ColeColeDielectric
- class pmrf.materials.ColeColeDielectric(ep_inf: Any = 1.0, dep_r: Any = 0.0, f_relax: Any = 1000000000.0, alpha: Any = 0.0, sigma: Any = 0.0, *, name: str | None = None, metadata: Any = None)
Bases:
AbstractDielectricCole-Cole dielectric: a single relaxation broadened by the exponent \(\alpha\).
Mathematical Formulation
\[\varepsilon_r(f) = \varepsilon_\infty + \frac{\Delta\varepsilon_r}{1 + \left(jf/f_r\right)^{1 - \alpha}} - j\frac{\sigma}{\omega\varepsilon_0}\]With \(\alpha = 0\) this reduces exactly to a single Debye pole.
References
Cole, K. S., & Cole, R. H. (1941). Dispersion and absorption in dielectrics. Journal of Chemical Physics, 9(4), 341-351.
- Parameters:
ep_inf (Param, default=1.0) – High-frequency limit of the relative permittivity.
dep_r (Param, default=0.0) – Permittivity increment (relaxation strength).
f_relax (Param, default=1e9) – Relaxation frequency in Hz.
alpha (Param, default=0.0) – Broadening exponent, in [0, 1).
sigma (Param, default=0.0) – Static bulk conductivity in S/m.
- properties(freq: Frequency) DielectricProperties
Evaluate the dielectric properties over a frequency axis.
- Parameters:
freq (Frequency) – The frequency axis to evaluate over.
- Returns:
Complex permittivity, permeability, and static conductivity.
- Return type:
jnp.ndarray