In the class, we learned that the energy cost of creating a vacancy in a crystal (εv) is balanced by the increase in configurational entropy. However, the amount of entropy gained by placing a single

In the class, we learned that the energy cost of creating a vacancy in a crystal (εv) is balanced by the increase in configurational entropy. However, the amount of entropy gained by placing a single vacancy in the crystal increases with the number of atomic sites in the crystal. Therefore, there may be a minimum number of atomic sites (N) that are needed to create sufficient entropy to stabilize a vacancy.

Assume a cube shaped crystal with atomic sites at the vertices of a primitive cubic lattice with a lattice spacing of 0.2 nm. Under what conditions can a crystal with edge length of 100 nm be perfect? Under what conditions can a 1 micron crystal be perfect?