Question

Calculate the theoretical density of the compound CaTiO3 (perowskite) which has a crystalline structure with a
elemental cell FCC: Atomic mass Ca 40.08 g / mol, atomic radius of Ca+2 0.099 nm; Atomic Mass Ti 47.88
g / mol, atomic radius of Ti 0.061 nm; Atomic mass O 16.00 g / mol, atomic radius of Ca-2 0.140 nm; (1 atom of
Ca / cell, vertices; 1 Ti atom / cell, central; 3 O atoms / cell, centered on faces)

Answer 1

Ans:- Here

Let r be the atomic radius

Given

r_Ca²⁺ = 0.099nm

r_O^2- = 0.140nm

r_Ti = 0.061nm

Let n be the number of unit cell

For FCC , n= 4

Let A be the atomic mass

A_Ca = 40.08 g/mol

A_O = 16.00 g/mol

A_Ti = 47.88 g/mol

Let V_c be the volume of unit cell

V_c = a³

     = (2r_Ca²⁺ + 2r_O^2- + 2r_Ti)³

     = (2x0.099+2x0.140+2x0.061)³

      = (0.6nm)³

       =(0.6x10^-7cm)³

       =(6x10^-8cm)³

        = 2.16x10^-22 cm³

Now N_a = Avagadros number = 6.023x10²³

V_cN_a = 2.16x10^-22x6.023x10²³

         = 130.0968 cm³ mol

Now Theoritical density

                      = 4(40.08+47.88+3x16) / 130.09856

                       =4.18 g/cm³