kinisi.arrhenius#

The two classes herein enable the determination of the activation energy from a diffusion-Arrhenius or -Super-Arrhenius plot. This includes the uncertainty on the activation energy from the MCMC sampling of the plot, with uncertainties on diffusion. Furthermore, the classes are build on the Relationship subclass, therefore it is easy to determine the Bayesian evidence for each of the models with the given data, enabling the distinction between Arrhenius and Super-Arrhenius diffusion.

class kinisi.arrhenius.StandardArrhenius(temperature, diffusion, bounds=((0, 1), (0, 1e+20)), diffusion_error=None)#

Bases: Relationship

Evaluate the data with a standard Arrhenius relationship. For attributes associated with the uravu.relationship.Relationship class see that documentation.

Args:

temperature (array_like): Temperature data in kelvin. diffusion (array_like): Diffusion coefficient data in cm^2s^{-1}. bounds (tuple): The minimum and maximum values for each parameters.

Defaults to ((0, 1), (0, 1e20)).

diffusion_error (array_like): Uncertainty in the diffusion coefficient data. Not necessary: if diffusion is list of uravu.distribution.Distribution objects.
ci_points (array_like, optional): The two percentiles at which confidence intervals should be: found for the variables. Default is [2.5, 97.5] (a 95 % confidence interval).

property activation_energy: uravu.distribution.Distribution#

Returns:: Activated energy distribution in electronvolt.

property preexponential_factor: uravu.distribution.Distribution#

Returns:: Preexponential factor.

property distribution: ndarray#

Returns:: A distribution of samples for the Arrhenius relationship that can be used for easy

plotting of credible intervals.

extrapolate(extrapolated_temperature)#

Extrapolate the diffusion coefficient to some un-investigated value. This can also be used for interpolation.

Param:: Temperature to return diffusion coefficient at.
Return type:: uravu.distribution.Distribution
Returns:: Diffusion coefficient at extrapolated temperature.

kinisi.arrhenius.arrhenius(abscissa, activation_energy, prefactor)#

Determine the diffusion coefficient for a given activation energy, and prefactor according to the Arrhenius equation.

Args:: abscissa (array_like): The abscissa data. activation_energy (float): The activation_energy value. prefactor (float): The prefactor value.

Return type:: ndarray
Returns:: The diffusion coefficient data.

class kinisi.arrhenius.SuperArrhenius(temperature, diffusion, bounds=[(0, 1), (0, 1e+20), (0, None)], diffusion_error=None)#

Bases: Relationship

Evaluate the data with a super-Arrhenius relationship. For attributes associated with the uravu.relationship.Relationship class see that documentation.

Args:

temperature (array_like): Temperature data in kelvin. diffusion (array_like): Diffusion coefficient data in cm^2s^{-1}. bounds (tuple): The minimum and maximum values for each parameters. Defaults to

[(0, 1), (0, 1e20), (0, temperature[0])].

diffusion_error (array_like): Uncertainty in the diffusion coefficient data. Not necessary: if diffusion is list of uravu.distribution.Distribution objects.
ci_points (array_like, optional): The two percentiles at which confidence intervals should be: found for the variables. Default is [2.5, 97.5] (a 95 % confidence interval).

property activation_energy: uravu.distribution.Distribution#

Returns:: Activated energy distribution in electronvolt.

property preexponential_factor: uravu.distribution.Distribution#

Returns:: Preexponential factor.

property T0: uravu.distribution.Distribution#

Returns:: Temperature factor for the VTF equation in kelvin.

property distribution: ndarray#

Returns:: A distribution of samples for the super Arrhenius relationship that can be used

for easy plotting of credible intervals.

extrapolate(extrapolated_temperature)#

Extrapolate the diffusion coefficient to some un-investigated value. This can also be used for interpolation.

Param:: Temperature to return diffusion coefficient at.
Return type:: uravu.distribution.Distribution
Returns:: Diffusion coefficient at extrapolated temperature.

kinisi.arrhenius.super_arrhenius(abscissa, activation_energy, prefactor, t_zero)#

Determine the rate constant for a given activation energy, prefactor, and t_zero according to the Vogel–Tammann–Fulcher equation.

Parameters:

abscissa (ndarray) – The abscissa data.
activation_energy (float) – The activation_energy value.
prefactor (float) – The prefactor value.
t_zero (float) – The T_0 value.

Return type:

ndarray

Returns:

The diffusion coefficient data.