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(units="m-3 Pa-1/2", S_0=1, E_S=0.2)
my_perm = Permeability(pre_exp=1, act_energy=0.2)

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#

import h_transport_materials as htm

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

Alternatively, 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

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",
)

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Defining a property

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