MHT-CET Chemistry · Solid State

Crystal Defects, Magnetic Properties and Semiconductors

Real crystals carry point defects — missing ions (Schottky), displaced ions (Frenkel), foreign atoms in place of or between the host atoms — and their electrical and magnetic behaviour follows from the band gap and from unpaired electrons.

All Solid State notes MHT-CET Chemistry strategy

Why this matters

26 PYQs, all EASY or MODERATE, all recall. Name the defect from its description or from an alloy (brass, stainless steel), pick the dopant that makes Si or Ge n-type or p-type, spot the ferromagnetic substance in a list, read a conductor off a band-gap table. Three short tables cover the lot.

Concept 1 of 3: Point Defects: Schottky, Frenkel, Impurity and Non-Stoichiometric

A defect is a break in the pattern at one lattice site. Either something is MISSING (vacancy; Schottky when a cation and an anion go together), DISPLACED to a hole (Frenkel), or FOREIGN — a different atom substituting for a host atom or squeezed between them. When the cation:anion ratio itself departs from the formula, the defect is non-stoichiometric.

Definition

Vacancy: a lattice site empty. Self-interstitial: a host atom in an interstitial site.
Schottky: equal numbers of cations and anions missing; neutrality kept, density FALLS. Ions of similar size, high coordination — NaCl, KCl, CsCl, AgBr.
Frenkel (dislocation defect): a smaller ion (usually the cation) leaves its site for an interstitial one; density UNCHANGED. Large size difference, low coordination — ZnS, AgCl, AgBr, AgI.
Substitutional impurity: a foreign atom of similar size replaces a host atom — brass (Zn for Cu), solid solutions of Cd in Ag. Interstitial impurity: a small foreign atom in a void — stainless steel (C between Fe atoms).
Non-stoichiometric: cation:anion ratio differs from the formula — metal excess (F-centres colour NaCl yellow; ZnO turns yellow on heating) or metal deficiency ( $\text{Fe}_{0.95}\text{O}$ , $\text{Ni}_{0.97}\text{O}$ ).

Defect	What happens	Effect on density	Examples
Schottky	Equal numbers of cations and anions missing	Decreases	NaCl, KCl, CsCl, AgBr
Frenkel	Ion leaves its site for an interstitial position	Unchanged	ZnS, AgCl, AgBr, AgI AgBr shows BOTH Schottky and Frenkel.
Substitutional impurity	Foreign atom replaces a host atom	Depends	Brass (Zn in Cu), Cd²⁺ in AgCl
Interstitial impurity	Small foreign atom in a void	Increases	Stainless steel (C in Fe) Brass is SUBSTITUTIONAL, steel is INTERSTITIAL — size decides.
Non-stoichiometric	Cation:anion ratio ≠ formula	Varies	( ext{Fe}_{0.95} ext{O}) (deficiency), NaCl with F-centres (excess)

Missing → Schottky, displaced → Frenkel, foreign → impurity, wrong ratio → non-stoichiometric.

Practise this conceptself-check · 4 quick reps

The same idea in a real exam question:

MHT-CET · 2023 · 10th May Shift 1 · Q62Easy

Example 1 · Solid State · Crystal Defects, Magnetic Properties and Semiconductors

In an ionic solid, equal number of cations and anions are missing from their regular positions in the crystal lattice creating vacancies. This is called

Calling every missing-ion picture Frenkel

Frenkel needs the ion to REAPPEAR in an interstitial site. If the ions are simply gone in equal numbers, it is Schottky. Read for the words 'interstitial position'.

Drill 4 more on point defects: schottky, frenkel, impurity and non-stoichiometric

Concept 2 of 3: Band Gap, n-Type and p-Type Doping

Conductivity is set by the gap between the filled valence band and the empty conduction band: no gap — conductor; small gap — semiconductor; large gap — insulator. Doping silicon or germanium (Group 14) with a Group 15 atom adds a spare electron (n-type); with a Group 13 atom it leaves a hole (p-type).

Definition

Band gap: conductor $E_g \approx 0$ (metals); semiconductor small (Si 1.12 eV, Ge 0.67 eV); insulator large (diamond 5.47 eV).
n-type: Si or Ge doped with P, As, Sb (Group 15, five valence electrons) — the extra electron carries current.
p-type: Si or Ge doped with B, Al, Ga, In (Group 13, three valence electrons) — the electron hole carries current.
Semiconductor conductivity RISES with temperature (more electrons cross the gap); a metal's falls.
Caesium, with the lowest work function, is used in photoelectric cells.

Dopant rule

\text{Group 15 (P, As, Sb)} \to n\text{-type};\qquad \text{Group 13 (B, Al, Ga, In)} \to p\text{-type}

Worked example

Four solids have band gaps 5.47 eV, 0.0 eV, 1.12 eV and 0.67 eV. Classify each.

Practise this conceptself-check · 4 quick reps

The same idea in a real exam question:

MHT-CET · 2023 · 11th May Shift 1 · Q80Easy

Example 2 · Solid State · Crystal Defects, Magnetic Properties and Semiconductors

n-type of semiconductor is formed when

Confusing 'n' with 'negative charge on the dopant'

n-type means the CARRIER is a negative electron, supplied by a Group 15 donor. The dopant itself is neutral. p-type means positive holes from a Group 13 acceptor. In, Ga, B and Al are always p-type.

Drill 6 more on band gap, n-type and p-type doping

Concept 3 of 3: Diamagnetic, Paramagnetic, Ferromagnetic

Unpaired electrons are tiny magnets. None — diamagnetic, weakly repelled by a field. A few, randomly oriented — paramagnetic, weakly attracted. Many, spontaneously aligned in domains — ferromagnetic, strongly attracted and able to stay magnetised. Of the exam's usual list (NaCl, H₂O, C₆H₆, O₂, CrO₂), only CrO₂ is ferromagnetic.

Definition

Diamagnetic: all electrons paired; repelled weakly. NaCl, $\text{H}_2\text{O}$ , benzene, $\text{N}_2$ , Zn, TiO $_2$ .
Paramagnetic: unpaired electrons, moments random; attracted weakly, magnetism lost when the field is removed. $\text{O}_2$ , $\text{Cu}^{2+}$ , $\text{Fe}^{3+}$ , NO.
Ferromagnetic: unpaired electrons aligned parallel in domains; strongly attracted, permanent magnets. Fe, Co, Ni, Gd, $\text{CrO}_2$ (magnetic tapes).
Antiferromagnetic (opposed, equal — MnO) and ferrimagnetic (opposed, unequal — $\text{Fe}_3\text{O}_4$ ) complete the list.
Nanoscale: melting point falls as a particle gets smaller — bulk Na 371 K, a $10^4$ -atom cluster ~303 K, a $10^3$ -atom cluster ~288 K.

Behaviour	Electrons	In a field	Examples
Diamagnetic	All paired	Weakly repelled	NaCl, H₂O, C₆H₆, N₂
Paramagnetic	Unpaired, random	Weakly attracted, temporary	O₂, Cu²⁺, Fe³⁺, NO O₂ is paramagnetic, never ferromagnetic.
Ferromagnetic	Unpaired, aligned in domains	Strongly attracted, permanent	Fe, Co, Ni, Gd, CrO₂ CrO₂ is the one ferromagnetic COMPOUND the paper lists.
Antiferromagnetic	Aligned opposite, equal	Net zero	MnO
Ferrimagnetic	Aligned opposite, unequal	Weakly attracted	Fe₃O₄, ferrites

Count unpaired electrons, then ask whether they line up.

Practise this conceptself-check · 4 quick reps

The same idea in a real exam question:

MHT-CET · 2023 · 15th May Shift 1 · Q57Easy

Example 3 · Solid State · Crystal Defects, Magnetic Properties and Semiconductors

Which among the following is ferromagnetic substance?

Picking O₂ because it is magnetic

O₂ has two unpaired electrons and is attracted to a magnet — but weakly and only while the field is on. That is paramagnetism. Ferromagnetic needs domains: Fe, Co, Ni, CrO₂.

Drill 2 more on diamagnetic, paramagnetic, ferromagnetic

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Band Gap, n-Type and p-Type Doping
Dopant rule
$\text{Group 15 (P, As, Sb)} \to n\text{-type};\qquad \text{Group 13 (B, Al, Ga, In)} \to p\text{-type}$

Reference tables (2)

Point Defects: Schottky, Frenkel, Impurity and Non-Stoichiometric5 rows

Defect	What happens	Effect on density	Examples
Schottky	Equal numbers of cations and anions missing	Decreases	NaCl, KCl, CsCl, AgBr
Frenkel	Ion leaves its site for an interstitial position	Unchanged	ZnS, AgCl, AgBr, AgI AgBr shows BOTH Schottky and Frenkel.
Substitutional impurity	Foreign atom replaces a host atom	Depends	Brass (Zn in Cu), Cd²⁺ in AgCl
Interstitial impurity	Small foreign atom in a void	Increases	Stainless steel (C in Fe) Brass is SUBSTITUTIONAL, steel is INTERSTITIAL — size decides.
Non-stoichiometric	Cation:anion ratio ≠ formula	Varies	( ext{Fe}_{0.95} ext{O}) (deficiency), NaCl with F-centres (excess)

Missing → Schottky, displaced → Frenkel, foreign → impurity, wrong ratio → non-stoichiometric.

Diamagnetic, Paramagnetic, Ferromagnetic5 rows

Behaviour	Electrons	In a field	Examples
Diamagnetic	All paired	Weakly repelled	NaCl, H₂O, C₆H₆, N₂
Paramagnetic	Unpaired, random	Weakly attracted, temporary	O₂, Cu²⁺, Fe³⁺, NO O₂ is paramagnetic, never ferromagnetic.
Ferromagnetic	Unpaired, aligned in domains	Strongly attracted, permanent	Fe, Co, Ni, Gd, CrO₂ CrO₂ is the one ferromagnetic COMPOUND the paper lists.
Antiferromagnetic	Aligned opposite, equal	Net zero	MnO
Ferrimagnetic	Aligned opposite, unequal	Weakly attracted	Fe₃O₄, ferrites

Count unpaired electrons, then ask whether they line up.

Watch out for (3)

Calling every missing-ion picture Frenkel
→ Point Defects: Schottky, Frenkel, Impurity and Non-Stoichiometric
Confusing 'n' with 'negative charge on the dopant'
→ Band Gap, n-Type and p-Type Doping
Picking O₂ because it is magnetic
→ Diamagnetic, Paramagnetic, Ferromagnetic

Test yourself on Solid State

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Related notes

Types of Solids — the classes these defects live in →