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The possibilities of modelling the diffraction profiles from bimodal microstructure in computer program MSTRUCT are demonstrated on two examples. A special “Double Component” profile effect can be utilized for such problems. At first it was applied to an analysis of a mixture of two nanocrystalline anatase powders with different crystallite sizes and the relative ratio of both components was determined from X-ray diffraction data. In the second case study, diffraction peaks from a pure polycrystalline copper sample treated by equal channel angular pressing were fitted using a two-phase model of large recrystallized defect-free grains and ultrafine crystallites with high dislocation density. The method is shown to be suitable for determination of the relative fraction of the microstructural components as well as other parameters (e.g. dislocation density).

We study the Anderson single-level quantum dot attached to two BCS superconducting leads with the same gap size. We reveal that a system with asymmetric tunnel coupling to the leads (ΓL = ΓR) can be related to the symmetric system with the same net coupling strength Γ = ΓL +ΓR. Surprisingly, it is the symmetric case which is the most general, meaning that all physical quantities in case of asymmetric coupling are fully determined by the symmetric ones. We give ready-to-use conversion formulas for the 0 − π phase transition boundary, on-dot quantities, and the Josephson current, and illustrate them on the NRG results of Oguri, Tanaka and Bauer [Phys. Rev. B 87, 075432 (2013)] for the three-terminal setup. We apply our theory to the recent 0 − π transition measurement of Delagrange et al. [Phys. Rev. B 93, 196437 (2016)] and determine the asymmetry of the experimental setup from the measured transition width. Finally, we establish that the widely assumed Kondo "universality" of physical quantities depending only on the ratio of the Kondo temperature and the superconducting gap TK /∆ cannot hold for asymmetric junctions.

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