This article reviews the transport of atoms through crystalline solids under the influence of external electric fields, chemical and isotopic concentration gradients and thermal gradients. The main emphasis is on the statistical and thermodynamic description of these phenomena via the theory of mobile lattice imperfections - vacancies and interstitial atoms. In discussing the various phenomena in detail (§ 5) extensive use is made of non-equilibrium thermodynamics as providing a convenient general formalism. Particular attention is given wherever possible to the physical interpretation of the descriptions provided by this formalism. An introductory survey of the properties of vacancies and interstitials in relation to diffusion phenomena is given in § 2. This includes a summary of the various defect models applicable to different solids - metals, ionic solids, semiconductors and insulators. Section 3 deals in greater detail with certain necessary aspects of the statistical thermodynamics of solids containing defects. Section 4 briefly summarizes the basic theory of non-equilibrium thermodynamics, oriented towards matter transport in crystalline solids; attention is drawn to several pitfalls in this approach. Finally, § 5 is the main object of the review; it applies the material developed in §§ 3 and 4. This section deals with (i) isothermal diffusion in metal alloys, including chemical diffusion, and isotopic tracer diffusion, particular attention being given to dilute systems, (ii) electrolytic conductivity, ionic mobility and both solute and solvent diffusion in ionic solids, special attention being given to the relation between these quantities and to a generalized form of the Nernst-Einstein relation, (iii) the Soret effect and thermal diffusion, especially in metals and dilute alloys, and (iv) thermoelectric phenomena in ionic solids. The article does not deal with grain boundary or surface diffusion and does not specifically discuss diffusion-controlled chemical reactions, sintering or creep. Discussions of these aspects of the subject are given in the works listed in the bibliography.

https://iopscience.iop.org/article/10.1088/0034-4885/27/1/305/pdf

Matter transport in solids

Optical properties of small inorganic and organic metal particles

Publisher Summary This chapter reviews the advances in the understanding of diffusion in metals, with appreciable emphasis on the experimental as well as the theoretical accomplishments. The theory of diffusion has followed two main approaches: (1) the more general thermodynamic approach in which the diffusing material is treated as a continuous medium and the atomic nature of the jump process is ignored, (2) The kinetic approach where a physical description is considered in terms of atomic defect movements. The kinetic approach is adopted in this chapter although thermodynamic equations are discussed, where necessary, to show the relationship between the two approaches. The theoretical and experimental results for self-diffusion in pure crystals, impurity diffusion in pure crystals, effects of solute additions on self-diffusion, diffusion in concentrated alloys, diffusion in an electrical gradient, diffusion in a chemical concentration gradient, and diffusion in a thermal gradient are presented in the chapter.

Diffusion in Metals

Solid-state batteries potentially offer increased lithium-ion battery energy density and safety as required for large-scale production of electrical vehicles. One of the key challenges toward high-performance solid-state batteries is the large impedance posed by the electrode-electrolyte interface. However, direct assessment of the lithium-ion transport across realistic electrode-electrolyte interfaces is tedious. Here we report two-dimensional lithium-ion exchange NMR accessing the spontaneous lithium-ion transport, providing insight on the influence of electrode preparation and battery cycling on the lithium-ion transport over the interface between an argyrodite solid-electrolyte and a sulfide electrode. Interfacial conductivity is shown to depend strongly on the preparation method and demonstrated to drop dramatically after a few electrochemical (dis)charge cycles due to both losses in interfacial contact and increased diffusional barriers. The reported exchange NMR facilitates non-invasive and selective measurement of lithium-ion interfacial transport, providing insight that can guide the electrolyte-electrode interface design for future all-solid-state batteries.

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Accessing the bottleneck in all-solid state batteries, lithium-ion transport over the solid-electrolyte-electrode interface

The haven ratio in fast ionic conductors

Experimental results are presented for the diffusion of silver in silver bromide single crystals for temperatures from 140\ifmmode^\circ\else\textdegree\fi{}C to the melting point. The results are obtained by the sectioning technique, using radioactive tracers. The observed diffusion coefficients fall below the values that would normally be expected from the electrical conductivity by a factor of 0.46 to 0.66. The discrepancy is ascribed to the simultaneous occurrence of two types of interstitialcy jumps, with corrections introduced for differing displacements of interstitials and tracer atoms and for correlation effects according to Bardeen and Herring. The resulting mobilities can be represented as $\ensuremath{\mu}={\ensuremath{\mu}}_{0}\mathrm{exp}(\ensuremath{-}\frac{U}{\mathrm{kT}})$ over a wide range of temperatures with ${\ensuremath{\mu}}_{0}=6.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3} \mathrm{and} 1.57\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ${\mathrm{cm}}^{2}$/volt-sec and $U=0.078 \mathrm{and} 0.225$ ev, respectively, for collinear and non-collinear jumps. These values are in reasonable agreement with theoretical calculations for silver chloride. The diffusion coefficient is observed to fall increasingly below expected values as the temperature approaches the melting point, and as a possible explanation it is surmised that the activation energy for collinear jumps drops gradually towards zero. A comparison is made to similar results which have been reported for diffusion of silver in silver chloride.

Diffusion of Silver in Silver Bromide and Evidence for Interstitialcy Migration

Observations of the motion of ions by means of both diffusion and electrical conductivity measurements usually show deviations from the normal Einstein relation. The interpretation of these deviations often leads to a fairly detailed picture of the types of defects present and the mechanisms of their motion. A correction must always be considered because of the fact that successive jumps of a tracer atom are correlated, as first discussed by Bardeen and Herring, and the origin of this effect is shown by treating diffusion as a random walk problem. For the interstitialcy mechanism a second correction is required because the effective displacement is larger for conductivity than diffusion, and this effect is illustrated with results on AgCl and AgBr. Possible mechanisms for ionic motion in crystals with the CsCl structure are described, and the present interpretation of results for CsBr, CsI, and TlCl is discussed. It appears that vacancy pairs may make an appreciable contribution to the diffusion. Experime...

Robert J. Friauf

Papers

Diffusion of Silver in Silver Bromide and Evidence for Interstitialcy Migration

Correlation Effects for Diffusion in Ionic Crystals

Interstitialcy motion in the silver halides

Diffusion of vacancies and vacancy pairs in NaCl

Perturbation Calculations ofF-Center Wave Functions with Point Ion and Pseudopotentials