## Integral Fuel Burnable Absorber (IFBA): Atomic number density calculation

Posted by Syeilendra Pramuditya on December 5, 2009

Integral Fuel Burnable Absorber (IFBA), is a thin layer of Zirconium Diboride (ZrB2) coating on fuel pellets [Ref.7,8]. It is a type of burnable poison developed by Westinghouse, to control the core reactivity in nuclear reactor operation. The quantity which is actually needed as an input for cell homogenization by using any lattice spectrum code, such as JAEA‘s SRAC/PIJ, is atomic number density of all materials, and atomic number density of IFBA is calculated as follow.

First of all, we will use these assumptions in this discussion:

- In reality, the thickness of IFBA coating on fuel pellet will vary depending on the required concentration of 10B, which is expressed in mg/cm 10B. However, here IFBA is modeled as a smeared material in the gap between fuel pellet and inner wall of the cladding.
- Zr in ZrB2 is assumed as natural Zirconium.
- B in ZrB2 is assumed as natural Boron.

Let us define a unit volume as a volume occupied by the gap of 1 cm long, therefore the shape of this unit volume is annular with inner radius being equal to fuel pellet radius and outer radius being equal to inner radius of the clad, therefore the volume of this annulus is:

Then the mass is calculated as follow:

Density of ZrB2 is 6.085 g/cc [Ref.1].

Atomic number density of ZrB2 is calculated as follow:

Molar mass of ZrB2 is 112.85 g/mol [Ref.1].

The molar mass of natural zirconium is 91.224 g/mol [Ref.6], then the total mass of Zr in the unit volume is:

Naturally occurring Boron is composed of two isotopes, with atomic number density fraction (abundance) as follow [Ref.2]:

- 10B 19.9%
- 11B 80.1%

Therefore,

Element which acts as the burnable poison is 10B, so actually we only interested in this element, the next task is to calculate the mass of 10B.

The total number of 10B in the unit volume is:

Atomic mass of 10B is 10.0129 amu [Ref.3], then the mass of one 10B atom in gram is [Ref.4]:

Then the total mass of 10B in the unit volume is:

The total number of 11B in the unit volume is:

Atomic mass of 11B is 11.0093 amu [Ref.5], then the total mass of 10B in the unit volume is:

As mentioned earlier, 10B concentration in IFBA is usually expressed in the unit of mg/cm, so if we keep the dimension of the unit volume, and since the length of our unit volume is 1 cm, we can define:

Now let say that your nuclear fuel design uses 1 mg/cm 10B, so:

Therefore, by using this model, instead of varying the thickness of IFBA layer, we simply use the fixed size of the pellet-clad gap, and then evaluate the atomic number densities of Zr, 10B, and 11B, or in other word, we “smear” the IFBA material in the gap.

**REFERENCES**

- http://en.wikipedia.org/wiki/Zirconium_diboride
- http://en.wikipedia.org/wiki/Boron
- http://wwwndc.jaea.go.jp/cgi-bin/nuclinfo2004?5,10
- http://en.wikipedia.org/wiki/Atomic_mass#Conversion_factor_between_atomic_mass_units_and_grams
- http://wwwndc.jaea.go.jp/cgi-bin/nuclinfo2004?5,11
- http://en.wikipedia.org/wiki/Zirconium
- http://www.westinghousenuclear.com/Products_&_Services/docs/flysheets/NF-FE-0028.pdf
- http://www.westinghousenuclear.com/Products_&_Services/docs/flysheets/NF-FE-0009.pdf

**Please let me know if you found any mistake in this post, thanks!**

**UPDATE**

- 2014.07 – Thanks for a correction by Mr. Joel Kulesza on Zr number density calculation (7.0911E+21 atom/cc).

## Leave a Reply