Calculating Density of Aluminium Using Debye Theory

[alfredbester]

I've calculates the density of aluminium using the debye theory.
I found The atom density n = 2.24E28 m^-3 at 600k (assumed to be the same as at room temperature).
Therefore the density is just the molecular mass m (m(grams) = (79amu / Avogadros number), multiplied by the atom density. Which I found to be 1000 kg m^-3.
I'm asked to compared to this with a true value of 2700 Kg m^-3.

My estimate just assumes all the mass is the atoms, but I'm not sure why the discrepancy is so large. I thought the majority of the mass of a solid was in the atoms.

 

[member 553083]

The discrepancy is due to the fact that the Debye model does not take into account the strong interatomic forces that exist in materials. These interatomic forces cause atoms to be packed more densely than what would be expected from a simple atom density calculation. The additional mass comes from these interatomic forces and the accompanying increased atomic packing density. This increased mass results in a higher true value than what was estimated using the Debye model.