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Frustrated microstructures composite PbS material’s size perspective from XRD by variant models of Williamson–Hall plot method

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Abstract

The coherent crystalline domain size of a particle is well understood and investigable from the broadening of X-ray diffraction (XRD) peaks by Williamson–Hall (WH) method in connection with a strain, and it has a correlation with the strain, stress, energy density, defects/dislocations. The coherent domain size of binary semiconducting material particles is being interlinked with the applications like sensors, solar systems, photo-detectors, photocatalyst, etc. In this work, the frustrated microstructure of PbS elucidated the perspective of different models of the WH method. Frustrated microstructural PbS nanomaterial was prepared, confirmed and rendered its microstructural analysis from the XRD data and scanning electron microscope. Eight various approaches as the variant models of the Williamson–Hall plotting methods have been tested. It includes the models like Balzar approach, UDM, USDM, UDEDM, mWHP model, Ehkl/E0 ratio model, direct fitting of simplified WH model with introducing new approach and the modified Kibasomba-WH model, which uses linearization of Scherrer equation with the WH method. This study lightens the USDM and UDEDM sizes in an account of a Zener constant. The other non-WH methods like the Scherrer formula method, modified Scherrer method, stress–strain methods and Halder–Wagner method are also included for comparison and to see their status in a cluster of frustrated structures. The sizes in connection with strain, stress, energy density, dislocation and stacking fault have also been investigated for the frustrated PbS nanomaterial.

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Acknowledgements

First author is thankful to Dr P R Arjunwadkar, Dr C M Dudhe and Dr R R Patil, Institute of Science, Nagpur, on meaningful discussion on concerned topics and criticizing the presented methods. We are also thankful to CELREF and EIVISE software’s authors and developers.

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Authors and Affiliations

  1. Maitreya, Modern School, Nagpur, 441111, India

    Nishant T Tayade

  2. Department of Physics (Formerly), Institute of Science, Nagpur, 440001, India

    Nishant T Tayade

  3. Department of Physics, Annasaheb Vartak College of Arts, K.M. College of Commerce and E.S. Andrades College of Science (affiliated to University of Mumbai), Palghar, 401202, India

    Manish P Tirpude

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  1. Nishant T Tayade
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  2. Manish P Tirpude
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Correspondence to Manish P Tirpude.

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Tayade, N.T., Tirpude, M.P. Frustrated microstructures composite PbS material’s size perspective from XRD by variant models of Williamson–Hall plot method. Bull Mater Sci 46, 20 (2023). https://doi.org/10.1007/s12034-022-02843-w

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