Compensation of the Meyer-Neldel Compensation Law for H diffusion in minerals

The Meyer-Neldel Rule (MNR), or compensation law, linearly relates the preexponent term to the logarithm of the excitation enthalpy for any process that is thermally driven in an Arrhenian manner, and MNR fits can be used to calibrate and validate laboratory experimental results. Both robust least squares linear regressions and nonrobust regressions on selected subsets for individual minerals with sufficient experimental data demonstrate that hydrogen diffusion in minerals obeys the MNR with differing MNR intercepts and gradients depending on the mineral. In particular, nominally anhydrous mantle minerals have very distinct and different MNR parameters compared to hydrous and crustal minerals, with garnet proving to be an outlier lying in between the two. Furthermore, the variations of the estimated intercepts and gradients of the various MNRs are not random, but remarkably they themselves fall on a striking linear trend. This observation, if more broadly true, has profound implications for materials sciences and understanding of solid-state physics, as it implies that the compensation rule is itself compensated.