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    Structural transformations in the (1−x)Na0.5Bi0.5TiO3−xBaTiO3 solid solution under high pressure: Comparison between x below and above the morphotropic phase boundary

    Constanze Rösche1,*, Thomas Malcherek1, Tiziana Boffa Ballaran2, Carsten Paulmann1, Ross John Angel3, Semën Gorfman4, and Boriana Mihailova1,†

    • *Contact author: constanze.roesche@uni-hamburg.de
    • †Contact author: boriana.mihailova@uni-hamburg.de

    Phys. Rev. B 112, 184102 – Published 3 November, 2025

    DOI: https://doi.org/10.1103/p74j-3j8p

    Abstract

    Single crystals of (1−x)Na0.5Bi0.5TiO3−xBaTiO3 (NBT−xBT) with a composition below (x=0.013) and above (x=0.074) the morphotropic phase boundary (MPB) were studied by in situ high-pressure x-ray diffraction with synchrotron radiation and Raman spectroscopy. We show that both compounds undergo a reversible pressure-induced phase transition to structures with Pnma symmetry, regardless of their symmetry at ambient conditions. The high-pressure phase resembles that recently reported for xMPB=0.048 [Sci. Rep. 14, 18799 (2024)], as the critical pressure pc gradually increases with x. However, the pathway of developing the high-pressure phase varies with the composition, revealing distinct ways of Ba incorporation into the NBT matrix for the pseudorhombohedral (x=0.013) and tetragonal (x=0.074) phases. For x<xMPB the Ba2+ cations are preferentially accommodated in the tetragonal-type nanodomains existing in the dominant pseudorhombohedral NBT matrix, whereas for x>xMPB, Ba2+ is dispersed in both the rhombohedral nanodomains and the dominant tetragonal matrix. Furthermore, for x=0.074 there are incommensurate structural modulations at ambient pressure, which up to pc remain unaffected by pressure, but vanish above pc.

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