Question

Calculate the concentration of vacancies in in fcc silver at 250oC given that the activation energyfor vacancy creation in silver is 79.5 kJ/mol. The units for your answer should be vacancies/cm3.

Answer 1

The concentration of vacancies in fcc silver is
`6.6105* 10^1^4 vacancies/cm^3`

Step-by-step explanation:

Given is - silver (fcc lattice)

Temperature = 250°C = 523K

Activation energy for vacancy creation ,
`Q_v` =79.5 kJ/mol

Silver has a fcc crystal lattice structure with basis

Lattice parameter = 0.49nm =
`4.09* 10^-^8`m

Now , let us calculate number of silver atoms"(lattice points)per
`cm^3`

`N=(4atoms/cell)/(4.09*10^-^8cm^3)`

=
`5.86*10^2^2 Ag` atoms/
`cm^3`

Concentration of vacancies is given by the formula -

`N_v =N_e_x_p(-Q_V)/(R.T_)`

here,

`N_v = concentration of vacancies \\`

`N= number of atoms`
`per`
`cm^3`

`Q_v=` Activation energy for vacancy creation

T = Temperature

R = constant =
`8.314 J K^-^1 mole^-^1`

Now , putting the given values in the formula -

`N_v= (5.85*10^2^2atomscm^-^3)exp((-79.5KJ/mole)/(8.314*JK^-^1mole^-^1))`

=
`6.6105*10^1^4vacnacies/cm^3`

Hence , the answer is
`6.6105*10^1^4vacnacies/cm^3`