How to Calculate Atom/B-cm Values for Nuclear Fuel Composition?

[emilmammadzada]

TL;DR Summary

How to Calculate Atom/B-cm Values for Nuclear Fuel Composition?

Hello everyone,

I came across the following atom/b-cm values for a specific nuclear fuel composition:
U-234.81c 1.1369e-06
U-235.81c 3.0421e-05
U-236.81c 2.4896e-06
U-238.81c 0.019613
Np-237.81c 4.6686e-05
Pu-236.81c 4.97e-10
Pu-238.81c 0.00011695
Pu-239.81c 0.0022076
Pu-240.81c 0.0013244
Pu-241.81c 0.00019375
Pu-242.81c 0.00029277
Am-241.81c 0.00010791
Am-242m.81c 9.2989e-06
Am-243.81c 0.00010017
Cm-242.81c 5.625e-06
Cm-243.81c 5.4321e-07
Cm-244.81c 6.724e-05
Cm-245.81c 1.7397e-05
Cm-246.81c 9.2285e-06
Zr-90.81c 0.0037456629
Zr-91.81c 0.00081683844
Zr-92.81c 0.00124855430
Zr-94.81c 0.00126529876
Zr-96.81c 0.00020384560
Mo-100.81c 9.04954512e-05
Mo-92.81c 0.0001360496577
Mo-94.81c 8.53224251e-05
Mo-95.81c 0.0001474173129
Mo-96.81c 0.0001548471529
Mo-97.81c 8.89909086e-05
Mo-98.81c 0.0002256070916

I am curious about the methodology and formula used to calculate these atom/b-cm values. Could someone explain the process or point me to relevant resources or references?

Thank you!

 

[Alexander Camargo]

To calculate the atomic density of a material, follow these steps

1 - add up all the atomic masses
2 - know the density of the material
3 - calculate the mass fraction for each radionuclide
4 - calculate the atomic density with the formula
((density*mass fraction*avogadro number)/total atomic mass)*1e-24)

5 - result in atoms/barn-cm

 

[emilmammadzada]

To calculate the atomic density of a material, follow these steps

1 - add up all the atomic masses
2 - know the density of the material
3 - calculate the mass fraction for each radionuclide
4 - calculate the atomic density with the formula
((density*mass fraction*avogadro number)/total atomic mass)*1e-24)

5 - result in atoms/barn-cm

Will each nuclide be written here as density or total density composition?

 

[Alexander Camargo]

Will each nuclide be written here as density or total density composition?

Atom Densities

 

[emilmammadzada]

Atom Densities

Isn't it separate for uranium and separate for neptunium in this composition?

 

[Alexander Camargo]

Isn't it separate for uranium and separate for neptunium in this composition?

use the formula to reverse engineer this and get this answer, because just looking at the data like this, I can't tell. Do you have the density of this material?

 

[emilmammadzada]

use the formula to reverse engineer this and get this answer, because just looking at the data like this, I can't tell. Do you have the density of this material?

I got this data from the serpent nuclear code input file. There was no fuel density given there, I just wonder how the content of such fuels is calculated. There is no information about density here
% --- 2D SFR Assembly based on MET-1000

% --- Materials

mat fuel sum tmp 807.15 vol 89.15304673765142 rgb 255 0 0 burn 1
U-234.81c 1.1369e-06
U-235.81c 3.0421e-05
U-236.81c 2.4896e-06
U-238.81c 0.019613
Np-237.81c 4.6686e-05
Pu-236.81c 4.97e-10
Pu-238.81c 0.00011695
Pu-239.81c 0.0022076
Pu-240.81c 0.0013244
Pu-241.81c 0.00019375
Pu-242.81c 0.00029277
Am-241.81c 0.00010791
Am-242m.81c 9.2989e-06
Am-243.81c 0.00010017
Cm-242.81c 5.625e-06
Cm-243.81c 5.4321e-07
Cm-244.81c 6.724e-05
Cm-245.81c 1.7397e-05
Cm-246.81c 9.2285e-06
Zr-90.81c 0.0037456629
Zr-91.81c 0.00081683844
Zr-92.81c 0.00124855430
Zr-94.81c 0.00126529876
Zr-96.81c 0.00020384560
Mo-100.81c 9.04954512e-05
Mo-92.81c 0.0001360496577
Mo-94.81c 8.53224251e-05
Mo-95.81c 0.0001474173129
Mo-96.81c 0.0001548471529
Mo-97.81c 8.89909086e-05
Mo-98.81c 0.0002256070916