Give any three characteristics of ionic crystals.

1. Solid state:

(i) Solid is the form of matter which possesses a definite shape and a definite volume.

(ii) If intermolecular forces $>$ thermal energy, substance exists as solid

2. Classification of Solids:

(i) Solids are classified into Crystalline (Regular arrangement of particles, anisotropic) and Amorphous (No regular arrangement of particles, isotropic).

(ii) Classification of crystalline solids: Ionic, Molecular, Covalent/Network, Metallic

3. Types of crystal systems.

(i) Cubic $(\mathrm{a} = \mathrm{b} = \mathrm{c}, \mathrm{\alpha } = \mathrm{\beta } = \mathrm{\gamma } = 90°)$

(ii) Tetragonal $(\mathrm{a} = \mathrm{b} \ne \mathrm{c}, \mathrm{\alpha } = \mathrm{\beta } = \mathrm{\gamma }= 90°)$

(iii) Orthorhombic/Rhombic $(\mathrm{a} \ne \mathrm{b} \ne \mathrm{c}, \mathrm{\alpha } = \mathrm{\beta } = \mathrm{\gamma }= 90°)$

(iv) Monoclinic $(\mathrm{a} \ne \mathrm{b} \ne \mathrm{c}, \mathrm{\alpha }=\mathrm{\gamma } = 90° \ne \mathrm{\beta })$

(v) Triclinic $(\mathrm{a} \ne \mathrm{b} \ne \mathrm{c}, \mathrm{\alpha } \ne \mathrm{\beta } \ne \mathrm{\gamma } \ne 90°)$

(vi) Rhombohedral/Trigonal $(\mathrm{a} = \mathrm{b} = \mathrm{c}, \mathrm{\alpha } = \mathrm{\beta } = \mathrm{\gamma } \ne 90°)$

(vii) Hexagonal $(\mathrm{a} = \mathrm{b} \ne \mathrm{c}, \mathrm{\alpha }=\mathrm{\beta } = 90°, \mathrm{\gamma } = 120°).$

4. Contribution by particles present at different positions:

Corner $=\frac{1}{8}$ Face-centre $=\frac{1}{2}$, Body-centre $= 1$, Edge-centre $=\frac{1}{4}$

5. Number of particles per unit cell of a cubic crystal:

(i) Simple $=8\times \frac{1}{8}=1$

(ii) Body-centred $=8\times \frac{1}{8}+1=2$

(iii) Face-centred $=8\times \frac{1}{8}+6\times \frac{1}{2}=4$

6. Voids:

If the number of close packed spheres be $\mathrm{N},$ then

The number of octahedral voids generated $= \mathrm{N}$ and the number of tetrahedral voids generated $= 2\mathrm{N}$

7. Relationship between radius $\left(\mathrm{r}\right)$ of an atom and edge length $\left(\mathrm{a}\right)$:

(i) Simple cubic $\mathrm{r} =\frac{\mathrm{a}}{\mathrm{2}}$

(ii) Face centred cubic $\mathrm{r} =\frac{\mathrm{a}}{\mathrm{2}\sqrt{\mathrm{2}}}$

(iii) Body centred cubic $\mathrm{r} =\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}\mathrm{a}$

8. Density of unit cell:

$\mathrm{d} =\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{a}}^{\mathrm{3}}\times {\mathrm{N}}_{\mathrm{A}}}\mathrm{g} {\mathrm{cm}}^{-\mathrm{3}}$

Where Z= No. of atoms in unit cell; $\mathrm{M}=\text{Atomic mass}$; $\mathrm{a}=\text{Edge length (in cm)}$

${\mathrm{N}}_{\mathrm{A}}=\text{Avogadro number}\mathrm{ }\left(6.022\times {10}^{23}\right)$

9. Packing efficiency:

ccp and hcp: $\text{Packing efficiency} =\frac{\text{Volume occupied by} 4 \text{spheres in the unit cell}}{\text{Total volume of the unit cell}}\times 100\%= 74\%$

BCC:

$\text{Packing efficiency} =\frac{\text{Volume occupied by} 2 \text{spheres in the unit cell}}{\text{Total volume of the unit cell}}\times 100\%= 68\%$

Simple cubic:

$\text{Packing efficiency} =\frac{\text{Volume of one atom}}{\text{Volume of the cubic unit cell}}\times 100\%= 52.4\%$

10. Imperfections/Defects in Solids.

(i) Any departure from perfectly ordered arrangement of constituent particles is called defect or imperfection.

(ii) Stoichiometric defects: When ratio between cations and anions remains the same. Two types are Schottky defect and Frenkel defect.

(iii) Non-stoichiometric defects: When ratio of cations and anions changes as a result of the defect. Metal excess and Metal deficiency are the two types of this defect.

(iv) Impurity defects: Adding impurities to crystalline solids to change their properties is called doping.