# Charge carrier interactions in ionic conductors: A classical molecular-dynamics and Monte Carlo study on AgI

30 Mar 2000-Journal of Chemical Physics (American Institute of Physics)-Vol. 112, Iss: 14, pp 6416-6423

TL;DR: In this article, the defect concentrations as well as defect energies, including excess energies, are computed as a function of temperature by molecular-dynamics and Monte Carlo simulations based on a classical semi-empirical potential.

Abstract: The equilibrium concentration of ionic and electronic charge carriers in ionic crystals as a function of temperature, concentration of dopants, and chemical environment is phenomenologically well understood as long as these point defects can be considered sufficiently dilute. However, there are cases, usually at temperatures close to the melting point, where the defects appear in higher concentrations. In these cases interactions come into play and cause anomalous increases in the conductivity or even phase transitions. Recently Hainovsky and Maier showed that for various Frenkel disordered materials this anomalous conductivity increase at high temperature can be described by a cube root term in the chemical potential of the defects. This quasi-Madelung approach does not only allow ionic conductivities and heat capacities to be computed, it also leads to a phenomenological understanding of the solid–liquid or superionic transition temperatures. In the present study we analyze this approach on the atomistic level for AgI: The defect concentrations as well as defect energies, including excess energies, are computed as a function of temperature by molecular-dynamics and Monte Carlo simulations based on a classical semiempirical potential. The simulations support the cube-root model, yield approximately the same interaction constants and show that the corrections in the chemical potential are of an energetic nature. In agreement with structural expectations, the simulations reveal that two different kinds of interstitials are present: Octahedral interstitials, which essentially determine the ionic transport at higher temperature, and tetrahedral ones, which remain substantially associated with the vacancies. It is shown how these refinements have to be introduced into the cube root.

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TL;DR: A review of the state of current knowledge concerning the crystal structures and conduction processes of superionic conductors can be found in this article, where the relative importance of factors such as bonding character and the properties of the mobile and immobile ions in promoting the extensive lattice disorder which characterizes superionic behaviour is assessed and the possibilities for predicting a priori which compounds will display high ionic conductivity discussed.

Abstract: Superionic conductors are compounds that exhibit exceptionally high values of ionic conductivity within the solid state. Indeed, their conductivities often reach values of the order of 1 Ω−1 cm−1, which are comparable to those observed in the molten state. Following Faraday's first observation of high ionic conductivity within the solids β-PbF2 and Ag2S in 1836, a fundamental understanding of the nature of the superionic state has provided one of the major challenges in the field of condensed matter science. However, experimental and theoretical approaches to their study are often made difficult by the extensive dynamic structural disorder which characterizes superionic conduction and the inapplicability of many of the commonly used approximations in solid state physics. Nevertheless, a clearer picture of the nature of the superionic state at the ionic level has emerged within the past few decades. Many different techniques have contributed to these advances, but the most significant insights have been provided by neutron scattering experiments and molecular dynamics simulations. This review will summarize the state of current knowledge concerning the crystal structures and conduction processes of superionic conductors, beginning with a comparison of the behaviour of two of the most widely studied binary compounds, AgI and β-PbF2. Each can be considered a parent of two larger families of highly conducting compounds which are related by either chemical or structural means. These include perovskite-structured oxides and Li+ containing spinel-structured compounds, which have important commercial applications in fuel cells and lightweight batteries, respectively. In parallel with these discussions, the relative importance of factors such as bonding character and the properties of the mobile and immobile ions (charge, size, polarizability, etc) in promoting the extensive lattice disorder which characterizes superionic behaviour will be assessed and the possibilities for predicting a priori which compounds will display high ionic conductivity discussed.

455 citations

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TL;DR: A survey of ionic conductivity in NASICONs can be found in this article, where the authors discuss the recent results from atomistic computer simulations on the dependence of conductivity as a function of composition, temperature, phase change and cation among others.

Abstract: Solid state ionic conductors are important from an industrial viewpoint. A variety of such conductors have been found. In order to understand the reasons for high ionic conductivity in these solids, there have been a number of experimental, theoretical and computational studies in the literature. We provide here a survey of these investigations with focus on what is known and elaborate on issues that still remain unresolved. Conductivity depends on a number of factors such as presence of interstitial sites, ion size, temperature, crystal structure etc. We discuss the recent results from atomistic computer simulations on the dependence of conductivity in NASICONs as a function of composition, temperature, phase change and cation among others. A new potential for modelling of NASICON structure that has been proposed is also discussed.

169 citations

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25 Sep 2018TL;DR: To understand and quantify the role of space-charge layers in all-solid-state batteries, a simple model is presented which allows to asses the interface capacitance and resistance caused by the space- charge layer.

Abstract: All-solid state batteries have the promise to increase the safety of Li-ion batteries. A prerequisite for high-performance all-solid-state batteries is a high Li-ion conductivity through the solid electrolyte. In recent decades, several solid electrolytes have been developed which have an ionic conductivity comparable to that of common liquid electrolytes. However, fast charging and discharging of all-solid-state batteries remains challenging. This is generally attributed to poor kinetics over the electrode-solid electrolyte interface because of poorly conducting decomposition products, small contact areas, or space-charge layers. To understand and quantify the role of space-charge layers in all-solid-state batteries a simple model is presented which allows to asses the interface capacitance and resistance caused by the space-charge layer. The model is applied to LCO (LiCoO2) and graphite electrodes in contact with an LLZO (Li7La3Zr2O12) and LATP (Li1.2Al0.2Ti1.8(PO4)3) solid electrolyte at several voltag...

67 citations

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TL;DR: In this paper, it is shown that the onset of this defect avalanche, which can be estimated by a cube root law, roughly corresponds to the Tammann temperature, and the investigation of simple compounds corroborates this picture and also the observation of a critical defect concentration.

Abstract: The validity of Tammann's rule is related to the fact that the unavoidable thermal generation of point defects leads to defect-defect interactions and finally to a breakdown of the structure. It is shown that the onset of this defect avalanche, which can be estimated by a cube root law, roughly corresponds to the Tammann temperature. The investigation of simple compounds corroborates this picture and also the observation of a critical defect concentration. Examples are given that Tammann's rule can be used to systematically search for new solid electrolytes.

62 citations

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TL;DR: The defect chemistry and d.c. transport characteristics of β-AgI are reconsidered by taking into account (i) two structurally different interstitial positions, (ii) short-range interactions via associations, (iii) anisotropy of the wurtzite structure, (iv) long-range defect-defect interactions via Coulomb forces, and (v) formation of highly conducting layers perpendicular to the c -axis via a disordered interface structure with stacking faults as mentioned in this paper.

Abstract: The defect chemistry and d.c. transport characteristics of β-AgI are reconsidered by taking into account (i) two structurally different interstitial positions, (ii) short-range interactions via associations, (iii) anisotropy of the wurtzite structure, (iv) long-range defect-defect interactions via Coulomb forces, and (v) formation of highly conducting layers perpendicular to the c -axis via a disordered interface structure with stacking faults. Besides microstructural characterization the analysis relies on the ionic conductivity data by impedance spectroscopy with conventional as well as micro-electrodes, and utilizes recent reports on the defect concentration and defect energies of β-AgI by molecular dynamics simulations and on AgI:Al 2 O 3 composites. Static valence sum calculations were performed to elucidate the ion conduction pathways and related migration barriers.

53 citations

##### References

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11 Feb 1988TL;DR: In this paper, the gear predictor -corrector is used to calculate forces and torques in a non-equilibrium molecular dynamics simulation using Monte Carlo methods. But it is not suitable for the gear prediction problem.

Abstract: Introduction Statistical mechanics Molecular dynamics Monte Carlo methods Some tricks of the trade How to analyse the results Advanced simulation techniques Non-equilibrium molecular dynamics Brownian dynamics Quantum simulations Some applications Appendix A: Computers and computer simulation Appendix B: Reduced units Appendix C: Calculation of forces and torques Appendix D: Fourier transforms Appendix E: The gear predictor - corrector Appendix F: Programs on microfiche Appendix G: Random numbers References Index.

21,073 citations

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TL;DR: In this article, a unified scheme combining molecular dynamics and density-functional theory is presented, which makes possible the simulation of both covalently bonded and metallic systems and permits the application of density functional theory to much larger systems than previously feasible.

Abstract: We present a unified scheme that, by combining molecular dynamics and density-functional theory, profoundly extends the range of both concepts. Our approach extends molecular dynamics beyond the usual pair-potential approximation, thereby making possible the simulation of both covalently bonded and metallic systems. In addition it permits the application of density-functional theory to much larger systems than previously feasible. The new technique is demonstrated by the calculation of some static and dynamic properties of crystalline silicon within a self-consistent pseudopotential framework.

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TL;DR: In this paper, the authors present a survey of interionic potential models for alkali halides, including the rigid ion potentials of Fumi and Tosi, and a major part of the section is devoted to deriving a new set of polarizable ion potential, which incorporate the ideas behind the lattice dynamical shell model.

Abstract: After an outline of work on rare-gas systems, which serves as a target for parallel work on alkali halides, and an initial brief survey of those parts of this parallel work for which results have been obtained, interionic potential models for alkali halides are considered in some detail. The rigid ion potentials of Fumi and Tosi are discussed and then a major part of the section is devoted to deriving a new set of polarizable ion potentials, which incorporate the ideas behind the lattice dynamical shell model. Extensions which include many-body terms in the potentials are considered briefly and finally the information which can be obtained from alkali halide diatomic molecules is discussed. In the third section methods of computer simulation for ionic liquids are outlined, concentrating on the molecular dynamics method, and some of the properties which can be obtained by analysing the ion trajectories are listed. Results from simulations, including some new work on LiF, NaCl and RbI, are reviewed.

551 citations

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TL;DR: In this paper, it was shown that the defect energy required for the formation of a defect pair greatly exceeds the thermal energy, kBT, in a typical ionic crystal, and the same is true of the ionic conductivity.

Abstract: Most ionic crystals have degrees of disorder well below 10-2, (i). The defect concentrations being small, only a limited fraction of ions can move at a time and carry charge through the crystal lattice. The ionic conductivities of these "normal" ionic crystals are therefore low at moderate temperatures. Typical values are ca. iO -4 (~ cm) -I in the case of igCl (~) and ca. I0 -~ (9 em) -I in the case of NaCI (j), both at 200 °C. In these "normal" crystals the energy required for the formation of a defect pair greatly exceeds the thermal energy, kBT. At 200 °C the factors are ca. 95 and 50 in the cases of AgCI and NaCI, respectively (2,9). The concentrations of acfects and mobile ions in a typical ionic crystal therefore strcngiy depenu on temperature, and the same is true of the ionic conductivity.

230 citations