Question

The energy of formtion of a vacancy in the copper crystal is about 1 eV. Calculate the concentration of vacancies at room temperature (300K) and just below the melting temperature, 1084^oC. The atomic mass of Cu is M_at = 63.54g*mol^-1 and the density at 293 K is 8.96cm^-3. Neglect the change in the density which is small.

Answer 1

Given,

Energy of formation of vacancy in Cu crystal = 1 eV = 1.6X10^-19J

Atomic mass = 63.54 g/mol

Density at 293K = 8.96 cm^-3

Concentration of vacancies = ?

Solution:

A missing of an atom in its site is generally called vacancy. It is calculated as

N_v = N e^(-E_a/KT)

Where Nv is number of vacancies per unit volume, N is number of atomic sites per unit volume {(Density*N_A)/Atomic mass}, N_A avagatro number and E_a is an activation energy for vacancy formation, k is boltzmann constant (1.38*10^-23J/K) and T is temparature in kelvin.

Therefore, at 300 K,
Density might be chage with respect to temperature. Since it is small change we can negligible in the calculations.

N_v = {(8.96 * 6.023*10²³) / 63.54} e^{(-1.6*10^-19) / 1.38*10^-23 *300}

     = 1.42*10⁶ cm^-3

and at 1084 + 273 K = 1357K

N_v = {(8.96 * 6.023*10²³) / 63.54} e^{(-1.6*10^-19) / 1.38*10^-23 *1357}

     = 1.66*10¹⁹ cm^-3