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

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{{#category_index:C|Cole-Cole relaxation model}}
 
{{#category_index:C|Cole-Cole relaxation model}}
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(k&#x014D;l k&#x014D;l) 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  
 
(k&#x014D;l k&#x014D;l) 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.
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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

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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 is given by

,

where Ro 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 104 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.