Question

Consider a sample of pure copper with dimensions of 1 cm x 1 cm x 1 cm. The sample is cold worked and has a dislocation density of 1010/cm2 . After a recrytstallizing anneal, the dislocation density is reduced to 104 /cm2 . If the average dislocation line energy is 5 eV/nm, calculate the energy change associated with this aspect of the recrystallization process.

It was said there was not enough information to answer, but this is all that was given

Answer 1

The dislocation density of the sample of pure copper = 10¹⁰ / cm²

Its dislocation density after a recrystallizing anneal = 10⁴ / cm²

Thechange in dislocation density = (10¹⁰ - 10⁴) / cm² = 9999990000 / cm²

The average dislocation line energy = 5 eV/nm​ = 5 eV/(10^-7 cm) = 5*10⁷ eV/cm

Then, the average dislocation line energy per cm² = (5*10⁷)² = 2.5*10¹⁵ eV

Therefore, the energy change associated with this aspect of the recrystallization process = 9999990000*2.5*10¹⁵ eV ~ 2.5*10²⁵ eV