crystal lattice and unit cell:

\(M=\frac { d\times { a }^{ 3 }\times NA }{ g } \)
d = Density of the material
a = Length of the edge of the cell.
N_A = Avogadro number
Z = No. of atoms
\(M=\frac { 10.5{ gcm }^{ -3 }{ (4.07\times { 10 }^{ -6 }cm) }^{ 3 }\times \left( 6.023\times { 10 }^{ 23 }{ mol }^{ -1 } \right) }{ 4 } \)
Atomic mass of silver M = 107.08 g mol^-1.

(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.

Formula is Ni_o.96 O_1.00
So the ration of Ni = O = 96.00
So if there are 100 atom of oxygen, as atoms of Ni
Let the number of atoms of Ni⁺² = x
The number of atoms of Ni⁺² = 96 - x
Charge on Ni = charge on O
So that oxygen has charge = 2
3 (96 - x) + 2x = 2(100)
288 - 3x + 2x = 200
-x = -88
x = 88
Percentage of Ni + 2 = (atom of Ni⁺² / total number of atoms of Ni 100.)
= 100.(94/98) x 100 = 96%
Percentage of Ni⁺³ = 100 - Ni⁺²
= 100 - 96 = 4%

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. 

i) In a simple cubic lattice atoms are present at the corners only, each atom at the corner is shared equally by eight other unit cells.
ii) The total number of atoms per unit cell \(\frac { { N }_{ c } }{ 8 } =8\times \frac { 1 }{ 8 } =1\) (N_c is the number of atoms at the corners.)

Frenkel defect

\(\operatorname{Density}(\rho)=\frac{\mathrm{nM}}{\mathrm{a}^{3} \mathrm{~N}_{\mathrm{A}}} \)
\(\rho=10 \mathrm{~g} \mathrm{~cm}^{-3} ; \mathrm{a}=100 \mathrm{pm}=1 \times 10^{-8} \mathrm{~cm} ; \mathrm{N}_{\mathrm{A}}=6.023 \times 10^{23} ; \mathrm{n}=4 ; \mathrm{M}=? \)
\(M=\frac{\rho \mathrm{a}^{3} \mathrm{N_{A}}}{n} \)
\(=\frac{10 \times\left(1 \times 10^{-8}\right)^{3} \times 6.023 \times 10^{23}}{4}  \)
\(=\frac{6.023}{4} \)
= 1.505 g /mol
No. of moles \(=\frac{\text { Mass }}{\text { Molar mass }}=\frac{1}{1.505}\)
= 0.664 moles
Hence number of atoms = 0.664 x 6.023 x 10²³ = 3.99 x 10²³ atoms

The imperfection occurs due to missing atoms, displaced atoms or extra atoms, is named as a point defect. Such defects arise due to imperfect packing during the original crystallisation or they may arise from thermal vibrations of atoms at elevated temperatures.

sc ⇒ 2r = a
⇒ r = a/2
bcc ⇒ 4r = \( \sqrt{3a} \) ⇒ r = \(\frac { \sqrt{3a}} {4}\)
fcc ⇒ 4r ⇒  \( \sqrt{2a} \) ⇒ r = \(\frac { \sqrt{2a}} {4} = \frac { a} {2\sqrt{2a}}\)
\(\left( \frac { a }{ 2 } :\frac { \sqrt { 3 } }{ 4 } a:\frac { a }{ 2\sqrt { 2 } } \right) \)

\(\left( \frac { r_{c^+} }{ r_{A^-} } \right) \) = \(\left( \frac { 0.98 \times 10^{-10 }}{ 1.81 \times 10^{-10} } \right) = 0.54\)
It is in the range of 0.414 to 0.732, hence the coordination number of each ion is 6.

(i) The defects in ionic solids is by adding impurity ions.
(ii) If the impurity ions are in different valance state from that of host, vacancies are created in the crystal lattice of the host.
(iii) For example, addition of CdCl₂ to silver chloride yields solid solutions where the divalent cation Cd²⁺ occupies the position of Ag⁺.
(iv) This will disturb the electrical neutrality of the crystal.
(v) In order to maintain the same, proportional number of Ag⁺ ions leaves the lattice.
(vi) This produces a cation vacancy in the lattice, such kind of crystal defects are called impurity defects.

(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.