12. Number of voids In close packed structure, there are  two main type of voids present in lattice, I.e. tetrahedral and octahedral voids. It is found that.

(¡)Number of octahedral voids =Number of particles in close packing(N)

(¡¡) Number of tetrahedral voids = 2×Number of particles present in close packing (N) 

           or,  

                  Tetrahedral voids = 2×Octahedral voids

13. Packing efficiency It is the fraction or percentage of total space filled by the particles, I.e 

 Packing efficiency = volume occupied by spheres in the unit cell/Total volume of unit cell ×100

14. Density (d) of the unit cell is calculated  by using the given expression.

          d= ZM/a³NA

Where, Z = Number of atom per unit cell,

               M = Molar mass or atomic mass 

               a = Edge length 

               a³= volume of cell 

                NA =Avogadro constant

   

15. Imperfections in solids A solid consist of an aggregate of large number of small crystals. These crystals have defect in them. These defects are of two types: Point defect and line defect.

16. Line defects are the irregularities from ideal arrangement in entire rows of lattice points. Where as point defects are the irregularities or deviation from ideal arrangement around a point in a crystalline solid.

These are further classified as stoichiometric defects, impurity defects and non-stoichiometric defects.

(i) Stoichiometric defects Point defect that do not disturb the stoichiometry of the solid are called stoichiometric defects (Intrinsic or thermodynamic defect) e.g.

 (ii) Non-stoichiometric defects Those imperfections in the crystals, which lead to change in the composition of solids are called non-stoichiometric defects.

(iii) Impurity defects Arise when foreign atoms are present in the lattice site or in the interstitial site. e.g. solid solution of CdCl2, AgCl.

17. Schottky defect A stoichiometric or vacancy defect, arises due to missing of equal number of cations and anions from the lattice and is shown by crystals having cation and anion of comparable size. e.g. CsCl, NaCl, AgBr etc. It decreases density of a substance.

18. Frenkel defect A stoichiometric or interstitial defect, arises when the smaller ion (usually cation) is dislocated from its normal site to an interstitial site. It results increase in conductivity but density of the crystal remains the same.

19. Metal excess defect can be due to anionic vacancies, e.g. on heating crystals of NaCl in presence of Na vapour, some anions leave lattice sites which are occupied by electrons called F-centres giving colour to crystals. These defects can also be generated due to presence of extra cations at interstitial sites, e.g. on heating, white ZnO it turns yellow as it loses oxygen and Zn²+ ions.