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    Coexisting commensurate and incommensurate cation ordering in the disordered rocksalt NaPb2SbS4 semiconductor

    Stavros Kozakos1, Nikolaos Vouroutzis1, Tyler J. Slade2,3, Hyungseok Lee2, Mercouri G. Kanatzidis2,*, and Nikolaos Frangis1,†

    • *Contact author: m-kanatzidis@northwestern.edu
    • †Contact author: frangis@auth.gr

    Phys. Rev. Materials 10, 064601 – Published 5 June, 2026

    DOI: https://doi.org/10.1103/3w11-zch3

    Abstract

    An electron diffraction (ED) and high-resolution transmission electron microscopy (HRTEM) study of the semiconductor system 2PbS+NaSbS2 (NaPb2SbS4) reveals strikingly complex, nanostructural properties despite its simple NaCl-type framework. We uncover the coexistence of commensurate and incommensurate cation ordering, nanoscale defect architectures, and quasiperiodic arrays of antiphase boundaries. In many areas, the dominant observed structure type corresponds to the NaCl type, with varying lattice parameters, denoting inhomogeneities in composition. In other areas, superstructure reflections were observed in the ED patterns. The HRTEM images reveal the existence of different nanocrystals, with long-range ordering of the cations. Three different commensurate modulated structures (superstructures) of the NaCl type of structure were observed. All the nanocrystals with ordering were observed to grow endotaxially within the matrix. Moreover, the local arrangement of several defects (orientation variants and antiphase boundaries) in a quasiperiodic way leads to the local formation of incommensurate modulated structures. Finally, in some cases, diffuse scattering intensity was observed in the ED patterns. The HRTEM images, together with the ED results, reveal a transition state between the phases with long- and short-range order. These findings clarify the structural behavior of this complex semiconductor and motivate further investigation of its structural and physical properties.

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