(I) Diamond has network structure, while sulphur does not.
(II) Due to this, particles of carbon are held at their positions firmly which makes diamond hard, brittle with extremely high melting point.

The empty spaces present between the metal atom or the ions when they are packed within the crystal are called voids.

Frenkel defect

(i) In ionic compounds, electricity is conducted by ions.
(ii) In solid state, ions are held together by A strong electrostatic forces and are not free to move about within the solid.
(iii) Hence, ionic solids do not conduct electricity in solid state
(iv) However, in molten state or in solution form, the ions are free to move and can conduct electricity.

ZnS exhibits Frenkel defect.

(i) The intermolecular forces of attraction that are present in solids are very strong.
(ii) The constituent particles of solids have fixed position.
(iii) Hence, solids have a definite volume.

\(\text { Density }(\rho)=\frac{\mathrm{nM}}{\mathrm{a}^{3} \mathrm{~N}_{\mathrm{A}}}  \)
\(\mathrm{n}=4, \mathrm{M}=\text { Molar mass of } \mathrm{KF}=58.1 \mathrm{~g} / \mathrm{mol}  \)
\(\rho=2.48 \mathrm{~g} \mathrm{~cm}^{-3}  \)
\(\mathrm{~N}_{\mathrm{A}}=6.023 \times 10^{23} \)
\(a^{3} =\frac{n M}{\rho N_{A}}=\frac{4 \times 58.1}{2.48 \times 6.023 \times 10^{23}}  \)
\(a^{3} =15.55 \times 10^{-23}  \)
\(a^{3} =0.1555 \times 10^{-21}  \)
\(a =\sqrt[3]{0.1555 \times 10^{-21}}  \)
\(a =0.5375 \times 10^{-7} \mathrm{~cm}=5.375 \times 10^{-8} \mathrm{~cm}=537.5 \mathrm{pm}  \)
\(d =\frac{a}{\sqrt{2}}(\text { for fcc })  [\therefore r = \frac{a\sqrt{2}}{4}]\)
\(=\frac{537.5}{1.414}=380.13 \mathrm{pm}\)
\(\therefore\) The distance between K⁺ and F^- in KF = 380.13 pm

Linear arrangement of spheres in one direction is repeated in two dimension (i.e.) more number of rows can be generated identical to the one dimensional arrangement such that all spheres of different rows align vertically as well as horizontal.
If we denote the first row as A type arrangement, then the above mentioned packing is called AAA type, because all rows are identical as the first one. In this arrangement each sphere is in contact with four of its neighbours.

The structural units of an ionic crystal are cations and anions. They are bound together by strong electrostatic attractive forces. To maximize the attractive force, cations are surrounded by as many anions as possible and vice versa. Hence they are hard and brittle.

(i) A basic repeating structural unit of a crystalline solid is called a unit cell.
(ii) A crystal is consisted of large number of unit cells.

Schottky defect:
(i) Schottky defect arises due to the missing of equal number of cations and anions from the crystal lattice.
(ii) This effect does not change the stoichiometry of the crystal.
(iii) Ionic solids in which the cation and anion are of almost of similar size show schottky defect. Ex: NaCl.
(iv) Presence of large number of schottky defects in a crystal, lowers its density.

Frenkel defect:
(i) Frenkel defect arises due to the dislocation of ions from its crystal lattice.
(ii) The ion which is missing from the lattice point occupies an interstitial position.
(iii) This defect is shown by ionic solids in which cation and anion differ in size.
(iv) Unlike Schottky defect, this defect does not affect the density of the crystal.
(v) For example AgBr, in this case, small Ag⁺ ion leaves its normal site and occupies an interstitial position.

Crystal defects are classified as follows
(i) Point defects
(ii) Line defects
(iii) Interstitial defects
(iv) Volume defects
Point defects are further classified as follows

(i) Solids have definite volume and shape 
(ii) Solids are rigid and incompressible
(iii) Solids have strong cohesive forces.
(iv) Their constituents have fixed positions and can only oscillate about their mean positions.

(i) The colour develops because of the presence of electrons in the 8 anionic sites.
(ii) These electron absorb energy from the visible region of radiation and get excited. 
(iii) For example when crystals of NaCl are heated in an atmosphere of sodium vapours, the sodium atoms get deposited on the surface of the crystal and the deposited Na atoms.
(iv) During this process, the Na atoms on the surface lose electrons to form Na⁺ ions 
(v) These electrons get excited by absorbing energy from the visible light and impart yellow colour to the crystals.

Metal excess defect:
(i) It arises due to the presence of more number of metal ions as compared to anions.
(ii) Examples: NaCl, KCl
(iii) The electrical neutrality of the crystal can be maintained by the presence of anionic vacancies equal to the presence of extra cation.

(iii) For example, when NaCI crystals are heated in the presence of sodium vapour, Na⁺ ions are formed and are deposited on the surface of the crystal.
(iv) Chloride ions (Cl^-) diffuse to the surface from the lattice point and combines with Na⁺ ion.
(v) The electron lost by the sodium vapour diffuse into the vacancy created by the Cl^- ions.
(vi) Such anionic vacancies which are occupied by unpaired electrons are called F centers. Hence, the formula of NaCl can be written as Na_1+xCl.
Metal deficiency defect:

(i) Metal deficiency defect arises due to the presence of less number of cations than the anions. This defect is observed in a crystal in which, the cations have variable oxidation states.
(ii) For example, In FeO crystal, some of the Fe²⁺ ions are missing from the crystal lattice. To maintain the electrical neutrality, twice the number of other Fe²⁺ ions in the crystal is oxidized to Fe³⁺ ions. In such cases, overall number of Fe²⁺ and Fe³⁺ ions is less than the O^2- ions.

The fundamental equation that gives a simple relation between the wavelength of the X-rays, the interplanar distance in the crystal and the angle of reflection is known as Bragg's equation.
nλ = 2dsinθ
Where n is the order of reflection
λ is the wavelength of X-rays
d is the interplanar distance in the crystal
θ is the angle of reflection 

Data:
Diffraction angle,
2θ = 14.8⁰ ∴ 8 = 7.4°
Interplanar distance, d = 0.400 nm
Order of reflection, n = 2
Formula:
nλ = 2dsinθ
∴ wavelength,
Solution:
\(\lambda =\frac { 2dsin\theta }{ 2 } \)
= dsinθ
= 0.400 sin 7.4^o
= 0.400 x 1.288 nm
= 0.0512 nm
λ = 0.0512 nm

Simple Cubic Lattice
100,101,111

\({ d }_{ hkl }=\frac { a }{ \sqrt { { h }^{ 2 }+{ k }^{ 2 }+{ l }^{ 2 } } } \)
\({ d }_{ 100 }=\frac { 1 }{ \sqrt { { 1 }^{ 2 }+0^{ 2 }+0^{ 2 } } } =1\)
\({ d }_{ 101 }=\frac { 1 }{ \sqrt { { 1 }^{ 2 }+0^{ 2 }+0^{ 2 } } } =\frac { 1 }{ \sqrt { 2 } } \)
\({ d }_{ 111 }=\frac { 1 }{ \sqrt { { 1 }^{ 2 }+1^{ 2 }+1^{ 2 } } } =\frac { 1 }{ \sqrt { 3 } } \)
\(\\ { d }_{ 100 }:{ d }_{ 101 }:{ d }_{ 111 }=1:\frac { 1 }{ \sqrt { 2 } } :\frac { 1 }{ \sqrt { 3 } } (or)\)
=1:0.707:0.577

(i) Yellow colour of ZnO is due to metal excess defect. Zinc oxide which is white in colour on heating loses oxygen and turns yellow.
\(ZnO\overset { Heating }{ \longrightarrow } { Zn }^{ + }+\frac { 1 }{ 2 } { O }_{ 2 }+{ 2e }^{ -1 }\)
(ii) The excess Zn²⁺ ion thus, formed get trapped into vacant interstitial sites and the electrons in the neighbouring interstitial sites.

(i) Covalent Solids: Silicon carbide, graphite.
(ii) Molecular Solids: Urea, benzene, ammonia, water and argon.
(iii) Ionic Solids: Zinc sulphide, potassium sulphate.
(iv) Metallic solids: Rubidium and tin.

Doping of NaCI with 10^-3 mol% SrCl₂ means that 100 moles of NaCl are doped with 10^-3 mol SrCl₂.
∴ 1mole of NaCl is doped with SrCl₂
\(=\frac { { 10 }^{ -3 } }{ 100 } \times 6.02\times { 10 }^{ 23 }=6.02\times 10^{ 18 }\)

(i) The intermolecular forces of attraction that are present in solids are very strong.
(ii) The constituent particles of solids cannot: move from their positions. They have fixed positions.
(iii) However, they can oscillate about their mean positions.
(iv) This is the reason solids are rigid.

(i) Frenkel defect arises due to the dislocation of ions from its crystal lattice.
(ii) The ion which is missing from the lattice point occupies an interstitial position.
(iii) This defect is shown by ionic solids in which cation and anion differ in size.
(iv) Unlike Schottky defect, this defect does not affect the density of the crystal.
For example AgBr, in this case, small Ag⁺ ion leaves its normal site and occupies an interstitial position.

\(\operatorname{Density}(\rho)=\frac{\mathrm{nM}}{\mathrm{a}^{3} \mathrm{~N}_{\mathrm{A}}} \)
\(\mathrm{n}=2, \mathrm{~N}_{\mathrm{A}}=6.023 \times 10^{23} ; \mathrm{a}=288 \mathrm{pm}=2.88 \times 10^{-8} \mathrm{~cm}, \rho=7.2 \mathrm{~g} \mathrm{~cm}^{-3} \)
\(\therefore M=\frac{\rho \times a^{3} \times N_{A}}{n} \)
\(=\frac{7.2 \times\left(2.88 \times 10^{-8}\right)^{3} \times 6.023 \times 10^{23}}{2} \)
\(=517.95 \times 10^{-1} \)
\(=51.795 \mathrm{~g} \mathrm{~mol}^{-1} \)
Number of moles (n) \(=\frac{\text { Mass }}{\text { Molar mass }}=\frac{208}{51.795}\)=4.02 moles
No. of atoms = No. of moles \(\times\) Avogadro number
=n \(\times\) N_A
\(=4.01 \times 6.023 \times 10^{23} \)
\(=24.15 \times 10^{23} \text { atoms }\)

There are seven types of unit cell, Cubic, tetragonal, orthorhombic, hexagonal, monoclinic, triclinic and rhombohedral. They differ in the arrangement of their crystallographic axes and angles.
i) Cubic: a = b = c; α = β = ૪ = 90^o.

ii) Tetragonal: a = b ≠ c; α = β = ૪ = 90°.

iii) Orthorhombic:  a  ≠ b  ≠ c; α = β = ૪ = 90°.

iv) Hexagonal: a = b ≠ c; α = β = 90^o, ૪ = 120^o. 

v) Monoclinic: a ≠ b ≠ c; α = ૪ = 90^o, β ≠ 90^o, 

vi) Triclinic: a ≠ b ≠ c; α  ≠ β ≠ ૪ ≠ 90^o.

vii) Rhombohedral:  a = b = c; α = β = ૪ ≠ 90^o. 

If the total number of M atoms is n, then the number of tetrahedral voids = 2n
Given that \(\left( \frac { 1 }{ 3 } \right) ^{rd}\) of tetrahedral voids are occupied.
i.,e \(\left( \frac { 1 }{ 3 } \right) \times 2n\) are occupied by N atoms
\(\therefore\)M : N = n : \(\left( \frac { 2 }{ 3 } \right) n\)
= 1 : \(\frac { 2 }{ 3 }\)
Hence M₃N₂ = 3 : 2

Lattice points are occupied by CO₂ molecules