# Difference between revisions of "Dictionary:Cole-Cole relaxation model"

Chrisdinneen (talk | contribs) (Fixed Equations) |
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{{#category_index:C|Cole-Cole relaxation model}} | {{#category_index:C|Cole-Cole relaxation model}} | ||

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(kōl kōl) A model for induced polarization (IP) effects in which the effective impedance varies as a power of the frequency. The complex resistivity <math>\rho (\omega) </math> is given by | (kōl kōl) A model for induced polarization (IP) effects in which the effective impedance varies as a power of the frequency. The complex resistivity <math>\rho (\omega) </math> is given by | ||

<center><math>\rho (\omega) = R_0 \left\{ 1-m\left[ 1-\frac {1}{\left(1+i\omega\tau\right)^c}\right] \right\} </math>,</center> | <center><math>\rho (\omega) = R_0 \left\{ 1-m\left[ 1-\frac {1}{\left(1+i\omega\tau\right)^c}\right] \right\} </math>,</center> | ||

− | where ''R''<sub>''o''</sub> is the dc resistivity, <math> \tau </math> is the time constant, and ''c'' is the frequency dependence. Typical ranges for parameters are ''m''=0.1 to 1.0, depending on the mineral content, <math>\tau </math> = 10<sup>-4</sup> to 10<sup>4</sup> depending on grain size, and ''c''=0.2 to 0.6 depending on the particle size distribution. Compare [[Dictionary:Warburg_impedance|''Warburg impedance'']], for which the value of ''c'' is 0.5. | + | where ''R''<sub>''o''</sub> is the dc resistivity, <math> \tau </math> is the time constant, and ''c'' is the frequency dependence. Typical ranges for parameters are ''m''=0.1 to 1.0, depending on the mineral content, <math>\tau </math> = 10<sup>-4</sup> to 10<sup>4</sup> depending on grain size, and ''c''=0.2 to 0.6 depending on the particle size distribution. Compare [[Special:MyLanguage/Dictionary:Warburg_impedance|''Warburg impedance'']], for which the value of ''c'' is 0.5. |

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## Revision as of 16:37, 2 March 2017

(kōl kōl) A model for induced polarization (IP) effects in which the effective impedance varies as a power of the frequency. The complex resistivity is given by

where *R*_{o} is the dc resistivity, is the time constant, and *c* is the frequency dependence. Typical ranges for parameters are *m*=0.1 to 1.0, depending on the mineral content, = 10^{-4} to 10^{4} depending on grain size, and *c*=0.2 to 0.6 depending on the particle size distribution. Compare *Warburg impedance*, for which the value of *c* is 0.5.