The Solid State • Topic 3 of 3

Imperfections & Properties

No real crystal is perfect. Irregularities from the ideal arrangement are called crystal defects or imperfections; when they involve only individual lattice points they are point defects. These defects control colour, conductivity and many useful properties.

In stoichiometric defects the ratio of cations to anions (and hence the chemical formula) stays unchanged. The two main types are:

  • Schottky defect — equal numbers of cations and anions are missing (a vacancy defect). It lowers density and appears in ionic solids with high coordination number and similar-sized ions (NaCl, KCl, CsCl, AgBr).
  • Frenkel defect — a smaller ion (usually the cation) shifts to an interstitial site (a dislocation defect). Density is unchanged; it occurs with a large ion-size difference (ZnS, AgCl, AgBr, AgI). AgBr shows both.

Non-stoichiometric defects change the cation:anion ratio. A metal excess defect arises when anion sites are vacant and balancing electrons are trapped there, forming F-centres that impart colour (NaCl heated in Na vapour turns yellow; LiCl turns pink). A metal deficiency defect occurs when some cations are missing and the charge is balanced by an ion in a higher oxidation state (e.g. $\text{Fe}_{0.95}\text{O}$, where some $\text{Fe}^{2+}$ becomes $\text{Fe}^{3+}$). Impurity defects arise when foreign ions occupy lattice sites; e.g. $\text{SrCl}_2$ added to NaCl introduces $\text{Sr}^{2+}$ replacing two $\text{Na}^+$, creating cation vacancies.

Electrical properties. Solids span an enormous conductivity range. Conductors (metals) have conductivity $\sim10^7\ \Omega^{-1}\text{m}^{-1}$ because the conduction band overlaps the valence band. Insulators have a very large band gap. Semiconductors have a small band gap, so conductivity rises with temperature. Doping a Group-14 element (Si, Ge) produces:

  • n-type semiconductor — doped with a Group-15 element (P, As); the extra electron carries the current (negative carriers).
  • p-type semiconductor — doped with a Group-13 element (B, Al, Ga); an electron-deficient hole acts as a positive carrier.

Magnetic properties depend on unpaired electrons. Diamagnetic (all electrons paired) are weakly repelled (NaCl, $\text{H}_2\text{O}$); paramagnetic (unpaired electrons) are weakly attracted and lose magnetism when the field is removed ($\text{O}_2$, $\text{Cu}^{2+}$). Ferromagnetic solids (Fe, Co, Ni, $\text{CrO}_2$) are strongly attracted and retain magnetism — their domains align in the same direction. Ferrimagnetic solids ($\text{Fe}_3\text{O}_4$) have unequal opposite domain alignment (small net moment), while antiferromagnetic solids (MnO) have equal opposite alignment that cancels to zero net moment.

Schottky vs Frenkel defect (stoichiometric point defects)
FeatureSchottky defectFrenkel defect
NatureVacancy defect — equal cations & anions missingDislocation defect — ion shifts to interstitial site
Effect on densityDecreases densityNo change in density
ConditionHigh coordination number; ions of similar sizeLarge difference in cation/anion size; low coordination number
ExamplesNaCl, KCl, CsCl, AgBrZnS, AgCl, AgBr, AgI
1
Worked Example
Which point defect lowers the density of an ionic crystal, and why?
Solution
  1. In a Schottky defect equal numbers of cations and anions are missing from their sites.
  2. The number of ions (mass) decreases while the volume stays the same.
  3. Therefore density (mass/volume) decreases.

Answer: The Schottky defect lowers density because ions are removed without changing the volume.

2
Worked Example
Why does the Frenkel defect not change the density of a crystal?
Solution
  1. In a Frenkel defect an ion only moves from its lattice site to an interstitial site.
  2. No ion leaves the crystal, so total mass is unchanged.
  3. The volume is unchanged, so density stays the same.

Answer: Because the ion is merely displaced (not removed), mass and volume are unchanged, so density is constant.

3
Worked Example
Explain how an F-centre gives colour to NaCl.
Solution
  1. Heating NaCl in sodium vapour creates anion ($\text{Cl}^-$) vacancies (metal excess defect).
  2. Electrons released by extra Na atoms occupy these anion vacancies, forming F-centres.
  3. These trapped electrons absorb visible light and get excited, imparting a yellow colour to the crystal.

Answer: Electrons trapped in anion vacancies (F-centres) absorb visible light, colouring NaCl yellow.

4
Worked Example
Silicon is doped with phosphorus. What type of semiconductor forms and what carries the current?
Solution
  1. Si is a Group-14 element with 4 valence electrons; P is Group-15 with 5.
  2. Four of P's electrons bond with Si; the fifth is free.
  3. This extra (negative) electron carries the current, so an n-type semiconductor forms.

Answer: An n-type semiconductor; the extra free electron is the current carrier.

5
Worked Example
Classify as diamagnetic, paramagnetic or ferromagnetic: (a) $\text{O}_2$, (b) NaCl, (c) Fe.
Solution
  1. $\text{O}_2$ has unpaired electrons, so it is paramagnetic.
  2. NaCl has all electrons paired, so it is diamagnetic.
  3. Iron has aligned domains and is strongly attracted, so it is ferromagnetic.

Answer: (a) paramagnetic, (b) diamagnetic, (c) ferromagnetic.

6
Worked Example
When $\text{SrCl}_2$ is added to NaCl, why are cation vacancies created?
Solution
  1. $\text{Sr}^{2+}$ carries two positive charges while $\text{Na}^+$ carries one.
  2. Each $\text{Sr}^{2+}$ replaces two $\text{Na}^+$ to maintain electrical neutrality.
  3. $\text{Sr}^{2+}$ occupies one $\text{Na}^+$ site; the other $\text{Na}^+$ site is left vacant — a cation vacancy.

Answer: One $\text{Sr}^{2+}$ replaces two $\text{Na}^+$, leaving one cation vacancy per added $\text{Sr}^{2+}$.

Key Points

  • Stoichiometric defects keep the formula: Schottky (cation + anion vacancies, density falls) and Frenkel (ion in interstitial site, density unchanged).
  • Non-stoichiometric: metal excess (anion vacancy + trapped electron = F-centre, gives colour) and metal deficiency (missing cation balanced by a higher-oxidation-state ion, e.g. $\text{Fe}_{0.95}\text{O}$).
  • Impurity defect: a higher-valent ion (e.g. $\text{Sr}^{2+}$ in NaCl) replaces two cations, creating cation vacancies.
  • Semiconductors: n-type (doped with Group 15, electron carriers); p-type (doped with Group 13, hole carriers).
  • Magnetism by unpaired electrons: diamagnetic (repelled), paramagnetic (weakly attracted), ferromagnetic (strong, retained), ferrimagnetic (unequal opposite, small net), antiferromagnetic (equal opposite, zero net).
Tap an option to check your answer0 / 4
Q1.Which defect decreases the density of an ionic solid?
Explanation: In a Schottky defect equal cations and anions are missing, reducing mass and hence density.
Q2.An n-type semiconductor is obtained when silicon is doped with:
Explanation: A Group-15 dopant such as P provides an extra electron, giving negative (n-type) charge carriers.
Q3.$\text{Fe}_3\text{O}_4$ (magnetite) is an example of a substance that is:
Explanation: In $\text{Fe}_3\text{O}_4$ the domains align in unequal opposite numbers, giving a net moment — it is ferrimagnetic.
Q4.F-centres in a crystal are responsible for:
Explanation: F-centres are electrons trapped in anion vacancies; they absorb visible light and impart colour to the crystal.