A Possible Common Mechanism for the Kink Behavior in the Ionic Diffusion of Solid Materials
摘要
Diffusion in solids is more complex than in simple liquids and gases, and it plays a fundamental role in the properties of functional materials and various solid-state phenomena. To understand the atomic transport mechanism in solid materials from a unified perspective, we investigated the ionic diffusivity in solids using a theoretical model proposed by the authors. The model is represented by the effective diffusion coefficient D(eff) = c D, where c (= n/N) is the vacancy concentration obtained from the extended theory of vacancy formation and D is the diffusion coefficient of the hopping ion written as D = D0exp( \(- E_{{\text{a}}}^{\left( D \right)}\) /kBT), where \(E_{{\text{a}}}^{\left( D \right)}\) is the activation energy per hopping ion defined as \(E_{{\text{a}}}^{\left( D \right)}\) = Δ \(Q/n\) (with ΔQ being a constant). The present model envisages that the mobile ions jumping from the interstitials can be attributed to vacancy formations. Thus, in this context, c and D are nonlinearly coupled. In this paper, we demonstrate that our model successfully describes the temperature dependence of the diffusion coefficients, including the ‘kink’ behavior observed experimentally. In addition, the model allows the estimation of vacancy concentrations solely from transport profiles, which are found to range between 10–14 and 10–6 for the ionic crystals studied. By comparing these results with those for metallic glass-forming materials, which also exhibit the kink behavior in the temperature dependence in the tracer diffusion coefficient, we identify a common mechanism irrespective of specific materials system.