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Theoretical Prediction for Thermo-Elastic Properties of TiO2 (Rutile Phase)

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Abstract

The equation of state plays a crucial role in calculating the elastic properties of nano TiO2 (Rutile phase). In this study, we used three different equations of state, namely Birch Murnaghan 3rd EOS, modified Lenard Jones EOS, and Vinet–Rydberg EOS to investigate the thermoelastic properties of titanium dioxide under high pressure. The obtained results for pressure calculations at different values of V/V0 are in good agreement with available experimental data, indicating that these EOSs can be used for calculating the thermoelastic properties of nanomaterials as well. In this research, we established the bulk modulus, first pressure derivative of bulk modulus, and the Grüneisen parameter. The theoretically calculated results were compared with the available data, and it was found that the ratio of γ/Ω (where Ω = V/V0), i.e., the variation of Grüneisen parameter with volume compression ratio remains constant for solids.

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References

  1. Al Shekh AM, Kareem S, Mawllod S (2022) Theoretical high pressure study of phonon density of state and Debye temperature of solid C60: Grüneisen approximation approach. Int J Thermodyn 25:10

    Article  Google Scholar 

  2. Al Sheikh AM, Al-Faris SJ, Jalal SK (2022) Grüneisen parameter variation consideration in theoretical high-pressure studies for C60. Iran J Sci Technol Trans Sci 46:689

    Article  Google Scholar 

  3. Jalal SK, Al-Sheikh AM, Al-Saqa RH (2021) High pressure effects on the phonon frequency spectrum of silicon nanoparticle. Iran J Sci Technol Trans Sci 45:391

    Article  Google Scholar 

  4. Kareem S, Mawllod S (2020) Size dependent thermodynamic properties of nanoparticles. Int J Thermodyn 23(4):245

    Article  Google Scholar 

  5. Liu LG (1978) A fluorite isotype of SnO2 and a new modification of TiO2: implications for the Earth’s lower mantle. Science 199:422

    Article  ADS  CAS  PubMed  Google Scholar 

  6. Su C, Hong BY, Tseng CM (2004) Sol–gel preparation and photocatalysis of titanium dioxide. Catal Today 96:119

    Article  CAS  Google Scholar 

  7. Banfield JF, Zhang H (2001) Nanoparticles and the environment—an introduction. Rev Mineral Geochem 44:01

    Article  CAS  Google Scholar 

  8. Chen HS, Su C, Chen JL, Yang TY, Hsu NM, Li WR (2011) Preparation and characterization of pure rutile TiO2 nanoparticles for photocatalytic study and thin films for dye-sensitized solar cells. J Nanomater 2011:1

    Article  Google Scholar 

  9. Swamy V et al (2003) Compression behavior of nanocrystalline anatase TiO2. Solid State Electron 125:111

    CAS  Google Scholar 

  10. Sun J (2005) A modified Lennard–Jones-type equation of state for solids strictly satisfying the spinodal condition. Phys Condens Matter 17(12):L103

    Article  Google Scholar 

  11. Birch F (1947) Finite elastic strain of cubic crystals. Phys Rev 71:809

    Article  ADS  CAS  MATH  Google Scholar 

  12. Vinet P, Ferrante J, Smith JR, Rose JH (1986) A universal equation of state for solids. J Phys C 92:467

    Article  Google Scholar 

  13. Vinet P, Ferrante J, Rose J, Smith JR (1987) Compressibility of solids. J Phys Res 19:9319

    Article  ADS  Google Scholar 

  14. Barton MA, Stacey FD (1985) The Grüneisen parameter at high pressure: a molecular dynamical study. Phys Earth Planet Interior 39:167

    Article  ADS  CAS  Google Scholar 

  15. Olsen JS, Gerard L, Jiang JZ (2002) High-pressure behavior of nano titanium dioxide. High Press Res 22:385

    Article  ADS  Google Scholar 

  16. Stacey FD (1995) Theory of thermal and elastic properties of the lower mantle and core. Phys Earth Planet Interiors 89:219

    Article  ADS  Google Scholar 

  17. Boehler R (1983) Melting temperature, adiabats, and Grüneisen parameter of lithium, sodium and potassium versus pressure. Phys Rev B 11:6754

    Article  ADS  Google Scholar 

  18. Ghazal AI, Al-Sheikh AM (2021) Thermo elastic properties of nano-TiO2 under high pressure using different equations of state. J Phys Phys Conf Ser 1999:012075

    Article  CAS  Google Scholar 

  19. Srivastava S, Pandey AK, Dixit CK (2023) Theoretical prediction of Grüneisen parameter for γ-Fe2O3. Comput Condens Matter 35:e00801

    Article  Google Scholar 

  20. Srivastava S, Pandey AK, Dixit CK (2023) Theoretical prediction for thermo elastic properties of carbon nanotubes (CNTs) at different pressure or compression using equation of states. J Math Chem 61:2098–2104

    Article  MathSciNet  CAS  MATH  Google Scholar 

  21. Srivastava S, Dixit CK, Pandey AK. Comparative study of elastic properties of some inorganic and organic molecular crystals by using isothermal EOS. SSRN. http://ssrn.com/abstract=4427891 or https://doi.org/10.2139/ssrn.4427891

  22. Pandey AK, Singh P, Srivastava S, Tripathi S, Dixit CK (2023) Theoretical prediction of Grüneisen parameter for nano Lead sulfide at different compressions. J Nanomater Mol Nanotechnol 12:2

    Google Scholar 

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Authors and Affiliations

  1. Institute of Engineering and Technology, Dr. Shakuntala Misra National Rehabilitation University, Lucknow, Uttar Pradesh, India

    Anjani K. Pandey

  2. Department of Physics, Dr. Shakuntala Misra National Rehabilitation University, Lucknow, Uttar Pradesh, India

    Chandra K. Dixit, Shivam Srivastava, Prachi Singh & Shipra Tripathi

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  1. Anjani K. Pandey
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  2. Chandra K. Dixit
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  3. Shivam Srivastava
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  4. Prachi Singh
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  5. Shipra Tripathi
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Correspondence to Anjani K. Pandey.

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Author and co authors of this manuscript have no involvement in any organization or affiliations with or entity with any financial interest or non-financial interest in the subject matter or nanomaterials discussed in this manuscript.

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Pandey, A.K., Dixit, C.K., Srivastava, S. et al. Theoretical Prediction for Thermo-Elastic Properties of TiO2 (Rutile Phase). Natl. Acad. Sci. Lett. (2023). https://doi.org/10.1007/s40009-023-01358-0

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  • DOI: https://doi.org/10.1007/s40009-023-01358-0

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