Imperfections in solids - class-XII

Silver halides show both Frenkel and Schotkky defects. For Frenkel defect the reason is that there is size difference between the sizes of silver and halide.

Schottky Defect: This defect occurs when oppositely charged ions leave their lattice site creating vacancies in such a way that electrical neutrality of crystal is maintained. It is generally seen in highly ionic compounds where a difference in size of cation and anion is small. 

So, an equal number of cations and anions vacancies are present in the crystals with Schottky Defect.

Frenkel defect is one in which atom is displaced from its lattice point to the interstitial site, creating a vacancy at the lattice point. Here, since dislocation of atom lattice point happens. So, it is also called as dislocation defect.

Given, sample of ferrous oxide is $Fe _{0.93}O _{1.00}$.

Let number of $Fe^{2+}$ ions is $x$ then number of $Fe^{3+}$ ions is $(0.93-x)$

Now, for electrical neutrality, $(+2)x + (+3)(0.93-x)=+2$

$\Rightarrow 2x+2.79 – 3x = 2$

$\Rightarrow x=0.79$

So, number of $Fe^{2+}$ ions $=0.79$

Number of $Fe^{3+}$ ions $=0.14$

So, fraction of $Fe^{2+}$ ions $= \cfrac {0.79}{0.93}=0.849$

$FeO$ has non stochiometric metal deficiency
defect in which number of $Fe^{2+}$ ions are lesser than $O^-$ ions as
compared to stochiometric formula. The neutrality is maintained to variable
oxidation state possessing capability of $Fe$.

NaCl is an ionic crystal that typically exhibits Schottky defects, which are a type of vacancy defect where ions are missing from their lattice sites.

When NaCl is doped with SrCl2, each Sr2+ ion replaces two Na+ ions to maintain electrical neutrality, creating one cationic vacancy per Sr2+ ion added. Thus, 10^-3 mole of SrCl2 introduces 10^-3 moles of cationic vacancies, which when multiplied by Avogadro's number gives 6.02 x 10^20 per mole.

When KC1 is heated in vapour of K, some of the Cl leave their lattice site and create anion vacancies. This chloride ion wants to combine with K vapour to form potassium chloride. For doing so K atom loses electrons form K ions. This released electron diffuses into the crystal to get entrapped in the anion vacancy called F-centre. When visible light falls on the crystal, this entrapped electron gains energy, goes to the higher level when it comes back to the ground state, energy is released in the form of light.

Given that $1$ $mol$ of $NaCl$ is doped with $\cfrac{10^{-3}}{100}$ $mol$ of $Sr^{+2}=10^{-5}$ $mol$

Schottky defect is shown in highly ionic compound, highly coordinated compounds, and where there is only a small difference in sizes of cations and anions of which the compound lattice is composed.

$180 \ Cu$ atoms are associated with $100 \ S$ atoms.

$NaCl$ is doped with $10^{-4}$ $mol%$ of $SrCl _2$, i.e., one mole of $NaCl$ will have $10^{-6}$ mol of $SrCl _2$

As temperature and number of defects are inversely propotional, with increase in temperature number of defects decreases. 

All statements are correct: Frenkel involves vacancy and interstitial sites, is stoichiometric, is called a dislocation defect, and is common in silver halides.

In ionic solids like NaCl and AgCl, electrical conductivity is primarily due to the migration of ions through vacancies or interstitial sites, not the movement of electrons.

Frenkel defect is typically observed in ionic solids where there is a large difference in size between the cation and anion, leading to a low coordination number. In this defect, smaller ions (usually cations) leave their normal lattice sites and occupy interstitial sites. Schottky defect is found in ionic solids with high coordination numbers where ions of similar sizes are missing.

10^-3 moles of SrCl2 in 100 moles of NaCl means 10^-5 moles of SrCl2 per mole of NaCl. This creates 10^-5 * 6.02 x 10^23 = 6.02 x 10^18 vacancies per mole.

An interstitial compound is a compound that is formed when an atom with a small enough radius sits in an interstitial hole in a metal lattice.  examples of small atoms are boron, carbon and nitrogen.  these compounds play important role in industries. Examples: TiH, Fe3H and Mn4N

Vacancy and Schottky defect which lead to decrease the density both are the types of a stoichiometric defect. In case of Frenkel defect and interstitial defect, there is no change in density of substance.

(a, b) In Frenkel defect, dislocation of cations takes place and there is no change in stoichiometry of the crystal.

Impurity defects are foreign atoms that replace some  of the atoms making up the solid or that squeeze into the interstices; they are important in the electrical behaviour of semiconductors, which are materials used in computer chips and other electronic devices.

Solution:- (C) $0.50$

AgBr, ZnS, and AgI all exhibit Frenkel defects due to the significant size difference between cations and anions.

Schottky defects involve the removal of ions from the lattice, which decreases the total mass of the crystal for the same volume, thus lowering the density.

Schottky defects are common in ionic compounds with high coordination numbers like NaCl, CsCl, and AgBr.

Vacancy defects decrease density because atoms leave the lattice. Interstitial defects increase density by adding atoms to voids. Impurity defects can either increase or decrease density depending on the size and mass of the impurity, but the statement that it must increase is not a universal rule, making it the most incorrect general claim.

Schottky defects are intrinsic or thermodynamic defects because they arise naturally in ionic crystals due to thermal vibrations, leading to the formation of vacancy pairs to maintain electrical neutrality.

I is False: In anti-fluorite, anions form FCC and cations occupy all tetrahedral voids. II is True: Radius ratio 20/95 = 0.21, which falls in the range for coordination number 4. III is True: This is the definition of Frenkel defect. IV is False: Density can decrease if the impurity atom is smaller or lighter.

Doping silicon with elements like phosphorus or boron introduces extra electrons or holes, which are classified as electronic defects, altering the electrical conductivity of the semiconductor.

Schottky defect arises due to a vacancies at cation sites and equal number of vacancies at anion sites.

Schottky defect arises due to a vacancies at cation sites and equal number of vacancies at anion sites.

Condition for Frankel defects in an ionic crystal is-

1. The size difference between the ions should be large.
   
2. Smaller ion (cation) move to interstitial site.

Frenkel defect is a defect which is created when an ion leaves its appropriate site in the lattice and occupies an interstitial site. A hole or vacancy is thus produced in the lattice.
Frenkel defect is exhibited in ionic compounds in which the radius ratio is low. The cations and anions differ much in their sizes and the ions have low co-ordination numbers. Examples are ZnS, AgBr, AgI, AgCl.
The Schottky defect is a defect which is produced when one cation and anion are missing from their respective positions leaving behind a pair of holes. The crystal as a whole remains neutral because the number of missing positive ions (cations) and negative ions (anions) is the same.

Schottky defect is the defect which is produced when one cation and anion are missing from their respective positions leaving behind a pair of holes. The crystal as a whole remains neutral because the number of missing positive ions (cations) and negative ions (anions) is the same.
For Schottky defect, co-ordination numbers of the ions should be high., Examples of ionic solids showing this defect are NaCl, CsCl, KCI, KBr etc.
Consequences of Schottky defect are as follows:
1. Density of the crystal decreases.
2. The crystal begins to conduct electricity to small extent by ionic mechanism.
3. The presence of too many voids lowers lattice energy or the stability of the crystal.

Frenkel defect is the defect which is created when an ion leaves its appropriate site in the lattice and occupies an interstitial site. A hole or vacancy is thus produced in the lattice.
Frenkel defect is exhibited in ionic compounds in which the radius ratio is low. The cations and anions differ much in their sizes and the ions have low co-ordination numbers. Examples are $ZnS, AgBr, AgI, AgCl$.

There are N atoms in a crystal with $N _1$ interstitial positions in
its structure. If there are n Frenkel defects in the crystal, then n is
equal to $\left (\dfrac{N}{N _1} \right )^{\dfrac{1}{2}} exp^{(-E _i/2KT)}$

Solids with Schottky defects conducts electricity to a small extent by the ionic mechanism. The defect is due to an unequal number of cation and anion vacancies because in it some cations leave vacant spaces

Frenkel defect is a defect is created when an ion leaves its appropriate site in the lattice and occupies an interstitial site. A hole or vacancy is thus produced in the lattice.
The electroneutrality of the crystal is maintained since the number of positive and negative ions is the same. Since positive ions are small in size, they usually leave their positions in the lattice and occupy interstitial positions.
Consequences of Frenkel defect:
1. The closeness of like charges tends to increase the dielectric constant of the crystal.
2. The crystal showing a Frenkel defect conducts electricity to a small extent by ionic mechanism.
3. The density of the crystal remains the same.
In metal excess defects caused by anion vacancies, one or more anions are missing from the lattice points which are occupied by electrons.
The overall electrical neutrality is maintained. When NaCl crystal is heated with Na vapours, this kind of defect is observed.
The electrons impart colour to the crystal (yellow colour to NaCl). These are known as F-centers (Farbe's centres).

Doping with $Ca^{2+}$ ions will create two vacant sites occupied by $K^+$ ions. One site will be occupied by $Ca^{2+}$ ions leaving one site. So, the density is lowered.

I. In an anti-flourite structure, anions form FCC lattice and cations occupy all tetrahedral voids.

Schottky defect is observed in the crystals of NaCl, CsCl, AgBr etc.

Frenkel defect is observed in the crystals of ZnS, AgBr, AgI, AgCl etc.

When Potassium chloride is heated in sodium vapour, we see that is acquires a yellow colour. The heating in excess sodium creates new lattice sites for sodium. To maintain the structure, an equal number of chloride sites are also created but the latter are vacant. The electron of the potassium atom that is ionized in the KCl matrix is trapped by the chloride ion vacancy. This trapped electron can be freed into the crystal by absorbing visible light and hence, the colour. A trapped electron at an anion vacancy is an electronic defect and it is known as F-centre.

Frenkel defect is exhibited in ionic compounds in which the radius ratio is low. The cations and anions differ much in their sizes and the ions have low co-ordination numbers. However, in Schottky defect the size of cation and anion

Schottky defect is the defect which is produced when one cation and anion is missing from their respective positions leaving behind a pair of holes. The crystal as a whole remains neutral because the number of missing positive ions (cations) and negative ions (anions) is the same.

Frenkel defect is a defect which is created when an ion leaves its appropriate site in the lattice and occupies an interstitial site. A hole or vacancy is thus produced in the lattice.
The electroneutrality of the crystal is maintained since the number of positive and negative ions is the same. Since positive ions are small in size, they usually leave their positions in the lattice and occupy interstitial positions.

A Schottky defect is a type of point defect in a solid crystal lattice. 

All alkali metal halides show the Schottky defect due to the formation of excess cations.
Thus Schottky defect will be noticed in $NaCl ; & ; KCl$.
Thus, option $(D)$ is right answer.

Schottky defect is indicated in the diagram as equal number of sodium cation and chloride anion are missing.
In Frenkel defect, a cation or anion leaves its regular site and occupies interstitial position.

(A) Frenkel defect tends to increase the dielectric constant of the crystal because of presence of the ions in interstitial sites.

Frenkel Defect: This
defect is shown by ionic
solids. The smaller ion is
dislocated from its normal
site to an interstitial site. Frenkel defect is
shown by ionic substance in which there is a large difference in
the size of ions.

$FeO$ shows metal deficiency defect. In crystal of $FeO$ some $Fe^{2+}$ cations are missing and the loss of positive charge is made up by the presence of required number of $Fe^{3+} $ ions.

In the given crystal equal number of cations and anions are missing (two ${K}^{+}$ and two ${Cl}^{-}$) from their normal lattice sites and the crystal maintains electrical neutrality. Hence, this is Schottky defect.

In F-centre defect in which an anionic vacancy in a crystal is filled by one or more unpaired electron. These electron absorb light in the visible region and emits colour. So, appearance of colour in solid alkali metal halides is generally due to F-centre.

(4) Density of crystal not $\uparrow$ es always it may remain constant sometimes.

$FeO$ has metal deficiency defect. Metal deficiency defect is supposed to arise when there are lesser number of positive ions than negative ions. In case of $FeO$, the positive ions are missing from their lattice sites. 

The additional negative charge is balanced by some nearby metal ion by acquiring one more positive charge. It happens in $FeO$ because $Fe$ has capacity of showing variable oxidation states.

$\cfrac {^nV}{N}=Ae^{-\Delta H _V/RT} \longrightarrow (x)$

$1.$ In frenkel defect there is no change in original density

In case of KCl, the cation and the anion are of comparable size while in case of LiI, the cation Li+ is very small as compared to the iodide ion, I-. Hence, KCl is more likely to show Schottky defect while LiI tends to show Frenkel defect. Thus, the statements 1 and 2 are true and 2 is correct explanation of 1.

F-centres are indeed responsible for the intense colors in alkali halides due to the excitation of trapped electrons. However, the color of NaCl with F-centres is yellow, not pink, making statement II incorrect.

Frenkel defect: This type of defect is created when an ion leaves its appropriate site in the lattice and occupies an interstitial site. A hole or vacancy is thus produced in the lattice.

Schottky defect: This type of defect is produced when one cation and anion are missing from their respective positions leaving behind a pair of holes.

The presence of ions in the vacant interstital sites along with lattice point is called interstital defect.

 When alkali metal halides are heated in an atmosphere of vapours of the alkali metal, anion vacancies are created. 

The statements A, C and D are correct.
(A) If three $Fe^{2+}$ ions are missing from their lattice in FeO,  there must be two $Fe^{3+}$ ions somewhere in the lattice.
The charge on three $Fe^{2+}$ ions is $3 \times (+2) = +6$
The charge on two $Fe^{3+}$ ions is $2 \times{3+} = +6$
Thus, the electrical neutrality is maintained.

F centers are color centres consisting of an electron trapped by a negative ion vacancy in an ionic crystal such as an alkali halide or an alkaline-earth fluoride or oxide.
As F-center have free unpaired electron, they are paramagnetic in nature and because of this free electron, they conduct electricity.
Also, because of this extra electron, they form n-type semiconductor.

As given,
$1$ g Germanium $\equiv  150$ ppm of Boron $=1.5 \times 10^{-4}$ g of Boron
$4%$ decrease in density of Ge occurs in one experiment due to replacement of Ge by B.

When light strikes a photographer $(AgBr)$ paper, it gives energy to the electrons present in the film. These energetic electrons when strike silver ions turn them to silver atoms. So eventually,  ions leave their lattice site and occupy interstitial sites. Since silver atoms are black in color so whenever light strikes a silver ion the photographic film will turn black.

$LiCl$ has non-stochiometric metal excess defect due to anion vacancies. The negative ions $(Cl^-)$ are missing from their lattice sites leaving the holes in which electrons are entrapped so that electrical neutrality is maintained.

When $LiCl$ is heated, $Li$ atoms gets deposited on the surface of the crystal. The $Cl^-$ ions diffuse into the surface and combine with $Li$ atoms to give $LiCl$. This is so because of loss of electrons by $Li$ atoms to form $Li^+$. The released electrons diffuse excess into crystal and occupy anionic sites. As a result, there is an excess of $Li$. The anionic sites occupied by unpaired electrons are F-centers which imparts a pink color to $LiCl$ crystals. The color is observed as a result of excitation of these electrons when they absorb energy from visible light falling on crystals.