Defining a property#

Most - if not all - H transport properties are thermally activated. Meaning they follow the Arrhenius law:

\(X = X_0 \ \exp{\left( \frac{-E_X}{k_B \ T} \right)}\)

Here, \(X_0\) is called the pre-exponential factor and \(E_X\) is the activation energy. \(T\) is the temperature and \(k_B\) is the Boltzman constant.

The Arrhenius law is sometimes written as: \(X = X_0 \ \exp{\left( \frac{-E_X}{R_g \ T} \right)}\) with \(R_g\) the gas constant.

Note, \(R_g\) and \(k_B\) are linked by Avogadro’s number \(N_A\).

\(R_g = N_A \ k_B\)

Arrhenius parameters#

Properties can be defined in HTM by using the ArrheniusProperty() class.

from h_transport_materials import ArrheniusProperty

my_property = ArrheniusProperty(pre_exp=1, act_energy=0.2)

More precise classes can also be used like Diffusivity(), Solubility(), Permeability(), RecombinationCoeff(), DissociationCoeff().

from h_transport_materials import Diffusivity, Solubility, Permeability

my_diff = Diffusivity(D_0=1, E_D=0.2)
my_sol = Solubility(S_0=1, E_S=0.2, law="henry")
my_perm = Permeability(pre_exp=1, act_energy=0.2, law="sievert")

Note, Solubility() has a units argument because depending on the material, the units can be m-3 Pa-1/2 (Sievert’s law of solubility) or m-3 Pa-1 (Henry’s law of solubility).

Temperature range#

A temperature range can be associated with a property.

from h_transport_materials import ArrheniusProperty

my_property = ArrheniusProperty(pre_exp=1, act_energy=0.2, range=(300, 400))

In this example, the property is defined over the 300-400 K temperature range (see Units for more information on units).

Property from experimental data#

It is possible to define an ArrheniusProperty() directly from (T,y) points. In this case, the Arrhenius parameters will be fitted automatically from the data points.

from h_transport_materials import ArrheniusProperty

my_property = ArrheniusProperty(
    data_T=[400, 500, 600, 700],
    data_y=[200, 300, 400, 500]
)
print(my_property)

Author:
Material:
Year: None
Isotope: None
Pre-exponential factor: 1.67×10³
Activation energy: 7.34×10⁻² eV/particle

Attach a material#

A material can be attached to a property. The simple case is to give the material as a string:

from h_transport_materials import ArrheniusProperty

my_property = ArrheniusProperty(
    pre_exp=1,
    act_energy=0.2,
    material="tungsten"
)

If the material already exists in the material database, the HTM object can be used instead:

from h_transport_materials import ArrheniusProperty, TUNGSTEN

my_property = ArrheniusProperty(
    pre_exp=1,
    act_energy=0.2,
    material=TUNGSTEN
)

Units#

HTM uses pint to automatically converts units. If no units are given, defaults units are assumed. The units are stored in a pint.UnitRegistry that can be accessed by h_transport_materials.ureg.

from h_transport_materials import Diffusivity, ureg

my_property = Diffusivity(
    D_0=1 * ureg.cm**2 * ureg.s**-1,
    E_D=20 * ureg.kJ * ureg.mol**-1,
)

print(my_property.pre_exp)
print(my_property.act_energy)

0.0001 meter ** 2 / second
0.20728539312524347 electron_volt / particle

This is extremely useful when units start getting complicated:

from h_transport_materials import Permeability, ureg

my_perm = Permeability(
    pre_exp=1 * ureg.mol * ureg.cm**-1 * ureg.hour**-1 * ureg.bar**-0.5,
    act_energy=20 * ureg.kcal * ureg.mol**-1,
)

print(my_perm.pre_exp)
print(my_perm.act_energy)

5.289911442149285e+19 particle / meter / pascal ** 0.5 / second
0.8672820848360187 electron_volt / particle

Most attributes of properties in HTM are pint.Quantity objects: pre-exponential factors, activation energies, temperature range. Visit the pint documentation to learn more.

Evaluate property at a given temperature#

It is possible to evaluate the value of a property at a given temperature.

from h_transport_materials import Diffusivity, ureg

D = Diffusivity(
    D_0=1 * ureg.cm**2 * ureg.s**-1,
    E_D=20 * ureg.kJ * ureg.mol**-1,
)
print(D.value(400 * ureg.K))

2.4446573022139513e-07 meter ** 2 / second

To visualise the temperature dependency of an Arrhenius property, see Plotting.

Add a reference#

References are very important in order to track the origin of the property. Three methods exist to add a reference to a property in HTM.

Method 1: Fields like author, year, and source can be added manually:

import h_transport_materials as htm

D = htm.Diffusivity(
    D_0=1,
    E_D=0.2,
    author="Shrek",
    year=2023,
    source="name of book"
)

Method 2: One can provide a source in the Bib format.

import h_transport_materials as htm

bibsource = """@article{my_shrek_reference,
    title = {Name of Book},
    doi = {10.1016/awesome.journal.2023.1234},
    journal = {An Awesome Journal},
    author = {Shrek},
    year = {2023},
    pages = {1--2},
}"""

D = htm.Diffusivity(
    D_0=1,
    E_D=0.2,
    source=bibsource
)

print(D.author)
print(D.year)
print(D.doi)

shrek
2023
10.1016/awesome.journal.2023.1234

Method 3: In the h_transport_materials directory, there is a references.bib file containing a most of the references of HTM. One can also append the source in the Bib format to references.bib and then add the reference to source. The previous example would then be:

import h_transport_materials as htm

D = htm.Diffusivity(
    D_0=1,
    E_D=0.2,
    source="my_shrek_reference"
)

Add notes#

Sometimes it is useful to add custom notes to a property.

import h_transport_materials as htm

D = htm.Diffusivity(
    D_0=1,
    E_D=0.2,
    note="this was measured under atmospheric pressure",
)

Defining a property

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