely charged ions (one cation + one anion) is missing from the lattice. The number of ions decreases while the crystal volume is unchanged, so the mass per unit volume — the density — DECREASES. …
- CBSE 2022Set ANNUAL1 markQ.Write an ionic compound which can exhibit both Schottky and Frenkel defect.
›Reveal solutionSolution
AgBr is the classic example of an ionic compound that exhibits both Schottky and Frenkel defects simultaneously.
A Schottky defect needs cation and anion of comparable size (so equal numbers of both can go missing from the lattice without huge strain), while a Frenkel defect needs a big size difference between cation and anion (so the smaller ion, usually the cation, can slip into an interstitial site).
…
- CBSE 2019Set 56/2/11 markQ.Out of KCl and AgCl, which one shows Schottky defect and why?(OR)Why does ZnO appear yellow on heating?
›Reveal solutionSolution
Part (a): KCl shows the Schottky defect (similar-sized ions, 6:6 coordination, equal cation/anion vacancies), while AgCl shows Frenkel (small, polarisable Ag+ goes interstitial). Part (b): on heating ZnO loses oxygen to become metal-excess; interstitial Zn2+ with trapped electrons (F-centres) absorb visible light, turning it yellow.
Part (a)
A Schottky defect is a pair of vacancies — one cation and one anion missing together — keeping the crystal electrically neutral. It is favoured when:
- the cation and anion are of comparable size, and
- the crystal has a high coordination number (small interstitial holes).
In KCl the radius ratio rK+/rCl−≈0.76 gives the 6:6 rock-salt structure; the interstitial holes are too small to accept a K+ ion, so removing an ion pair is energetically cheaper than pushing a cation interstitial — hence Schottky. …
- CBSE 2017Set ANNUAL1 markQ.What is Schottky defect ?
›Reveal solutionSolution
Schottky defect = missing equal numbers of cation-anion pairs from an ionic crystal lattice.
In an ionic solid, a Schottky defect arises when an equal number of cations and anions are missing from their normal lattice sites (leaving behind vacancies), typically in ionic compounds with similar-sized cations and anions and high coordination numbers, such as NaCl, KCl, CsCl. Since equal numbers of positive and negative ions leave the lattice, electrical neutrality of the crystal is maintained. It …
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