isovec 1.2.2

A package to calculate atomic, weight or volume composition of (custom) elements, molecules and mixtures, down to isotopic composition.

isoVec

Description

isoVec is a framework to build complex mixtures of materials and get atomic (mole), weight or volume percentages of each of its substances down to the isotopic composition (the isotope vector, hence the name). The information on relative atomic weights of isotopes, as well as their abundance in natural occuring elements, is taken from "Atomic Weights and Isotopic Compositions with Relative Atomic Masses" by the NIST Physical Measurement Laboratory [1]. This information is embedded in the form of Isotope and Element classes. The user can also create custom Elementss and specify the isotopic composition manually. Molecules are made from Elements and Mixtures can be made from Elements, Molecules and other Mixtures. A thorough example is given in Section 'Example'.

Installation

The source code of the most recent development version is hosted on GitHub. The binary installers and the source code of stable releases is available on the project site on the Python Package Index (PyPI) and can be simply installed from the repository via

pip install isovec

There are no additional dependencies other than core Python packages of Python 3.10.

Example

The composition of the atmosphere of the Earth may serve as an example how to use isoVec. The constituents and their mole fractions are taken from the respective Wikipedia article and are as of April 2022:

Constituent	Mole Fraction
Nitrogen (N2)	78.084 %
Oxygen (O2)	20.946 %
Argon (Ar)	0.9340 %
Carbon dioxide (CO2)	417 ppm
Neon (Ne)	18.18 ppm
Helium (He)	5.24 ppm
Methane (CH4)	1.87 ppm
Krypton (Kr)	1.14 ppm

It may be noted, that these values are often given as a volume fraction in other literature. For a mixture of ideal gases (which is the case for air), volume and mole fractions are equal. Furthermore the amount of substance (mole) and number of particles (e.g. atoms) are proportional in an element, being connected via the Avogadro constant $N_\mathrm{A}$. Here, the terms mole and atomic fraction can be used interchangeably. In general, and especially when dealing with molecules containing multiple atoms per particle, this is not strictly correct, but is done regardless in the API for the sake of convenience. One should be aware of this and always consider the current context.

Let's assume for the following, that isoVec is imported with the following (shorter) alias. Keep in mind, that all content is packed inside the given namespace.

import isovec as iso

Element

Natural occuring elements are already implemented and can be accessed via its symbol and "_nat". Nitrogen for example is called with N_nat. For the sake of this tutorial, we will define nitrogen again by ourselfs. Furthermore, an extensive library of isotopes is implemented. Each Isotope is acessed via the elements symbol, followed by an underscore "_" and its mass number (that is protons + neutrons). Nitrogen-14 is therefore called via N_14. An Element can only be composed of its respective isotopes, so Isotope objects with the same atomic number Z.

A custom Element is created with a unique name and its composition as a dictionary:

nitrogen = iso.Element("nitrogen", {
    iso.N_14: 9.963600E-01,
    iso.N_15: 3.640000E-03
})

In composition dictionaries, positive values refer to an atomic fraction (as done before), while negative values refer to a weight fraction. Whatever information is available or more convenient may be used, but atomic and weight fractions cannot be mixed inside one composition dictionary. If the keyword argument mode is supplied with either "atomic", "weight" or other short forms thereof, signs are ignored and the values of the dictionary are interpreted accordingly, making the construction call more verbose. Alternatively, fraction-specific constructor methods can be called on the class, namely from_atomic() and from_weight(), in which case the keyword mode doesn't need to be supplied. Otherwise, the syntax is identical to the ordinary constructor call. The given composition doesn't necessarily need to add up to unity. Instead, each fraction is normalised by the total sum of given fractions.

The molar mass of an element is calculated automatically, but could be overwritten when supplying the keyword argument M=value in the constructor. Optionally, the density of the element can be supplied with the keyword argument rho=value, since densities of elements cannot be calculated automatically by the given informations. The keyword argument data is a dictionary, containing string keys and float values. It serves the purpose of storing additional data (and can later be used to calculate mean values of those quantities). The described behaviour of the constructur also applies to the following classes, if not stated otherwise. Furthermore, instances of Elements and the following classes can be (deep)copied by calling the copy() method on the instance. Properties like density rho, molar mass M, name, symbol and data can be altered from the original, by supplying these as keyword arguments.

Molecule

The composition for a Molecule is the number of atoms per Element. Therefore, only the "atomic" mode is valid, or in short positive values in the composition dictionary. However, this class isn't strictly limited to molecules, but can be used for crystalline or amorphous structures with a stochiometric distribution.

Using the implemented natural Elements, the Molecule for carbon dioxide is given by:

carbon_dioxide = iso.Molecule("carbon dioxide", {
    iso.C_nat: 1,
    iso.O_nat: 2
})

Likewise, the other Molecules are given as:

methane = iso.Molecule("methane", {
    iso.C_nat: 1,
    iso.H_nat: 4
})
nitrogen2 = iso.Molecule("molecular nitrogen", { iso.N_nat: 2})
oxygen2 = iso.Molecule("molecular oxygen", { iso.O_nat: 2})

Note, that the molar mass of the entire molecule is calculated by default.

Mixture

Mixtures can contain several pure Elements, Molecules and also other Mixtures. In contrast to Element and Molecule, it is also possible to supply volume fractions in the composition, provided that all constituents have a density defined. This can be invoked either by supplying the keyword argument mode="volume" to the constructor, or calling the specific constructor from_volume().

According to the table from the introduction, a Mixture for air is defined by the following:

air = iso.Mixture("air", {
    nitrogen2:                  78.084E-02,  # Molecule
    oxygen2:        iso.percent(20.946),     # Molecule
    iso.Ar_nat:     iso.percent( 0.9340),    # Element
    carbon_dioxide:            417.0E-06,    # Molecule
    iso.Ne_nat:        iso.ppm( 18.18),      # Element
    iso.He_nat:        iso.ppm(  5.24),      # Element
    methane:           iso.ppm(  1.87),      # Molecule
    iso.Kr_nat:        iso.ppm(  1.14)       # Element
})

Note the use of convencience functions for conversion, an extensive list can be found in the source code file "conversion.py" When all constituents have their density defined, the density of the Mixture can also be calculated automatically.

The entered material hierarchy can be printed in a tree-like structure by invoking print_tree_input() on any substance we want to inspect:

air.print_tree_input(weight=True)

The percentage refers to the fraction in the parent and will sum up to 100 % on their 'sibling' level. Setting the keywords weight or volume to True also calculates the weight and volume percent of each node respectively (where applicable), in addition to the atomic percentage that is printed by default (but can be deactivated via the keyword atomic). This yields the following (excerpt of the) output:

Mixture "air": 28.9660 g/mol
├── Molecule "molecular nitrogen":  78.0775 at.%  |   75.5097 wt.%  |  28.0134 g/mol
│   └── Element "natural nitrogen": 100.0000 at.%  |  100.0000 wt.%  |  14.0067 g/mol
│       ├── Isotope "N-14":  99.6360 at.%  |   99.6102 wt.%  |  14.0031 g/mol
│       └── Isotope "N-15":   0.3640 at.%  |    0.3898 wt.%  |  15.0001 g/mol
├── Molecule "molecular oxygen":  20.9443 at.%  |   23.1372 wt.%  |  31.9988 g/mol
│   └── Element "natural oxygen": 100.0000 at.%  |  100.0000 wt.%  |  15.9994 g/mol
│       ├── Isotope "O-16":  99.7570 at.%  |   99.7290 wt.%  |  15.9949 g/mol
│       ├── Isotope "O-17":   0.0380 at.%  |    0.0404 wt.%  |  16.9991 g/mol
│       └── Isotope "O-18":   0.2050 at.%  |    0.2306 wt.%  |  17.9992 g/mol
├── Element "natural argon":   0.9339 at.%  |    1.2880 wt.%  |  39.9478 g/mol
│   ├── Isotope "Ar-36":   0.3336 at.%  |    0.3004 wt.%  |  35.9675 g/mol
│   ├── Isotope "Ar-38":   0.0629 at.%  |    0.0598 wt.%  |  37.9627 g/mol
│   └── Isotope "Ar-40":  99.6035 at.%  |   99.6399 wt.%  |  39.9624 g/mol
   [...]

The format of the fraction values and the physical properties can be given by supplying the keywords frac_fmt and prop_fmt respectively with a format string.

The method rule_of_mixtures() can be used to calculate mean values of quantities saved in the data dictionary via the rule of mixtures. For that, all constituents must have the respective key-value pair stored in their data dictionary.

Elemental & Isotopic Composition

To obtain the elemental composition, the method get_elements() can be called upon a substance, yielding an ordered dictionary with elements and their respective summed fractions. With the mode keyword argument, fractions can be fetched in terms of "atomic" or "weight". For the mixture of air, the following code

element_vector = air.get_elements(mode="atomic")
for element, at_frac in element_vector.items():
    print(f"{element.symbol:>2}: {at_frac:.4E}")

yields the elemental composition:

 H: 3.7565E-06
He: 2.6315E-06
 C: 2.1036E-04
 N: 7.8428E-01
 O: 2.1080E-01
Ne: 9.1301E-06
Ar: 4.6906E-03
Kr: 5.7251E-07

Similarly, get_isotopes() yields the isotopic composition of a substance. Additionally, the keyword argument use_natural can be used to represent the isotopic composition of a natural Element with a surrogate Isotope object. This surrogate object represents an element with natural occuring abundance. use_natural=True applies this behaviour to all natural elements. Alternatively, a collection (iterable) of natural Element objects can be passed as the argument, limiting the behaviour to those specified. Note that custom made elements are not subject to that behaviour, unless the keyword argument natural=True was specified in their constructor. The (atomic) isotopic composition of air - considering natural oxygen as one - can be fetched with the following code:

isotope_vector = air.get_isotopes(mode="atomic", use_natural=(iso.O_nat,))
for isotope, at_frac in isotope_vector.items():
    isotope_name = isotope.name.replace("-0", "-nat")  # surrogate Isotopes have a mass number of zero
    print(f"{isotope_name:>6}: {at_frac:.4E}")

yields the isotope vector (with all oxygen isotopes, that are part of a natural composition Element, being condensed into a surrogate Isotope object):

   H-1: 3.7560E-06
   H-2: 4.3200E-10
  He-3: 3.5263E-12
  He-4: 2.6315E-06
  C-12: 2.0811E-04
  C-13: 2.2508E-06
  N-14: 7.8143E-01
  N-15: 2.8548E-03
 O-nat: 2.1080E-01
   [...]

The composition can also be printed in a tree-hierarchy. Both atomic and weight fractions can be fetched and are limited to Element and Isotope objects. The following code

air.print_tree_composition(weight=True)

yields the composition tree:

Mixture "air": 28.9660 g/mol
├── Molecule "molecular nitrogen": 28.0134 g/mol
│   └── Element "natural nitrogen":  78.4281 at.%  |   75.5097 wt.%  |  14.0067 g/mol
│       ├── Isotope   "N-14":  78.1426 at.%  |   75.2154 wt.%  |  14.0031 g/mol
│       └── Isotope   "N-15":   0.2855 at.%  |    0.2943 wt.%  |  15.0001 g/mol
├── Molecule "molecular oxygen": 31.9988 g/mol
│   └── Element "natural oxygen":  21.0383 at.%  |   23.1372 wt.%  |  15.9994 g/mol
│       ├── Isotope   "O-16":  20.9872 at.%  |   23.0744 wt.%  |  15.9949 g/mol
│       ├── Isotope   "O-17":   0.0080 at.%  |    0.0093 wt.%  |  16.9991 g/mol
│       └── Isotope   "O-18":   0.0431 at.%  |    0.0534 wt.%  |  17.9992 g/mol
├────── Element "natural argon":   0.4691 at.%  |    1.2880 wt.%  |  39.9478 g/mol
│       ├── Isotope  "Ar-36":   0.0016 at.%  |    0.0039 wt.%  |  35.9675 g/mol
│       ├── Isotope  "Ar-38":   0.0003 at.%  |    0.0008 wt.%  |  37.9627 g/mol
│       └── Isotope  "Ar-40":   0.4672 at.%  |    1.2834 wt.%  |  39.9624 g/mol
├── Molecule "carbon dioxide": 44.0095 g/mol
│   ├── Element "natural carbon":   0.0209 at.%  |    0.0173 wt.%  |  12.0107 g/mol
│   │   ├── Isotope   "C-12":   0.0207 at.%  |    0.0171 wt.%  |  12.0000 g/mol
│   │   └── Isotope   "C-13":   0.0002 at.%  |    0.0002 wt.%  |  13.0034 g/mol
│   └── Element "natural oxygen":   0.0419 at.%  |    0.0461 wt.%  |  15.9994 g/mol
│       ├── Isotope   "O-16":   0.0418 at.%  |    0.0459 wt.%  |  15.9949 g/mol
│       ├── Isotope   "O-17":   0.0000 at.%  |    0.0000 wt.%  |  16.9991 g/mol
│       └── Isotope   "O-18":   0.0001 at.%  |    0.0001 wt.%  |  17.9992 g/mol
   [...]

Compared to the fetching algorithms shown before, these compositions are not summed for each Element or Isotope, but the percentage can be traced back to each individual component. For example, the amount of "natural oxygen" and its Isotopes are listed in the Molecule "molecular oxygen" $(\mathrm{O_2})$ and the Molecule "carbon dioxide" $(\mathrm{CO_2})$ individually.

Changelog

For a history of changes, refer to the file CHANGELOG.md in the source code distributions or directly on the GitHub repository.

References

1. Coursey, J.S., Schwab, D.J., Tsai, J.J., and Dragoset, R.A. (2015), Atomic Weights and Isotopic Compositions (version 4.1). [Online] Available: https://www.nist.gov/pml/atomic-weights-and-isotopic-compositions-relative-atomic-masses [Accessed 23 July 2023]. National Institute of Standards and Technology, Gaithersburg, MD.