Atomic density of Oxygen in a composite

Dear experts, how can I calculate the atomic density of Oxygen in a composite of 05 percent PuO2 and 95 percent UO2 (in atoms/barn-cm)? (5% U235 enriched)

emilmammadzada said:

TL;DR Summary: Atomic density of Oxygen in a composite

Dear experts, how can I calculate the atomic density of Oxygen in a composite of 05 percent PuO2 and 95 percent UO2 (in atoms/barn-cm)? (5% U235 enriched)

Usually, one would use a mixed materials approach. One has 5% PuO₂ (by weight/mass) and 95% UO₂, and determine the number of moles of each. Then the atomic fraction is just the moles of O in the total moles of the mixture.

Atomic wise, one has two atoms of O for each atom of U, Pu, so 0.66 roughly for the atomic fraction. One can find the density based on the densities of the compounds, 10.96 g/cm³ for UO₂ and 11.46 g/cm³ for PuO₂, which are the theoretical densities (TD) assuming 100% dense, so one may adjust for whatever lower density (e.g., 95% of TD) one expects.

Astronuc said:

Usually, one would use a mixed materials approach. One has 5% PuO₂ (by weight/mass) and 95% UO₂, and determine the number of moles of each. Then the atomic fraction is just the moles of O in the total moles of the mixture.

Atomic wise, one has two atoms of O for each atom of U, Pu, so 0.66 roughly for the atomic fraction. One can find the density based on the densities of the compounds, 10.96 g/cm³ for UO₂ and 11.46 g/cm³ for PuO₂, which are the theoretical densities (TD) assuming 100% dense, so one may adjust for whatever lower density (e.g., 95% of TD) one expects.

Dear expert, I could not fully understand this answer. Is there a formula to calculate this or a resource that will show how to calculate the oxygen of atomic density in this mixed mixture?Are there any examples on this subject? My aim is to find theoretically the atomic density of oxygen in this mixture.

emilmammadzada said:

I could not fully understand this answer. Is there a formula to calculate this or a resource that will show how to calculate the oxygen of atomic density in this mixed mixture?Are there any examples on this subject?

This is a very basic chemistry problem - the atomic density of a given element in a compound.

One starts with the mass density, the convert to the number of moles or atoms per unit volume.

Astronuc said:

This is a very basic chemistry problem - the atomic density of a given element in a compound.

One starts with the mass density, the convert to the number of moles or atoms per unit volume.

Dear expert, can you explain with the example I asked? Just showing the formulation will be enough for me to understand.This subject seems complicated to me, I have a little insufficient knowledge of chemistry.I would be happy if you could explain the question I asked or a simple chemistry example.

emilmammadzada said:

Dear expert, can you explain with the example I asked? Just showing the formulation will be enough for me to understand.This subject seems complicated to me, I have a little insufficient knowledge of chemistry.I would be happy if you could explain the question I asked or a simple chemistry example.

Does one know how to convert from mass (g) to moles (g-mole) to atoms? Is one familiar with Avogadro's number, 6.022×10²³ atoms/g-mole?

Density is just mass/volume (g/cm³). To find the number of moles per unit volume, one multiplies by the number moles per unit mass, which is just the atomic or molecular mass.

If I have 239 grams of ²³⁹Pu, then I have 1 mole of ²³⁹Pu, since the atomic mass is 239 amu. To convert that to atoms, one multiplies by Avogadro's number, to obtain the number atoms in the mass.

It is more complicated when there are isotopes involved, since Pu is usually some combination of Pu-239, -240, -241, -242 and possibly some -243, and U is predominately U-238 with some U-235, depending on enrichment. So one might have Pu with an atomic mass of 239.6 and U with an atomic mass of 237.85.

In the OP example, one has to determine the moles of PuO₂ and UO₂ in the mixture, using the steps above, then use the stoichiometric value of 2 moles of O per 1 mole of U or Pu. I have given the density for the oxides in a previous post.

This is a fairly complicated calculation and you need more information to do it correctly, specifically you need to know the densities (usually in g/cc). You also need to know the "plutonium vector" of the plutonium oxide. Does the uranium oxide contain any U234 or U236?

If you know the densities separately, the process can be briefly described as:
1. Find the molecular mass of the uranium. This depends on the enrichment, which is defined as the mass fraction of U235.
2. Find the molecular mass of the UO2
3. Once you have the molecular mass of UO2 and the density of UO2, you can find the number density of pure UO2.
4. Once you have the number density of UO2, you can back out the number densities of the individual isotopes.
4. Repeat the process for the PuO2. You will need the plutonium composition.
5. Combine the UO2 and PuO2 using the mass fractions given.

Be careful not to mix up mass fractions and atom fractions.