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Specific Heat and its Related Parameters in Si Nanoparticles

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Abstract

The specific heat for Si nanoparticles is calculated from the nanosize dependence of the Gruneisen parameter using the Gruneisen equation, which includes lattice thermal expansion, lattice volume, and bulk modulus. The results were comparable to the size dependent lattice volume under hydrostatic pressure. The reduction in specific heat from its bulk value to near zero for nanoparticles of critical size is comparably explained according to that of thermal expansion. The size dependent vibrational frequency derived from the nanosize dependent Gruneisen parameter, as well as the size dependent mean square atomic displacement and atomic spring constant, are used to evaluate the findings. Additionally, the nanosize dependent melting temperature and lattice anharmonicity are described using the Lennard–Jones equation principles. Lastly, whereas MSD decreases to zero at the critical size of solid nanoparticles, melting occurs at zero temperature.

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Acknowledgements

Authors would like to acknowledge the financial support under grand no. (3/1/39-212022) from College of Science at the Salahaddin University-Erbil in Kurdistan Region, Iraq.

Funding

This work was fully funded by the College of Science in the University of Salahaddin-Erbil (Grant number3/1/39–212022).

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Authors and Affiliations

  1. Department of Physics, College of Science, Salahaddin University-Erbil, Kurdistan Region, Erbil, 44001, Iraq

    M. S. Omar & Botan Jawdat Abdullah

  2. Department of Physics, College of Education, Salahaddin University-Erbil, Erbil, 44001, Kurdistan Region, Iraq

    Ayoub Sabir Karim

  3. Department of General Science, Charmo University, Kurdistan Region, Sulaimani, 46001, Iraq

    Sirwan Karim Jalal

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  1. M. S. Omar
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  2. Botan Jawdat Abdullah
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  4. Sirwan Karim Jalal
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [Mustafa Saeed Omar], [Botan Jawdat Abdullah], [Ayoub Sabir Karim] and [Sirwan Karim Jalal]. All authors read and approved the final manuscript.

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Correspondence to Botan Jawdat Abdullah.

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Omar, M.S., Abdullah, B.J., Karim, A.S. et al. Specific Heat and its Related Parameters in Si Nanoparticles. Silicon 15, 4049–4056 (2023). https://doi.org/10.1007/s12633-023-02316-7

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  • DOI: https://doi.org/10.1007/s12633-023-02316-7

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