Reconciling different equations for proton conduction using the Meyer-Neldel compensation rule

Proton conduction in nominally anhydrous minerals is the likely explanation for moderate values of electrical resistivity observed in the lithospheric and sublithospheric mantle. However, results from the various laboratories making the controlled measurements on mantle minerals, predominantly olivine, are not in agreement with one another. Importantly, the groups use different formalisms to fit their experimental data. In this paper, we show that neither of the two formalisms employed by the various laboratories is consistent with the Meyer-Neldel Rule (MNR), or Compensation Law, by which the preexponent term of the Arrhenian equation is linearly related to the activation energy term. We also demonstrate why the formalism of Karato and colleagues can be used at low water contents (100 wt ppm and below), whereas at higher water contents (above 300 wt ppm), the formalism of Yoshino's and Poe's labs needs to be employed. A new MNR self-consistent formalism is presented that is applicable over all water contents. MNR consistency appears to operate for most processes that can be described by an Arrhenius equation, so its adoption through an MNR consistent formalism is highly recommended when fitting experimental observations.