Imperfections In Solids : Defects In Crystals

Q: What are point defects in crystals?

Point defects are irregularities around a single lattice point: missing particles (vacancies), extra particles in voids (interstitials), displaced ions, or foreign ions. They are divided into stoichiometric defects, non-stoichiometric defects and impurity defects.

Q: What is the difference between Schottky and Frenkel defects?

In a Schottky defect equal numbers of cations and anions are missing, so density decreases; it occurs in NaCl, KCl and CsCl. In a Frenkel defect a smaller ion leaves its site for an interstitial position, so density is unchanged; it occurs in ZnS, AgCl and AgI. Both keep the formula unchanged.

Q: What are F-centres?

F-centres are anion vacancies that hold trapped electrons. They form, for example, when NaCl is heated in sodium vapour. The electrons absorb visible light, so NaCl becomes yellow, LiCl pink and KCl violet.

Q: Why does ZnO turn yellow on heating?

On heating, zinc oxide loses a little oxygen. The extra zinc ions move into interstitial sites and the released electrons occupy neighbouring interstitial sites. This metal excess defect makes the solid yellow; it turns white again on cooling.

Q: Why is ferrous oxide non-stoichiometric?

In ferrous oxide some iron(II) sites are empty. To keep the crystal neutral, two iron(II) ions are oxidised to iron(III) for every vacancy. The real composition is about Fe0.93O to Fe0.96O, a metal deficiency defect.

Q: How does adding SrCl2 to NaCl create vacancies?

Each strontium ion replaces two sodium ions to keep the charge balanced but occupies only one lattice site. So every strontium ion added leaves one cation site empty, and the number of cation vacancies equals the number of strontium ions.

Q: Are crystal defects in the NEET syllabus?

No. Point defects were removed from NEET, together with the rest of Solid State, from 2024. JEE Advanced 2026 still lists point defects under Solid State.

Q: What type of defect questions come in JEE Advanced?

JEE Advanced asks you to identify Schottky, Frenkel, metal excess or metal deficiency defects, predict their effect on density and colour, find the fraction of M3+ in formulas like Fe0.93O, and count vacancies created by doping with divalent impurities.

ChemistrySolid StateFor JEE aspirants

Imperfections in solids, or defects in crystals, are departures from the perfectly regular arrangement of particles. Every real crystal has them, because crystals grow fast, contain impurities and are formed at temperatures where some particles are knocked out of place. Point defects are the ones tested: Schottky and Frenkel defects (formula unchanged), metal excess and metal deficiency defects (formula changed), and impurity defects. Each changes density, colour or conductivity in a predictable way. Point defects remain in the JEE Advanced syllabus only.

On this page1Why defects form2Types of defects3Vacancy and interstitial4Schottky5Frenkel6Metal excess7Metal deficiency8Impurity defects

Key Formulas - Quick Reference

★ Must learn Schottky: equal cation and anion vacancies; $ρ_{e x p} < ρ_{t h}$ ; formula unchanged.
★ Must learn Frenkel: ion (usually cation) shifted to an interstitial site; $ρ$ unchanged; formula unchanged.
★ Must learn Fraction of sites vacant (Schottky) $= \frac{ρ _{t h} - ρ _{e x p}}{ρ _{t h}}$ ; % missing $= \frac{ρ _{t h} - ρ _{e x p}}{ρ _{t h}} \times 100$ .
★ Must learn Mixed valence in $M_{x} O$ ( $x < 1$ ): $3 y + 2 (x - y) = 2$ ; % $M^{3 +} = \frac{y}{x} \times 100$ .
Impurity defect: each $S r^{2 +}$ (or $C d^{2 +}$ ) added creates one cation vacancy.
Metal excess: anion vacancies holding electrons (F-centres) or extra cations in interstitial sites (ZnO).
Density with defects: $d = \frac{Z _{e f f} M}{N _{A} a ^{3}}$ with $Z_{e f f}$ reduced by the fraction missing.

1. Why Real Crystals Have Defects

An ideal crystal would have every lattice point occupied at 0 K. Real crystals depart from this because:

they grow at a finite rate, so particles do not always reach their correct sites (faster crystallisation, more defects);
they contain impurities from their surroundings;
at any temperature above 0 K, thermal energy knocks some particles out of their sites. Defects therefore increase with temperature.

A crystal defect (imperfection) is any irregularity in the arrangement of the constituent particles. Defects are classified by their extent as point defects (around one lattice point), line defects (along a row of lattice points) and plane defects (over a whole plane).

Figure 1: The family tree of crystal defects. This concept concentrates on point defects, the ones that change density, colour and conductivity.

Figure 2: A line defect: an extra half-plane of atoms squeezed into the upper part of the crystal. The irregularity runs along a whole row (a line) of lattice points, not just one site.

Line and plane defects matter for the strength of metals. Point defects matter for chemistry, because they change density, colour, conductivity and even the formula of a compound. The rest of this page is about point defects, which fall into three groups:

Stoichiometric defects: the ratio of cations to anions stays exactly as in the formula.
Non-stoichiometric defects: the ratio changes, so the formula is no longer a simple whole-number ratio.
Impurity defects: foreign ions replace some of the host ions.

2. Stoichiometric Defects in Non-Ionic Solids

Figure 3: The two simplest point defects in a non-ionic (atomic or molecular) crystal. A vacancy lowers the density; an interstitial raises it.

Vacancy defect: some lattice sites are empty. Mass drops while volume stays the same, so density decreases. Vacancies also form when a substance is heated.
Interstitial defect: some particles occupy positions between regular sites. Mass rises for the same volume, so density increases.

These two simple defects occur in non-ionic solids. In ionic solids the crystal must stay electrically neutral, so vacancies and interstitials appear in the linked forms named after Schottky and Frenkel.

Quick Recall: tap to check

Name the three classes of defects by extent.

Point, line and plane defects.

Why do defects increase with temperature?

Thermal energy knocks more particles out of their sites.

Which simple defect raises the density of a non-ionic solid?

The interstitial defect.

3. Schottky Defect

Figure 4: Schottky defect. A cation and an anion are both missing, so the crystal stays neutral and its formula is unchanged, but it gets lighter:

ρ_{e x p} < ρ_{t h}

It is a vacancy defect in an ionic solid: equal numbers of cations and anions are missing, so the crystal stays neutral.
Density decreases, because particles are lost but the volume is unchanged.
It appears in ionic compounds whose cation and anion are of similar size and which have high coordination numbers: NaCl, KCl, CsCl, KBr, AgBr.
The number is significant: NaCl has about $1 0^{6}$ Schottky pairs per cm $^{3}$ at room temperature (out of about $1 0^{22}$ ions).

Measured density gives the fraction of missing formula units directly:

fraction missing = \frac{ρ _{t h} - ρ _{e x p}}{ρ _{t h}}

Key idea

Schottky = a cation-anion pair missing: neutral, formula unchanged, density lower.

4. Frenkel (Dislocation) Defect

Figure 5: Frenkel (dislocation) defect. The smaller ion leaves its site for an interstitial void. Nothing leaves the crystal, so the density is unchanged, but a vacancy-interstitial pair forms.

The smaller ion (usually the cation) leaves its site and moves into an interstitial site. This creates a vacancy at the old site and an interstitial defect at the new one.
Nothing leaves the crystal, so the density does not change.
It appears in ionic solids with a large difference in ion size and low coordination number: ZnS, AgCl, AgBr, AgI.
AgBr shows both Schottky and Frenkel defects.

Schottky defect

Cation + anion both missing. Density decreases. Similar-size ions, high CN: NaCl, KCl, CsCl. Formula unchanged.

Frenkel defect

Cation moved to an interstitial site. Density unchanged. Very different sizes, low CN: ZnS, AgCl, AgI. Formula unchanged. (AgBr shows both.)

Figure 6: A quick density check identifies the defect. Losing particles (Schottky, vacancy) lowers

ρ

; moving them (Frenkel) keeps it; adding them (interstitial) raises it. Bar heights are exaggerated for clarity.

Exam Trick Schottky = subtract, Frenkel = shift. Schottky removes a pair (density falls); Frenkel only shifts an ion (density stays). The silver halides love Frenkel because

A g^{+}

is small and mobile.

Key idea

Frenkel = small ion moves to a void: vacancy + interstitial pair, density unchanged.

Quick Recall: tap to check

Which defect lowers the density of an ionic crystal?

Schottky (and simple vacancies).

Why does ZnS show Frenkel, not Schottky, defects?

Z n^{2 +}

is much smaller than

S^{2 -}

and fits into interstitial voids; the coordination number is low (4).

Does a Frenkel defect change the formula?

No. Both Schottky and Frenkel are stoichiometric.

5. Non-Stoichiometric Defects

Many inorganic solids contain cations and anions in a ratio slightly different from the ideal formula, while the crystal stays neutral. These non-stoichiometric defects are of two types.

5.1 Metal excess due to anion vacancies: F-centres

Figure 7: F-centres (from German Farbenzentren, colour centres). Electrons trapped in anion vacancies absorb visible light, giving the crystal colour and making it slightly conducting.

Heat NaCl crystals in sodium vapour. Na atoms deposit on the surface.
The $C l^{-}$ ions diffuse to the surface and combine with Na atoms, which lose electrons: Na → $N a^{+}$ + $e^{-}$ .
The released electrons diffuse back into the crystal and occupy the anion vacancies left by the $C l^{-}$ ions.
The crystal now has an excess of sodium ( $N a_{1 + δ} Cl$ ). The anion sites holding unpaired electrons are F-centres.

Electrons in F-centres absorb visible light and re-emit it, so the crystal becomes coloured: NaCl turns yellow, excess lithium makes LiCl pink, and excess potassium makes KCl violet (lilac). These crystals are also paramagnetic and slightly conducting.

5.2 Metal excess due to extra cations in interstitial sites

Figure 8: Metal excess by extra cations. Heated ZnO loses oxygen; the extra

Z n^{2 +}

ions move into interstitial sites and the released electrons occupy neighbouring interstitial sites, so ZnO turns yellow.

Zinc oxide is white at room temperature but turns yellow on heating. It loses oxygen:

ZnO Δ Z n^{2 +} + \frac{1}{2} O_{2} + 2 e^{-}

The excess $Z n^{2 +}$ ions move into interstitial sites and the electrons into neighbouring interstitial sites. The crystal becomes $Z n_{1 + x} O$ , coloured and weakly conducting. On cooling it turns white again.

5.3 Metal deficiency

Figure 9: Metal deficiency. Some

F e^{2 +}

sites are empty and the missing charge is made up by oxidising neighbouring

F e^{2 +}

F e^{3 +}

, so FeO is really about

F e_{0.95} O

Compounds of metals with variable valency can have fewer metal ions than the formula demands. In FeO, some $F e^{2 +}$ sites are empty and, for each vacancy, two neighbouring $F e^{2 +}$ ions become $F e^{3 +}$ . Ferrous oxide is really about $F e_{0.93} O$ to $F e_{0.96} O$ . Similar behaviour: NiO, FeS, $C u_{2} O$ .

Figure 10: The charge-balance route for questions like

F e_{0.93} O

. Divide by

x

, not by 1, for the percentage of metal ions.

JEE Advanced Non-stoichiometric oxides are semiconductors. In metal-deficient

F e_{1 - x} O

N i_{1 - x} O

, an electron can hop from

M^{2 +}

to a neighbouring

M^{3 +}

; the positive 'hole' moves, so they are p-type semiconductors. In metal-excess

Z n_{1 + x} O

the loosely held interstitial electrons carry current, so it is n-type. Heating raises the number of defects and therefore the conductivity, the reverse of a metal.

Key idea

Metal excess: extra electrons (F-centres, or interstitial cations with their electrons). Metal deficiency: cation vacancies balanced by higher-valent cations.

6. Impurity Defects

Figure 11: Impurity defect. A divalent cation replaces two

N a^{+}

ions but occupies only one site, so each

S r^{2 +}

creates one cation vacancy. The number of vacancies equals the number of

S r^{2 +}

ions added.

If molten NaCl containing a little $SrC l_{2}$ is crystallised, some $N a^{+}$ sites are taken by $S r^{2 +}$ . Each $S r^{2 +}$ replaces two $N a^{+}$ ions but occupies only one site, so one cation site is left vacant. The number of cation vacancies equals the number of $S r^{2 +}$ ions. Another example: $CdC l_{2}$ dissolved in AgCl.

Exam Trick One divalent impurity = one cation vacancy. For

x

mol %

SrC l_{2}

in NaCl, vacancies per mole of NaCl

= \frac{x}{100} \times N_{A}

Defect	What happens	Density	Formula	Examples
Vacancy	sites empty (non-ionic)	decreases	same	metals near melting
Interstitial	extra particles in voids (non-ionic)	increases	same	C in Fe
Schottky	cation + anion missing	decreases	same	NaCl, KCl, CsCl, AgBr
Frenkel	cation moved to a void	unchanged	same	ZnS, AgCl, AgBr, AgI
Metal excess (F-centre)	anion vacancy holds $e^{-}$	decreases slightly	changes	NaCl in Na vapour
Metal excess (interstitial)	extra cation + $e^{-}$ in voids	increases slightly	changes	ZnO on heating
Metal deficiency	cation vacancy + higher valence	decreases	changes	FeO, NiO
Impurity	$S r^{2 +}$ replaces 2 $N a^{+}$	depends	doped	$SrC l_{2}$ in NaCl

Key idea

Impurity defects create vacancies by charge balance: count the extra charge, and that many cation sites empty.

Quick Recall: tap to check

Why does NaCl heated in Na vapour turn yellow?

Anion vacancies trap electrons (F-centres) which absorb visible light.

Why is FeO written as

F e_{0.95} O

Some

F e^{2 +}

sites are empty; their charge is made up by

F e^{3 +}

ions (metal deficiency).

Vacancies per mole when NaCl is doped with

1 0^{- 3}

mol %

SrC l_{2}

1 0^{- 5} \times 6.022 \times 1 0^{23} = 6.02 \times 1 0^{18}

6.1 The whole concept at a glance

Figure 12: Crystal defects on one page, with the density and colour effects that questions test.

7. Solved Examples

Solved Example 1

Which statement about the defect shown is incorrect?
(A) The defect is known as a Schottky defect
(B) The density of the compound decreases
(C) NaCl(s) is an example that generally shows this defect
(D) The stoichiometry of the compound changes slightly

Solution:

Figure 13: The lattice in Solved Example 1. Two cation and two anion sites are empty: a Schottky defect.

Answer: (D). Equal numbers of cation and anion sites are empty, so this is a Schottky defect: the density falls, NaCl typically shows it, and the cation-anion ratio is unchanged. So (D) is the incorrect statement.

Solved Example 2

Ferrous oxide (FeO) is experimentally found to have the formula

F e_{0.93} O

. Find the percentage of Fe ions in the +3 state.

Solution:

Take 93 Fe ions per 100 O ions, and let $x$ of them be $F e^{3 +}$ . Charge balance with 100 $O^{2 -}$ :

3 x + 2 (93 - x) = 200 \Rightarrow x = 14

% F e^{3 +} = \frac{14}{93} \times 100 = 15.05%

So about 15% of the iron is $F e^{3 +}$ and 85% is $F e^{2 +}$ .

Solved Example 3

Calcium crystallises in an fcc unit cell with a = 0.556 nm (

M = 40

g mol

^{- 1}

). Calculate the density if it contains (i) 0.1% Frenkel-type defects, (ii) 0.1% Schottky-type (vacancy) defects.

Solution:

$a = 0.556 \times 1 0^{- 7}$ cm, so $a^{3} N_{A} = (0.556 \times 1 0^{- 7})^{3} \times 6.022 \times 1 0^{23} = 103.5$ cm $^{3}$ mol $^{- 1}$ .

(i) Frenkel defects move atoms without removing them: $Z = 4$ .

d = \frac{4 \times 40}{103.5} = 1.546 g cm^{- 3}

(ii) 0.1% of sites empty: $Z_{e f f} = 4 \times 0.999 = 3.996$ .

d = \frac{3.996 \times 40}{103.5} = 1.545 g cm^{- 3}

Solved Example 4

NaCl is doped with

1 0^{- 3}

mol % of

SrC l_{2}

. What is the concentration of cation vacancies per mole of NaCl?

Solution:

$1 0^{- 3}$ mol % means $1 0^{- 3}$ mol of $SrC l_{2}$ per 100 mol of NaCl, that is $1 0^{- 5}$ mol per mole of NaCl. Each $S r^{2 +}$ creates one cation vacancy:

vacancies = 1 0^{- 5} \times 6.022 \times 1 0^{23} = 6.02 \times 1 0^{18} mol^{- 1}

Solved Example 5

Which defect decreases the density of a crystal?
(A) Frenkel
(B) Schottky
(C) interstitial
(D) F-centre formed by extra cations in interstitial sites

Solution:

Answer: (B). A Schottky defect removes cation-anion pairs while the volume stays the same. Frenkel leaves density unchanged; interstitial defects increase it.

Solved Example 6

A sample of nickel oxide has the formula

N i_{0.98} O

. What fraction of nickel exists as

N i^{3 +}

Solution:

Let $y$ be $N i^{3 +}$ per formula unit: $3 y + 2 (0.98 - y) = 2$ , so $y = 0.04$ .

Fraction $= \frac{0.04}{0.98} = 0.0408$ , about 4.1%.

Solved Example 7

The theoretical density of KCl is 1.99 g cm

^{- 3}

but a crystal is found to have 1.98 g cm

^{- 3}

. Assuming only Schottky defects, what percentage of formula units is missing?

Solution:

% missing = \frac{1.99 - 1.98}{1.99} \times 100 = 0.50%

Solved Example 8

Which compound shows both Schottky and Frenkel defects?
(A) NaCl
(B) ZnS
(C) AgBr
(D) CsCl

Solution:

Answer: (C). AgBr has Schottky defects like the alkali halides, and its small, mobile $A g^{+}$ ions also move into interstitial sites (Frenkel).

Practice Questions

What type of defect does AgCl mainly show, and how does it affect density?Answer: Frenkel; density unchanged.
Why does white ZnO turn yellow on heating?Answer: It loses oxygen; extra $Z n^{2 +}$ and electrons occupy interstitial sites (metal excess).
NaCl is doped with $1 0^{- 4}$ mol % $SrC l_{2}$ . Cation vacancies per mole?Answer: $1 0^{- 6} \times 6.022 \times 1 0^{23} = 6.02 \times 1 0^{17}$ .
Find the percentage of Fe as $F e^{3 +}$ in $F e_{0.95} O$ .Answer: $3 y + 2 (0.95 - y) = 2$ , $y = 0.10$ ; $\frac{0.10}{0.95} = 10.5%$ .
What colour does KCl take when heated in potassium vapour, and why?Answer: Violet (lilac), from F-centres.
Name two defects that do not change the formula of an ionic solid.Answer: Schottky and Frenkel.
Which defect is a line defect: F-centre, edge dislocation, Frenkel?Answer: Edge dislocation.

Common Mistakes to Avoid

Watch out

Saying Frenkel defects lower density. Nothing leaves the crystal, so density is unchanged.
Calling Schottky and Frenkel defects non-stoichiometric. Both keep the formula ratio exactly.
Thinking F-centres are cation vacancies. They are anion vacancies that trap electrons.
Dividing by 1 instead of by $x$ in $M_{x} O$ problems: % $M^{3 +}$ $= \frac{y}{x} \times 100$ .
Assuming one $S r^{2 +}$ creates two vacancies. It replaces two $N a^{+}$ but occupies one site, leaving one vacancy.
Listing NaCl as a Frenkel example. $N a^{+}$ and $C l^{-}$ are too similar in size; NaCl shows Schottky defects.
Believing defects vanish on heating. Their number increases with temperature.
Treating a screw or edge dislocation as a plane defect. Dislocations are line defects.

Frequently Asked Questions

What are point defects in crystals?

Point defects are irregularities around a single lattice point: missing particles (vacancies), extra particles in voids (interstitials), displaced ions, or foreign ions. They are divided into stoichiometric defects, non-stoichiometric defects and impurity defects.

What is the difference between Schottky and Frenkel defects?

In a Schottky defect equal numbers of cations and anions are missing, so density decreases; it occurs in NaCl, KCl and CsCl. In a Frenkel defect a smaller ion leaves its site for an interstitial position, so density is unchanged; it occurs in ZnS, AgCl and AgI. Both keep the formula unchanged.

What are F-centres?

F-centres are anion vacancies that hold trapped electrons. They form, for example, when NaCl is heated in sodium vapour. The electrons absorb visible light, so NaCl becomes yellow, LiCl pink and KCl violet.

Why does ZnO turn yellow on heating?

On heating, zinc oxide loses a little oxygen. The extra zinc ions move into interstitial sites and the released electrons occupy neighbouring interstitial sites. This metal excess defect makes the solid yellow; it turns white again on cooling.

Why is ferrous oxide non-stoichiometric?

In ferrous oxide some iron(II) sites are empty. To keep the crystal neutral, two iron(II) ions are oxidised to iron(III) for every vacancy. The real composition is about Fe0.93O to Fe0.96O, a metal deficiency defect.

How does adding SrCl2 to NaCl create vacancies?

Each strontium ion replaces two sodium ions to keep the charge balanced but occupies only one lattice site. So every strontium ion added leaves one cation site empty, and the number of cation vacancies equals the number of strontium ions.

Are crystal defects in the NEET syllabus?

No. Point defects were removed from NEET, together with the rest of Solid State, from 2024. JEE Advanced 2026 still lists point defects under Solid State.

What type of defect questions come in JEE Advanced?

JEE Advanced asks you to identify Schottky, Frenkel, metal excess or metal deficiency defects, predict their effect on density and colour, find the fraction of M3+ in formulas like Fe0.93O, and count vacancies created by doping with divalent impurities.

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