# Density of defects help!

1. Mar 16, 2012

### Arran

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

NV/NL=exp(-Δhf/kT)

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

3. The attempt at a solution

Equilibrium density of vacancies = NV/NL=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.

2. Apr 11, 2012

### newyork7

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

3. Apr 11, 2012

### Arran

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 dont see how to describe this with the given equation though. . .