galpynostatic.utils module
Internal unitless parameters functions.
- galpynostatic.utils.logell(c_rate, d, z, dcoeff)
Obtain log value in base 10 of \(\ell\) internal parameter.
\(\ell = \frac{d^2 C_{rate}}{z t_h D}\) where \(d\) is the particle size, \(C_{rate}\) is the galvanostatic charging rate, \(z\) is a geometrical factor, \(D\) is the diffusion coefficient and \(t_h\) is the time equivalent to one hour in suitable time units, here 3600 seconds.
- Parameters:
c_rate (float or int or array-like) – C-rate values.
d (float) – Characteristic diffusion length (particle size) in \(cm\).
z (int) – Geometric factor: 1 for planar, 2 for cylinder and 3 for sphere.
dcoeff (float) – Diffusion coefficient, \(D\), in \(cm^2/s\).
- Returns:
logell – The log 10 value of \(\ell\) internal parameter.
- Return type:
float or array-like
- galpynostatic.utils.logxi(c_rate, dcoeff, k0, z)
Obtain log value in base 10 of \(\Xi\) internal parameter.
\(\Xi = k^0 \sqrt{\frac{t_h}{C_{rate} D}}\) where \(k^0\) is the kinetic rate constant, \(t_h\) is the time equivalent to one hour in suitable time units, here 3600 seconds, \(C_{rate}\) is the galvanostatic charging rate and \(D\) is the diffusion coefficient.
- Parameters:
c_rate (float or int or array-like) – C-rate values.
dcoeff (float) – Diffusion coefficient, \(D\), in \(cm^2/s\).
k0 (float) – Kinetic rate constant, \(k^0\), in \(cm/s\).
z (int) – Geometric factor: 1 for planar, 2 for cylinder and 3 for sphere.
- Returns:
logxi – The log 10 value of \(\Xi\) internal parameter.
- Return type:
float or array-like
- galpynostatic.utils.logcrate(xi_log, dcoeff, k0, z)
Obtain log value in base 10 of the C-rate.
\(C_{rate} = \dfrac{t_h}{D}(\dfrac{k^0}{\Xi})\) where \(k^0\) is the kinetic rate constant, \(t_h\) is the time equivalent to one hour in suitable time units, here 3600 seconds, \(\Xi\) is the kinetic parameter of the model and \(D\) is the diffusion coefficient.
- Parameters:
xi_log (float or int or array-like) – The log 10 value of \(\Xi\).
dcoeff (float) – Diffusion coefficient, \(D\), in \(cm^2/s\).
k0 (float) – Kinetic rate constant, \(k^0\), in \(cm/s\).
z (int) – Geometric factor: 1 for planar, 2 for cylinder and 3 for sphere.
- Returns:
log_crate – The log 10 value of the C-rate.
- Return type:
float or array-like
- galpynostatic.utils.logd(xi_log, l_log, dcoeff, k0, z)
Obtain log value in base 10 of the characteristic diffusion length d.
\(d = \sqrt(\dfrac{\ell z t_h D}{C_{rate}})\) where \(k^0\) is the kinetic rate constant, \(t_h\) is the time equivalent to one hour in suitable time units, here 3600 seconds, \(C_{rate}\) is the galvanostatic charging rate, \(\Xi\) and \(\ell\) are the kinetic parameter and finite diffusion parameter of the model, z the geometric factor of the particle and \(D\) is the diffusion coefficient.
- Parameters:
xi_log (float or int or array-like) – The log 10 value of \(\Xi\).
l_log (float or int or array-like) – The log 10 value of \(\ell\).
dcoeff (float) – Diffusion coefficient, \(D\), in \(cm^2/s\).
k0 (float) – Kinetic rate constant, \(k^0\), in \(cm/s\).
z (int) – Geometric factor: 1 for planar, 2 for cylinder and 3 for sphere.
- Returns:
logd – The log 10 value of the diffusion length.
- Return type:
float or array-like