Calculate the energy for vacancy formation in silver, given that the equilibrium number of vacanciesat 800°C (1073 K) is 3.6 × 1023m–3. The atomic weight and density (at 800°C) for silver are, respectively, 107.9 g/mol and 9.5 g/cm3. (hint: see example problem in Lecture 9for part of the solution)

1.10 eV/atom

Explanation:

The energy for vacancy formation can be calculated by solving the following equation for Qv:

      (1)  

where Qv: is the energy required for vacancy formation, k: is the Boltzmann constant, T: is the temperature, N: is the concentration of atomic sites and Nv: is the vacancy concentration.  

We have that:

Nv = 3.6x10²³ m⁻³

T = 1073 K      

k = 8.62x10⁻⁵ eV/K    

Hence, to calculate the energy for vacancy formation first we need to find N:

where ρ: is the density = 9.5 g/cm³, : is the Avogadro constant = 6.022x10²³ atoms/mol, and A: is the atomic weight = 107.9 g/mol.    

Now, the energy for vacancy formation is:

Therefore, the energy for vacancy formation in silver is 1.10 eV/atom.  

I hope it helps you!

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