Integral Fuel Burnable Absorber (ifba) - Zirconium Diboride - Zrb2

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INTEGRAL FUEL BURNABLE ABSORBER (IFBA) - Atomic Number Density Calculation -

Integral Fuel Burnable Absorber (IFBA), is a thin layer of Zirconium Diboride (ZrB2) coating on fuel pellets [Ref.,]. 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 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.

COOLANT

CLADDING

GAP+IFBA FUEL

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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: R fuel = Rinner = 0.4095 cm Rgap = Router = 0.4177 cm L = 1 cm 2 2 V = A × L = π × ( Router − Rinner )  × L

V = π × ( 0.4177 2 − 0.40952 )  × 1 V = 0.02131 cm3

Then the mass is calculated as follow: Density of ZrB2 is 6.085 g/cc [Ref.]. m = ρ × V = 6.085 × 0.02131 m = 0.12967 g Atomic number density of ZrB2 is calculated as follow: N ZrB 2 =

ρ N Av M ZrB 2

ρ = density of ZrB2 [g/cc] N Av = Avogadro's number [atom/mol] M ZrB 2 = molar mass of ZrB2 [g/mol] Molar mass of ZrB2 is 112.85 g/mol [Ref.]. N ZrB 2 =

6.085 × 6.022 ×1023 = 3.247 × 1022 atom/cc 112.85

N Zr = N ZrB 2 = 3.247 ×1022 atom/cc N B = 2 × N ZrB 2 = 2 × 3.247 ×1022 = 6.494 ×1022 atom/cc The molar mass of natural zirconium is 91.224 g/mol [Ref.], then the total mass of Zr in the unit volume is: Zr mass = 0.02131×

91.224 × 3.247 × 1022 = 0.10482 g 23 6.022 ×10

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

10

•

11

B 19.9% B 80.1%

Therefore, N B10 = 0.199 × N B = 0.199 × 6.494 × 1022 = 1.2923 ×1022 atom/cc N B11 = 0.801× N B = 0.801× 6.494 × 1022 = 5.2017 ×1022 atom/cc

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: 10

B = 0.02131×1.2923 ×1022 = 2.7539 × 1020 atom

Atomic mass of 10B is 10.0129 amu [Ref.], then the mass of one 10B atom in gram is [Ref.]: 1 amu =

Mu g N Av

⇒

10.0129 amu =

10.0129 g 6.022 ×1023

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

B mass =

10.0129 × 2.7539 ×1020 = 4.5789 × 10−3 g 23 6.022 ×10

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

B = 0.02131× 5.2017 ×1022 = 1.1085 ×1021 atom

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

B mass =

11.0093 ×1.1085 ×1021 = 2.0265 ×10−2 g 23 6.022 × 10

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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: 4.5789 mg/cm 10 B = 1.2923 × 1022 atom/cc 10 B 1 mg/cm 10 B = 2.8223 ×1021 atom/cc 10 B Now let say that your nuclear fuel design uses 1 mg/cm 10B, so: 10

B = 2.8223 ×1021 atom/cc

11

B = 1.1360 ×1022 atom/cc

Zr = 1.4182 × 1022 atom/cc 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 “smeared” the IFBA material in the gap.

REFERENCES 1. http://en.wikipedia.org/wiki/Zirconium_diboride 2. http://en.wikipedia.org/wiki/Boron 3. http://wwwndc.jaea.go.jp/cgi-bin/nuclinfo2004?5,10 4. http://en.wikipedia.org/wiki/Atomic_mass#Conversion_factor_between_atomic_mass_units _and_grams 5. http://wwwndc.jaea.go.jp/cgi-bin/nuclinfo2004?5,11 6. http://en.wikipedia.org/wiki/Zirconium 7. http://www.westinghousenuclear.com/Products_&_Services/docs/flysheets/NF-FE-0028.pdf 8. http://www.westinghousenuclear.com/Products_&_Services/docs/flysheets/NF-FE-0009.pdf 4 of 4