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.

 

[Nate810]

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.

 

[kyle8921]

I would first commend the individual for using the Debye theory to calculate the density of aluminium. This is a valid and widely accepted method for determining the properties of materials at the atomic level. However, I would also point out that the calculation provided may not accurately reflect the true density of aluminium.

There are a few reasons why the calculated value of 1000 kg m^-3 is significantly lower than the true value of 2700 kg m^-3. First, the assumption that the atom density at 600K is the same as at room temperature may not be accurate. The density of materials can change with temperature, so it is important to consider the specific conditions under which the calculation is being performed.

Additionally, the calculation only takes into account the mass of the atoms, but does not account for the spaces between the atoms or any other structural components of the material. In reality, the density of a solid is determined by the packing of atoms and the presence of any void spaces or additional structures.

Furthermore, the Debye theory is based on certain assumptions and simplifications, and may not accurately capture all the complexities of the material. It is important to consider the limitations of any theoretical model and compare the results to experimental data.

In conclusion, while the use of Debye theory is a valid approach, it is important to carefully consider the assumptions and limitations of the calculation and compare the results to experimental data in order to accurately determine the density of a material.