# Copyright 2019 TerraPower, LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Boron carbide; a very typical reactor control material.
Note that this material defaults to a theoretical density fraction of 0.9, reflecting
the difficulty of producing B4C at 100% theoretical density in real life. To get
different fraction, use the `TD_frac` material modification in your assembly definition.
"""
from armi import runLog
from armi.materials import material
from armi.nucDirectory import nuclideBases
from armi.utils.units import getTc
DEFAULT_THEORETICAL_DENSITY_FRAC = 0.90
DEFAULT_MASS_DENSITY = 2.52
[docs]class B4C(material.Material):
enrichedNuclide = "B10"
propertyValidTemperature = {"linear expansion percent": ((25, 500), "C")}
[docs] def updateTD(self, td: float) -> None:
self.theoreticalDensityFrac = td
self.clearCache()
[docs] def setNewMassFracsFromMassEnrich(self, massEnrichment):
r"""
Calculate the mass fractions for a given mass enrichment and set it on any parent.
Parameters
----------
massEnrichment : float
The mass enrichment as a fraction.
Returns
-------
boron10MassGrams, boron11MassGrams, carbonMassGrams : float
The resulting mass of each nuclide/element
Notes
-----
B-10: 10.012 g/mol
B-11: 11.009 g/mol
Carbon: 12.0107 g/mol
4 moles of boron/1 mole of carbon
grams of boron-10 = 10.012 g/mol* 4 mol * 0.199 = 7.969552 g
grams of boron-11 = 11.009 g/mol* 4 mol * 0.801 = 35.272836 g
grams of carbon= 12.0107 g/mol * 1 mol = 12.0107 g
from number enrichment mi:
mB10 = nB10*AB10 /(nB10*AB10 + nB11*AB11)
"""
if massEnrichment < 0 or massEnrichment > 1:
raise ValueError(
"massEnrichment {} is unphysical for B4C".format(massEnrichment)
)
b10AtomicMass = nuclideBases.byName["B10"].weight
b11AtomicMass = nuclideBases.byName["B11"].weight
b10NumEnrich = (massEnrichment / b10AtomicMass) / (
massEnrichment / b10AtomicMass + (1 - massEnrichment) / b11AtomicMass
)
b11NumEnrich = 1.0 - b10NumEnrich
cAtomicMass = nuclideBases.byName["C"].weight
boron10MassGrams = b10AtomicMass * b10NumEnrich * 4.0
boron11MassGrams = b11AtomicMass * b11NumEnrich * 4.0
carbonMassGrams = cAtomicMass
gTotal = boron10MassGrams + boron11MassGrams + carbonMassGrams
boron10MassGrams /= gTotal
boron11MassGrams /= gTotal
carbonMassGrams /= gTotal
if self.parent:
self.parent.setMassFracs(
{"B10": boron10MassGrams, "B11": boron11MassGrams, "C": carbonMassGrams}
)
return boron10MassGrams, boron11MassGrams, carbonMassGrams
[docs] def setDefaultMassFracs(self) -> None:
r"""B4C mass fractions. Using Natural B4C. 19.9% B-10/ 80.1% B-11
Boron: 10.811 g/mol
Carbon: 12.0107 g/mol.
4 moles of boron/1 mole of carbon
grams of boron-10 = 10.01 g/mol* 4 mol * 0.199 = 7.96796 g
grams of boron-11 = 11.01 g/mol* 4 mol * 0.801 = 35.27604 g
grams of carbon= 12.0107 g/mol * 1 mol = 12.0107 g
total=55.2547 g.
Mass fractions are computed from this.
"""
massEnrich = self.getMassEnrichmentFromNumEnrich(naturalB10NumberFraction=0.199)
gBoron10, gBoron11, gCarbon = self.setNewMassFracsFromMassEnrich(
massEnrichment=massEnrich
)
self.setMassFrac("B10", gBoron10)
self.setMassFrac("B11", gBoron11)
self.setMassFrac("C", gCarbon)
self.refDens = DEFAULT_MASS_DENSITY
# TD reference : Dunner, Heuvel, "Absorber Materials for control rod systems of fast breeder reactors"
# Journal of nuclear materials, 124, 185-194, (1984)."
self.theoreticalDensityFrac = (
DEFAULT_THEORETICAL_DENSITY_FRAC # normally is around 0.88-93.
)
[docs] @staticmethod
def getMassEnrichmentFromNumEnrich(naturalB10NumberFraction: float) -> float:
b10AtomicMass = nuclideBases.byName["B10"].weight
b11AtomicMass = nuclideBases.byName["B11"].weight
return (
naturalB10NumberFraction
* b10AtomicMass
/ (
naturalB10NumberFraction * b10AtomicMass
+ (1.0 - naturalB10NumberFraction) * b11AtomicMass
)
)
[docs] def pseudoDensity(self, Tk: float = None, Tc: float = None) -> float:
"""
Return density that preserves mass when thermally expanded in 2D.
Notes
-----
- applies theoretical density of B4C to parent method
"""
return (
material.Material.pseudoDensity(self, Tk, Tc) * self.theoreticalDensityFrac
)
[docs] def density(self, Tk: float = None, Tc: float = None) -> float:
"""
Return density that preserves mass when thermally expanded in 3D.
Notes
-----
- applies theoretical density of B4C to parent method
"""
return material.Material.density(self, Tk, Tc) * self.theoreticalDensityFrac
[docs] def linearExpansionPercent(self, Tk: float = None, Tc: float = None) -> float:
"""Boron carbide expansion. Very preliminary."""
Tc = getTc(Tc, Tk)
self.checkPropertyTempRange("linear expansion percent", Tc)
deltaT = Tc - 25
dLL = deltaT * 4.5e-6
return dLL * 100