Coherency strain and its effect on ionic conductivity and diffusion in solid electrolytes – an improved model for nanocrystalline thin films and a review of experimental data

Abstract

A phenomenological and analytical model for the influence of strain effects on atomic transport in columnar thin films is presented. A model system consisting of two types of crystalline thin films with coherent interfaces is assumed. Biaxial mechanical strain ε₀ is caused by lattice misfit of the two phases. The conjoined films consist of columnar crystallites with a small diameter l. Strain relaxation by local elastic deformation, parallel to the hetero-interface, is possible along the columnar grain boundaries. The spatial extent δ₀ of the strained hetero-interface regions can be calculated, assuming an exponential decay of the deformation-forces. The effect of the strain field on the local ionic transport in a thin film is then calculated by using the thermodynamic relation between (isostatic) pressure and free activation enthalpy ΔG^#. An expression describing the total ionic transport relative to bulk transport of a thin film or a multilayer as a function of the layer thickness is obtained as an integral average over strained and unstrained regions. The expression depends only on known material constants such as Young modulus Y, Poisson ratio ν and activation volume ΔV^#, which can be combined as dimensionless parameters. The model is successfully used to describe own experimental data from conductivity and diffusion studies. In the second part of the paper a comprehensive literature overview of experimental studies on (fast) ion transport in thin films and multilayers along solid–solid hetero-interfaces is presented. By comparing and reviewing the data the observed interface effects can be classified into three groups: (i) transport along interfaces between extrinsic ionic conductors (and insulator), (ii) transport along an open surface of an extrinsic ionic conductor and (iii) transport along interfaces between intrinsic ionic conductors. The observed effects in these groups differ by about five orders of magnitude in a very consistent way. The modified interface transport in group (i) is most probably caused by strain effects, misfit dislocations or disordered transition regions.