The degree of decoupling between ionic conduction and structural relaxation is a key quantity to characterize good ionic conductors. On the other hand, it is known that the fragility of the materials plays an important role in diverse properties of disordered materials. In the present report, the relation between the decoupling index and the fragility is studied based on the Bond Strength-Coordination Number Fluctuation (BSCNF) model developed by ourselves. The analytical expression derived from the model indicates that the decoupling index, defined as the ratio between the structural and conductivity relaxation times evaluated at the glass transition temperature, could depend or not on the fragility. Such kind of behavior have been reported for instance, in polymer electrolytes and in AgI-containing oxide glasses, respectively. These results indicate that the BSCNF model could provide a good reference to understand the fundamental properties of structurally disordered ionic conductors.

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_a^( D ) /kBT), where E_a^( D ) is the activation energy per hopping ion defined as E_a^( D ) = 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.

The thermal expansion is one of the fundamental physical properties of the materials that reflects the anharmonicity of the interatomic potential. The description and understanding of thermal expansion are important in the applications of the materials. From the fundamental science point of view, the thermal expansion in glassy materials is also related directly to the relaxation behavior, a topic of current interest in condensed matter physics. However, the estimation of the thermal expansion coefficient of the materials having complex structures is not easy. In the present study, motivated by a previous work on Lindeman’s like rule between the thermal expansion coefficient and the glass transition temperature, we developed a model for the thermal expansion coefficient of metallic glasses by using a parametrized form of the interatomic potential and the Debye model for the distribution of atomic oscillations. The obtained analytical expression enables us to estimate the temperature dependence of the thermal expansion coefficient just from the glass transition temperature. However, the analysis based on the model indicates that the temperature dependence is weak compared to the experimental data. This observation suggests that we must go beyond the Debye model to treat the thermal expansion of glassy materials.

The ionic conductivity in aliovalently substituted solid solution Pb1–xRxSnF4+x (R = Y, Nd, Gd) is examined within an extended theoretical framework incorporating defect thermodynamics. Experimentally, the temperature dependence of the ionic conductivity exhibits two Arrhenius-like regimes with different activation energies and depending on the R content it displays either a downward- or upward-convex pattern. The present study provides a unified interpretation to these contrasting patterns of the ionic conductivity within a single defect-thermodynamic model. The results suggest that the ionic transport is governed by the coupling between thermally activated vacancy formation and ionic diffusion, and that the downward- or upward-convex crossover behavior is determined by the relationship between the parameters corresponding to the potential well depth and the diffusion-related parameter . The carrier number increases significantly with increasing temperature, reaching two orders of magnitude higher than that of β-PbSnF4.

The bond fluctuation model of superionic conductors proposed by one of the authors (MA) predicts that there must be a close relationship between the electronic polarizability and the ionic conduction in solids. Guided by this model, the relation between the nonlinear optical constants and the ion transport properties in crystalline and glassy ion conducting materials were studied previously. Those studies revealed that the nonlinear optical constant increases with the increase of the ionic conductivity. It was also noted that the optical properties could be also related with the structural relaxation. All these notions suggest the possibility that the optical properties of ionic conductors are interrelated with the mechanical properties of the materials. In the present study, such a possibility is investigated and corroborated using an anharmonic interatomic potential based theoretical model. Furthermore, it is shown that the previously found relation between the optical and the ionic transport properties can be understood analytically from the same interatomic potential point of view.

The Stokes-Einstein (SE) law has been widely used in the analysis of transport properties in the liquid state. However, recent studies have revealed that not all the systems obey this law. Particularly, large deviations from the SE law have been reported for systems that exhibit high ionic conduction in the glassy state. Although this observation has strong implication in the development of electrolyte materials, few fundamental studies on the subject have been done. In a recent study, based on the Bond Strength-Coordination Number Fluctuation model of structural relaxation developed in our group, it was pointed out that the correlated ionic motion starts at a temperature much higher than the glass transition temperature. With the objective to gain a further understanding on that behavior, in the present study we analyzed the temperature dependence of the degree of deviation from the SE law in the melts of AgI–AgPO3 and M–PO3 (M = Mg, Ca, Sr, Ba). The result reveals clearly that the deviation from the SE law increases with the decrease of temperature of the melt, which contrast with the behavior found in other systems. It is also noted that the behavior of the above mentioned two systems differ, and that such difference reflects the degree of ion transport.

The understanding of the non-Arrhenius transport properties in glass-forming materials is of great importance from both, fundamental and applied points of views. In the present paper, we show that our model, the bond strength-coordination number fluctuation (BSCNF) model describes the temperature dependence of the non-Arrhenius transport coefficients in a wide temperature range. The BSCNF model also enables to characterize the glass-forming materials in terms of the mean values of the bond strength E0, the coordination number Z0 and their fluctuations ΔE and ΔZ of the structural units that form the melts. Importantly, in the light of the BSCNF model, one can discuss the physical implications of the materials that extend from the strong to fragile systems in a systematic way compared to other popular models. In addition, we present a new theory of the vacancy formation, and briefly mention that the extended theory along with the BSCNF model can be applied to discuss the freezing of defects.

Noble metal chalcogenides are attracting considerable interest as thermoelectric materials. These materials exhibit superionic conduction at high temperatures. This fact is certainly affecting the peculiar thermoelectric properties of these materials. However, few attentions have been paid to this fact. The Seebeck coefficient which gives the magnitude of the induced voltage in response to a temperature gradient is a fundamental quantity that characterizes the thermoelectric material. In the present report, a theoretical expression for the electronic Seebeck coefficient of superionic conductors is derived from the point of view of the Bond Fluctuation Model of ionic conduction proposed by the author. According to this model, the transport of ions is accompanied by a fluctuation in the electronic cloud surrounding the moving ion. Such a process affects the electronic properties of the materials. It is shown that the model captures the peculiar temperature dependence of the Seebeck coefficient observed experimentally.

Among the various MX2-type compounds, only a limited number of them exhibit high ionic conduction. Is there any index that demarcates such compounds? The present study focuses on the molecular shape of these type of compounds having the nominal number of valence electrons N = 16. Interestingly, we note that compounds having a bent shape in the molecular state exhibit high ionic conduction in the solid phase. What is the origin of this correlation? In the field of quantum chemistry, the molecular shape has been understood based on the Walsh rule. On the other hand, with the objective to understand the ionic transport mechanism from the electronic theory point of view, the author proposed many years ago, the bond fluctuation model of ionic conduction. In the present study, the origin of the correlation mentioned above is discussed by exploiting the physical background of the Walsh rule in connection with the bond fluctuation model. It is concluded that the hybridization between the electronic orbitals not accounted in the nominal counting of valence electrons and the degree of charge transfer between the constituent atoms controls the behavior.

The bond fluctuation model of ionic conductors suggests that the high ionic conductivity is related with the low structural stability of the materials. A physical quantity that is related with the structural stability is the bulk modulus. Some years ago, a microscopic empirical model of bulk modulus has been proposed. The model applied to diverse materials showed a good agreement with the experimental values. It is of considerable interest to verify if such a model works in materials that exhibit high ionic conduction at high temperatures. Our analysis indicates that the temperature dependence of the bulk modulus described by the model is weak when compared with the experimental values. The result indicates that considering merely the effect of thermal expansion is not sufficient to account for the temperature variation of the bulk modulus. In particular, it is shown that such a variation is large in ionic conductors. This observation is interesting from the materials design point of view, because, recent studies consider that the bulk modulus is an important quantity that controls the performance of solid electrolytes. A possible way to extend the model is discussed briefly.

The temperature dependence of the diffusion coefficient in metallic glass-forming systems do not follow the Arrhenius behavior over a wide temperature range. Instead, it exhibits a kink behavior at around the glass transition temperature. Some researchers associate this behavior to the difference in the diffusion mechanism operating in the glassy and the supercooled liquid state, whereas others do not support this view. In addition, usually, the temperature dependence of the diffusion coefficient is analyzed by splitting the temperature range into two regions, above and below the glass transition temperature. In the present study, we developed an analytical theory that describes the continuous variation of the diffusion coefficient across a temperature where the kink behavior is observed. According to the theory, the kink behavior arises from the freezing of free volume available for diffusion by lowering the temperature. A connection to the vacancy mechanism of diffusion has been also pointed out.

The theory of the vacancy formation in crystals has been extended by generalising the vacancy formation energy that depends on the number of vacancies resulting from thermal activation. This extension enables to describe the freezing of defect concentrations at lower temperature, while the derived vacancy concentration reduces to the Boltzmann-Arrhenius law at higher temperature. The implications of the low-temperature patterns and its relevance to non-equilibrium process in the defect concentrations have been also touched upon. In addition, based on the approach explored, we further construct a model for the ionic conductivity in the intrinsic and extrinsic regions, which is formulated by focusing on the relation between the number concentration and the mobility of ionic charge carriers. A theoretical background to the continuity (knee) across which the both ionic conductivity patterns are smoothly connected is corroborated by the present work.

An empirical relation that correlates the optical dielectric constant and the electronegativity difference in A N B 8- N type binary compounds is presented. The relation uses only one numerical constant common to all I-VII, II-VI and III-V compounds. The simplicity of the relation provides a clue to understand the role of the charge transfer from one atom to another in the origin of the optical dielectric constant. It is also shown that the optical dielectric constant correlates better with the Pauling ionicity scale than with the Phillips ionicity scale. The possible physical background of the found relation is discussed based on the results obtained.

In recent years, much attention has been devoted to understand the behavior of the particle size dependence of the ionic conductivity. In the present study, a model for the particle size dependence of the ionic conductivity is proposed by considering that the particle can be separated into the core and shell regions, and that the size effect can be expressed by the size dependence of their constituents. In the model, the cohesive energy and the surface tension are related to the activation energy of ion transport in the core and shell regions, respectively. The model indicates that the conductivity increases by decreasing the particle size up to a certain size, and decreases below that size. The result indicates that there is an optimal particle size for the ionic conductivity.

The relation between the annealing temperature dependence of the structural inhomogeneity and the diffusion coefficient in a metallic glass forming system Zr-Ti-Cu-Ni-Be is studied by using reported experimental data. It is shown that the diffusion coefficient increases with the increase of the correlation length of the structural inhomogeneity. Interestingly, the result found resembles the behavior known in superionic glasses. A discussion on the found relationship is given by exploiting the model for the superionic glasses proposed by the author. Based on the model, an inhomogeneity dependent diffusivity maximum is predicted.

An empirical relation that correlates the optical dielectric constant and the electronegativity difference in ANB8-N type binary compounds is presented. The relation uses only one numerical constant common to all I-VII, II-VI and III-V compounds. The simplicity of the relation provides a clue to understand the role of the charge transfer from one atom to another in the origin of the optical dielectric constant. It is also shown that the optical dielectric constant correlates better with the Pauling ionicity scale than with the Phillips ionicity scale. The possible physical background of the found relation is discussed based on the results obtained.

The understanding of fundamental materials properties is indispensable for the development of functional materials. Some years ago, it has been reported that the fragility in poly (ethylene oxide)-based Li+ ion conductors decreases with the Li+ ion content. The behavior was considered as unexpected and the origin unclear. In the present study, it is shown that the Bond Strength-Coordination Number Fluctuation (BSCNF) model of structural relaxation developed by the present authors provides an explanation to the observed behavior. The analysis based on the BSCNF model indicates that the cooperativity, or the number of correlated structural units involved in the network relaxation decreases with the Li+ ion content.

Nanomaterials exhibit unusual physical properties when compared to bulk materials. To exploit the properties of the nanomaterials, it is important to understand the fundamental properties of the materials. In the present study, a theoretical formula for the particle size dependence of the Grüneisen parameter is derived. Since the Grüneisen parameter is a quantity that reflects the anharmonicity of lattice vibrations, it could be useful to study the diverse properties related to lattice dynamical properties of the materials. In the present report, the derived model has been applied to study the size and dimensionality dependence of the Grüneisen parameter of elemental metallic materials. The result reveals that the Grüneisen parameter increases with the decrease of particle size. The result also reveals that the size effect is more pronounced in nanoparticles than in nanowires and nanofilms.

The temperature dependence of the viscosity of some metallic glass forming liquids (MGFLs) exhibits an unusual behavior. At high temperature, the temperature dependence is quite weak, whereas at low temperature, the viscosity varies exponentially. Recently, this type of behavior are attracting much attention, because it can be considered as a manifestation of the fragile-to-strong transition. Well known classic viscosity models do not describe such kind of behavior over a wide temperature range. In the present report, it is shown that a modified version of the Bond Strength-Coordination Number Fluctuation (BSCNF) model describes the behavior observed in MGFLs. For the convenience of the readers, a brief review of the BSCNF model is also given.