from collections import OrderedDict
import os
import re
from xml.etree import ElementTree as ET
import openmc.checkvalue as cv
from openmc.data import NATURAL_ABUNDANCE, atomic_mass, \
isotopes as natural_isotopes
[docs]class Element(str):
"""A natural element that auto-expands to add the isotopes of an element to
a material in their natural abundance. Internally, the OpenMC Python API
expands the natural element into isotopes only when the materials.xml file
is created.
Parameters
----------
name : str
Chemical symbol of the element, e.g. Pu
Attributes
----------
name : str
Chemical symbol of the element, e.g. Pu
"""
def __new__(cls, name):
cv.check_type('element name', name, str)
cv.check_length('element name', name, 1, 2)
return super().__new__(cls, name)
@property
def name(self):
return self
[docs] def expand(self, percent, percent_type, enrichment=None,
enrichment_target=None, enrichment_type=None,
cross_sections=None):
"""Expand natural element into its naturally-occurring isotopes.
An optional cross_sections argument or the :envvar:`OPENMC_CROSS_SECTIONS`
environment variable is used to specify a cross_sections.xml file.
If the cross_sections.xml file is found, the element is expanded only
into the isotopes/nuclides present in cross_sections.xml. If no
cross_sections.xml file is found, the element is expanded based on its
naturally occurring isotopes.
Parameters
----------
percent : float
Atom or weight percent
percent_type : {'ao', 'wo'}
'ao' for atom percent and 'wo' for weight percent
enrichment : float, optional
Enrichment of an enrichment_taget nuclide in percent (ao or wo).
If enrichment_taget is not supplied then it is enrichment for U235
in weight percent. For example, input 4.95 for 4.95 weight percent
enriched U. Default is None (natural composition).
enrichment_target: str, optional
Single nuclide name to enrich from a natural composition (e.g., 'O16')
.. versionadded:: 0.12
enrichment_type: {'ao', 'wo'}, optional
'ao' for enrichment as atom percent and 'wo' for weight percent.
Default is: 'ao' for two-isotope enrichment; 'wo' for U enrichment
.. versionadded:: 0.12
cross_sections : str, optional
Location of cross_sections.xml file. Default is None.
Returns
-------
isotopes : list
Naturally-occurring isotopes of the element. Each item of the list
is a tuple consisting of a nuclide string, the atom/weight percent,
and the string 'ao' or 'wo'.
Raises
------
ValueError
No data is available for any of natural isotopes of the element
ValueError
If only some natural isotopes are available in the cross-section data
library and the element is not O, W, or Ta
ValueError
If a non-naturally-occurring isotope is requested
ValueError
If enrichment is requested of an element with more than two
naturally-occurring isotopes.
ValueError
If enrichment procedure for Uranium is used when element is not
Uranium.
ValueError
Uranium enrichment is requested with enrichment_type=='ao'
Notes
-----
When the `enrichment` argument is specified, a correlation from
`ORNL/CSD/TM-244 <https://doi.org/10.2172/5561567>`_ is used to
calculate the weight fractions of U234, U235, U236, and U238. Namely,
the weight fraction of U234 and U236 are taken to be 0.89% and 0.46%,
respectively, of the U235 weight fraction. The remainder of the
isotopic weight is assigned to U238.
When the `enrichment` argument is specified with `enrichment_target`, a
general enrichment procedure is used for elements composed of exactly
two naturally-occurring isotopes. `enrichment` is interpreted as atom
percent by default but can be controlled by the `enrichment_type`
argument.
"""
# Check input
if enrichment_type is not None:
cv.check_value('enrichment_type', enrichment_type, {'ao', 'wo'})
if enrichment is not None:
cv.check_less_than('enrichment', enrichment, 100.0, equality=True)
cv.check_greater_than('enrichment', enrichment, 0., equality=True)
# Get the nuclides present in nature
natural_nuclides = {name for name, abundance in natural_isotopes(self)}
# Create dict to store the expanded nuclides and abundances
abundances = OrderedDict()
# If cross_sections is None, get the cross sections from the
# OPENMC_CROSS_SECTIONS environment variable
if cross_sections is None:
cross_sections = os.environ.get('OPENMC_CROSS_SECTIONS')
# If a cross_sections library is present, check natural nuclides
# against the nuclides in the library
if cross_sections is not None:
library_nuclides = set()
tree = ET.parse(cross_sections)
root = tree.getroot()
for child in root.findall('library'):
nuclide = child.attrib['materials']
if re.match(r'{}\d+'.format(self), nuclide) and \
'_m' not in nuclide:
library_nuclides.add(nuclide)
# Get a set of the mutual and absent nuclides. Convert to lists
# and sort to avoid different ordering between Python 2 and 3.
mutual_nuclides = natural_nuclides.intersection(library_nuclides)
absent_nuclides = natural_nuclides.difference(mutual_nuclides)
mutual_nuclides = sorted(list(mutual_nuclides))
absent_nuclides = sorted(list(absent_nuclides))
# If all naturally ocurring isotopes are present in the library,
# add them based on their abundance
if len(absent_nuclides) == 0:
for nuclide in mutual_nuclides:
abundances[nuclide] = NATURAL_ABUNDANCE[nuclide]
# If some naturally occurring isotopes are not present in the
# library, check if the "natural" nuclide (e.g., C0) is present. If
# so, set the abundance to 1 for this nuclide.
elif (self + '0') in library_nuclides:
abundances[self + '0'] = 1.0
elif len(mutual_nuclides) == 0:
msg = ('Unable to expand element {} because the cross '
'section library provided does not contain any of '
'the natural isotopes for that element.'
.format(self))
raise ValueError(msg)
# If some naturally occurring isotopes are in the library, add them.
# For the absent nuclides, add them based on our knowledge of the
# common cross section libraries (ENDF, JEFF, and JENDL)
else:
# Add the mutual isotopes
for nuclide in mutual_nuclides:
abundances[nuclide] = NATURAL_ABUNDANCE[nuclide]
# Adjust the abundances for the absent nuclides
for nuclide in absent_nuclides:
if nuclide in ['O17', 'O18'] and 'O16' in mutual_nuclides:
abundances['O16'] += NATURAL_ABUNDANCE[nuclide]
elif nuclide == 'Ta180' and 'Ta181' in mutual_nuclides:
abundances['Ta181'] += NATURAL_ABUNDANCE[nuclide]
elif nuclide == 'W180' and 'W182' in mutual_nuclides:
abundances['W182'] += NATURAL_ABUNDANCE[nuclide]
else:
msg = 'Unsure how to partition natural abundance of ' \
'isotope {0} into other natural isotopes of ' \
'this element that are present in the cross ' \
'section library provided. Consider adding ' \
'the isotopes of this element individually.'
raise ValueError(msg)
# If a cross_section library is not present, expand the element into
# its natural nuclides
else:
for nuclide in natural_nuclides:
abundances[nuclide] = NATURAL_ABUNDANCE[nuclide]
# Modify mole fractions if enrichment provided
# Old treatment for Uranium
if enrichment is not None and enrichment_target is None:
# Check that the element is Uranium
if self.name != 'U':
msg = ('Enrichment procedure for Uranium was requested, '
'but the isotope is {} not U'.format(self))
raise ValueError(msg)
# Check that enrichment_type is not 'ao'
if enrichment_type == 'ao':
msg = ('Enrichment procedure for Uranium requires that '
'enrichment value is provided as wo%.')
raise ValueError(msg)
# Calculate the mass fractions of isotopes
abundances['U234'] = 0.0089 * enrichment
abundances['U235'] = enrichment
abundances['U236'] = 0.0046 * enrichment
abundances['U238'] = 100.0 - 1.0135 * enrichment
# Convert the mass fractions to mole fractions
for nuclide in abundances.keys():
abundances[nuclide] /= atomic_mass(nuclide)
# Normalize the mole fractions to one
sum_abundances = sum(abundances.values())
for nuclide in abundances.keys():
abundances[nuclide] /= sum_abundances
# Modify mole fractions if enrichment provided
# New treatment for arbitrary element
elif enrichment is not None and enrichment_target is not None:
# Provide more informative error message for U235
if enrichment_target == 'U235':
msg = ("There is a special procedure for enrichment of U235 "
"in U. To invoke it, the arguments 'enrichment_target'"
"and 'enrichment_type' should be omitted. Provide "
"a value only for 'enrichment' in weight percent.")
raise ValueError(msg)
# Check if it is two-isotope mixture
if len(abundances) != 2:
msg = ('Element {} does not consist of two naturally-occurring '
'isotopes. Please enter isotopic abundances manually.'
.format(self))
raise ValueError(msg)
# Check if the target nuclide is present in the mixture
if enrichment_target not in abundances:
msg = ('The target nuclide {} is not one of the naturally-occurring '
'isotopes ({})'.format(enrichment_target, list(abundances)))
raise ValueError(msg)
# If weight percent enrichment is requested convert to mass fractions
if enrichment_type == 'wo':
# Convert the atomic abundances to weight fractions
# Compute the element atomic mass
element_am = sum(atomic_mass(nuc)*abundances[nuc] for nuc in abundances)
# Convert Molar Fractions to mass fractions
for nuclide in abundances:
abundances[nuclide] *= atomic_mass(nuclide) / element_am
# Normalize to one
sum_abundances = sum(abundances.values())
for nuclide in abundances:
abundances[nuclide] /= sum_abundances
# Enrich the mixture
# The procedure is more generic that it needs to be. It allows
# to enrich mixtures of more then 2 isotopes, keeping the ratios
# of non-enriched nuclides the same as in natural composition
# Get fraction of non-enriched isotopes in nat. composition
non_enriched = 1.0 - abundances[enrichment_target]
tail_fraction = 1.0 - enrichment / 100.0
# Enrich all nuclides
# Do bogus operation for enrichment target but overwrite immediatly
# to avoid if statement in the loop
for nuclide, fraction in abundances.items():
abundances[nuclide] = tail_fraction * fraction / non_enriched
abundances[enrichment_target] = enrichment / 100.0
# Convert back to atomic fractions if requested
if enrichment_type == 'wo':
# Convert the mass fractions to mole fractions
for nuclide in abundances:
abundances[nuclide] /= atomic_mass(nuclide)
# Normalize the mole fractions to one
sum_abundances = sum(abundances.values())
for nuclide in abundances:
abundances[nuclide] /= sum_abundances
# Compute the ratio of the nuclide atomic masses to the element
# atomic mass
if percent_type == 'wo':
# Compute the element atomic mass
element_am = 0.
for nuclide in abundances.keys():
element_am += atomic_mass(nuclide) * abundances[nuclide]
# Convert the molar fractions to mass fractions
for nuclide in abundances.keys():
abundances[nuclide] *= atomic_mass(nuclide) / element_am
# Normalize the mass fractions to one
sum_abundances = sum(abundances.values())
for nuclide in abundances.keys():
abundances[nuclide] /= sum_abundances
# Create a list of the isotopes in this element
isotopes = []
for nuclide, abundance in abundances.items():
isotopes.append((nuclide, percent * abundance, percent_type))
return isotopes