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.

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Interface strain and its influence on the ionic transport along hetero-interfaces has gained a lot of attention over the last decade and is controversially discussed. We investigate the relaxation of mismatch induced interfacial strain as a function of the degree of orientation/texture of the columnar crystallites and assess the impact on the oxygen ion conductivity in Er2O3/YSZ multilayer systems. Results from X-ray diffraction clearly show, that the width of the strained hetero-interface region increases with an increasing degree of orientation of the crystallites. The combined impact of film texture and strain at the hetero-interfaces of the film on the ionic conductivity however is not easily deduced from these measurements. The samples with the highest degree of orientation, i.e. with only one azimuthal variant, show strong anisotropic electrical properties. In samples with a lower degree of orientation, i.e. samples with a fiber texture, anisotropic properties cannot be detected, possibly due to a geometrical averaging of the electrical properties. The expected strain induced monotonic increase of the ionic conductivity with decreasing layer thickness and thus increasing interfacial influence could only be detected for samples with a fiber texture and a considerable degree of crystallite misorientation. This leads to the important conclusion that the texture and therefore the nature of the grain boundaries and their network influence the ionic conductivity of the multilayer thin films in the same order of magnitude as the misfit induced interface strain. Thus, the potential design of strain-controlled ionic conductors requires additionally the control of the microstructure in terms of grain orientation.

In this study the strain states in alternating multilayers of an extrinsic O2− ion conductor yttria stabilized zirconia (YSZ) and an insulator RE2O3 (RE = Er, Y) are investigated as a function of the layer thickness. Multilayers with narrow columnar crystallites and coherent phase boundaries were grown by pulsed laser deposition (PLD). A detailed strain analysis is performed by X-Ray Diffraction XRD, measuring distinct reflections in and perpendicular to the interface planes. Because of small columnar crystallites in the layers, the interfacial strain decays by shear with increasing distance from the interface. The extent of the strained interface regions in the YSZ layers is estimated from XRD data. By using a quantitative analytical model based on the pressure dependence of the free migration enthalpy for vacancies the results are compared to former published experimental data on O2− ion conductivity and diffusion.