Defects in crystal Questions in English

(B) Non-stoichiometric compounds are those in which the ratio of the elements present does not correspond to simple whole numbers as indicated by the chemical formula.
$Fe_{0.98}O$ is a classic example of a metal-deficient non-stoichiometric compound where the actual ratio of $Fe$ to $O$ deviates from $1:1$ due to the presence of $Fe^{3+}$ ions to maintain electrical neutrality.

(B) In a $Schottky$ defect,an equal number of cations and anions are missing from their lattice sites.
This creates vacancies in the crystal lattice,which leads to a decrease in the overall mass of the crystal while the volume remains constant.
Therefore,the density of the crystal decreases.
Thus,the correct option is $(b)$.

(D) $F$-centres are formed when anionic vacancies are occupied by unpaired electrons.
$1$. These electrons are trapped in the voids of the crystal lattice.
$2$. They absorb energy from visible light,which imparts colour to the crystals.
$3$. The presence of these free electrons increases the electrical conductivity of the crystal.
Therefore,all the given statements are correct.

(A) When $SrCl_2$ is added to $NaCl$,each $Sr^{2+}$ ion replaces two $Na^+$ ions in the crystal lattice.
One $Sr^{2+}$ ion occupies the site of one $Na^+$ ion,while the other $Na^+$ site remains vacant to maintain electrical neutrality.
Therefore,the number of cation vacancies created is equal to the number of $Sr^{2+}$ ions added.
Given that the concentration of $SrCl_2$ is $10^{-3} \ mol \ \%$,the concentration of cation vacancies will be $1 \times 10^{-3} \ mol \ \%$.

(C) When $NaCl$ is heated in an atmosphere of sodium vapor,sodium atoms deposit on the surface of the crystal.
$Cl^{-}$ ions diffuse to the surface to combine with $Na$ atoms,creating anion vacancies.
Electrons released by the ionization of $Na$ atoms occupy these anionic sites to maintain electrical neutrality.
These trapped electrons,known as $F$-centers,absorb energy from visible light and impart a yellow color to the $NaCl$ crystal.

(D) Frenkel defect occurs when an ion,usually a smaller cation,leaves its normal lattice site and occupies an interstitial site,thereby creating a vacancy at the original site and an interstitial defect at the new position.

(C) $AgBr$ exhibits Frenkel defect due to the large difference in the size of $Ag^{+}$ and $Br^{-}$ ions.
It also shows Schottky defect.

(D) Schottky defects occur in highly ionic compounds which have high coordination numbers and small difference in the sizes of cations and anions. $NaCl$,$KCl$,and $CsCl$ all exhibit this type of defect. Therefore,the correct option is $D$.

(D) The Schottky defect occurs when an equal number of cations and anions are missing from their lattice sites,maintaining the electrical neutrality of the crystal. This leads to a decrease in the density of the crystal.

(A) The correct answer is $A$.
Schottky defect is a type of point defect in ionic crystals where an equal number of cations and anions are missing from their lattice sites,maintaining the electrical neutrality of the crystal.

(A) The correct answer is $(A)$. An impurity present in a crystal lattice does not establish thermal equilibrium. Impurities can diffuse through the crystal,act as scattering centers for charge carriers,and introduce new electronic energy levels within the band gap of the semiconductor or crystal.

(C) $Frenkel$ defect involves the migration of an ion from its lattice site to an interstitial site within the same crystal.
Since no ions are missing from the crystal as a whole,the total mass and volume remain constant.
Therefore,there is no effect on the density of the ionic solid.

(A) Point defects are irregularities or deviations from the ideal arrangement around a point or an atom in a crystalline substance.
These defects are primarily observed in $Ionic \ solids$ because they possess a regular,repeating lattice structure.
Examples of point defects include stoichiometric defects (like $Schottky$ and $Frenkel$ defects),non-stoichiometric defects,and impurity defects.

(C) In $AgBr$ crystals,the size of the $Ag^{+}$ ion is significantly smaller than the $Br^{-}$ ion.
Due to this large difference in ionic sizes and the low coordination number,$AgBr$ exhibits both Frenkel and Schottky defects.
However,it is most commonly cited for exhibiting both types of defects.

(C) The correct answer is $(C)$.
Frenkel and Schottky defects are types of point defects in ionic solids.
These are considered stoichiometric crystal defects because they do not change the stoichiometry of the crystal.

(D) In metal excess defect,when holes created by the missing of anions are occupied by electrons,these sites are called $F$-centres (Farbe centres). These electrons absorb energy from visible light and get excited,which is responsible for the colour in the crystal.

(C) Frenkel defect is typically shown by ionic crystals where there is a large difference in the size of ions,such as $AgCl$,$AgBr$,and $ZnS$.
$KBr$ consists of ions of similar sizes,which makes it favor the formation of Schottky defect rather than Frenkel defect.
Therefore,the correct option is $(C)$.

(C) When a cation shifts from its original lattice site to an interstitial position,the defect is known as a $Frenkel$ defect. This defect is common in ionic crystals where the cation is smaller than the anion.

(D) . $F$-centres (from the German word $\text{Farbe}$ meaning colour) are the sites where anions are missing from the lattice and electrons are trapped in the resulting vacancy to maintain electrical neutrality. These trapped electrons are responsible for the colour of the crystal.

(A) $Schottky$ defect is a type of point defect that occurs in the crystal lattice of a $solid$. It arises when oppositely charged ions leave their lattice sites,creating vacancies to maintain electrical neutrality.

(A) The fraction of unoccupied sites (vacancies) is given by the formula: $\text{Fraction} = \frac{\rho_{\text{X-ray}} - \rho_{\text{pyknometric}}}{\rho_{\text{X-ray}}}$
Given: $\rho_{\text{X-ray}} = 2.178 \times 10^3 \ kg \ m^{-3}$ and $\rho_{\text{pyknometric}} = 2.165 \times 10^3 \ kg \ m^{-3}$
Difference $= (2.178 - 2.165) \times 10^3 = 0.013 \times 10^3 \ kg \ m^{-3}$
Fraction $= \frac{0.013 \times 10^3}{2.178 \times 10^3} = \frac{0.013}{2.178} \approx 5.96 \times 10^{-3}$

(B) In the provided diagram,an equal number of cations $(Na^{+})$ and anions $(Cl^{-})$ are missing from their respective lattice sites,creating vacancies $(Box)$.
This is the characteristic feature of a Schottky defect,which is a type of stoichiometric point defect in ionic crystals.

(A) Ferrous oxide $(FeO)$ is a non-stoichiometric compound.
In reality,it is difficult to obtain a perfectly stoichiometric $FeO$ sample because it usually contains a slight excess of oxygen,making its composition range from $Fe_{0.95}O$ to $Fe_{0.98}O$.
Therefore,it is often referred to as a non-stoichiometric compound.

(C) Non-stoichiometric compounds are those in which the ratio of elements does not correspond to simple whole numbers. $FeO$ is a classic example of a metal-deficient non-stoichiometric oxide,often represented as $Fe_{1-x}O$ where $x$ is a small fraction. While $Fe_3O_4$ and $Fe_2O_3$ are generally considered stoichiometric,$FeO$ is the most prominent non-stoichiometric compound among the options provided.

(C) $KBr$ exhibits Schottky defect. It does not exhibit Frenkel defect because the difference in the size of the cation $(K^+)$ and anion $(Br^-)$ is small.

(B) In the given diagram,an equal number of $Na^{+}$ and $Cl^{-}$ ions are missing from their respective lattice sites.
This is the characteristic feature of a Schottky defect,which occurs in ionic solids to maintain electrical neutrality.

(D) The color of metal ions in a flame is due to the presence of $F$-centers.
These $F$-centers are formed due to metal excess defect,where anionic sites are occupied by unpaired electrons.
When these electrons absorb energy from the visible light,they get excited and emit radiation in the visible region,which imparts color to the flame.

(D) Frenkel defect occurs in ionic crystals where the smaller ion (usually cation) is dislocated from its lattice site to an interstitial site.
This defect is typically observed in compounds with a large difference in size between the cation and the anion.
$AgBr$,$AgI$,and $ZnS$ all exhibit Frenkel defects due to the small size of the cations ($Ag^+$ and $Zn^{2+}$) relative to the anions.
Therefore,the correct answer is all of the above.

(A) Schottky defect is a type of point defect in ionic crystals where an equal number of cations and anions are missing from their lattice sites,maintaining electrical neutrality. $NaCl$ is a classic example of an ionic compound that exhibits Schottky defect due to the similar size of its ions. $AgCl$ and $TlCl$ typically exhibit Frenkel defects,while $MgCl_2$ is not a standard example for Schottky defects.

(A) $F$-centers (from the German word $Farbenzenter$,meaning color centers) are formed when anionic vacancies in an ionic crystal are occupied by unpaired electrons.
These electrons absorb light from the visible region,which imparts color to the crystal.
Therefore,$F$-centers are lattice sites containing electrons.

(D) Schottky defect is a type of point defect in ionic crystals. It is generally observed in ionic compounds with high coordination numbers and where the cations and anions are of similar size. Examples include $NaCl$,$KCl$,and $CsCl$.

(A) Schottky defect is a type of point defect in ionic crystals where an equal number of cations and anions are missing from their lattice sites.
This maintains the electrical neutrality of the crystal.
Therefore,the structure possesses an equal number of cation and anion vacancies.

(B) $(1)$ False: Frenkel defect occurs in ionic solids where there is a large difference in the size of ions.
$(2)$ True: Frenkel defect is also known as a dislocation defect because the ion leaves its lattice site and occupies an interstitial site.
$(3)$ True: $F$-centers are formed when electrons are trapped in anion vacancies,which are created due to metal excess defect.
$(4)$ False: Schottky defect leads to a decrease in the density of the crystal,thus changing its physical properties.

(D) An $F$-center (from the German word $Farbenzentrum$,meaning color center) is a type of crystallographic defect in which an anionic vacancy in a crystal lattice is occupied by one or more unpaired electrons.
$1$. Electrons are trapped in the vacant sites of the crystal lattice to maintain electrical neutrality.
$2$. These trapped electrons absorb light from the visible region,which imparts color to the crystal.
$3$. The presence of these free electrons also contributes to the electrical conductivity of the crystal.
Therefore,all the given statements are correct.

(B) When $SrCl_2$ is added to $NaCl$,each $Sr^{2+}$ ion replaces two $Na^+$ ions to maintain electrical neutrality.
One $Sr^{2+}$ ion creates one cation vacancy.
Concentration of $SrCl_2 = 2 \times 10^{-3} \, mol \% = \frac{2 \times 10^{-3}}{100} = 2 \times 10^{-5} \, mol$ per $100 \, mol$ of $NaCl$.
Number of cation vacancies per mole of $NaCl = 2 \times 10^{-5} \times N_A$.
$= 2 \times 10^{-5} \times 6.022 \times 10^{23} \, mol^{-1}$.
$= 12.044 \times 10^{18} \, mol^{-1}$.

(B) $Schottky$ defect is a type of point defect in ionic crystals where an equal number of cations and anions are missing from their lattice sites to maintain electrical neutrality.
This results in a decrease in the density of the crystal.
Therefore,the correct statement is that an equal number of cations and anions are missing.

(A) Schottky defect is a type of point defect in ionic crystals where an equal number of cations and anions are missing from their lattice sites to maintain electrical neutrality.
Since the number of missing cations equals the number of missing anions,the number of vacancies created for both is equal.
Therefore,the reason correctly explains why the Schottky defect maintains electrical neutrality by having an equal number of vacancies for both ions.
Thus,both assertion and reason are true,and the reason is the correct explanation of the assertion.

(A) Frenkel defect occurs in ionic crystals where there is a large difference in the size of the ions.
This typically happens when the smaller ion (usually the cation) can easily fit into the interstitial sites of the crystal lattice.
This condition is generally satisfied when the radius ratio $(r_+ / r_-)$ is low,indicating a significant difference in the ionic radii.

(B) Most ionic crystals,especially those with high coordination numbers and similar sized cations and anions (like $NaCl$),exhibit $Schottky$ defects. In this defect,an equal number of cations and anions are missing from their lattice sites,maintaining electrical neutrality.

(A) Schottky defect and Frenkel defect are types of point defects in ionic crystals.
Point defects are irregularities or deviations from ideal arrangement around a point or an atom in a crystalline substance.

(C) $Schottky$ defect is a type of point defect in ionic crystals.
It occurs when an equal number of cations and anions are missing from their lattice sites,maintaining the electrical neutrality of the crystal.
Therefore,the correct option is $C$.

(A) Schottky defect is a type of point defect in ionic crystals where an equal number of cations and anions are missing from their lattice sites.
This defect is typically observed in ionic compounds that have a $High \ coordination \ number$ and where the sizes of the cations and anions are $similar$ (i.e.,the radius ratio is close to $1$).
Examples include $NaCl$,$KCl$,and $CsCl$.

(C) When $Sr^{2+}$ ions are added to $NaCl$,each $Sr^{2+}$ ion replaces two $Na^+$ ions to maintain electrical neutrality.
One $Sr^{2+}$ ion creates one cation vacancy.
Given concentration of $SrCl_2 = 10^{-4} \, \text{mole} \% = \frac{10^{-4}}{100} = 10^{-6} \, \text{mole}$.
Number of $Sr^{2+}$ ions = $10^{-6} \times N_A = 10^{-6} \times 6.02 \times 10^{23} = 6.02 \times 10^{17} \, \text{mol}^{-1}$.
Since each $Sr^{2+}$ ion creates one cation vacancy,the concentration of cation vacancies is $6.02 \times 10^{17} \, \text{mol}^{-1}$.

(D) $AgBr$ is a unique ionic solid that exhibits both Schottky and Frenkel defects.
Due to the small size of the $Ag^{+}$ ion,it can easily occupy interstitial sites,leading to Frenkel defects.
Simultaneously,it also shows Schottky defects due to the missing of equal numbers of cations and anions from their lattice sites.

(D) When electrons are trapped in anion vacancies,these are called $F$-centres (from the German word $Farbenzentrum$,meaning colour centre). These centres are responsible for the colour of the crystal.

(D) In $Schottky$ defect,ions leave the lattice,so density decreases. This is a correct statement.
$FeO_{0.98}$ shows metal deficiency defect because the ratio of $Fe$ to $O$ is less than $1:1$. This is a correct statement.
$NaCl_{(s)}$ is an insulator,$Si$ is a semiconductor,$Ag$ is a conductor,and quartz is a piezoelectric crystal. This is a correct statement.
Frenkel defect occurs in ionic compounds where there is a large difference in the size of the cation and anion (cation is much smaller than the anion). Therefore,the statement that it is favoured when sizes are almost equal is incorrect.

(B) Frenkel defect is a type of point defect where an ion leaves its lattice site and occupies an interstitial site.
Because the ion remains within the crystal,the overall density of the solid remains unchanged.
This is known as a dislocation defect.
Schottky defects involve the loss of ions from the lattice,which decreases the density of the crystal.