Calculate the fraction of atom sites that are vacant for sil

Calculate the fraction of atom sites that are vacant for silver at 553°C. Assume an energy for vacancy formation of 0.63 eV/atom.

Solution

Ans- The fraction of atom sites that are vacant for silver is given by the division of the number of vacancies to the total number of atomic sites. we can calculate by using the following equation as

N_v / N = exp(-Q_v /K_BT) ------------------------1

where , Qv= energy required for vacancy formation ( in eV)

k = Boltzmann’s constant ( 8.62 x 10^-5 eV)

T = temperature (in kelvin

given temperature of silver at which the atom sites are vacant is 553 ⁰C. Convert the unit into Kelvin,

T=(553+273)K

=826 k

now, using equation 1 we get

   N_v / N = exp(-Q_v /K_BT)

   N_v / N = exp(- 0.63 /  8.62 * 10^-5 *826)

=exp(-8.84)

N_v / N   =1.45 * 10^-4