Optimizing the Proton Conductivity with the Isokinetic Temperature in Perovskite‐Type Proton Conductors According to Meyer–Neldel Rule

Abstract

Perovskite‐type metal oxides such as Y‐doped BaMO3 (M = Zr/Ce) have drawn considerable attention as proton‐conducting electrolytes for intermediate temperature ceramic electrochemical cells. Improving the proton conductivity at lower temperatures requires a comprehensive understanding of the proton conduction mechanism. By applying high pressure or varying the Ce content of Y‐doped BaMO3, it is demonstrated that the proton conductivity follows the Meyer–Neldel rule (MNR) well. In the Arrhenius plot, the conductivities intersect at an isokinetic temperature, where the proton conductivity is independent of activation energy. Considering the relationship between isokinetic temperature and lattice vibration frequency, a high isokinetic temperature is observed in materials with stiff lattices, consisting of light atoms and small MO bond length. Based on consideration of the MNR, it is suggested that the enhancement of proton conductivity at low temperature can be well achieved by tuning lattice vibration frequency toward a desired isokinetic temperature.

Considering the Role of Ion Transport in Diffuson‐Dominated Thermal Conductivity

“…The resulting interpretation is consistent with the multi excitation entropy approach, but it leads to a physical interpretation of the coupling constant N , here related to the characteristic phonon occupation $${\tilde n^0}$$. [ 32,33,59 ] This can be shown by considering that $$\;{\tilde n^0}$$ represents the average occupation of mode hν at the isokinetic temperature T iso according to the Bose–Einstein distribution function (Equation (5), Note S10, Supporting Information): $$\[ \begin{array}{*{20}{c}}{{{\tilde n}^0} = {{\left( {{{\rm{e}}^{\frac{{h\nu }}{{{k_{\rm{B}}}{T_{{\rm{iso}}}}}}}} - 1} \right)}^{ - 1}}}\end{array} \]$$which can be algebraically solved for k B T iso (Equation (6), Figure 7 right) leading to $$\[ \begin{array}{*{20}{c}}{{k_{\rm{B}}}{T_{{\rm{iso}}}} = \frac{{h\nu }}{{\ln \left( {1 + \frac{1}{{\;{{\tilde n}^0}}}} \right)}}\;}\end{array} \]$$…”

“…[ 32,33 ] However, lacking a consistent definition of N , ln( N ) is empirically treated as a coupling constant. [ 32,33 ] Thus, a deeper understanding of Meyer–Neldel behavior is still needed to develop a predictive theory based on the vibrational spectrum of the ion conductor.…”

“…By expounding upon the known multi‐excitation entropy model [ 32,33 ] using phonon occupation fluctuation considerations, we show that the inverse Meyer–Neldel slope can be related to the vibrational modes contributing to ionic conduction and a characteristic average phonon occupation $${\tilde n^0}$$ (for details see: Note S10, Supporting Information) as, [ 29 ] $$\[ \begin{array}{*{20}{c}}{\ln \left( {{\sigma _0}} \right) \propto \frac{{\Delta {S_{\rm{m}}}}}{{{k_{\rm{B}}}}} \approx \frac{{{E_{\rm{A}}}}}{{h\nu \;{{\tilde n}^0}}}}\end{array} \]$$…”

“…[32,33] Essentially, the multiexcitation entropy model applied to ionic conductors considers that the migrational entropy arises from a multiplicity of statistical microstates associated with the absorption of phonon excitations by the mobile ions. This leads to the result that the inverse slope of the Meyer-Neldel plot (Figure 7) relates to an energy scale, corresponding to the isokinetic temperature T iso (slope −1 = k B T iso ), [33] and is suggested to be related to a characteristic vibrational mode, hν, as well as a characteristic number of vibrations N (slope −1 = hν/ln (N), Figure 7). [32,33] However, lacking a consistent definition of N, ln(N) is empirically treated as a coupling constant.…”

Relating critical phonon occupation to activation barrier in fast lithium-ion conductors

“…23,24 Still, the phenomenological implementation of the multi-excitation theory has been used to explain Meyer-Neldel behavior in diverse physical systems, including ionic conductors. 26,47 Because 𝑛 c cannot be treated as an independent variable, i.e. its value cannot change independent of the frequency, the Taylor expansion in frequency (Eq.…”