The Solid State Notes - Chemistry Class 12

The Solid State Notes

1. Solids have definite mass volume and shape due to the fixed positions of their constituent particles.

2. They may be crystalline (i.e having long-range order of constituents) or amorphous (i.e having short-range order of constituents).

3. The crystal lattice is the three-dimensional arrangement of constituents or points in a crystalline solid.  the smallest repeating unit of the crystal lattice is called the unit cell.

There are seven primitive unit cells whose possible variations as centered unit cells are listed below.

Systems	Paramiters	Interaxial angles	Examples
Triclinic	`a\ne b\ne c`	`\alpha\ne\beta\ne\gamma\ne90^\circ`	`K_2Cr_2O_7`, `CuSO_{4}∙5H_2O`, `H_3BO_3`
Monoclinic	`a\ne b\ne c`	`\alpha=\gamma=90^\circ\ne\beta`	`Na_2SO_4∙10H_2O`, `Na_2B_4O_7∙10H_2O`, Monoclinic Sulphur
Orthorhombic	`a\ne b\ne c`	`\alpha=\beta=\gamma=90^\circ`	`KNO_3`, `K_2SO_4`, `BaSO_4`, `PbCO_3`, Rhombic Sulphur
Tetragonal	`a=b\ne c`	`\alpha=\beta=\gamma=90^\circ`	White tin, `SnO_2`, `TiO_2`, `NiSO_4`
Cubic	`a=b=c`	`\alpha=\beta=\gamma=90^\circ`	`NaCl`, `KCL`, `CsCl`, `ZnS`, `CaF_2`, Diamond
Hexagonal	`a=b\ne c`	`\alpha=\beta=90^\circ`,`\gamma=120^\circ`	`ZnO`, `CdS`, `HgS`, Graphite
Rhombohedral	`a=b=c`	`\alpha=\beta=\gamma\ne90^\circ`	`NaNO_3`, `ICI`, Calcite, Quartz

4. Types of the cubic unit cell

• In the simple-cubic unit cell (sc) are the eight corners of the cube are occupied by atoms ions or molecules.
• In a body-centred cubic unit cell (bcc)  the  constituent  particles occupy all eight corners of the cube and one particle is located at the body center of the cube
• In face-centred cubic unit cell (fcc) The constituent particles occupy all the the 8 corners of the cube and also so the the centre of the  six  faces of the cube

5. In hcp structure order is ABABAB…

6. In ccp it is ABCABC…

7. Unit cell parameters

Type/Feature	sc	bcc	fcc
Number of atom per unit cell, Z	1	2	4
Radius of atom, r	`a/2`	`\sqrt3\frac a4`	`\frac a{2\sqrt2}`
Packing Fraction	`52.4%`	`68%`	`74%`
CN	—	8	12

8. Ionic radius for fcc structure, `r_a+r_c=\frac a2`
    for bcc structure, `r_c+r_a=\frac{\sqrt{3a}}2`
    Where `r_a` & `r_c` = radius of cation and anion respectively.

9. The density of unit cell, `d=\frac{Z\times M}{a^3\times N_A}`
    Where `Z` = number of atoms per unit cell
    `M` = atomic or molecular mass
    `N_a` = Avogadro's number
    `a^3` = volume and `a` = edge length

10. If the number of atoms `=N`

    Then, the number of tetrahedral voids `= 2\times N`

    And number of octahedral voids `= N`

11. Schottky defect (a stoichiometric point defect) is due to the missing of an equal number of atoms from their sites and hence, resulting in a decrease in density. It is found in `NaCl`, `KCI`, `AgBr` etc.

12. Frenkel defect (a stoichiometric defect) is due to the occupation of an interstitial site by an atom leaving its original site vacant. Hence, density remains the same throughout, e.g. `AgBr`, `AgCl` etc.

13. F-centres (or Farbenzenter) are electron field vecancy of anion, generated due to metal excess defect.

14. Semiconductors have conductivity in between conductors  and insulators and are of two types:

• p-type (group 13 elements is added into element of group 14)
• n-type (group 15 element is added into element of group 14)

15. Paramagnetic substances show magnetic behaviour only under the influence of the applied magnetic field.

16. Ferromagnetic substances exhibit magnetism even when applied magnetic field is removed.

17. Ferrimagnetic substances exhibit some magnetic character due to alignment of the electron spins in parallel and antiparallel direction in in an equal numbers.