A new model for X-ray scattering from thin films of layered crystals containing defects

What is it about?

This paper describes a new theoretical model for the effects that defects have on the X-ray diffraction patterns from thin films of layered materials. This is done with specific reference to the Aurivillius family of layered ferroelectric oxide materials. This structure has ‘m’ blocks with the perovskite structure and general formula [Am-1BmO3m+1]2+ interspersed with fluorite-structured [Bi2O2]2- layers. This is a bit like a crystalline “mille-feuille” pastry-cake, where the pastry layers are the fluorite layers and the cream & fruit represent the perovskite blocks. Examples of the family include SrBi2Ta2O9 (SBT) with m = 2 and bismuth titanate (BiT) Bi4Ti3O12 with m = 3. Any layered crystal structure brings with it the potential for the generation of a variety of crystalline defects, including regions where the layers of the structure are out-of-registry. Examples of such defects include out-of-phase boundaries (OPBs) and stacking faults. It is important that we have an understanding of the ways these defects occur in layered materials, especially in relation to crystal growth, and how they affect film properties. Developing such an understanding will be vital for future applications, especially in the electronics industry. Traditionally, cross-sectional transmission electron microscopy has been the tool-of-choice for characterising these defects, but this is inherently destructive and only examines very small areas. X-ray diffraction is a much easier characterization tool to use. It is non-destructive and can look at large areas of the sample. It has been noted by previous workers that OPBs affect the X-ray diffraction patterns from thin films containing them in quite specific ways, especially through the splitting of particular diffraction peaks. However, until now there has been no theory that could explain which peaks would be split, or how the characteristics of the peak splitting relate to the structural parameters describing the defects. Such parameters include the magnitude of the step at the defect boundary and the defect spatial density. This paper presents, for the first time, an analytical theory that explains these relationships and applies it to the OPBs occurring in thin films of SBT and BiT. Good agreement between theory and experiment has been demonstrated.

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Photo by amirali mirhashemian on Unsplash

Photo by amirali mirhashemian on Unsplash

Why is it important?

Materials with layered crystal structures are ubiquitous in nature, and many of them have found important applications. Examples include: The clay minerals such as kaolinite, widely used in industrial applications such as ceramics, the paper industry and cosmetics; Transition metal dichalcogenides such as MoS2, which are showing great promise for future transistors, sensors and energy storage; The layered cuprates such as yttrium barium copper oxide that are high-temperature superconductors and are now being applied in superconducting magnets. The Aurivillius ferroelectrics have applications in high temperature piezoelectric sensors, non-volatile memories and photocatalysis. Recently, examples of Aurivillius compounds containing transition metal ions such as Fe and Mn have been shown to "multiferroics", coupling ferroelectricity with ferromagnetism. These offer new possibilities for applications in low-power non-volatile memories. The theoretical model presented in the paper is general and should be easily applicable to describing the X-ray diffraction patterns from thin films of any layered structure containing OPBs. Examples of other layered structures where it might be applied include Ruddlesden Popper phases which have potential applications in solar cells, energy storage and catalysis.

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