Imperfections in Solids — Revision Notes

⚡ 30-Second Revision

Point Defects: — Localized deviations from ideal crystal structure.
Stoichiometric Defects: — Maintain ideal cation:anion ratio.

- Vacancy: Missing atom/ion. Decreases density. - Interstitial: Extra atom/ion in interstitial site. Increases density. - Frenkel: Ion leaves lattice site, occupies interstitial. Density unchanged. (AgCl, ZnS, AgBr). - Schottky: Equal number of cation/anion vacancies. Decreases density. (NaCl, KCl, CsCl, AgBr).

Non-Stoichiometric Defects: — Alter cation:anion ratio.

- Metal Excess: Anion vacancies (F-centres, color, n-type) or interstitial cations (n-type). - Metal Deficiency: Cation vacancies (p-type). (e.g., $Fe_{0.95}O$).

Impurity Defects: — Foreign atoms.

- Substitutional: Impurity replaces host (e.g., doping Si with P/B, $Sr^{2+}$ in NaCl $ightarrow$ cation vacancies). - Interstitial: Impurity in interstitial site (e.g., C in Fe).

F-centre: — Anion vacancy + trapped electron $ightarrow$ color, n-type semiconductor.
Doping: — Adding impurities to semiconductors.

- n-type: Group 14 + Group 15 (excess $e^-$). - p-type: Group 14 + Group 13 (electron holes).

2-Minute Revision

Imperfections in solids are deviations from perfect crystal order, crucial for material properties. They arise due to thermodynamics (entropy increase) or kinetic factors. Point defects are the most relevant for NEET.

Stoichiometric defects maintain the compound's ideal ratio. Frenkel defects involve an ion moving to an interstitial site, keeping density unchanged (e.g., AgCl, ZnS). Schottky defects involve missing pairs of cations and anions, decreasing density (e.g., NaCl, KCl). AgBr uniquely exhibits both.

Non-stoichiometric defects alter the ideal ratio. Metal excess can be due to anion vacancies (forming F-centres, which cause color and n-type semiconduction, e.g., yellow NaCl) or interstitial cations (e.g., ZnO). Metal deficiency involves cation vacancies, compensated by higher-valent metal ions, leading to p-type semiconduction (e.g., $Fe_{0.95}O$).

Impurity defects involve foreign atoms. Doping semiconductors is a key example: Group 15 impurities in Group 14 elements create n-type (electron-rich) semiconductors, while Group 13 impurities create p-type (hole-rich) semiconductors. Doping NaCl with $SrCl_2$ creates cation vacancies to maintain charge neutrality.

5-Minute Revision

Crystal imperfections, or defects, are deviations from the ideal, perfectly ordered arrangement of atoms or ions in a solid. These are thermodynamically favored at temperatures above absolute zero due to the increase in entropy. They are classified by dimensionality, with point defects being most important for NEET.

Point Defects:

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Stoichiometric Defects: — Maintain the compound's ideal cation:anion ratio.

* Vacancy Defect: A particle is missing from its lattice site. Decreases density. (e.g., non-ionic solids). * Interstitial Defect: An extra particle occupies an interstitial site. Increases density.

(e.g., non-ionic solids). * Frenkel Defect: An ion (usually cation) leaves its lattice site and occupies an interstitial site within the same crystal. Density remains unchanged. Common in compounds with large ion size difference and low coordination number (e.

g., AgCl, ZnS, AgBr). * Schottky Defect: An equal number of cations and anions are missing from their lattice sites. Density decreases. Common in compounds with similar ion sizes and high coordination number (e.

g., NaCl, KCl, CsCl, AgBr).

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Non-Stoichiometric Defects: — Alter the ideal cation:anion ratio, common in transition metal compounds due to variable valency.

* Metal Excess Defects: Excess metal ions. * Due to Anion Vacancies: Anion missing, electron trapped in its place $ightarrow$ F-centre. Imparts color (e.g., yellow NaCl, violet KCl) and causes n-type semiconduction.

* Due to Interstitial Cations: Extra cation in interstitial site, electron in adjacent interstitial site. Causes n-type semiconduction (e.g., ZnO turns yellow on heating). * Metal Deficiency Defects: Deficiency of metal ions.

Cation vacancies are compensated by adjacent metal ions having higher oxidation states. Causes p-type semiconduction (e.g., $Fe_{0.95}O$).

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Impurity Defects: — Foreign atoms present.

* Substitutional Impurity: Impurity replaces host atom. Example: Doping silicon with phosphorus (Group 15) creates n-type semiconductors (excess electrons). Doping silicon with boron (Group 13) creates p-type semiconductors (electron holes). Doping NaCl with $SrCl_2$: $Sr^{2+}$ replaces $Na^+$, creating one $Na^+$ vacancy per $Sr^{2+}$ to maintain charge neutrality, increasing ionic conductivity.

Key Takeaways:

Density changes: Schottky/Vacancy (decrease), Interstitial (increase), Frenkel (no change).
Electrical conductivity: F-centres (n-type), Metal excess (n-type), Metal deficiency (p-type), Doping (n-type or p-type).
AgBr is unique, showing both Frenkel and Schottky defects.
F-centres are anion vacancies with trapped electrons, causing color.

Prelims Revision Notes

Imperfections in Solids: NEET Quick Recall

1. Definition: Any deviation from the perfectly ordered, periodic arrangement of particles in a crystalline solid.

2. Causes:

* Thermododynamic stability (entropy increase at $T > 0 K$). * Kinetic factors (rapid cooling, impurities during crystallization).

3. Types of Point Defects (Most Important for NEET):

* Stoichiometric Defects (Maintain stoichiometry): * Vacancy Defect: Missing atom/ion from lattice site. $ightarrow$ Decreases density. * Interstitial Defect: Extra atom/ion in interstitial site.

$ightarrow$ Increases density. * Frenkel Defect: Ion leaves lattice site, occupies interstitial site within same crystal. $ightarrow$ Density unchanged. * Favored by: Large size difference between ions (cation usually smaller), low coordination number.

* Examples: AgCl, ZnS, AgBr, CaF$_2$. * Schottky Defect: Equal number of cations and anions missing from lattice sites. $ightarrow$ Decreases density. * Favored by: Similar ion sizes, high coordination number.

* Examples: NaCl, KCl, CsCl, AgBr. * Note: AgBr exhibits both Frenkel and Schottky defects.

* Non-Stoichiometric Defects (Alter stoichiometry): Common in transition metal compounds (variable valency). * Metal Excess Defects: Excess metal ions. * Due to Anion Vacancies: Anion missing, electron trapped in vacancy.

$ightarrow$ F-centre. * Causes: Color (e.g., NaCl yellow, KCl violet, LiCl pink). * Electrical property: n-type semiconductor (due to free electrons). * Due to Interstitial Cations: Extra cation in interstitial site, electron in adjacent interstitial site.

$ightarrow$ n-type semiconductor. * Example: ZnO (white when cold, yellow when hot due to $Zn^{2+}$ interstitials and electrons). * Metal Deficiency Defects: Deficiency of metal ions. * Due to Cation Vacancies: Cation missing, charge balanced by adjacent metal ions acquiring higher oxidation state.

$ightarrow$ p-type semiconductor. * Example: $Fe_{0.95}O$ (some $Fe^{2+}$ missing, compensated by $Fe^{3+}$).

* Impurity Defects (Foreign atoms present): * Substitutional Impurity: Foreign atom replaces host atom. * Doping in Semiconductors: * n-type: Group 14 (Si, Ge) doped with Group 15 (P, As, Sb).

$ightarrow$ Excess electrons (majority carriers). * p-type: Group 14 (Si, Ge) doped with Group 13 (B, Al, Ga). $ightarrow$ Electron holes (majority carriers). * Ionic Solids: Doping NaCl with $SrCl_2$.

$Sr^{2+}$ replaces $Na^+$. For every $Sr^{2+}$ ion, one $Na^+$ vacancy is created to maintain charge neutrality. $ightarrow$ Increases ionic conductivity.

4. Key Effects to Remember:

* Density: Schottky/Vacancy (decrease), Interstitial (increase), Frenkel (no change). * Color: F-centres. * Electrical Conductivity: F-centres (n-type), Doping (n-type/p-type), Schottky/Frenkel (slight increase due to ion/vacancy mobility), Impurity defects (e.g., $SrCl_2$ in NaCl $ightarrow$ increased ionic conductivity).

5. Important Examples:

* AgBr: Both Frenkel and Schottky. * NaCl + Na vapor: Yellow color due to F-centres. * ZnO + heat: Yellow color due to interstitial $Zn^{2+}$ and electrons. * $Fe_{0.95}O$: Metal deficiency defect. * Si + P: n-type semiconductor. * Si + B: p-type semiconductor. * NaCl + $SrCl_2$: Cation vacancies.

Vyyuha Quick Recall

To remember the density effects of Frenkel and Schottky defects: Frenkel: Forgets to change density (Density Fixed). Schottky: Shrinks density (Density Sinks).