How Does Melting Temperature Affect the Density of Vacancies in Copper?

[Arran]

Homework Statement

Consider a crystal of copper with the f.c.c. structure. Suppose the energy costs for creating a one-atom vacancy in the material is 1.1eV. The melting temperature of the material is 1356K. Estimate equilibrium density of vacancies in the material.

Homework Equations

N_V/N_L=exp(-Δhf/kT)

where N_V is the number of vacancies,
N_L is the number of lattice sites,
Δhf is the energy required to create a one-atom vacancy,
& k is boltzmann's constant

The Attempt at a Solution

Equilibrium density of vacancies = N_V/N_L=exp(-Δhf/kT)=
=exp(-1.1*1.6*10^-19/1.38*10^-23*300)=3.45*10^-19

I think I understand the equation and am able to derive it. However, I don't understand the relevance of the melting temperature. I assume the "equilibrium" implies room temperature, so I use T=300K. Also I don't see the relevance of the crystal structure, f.c.c.

Please help me. I feel as though I am missing the point of the equation :)

 

[newyork7]

I'm pretty sure for T you are supposed to use the melting point of copper i.e 1357.77K.

 

[Arran]

I'm pretty sure for T you are supposed to use the melting point of copper i.e 1357.77K.

But the formula implies (to me anyway) that the density of defects is temperature dependent, which makes sense. So as T goes to zero, so too does the density of defects. As T goes to infinity, the defect density goes to unity.

My only idea about the melting point is that at this temperature (T=1357.77K) the density of defects somehow saturates or reaches unity or some such. I don't see how to describe this with the given equation though. . .