Calculate the fraction of vacancies for copper at i its melt

Calculate the fraction of vacancies for copper at (i) its melting point (1357 K) assuming the vacancy formation energy is 0.90 eV/atom, then (ii) at room temperature (298 K). (iii) Calculate the ratio of the melting point fraction to the room temperature fraction

Solution

i) Nv / N = exp(-Qv / kT)

Nv / N = exp ( - 0.90 eV/atom / (8.62 x 10^-5 eV/atomK)(1357) )

= 4.56 x 10^-4

ii) Nv / N = exp ( - 0.90 eV/atom / (8.62 x 10^-5 eV/atomK)(298) )

= 2.07 x 10^-3

iii) Ration = (4.56 x 10^-4 ) / (2.07 x 10^-3 ) = 0.22