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. 2022 Sep 9;12:15242. doi: 10.1038/s41598-022-19552-3

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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(a) Pseudo first-order and pseudo second-order kinetic models for degradation of 10 ppm MB in presence of sample S4 as catalyst and ZrO₂ balls with 350 RPM in speed at different temperatures: 20 °C (black curve), 40 °C (red curve), and 70 °C (blue curve). (b) LNK Vs 1/T Plot for the experimental data for the evaluation of thermodynamic Parameters of the degradation of MB. (c) Activation energy for decomposition of MB by piezo catalyst based on Arrhenius equation.