Exploring the High-Pressure Equation of State in Earth’s Mantle with a Focus on the MgSiO<sub>3</sub>−MgO System

Issues » Volume 47, Issue 6

Exploring the High-Pressure Equation of State in Earth’s Mantle with a Focus on the MgSiO₃−MgO System

S. Gaurav$^{1}$, S. Shankar$^{2}$, Arvind Mishra$^{3}$, S. Kanwar$^{1}$, Pratibha K$^{1}$

$^{1}$Department of Applied Physics, Amity University, Amity Road, Sector 125, 122413 Noida, India
$^{2}$Experimental Research Laboratory, Department of Applied Physics, ARSD College, University of Delhi, Dhaula Kuan Enclave I, 110021 New Delhi, India
$^{3}$Department of Applied Science and Humanities, G. L. Bajaj Institute of Technology and Management, 201303 Noida, India

Received: 16.01.2024; final version - 25.09.2024. Download: PDF

The thermodynamic characteristics of the MgSiO₃−MgO system are determined using a modified form of the Shanker equation of state (EOS) known as the ‘Higher Order Shanker (HOS) EOS’. This adaptation incorporates higher-order terms into the Shanker EOS. The Higher Order Shanker (HOS) EOS is evaluated against Stacey criteria to ensure consistency in the variation of the pressure dependence of the isothermal bulk modulus. In a comparative analysis, the thermodynamic properties obtained from the Higher Order Shanker (HOS) EOS are contrasted with those derived from established classical EOS models, alongside electronic contribution analysis. This demonstrates the reliability of the proposed Higher Order Shanker (HOS) EOS for computing thermodynamic properties for similar systems under higher pressures. Furthermore, expressions for the bulk modulus and its pressure derivatives are formulated and extended to the theoretical limit of infinite pressure. These derived expressions are valuable for conducting more intricate analysis of higher-order thermoelastic properties.

Key words: equation of state, Stacey criteria, thermal expansion, Grüneisen parameter.

URL: https://mfint.imp.kiev.ua/en/abstract/v47/i06/0601.html

DOI: https://doi.org/10.15407/mfint.47.06.0601

PACS: 05.70.Ce, 62.20.de, 62.50.-p, 64.30.Jk, 65.40.De, 91.32.Gh, 91.60.Gf

Citation: S. Gaurav, S. Shankar, Arvind Mishra, S. Kanwar, and Pratibha K, Exploring the High-Pressure Equation of State in Earth’s Mantle with a Focus on the MgSiO₃−MgO System, Metallofiz. Noveishie Tekhnol., 47, No. 6: 601-617 (2025)

REFERENCES

O. L. Anderson, Equations of State of Solids for Geophysics and Ceramic Science (New York: NY: 1995; online edn, Oxford Academic: 2023).
F. D. Stacey, B. J. Brennan, and R. D. Irvine, Geophysical Surveys, 4, No. 3: 189 (1981).
F. D. Stacey, Rep. Prog. Phys., 73, No. 4: 046801 (2010).
A. Keane, Aust. J. Phys., 7, No. 2: 322 (1954).
F. D. Murnaghan, Proc. Natl. Acad. Sci., 30, No. 9: 244 (1944).
J. Shanker, K. Sunil, and B. S. Sharma, Phys. Earth Planet. Inter., 262: 41 (2017).
S. S. Kushwah and J. Shanker, Phys. B, 253, Nos. 1–2: 90 (1998).
F. D. Stacey, Phys. Earth Planet. Inter., 89, Nos. 3–4: 219 (1995).
S. Gaurav, S. Shankar, A. Raghav, P. Kumari, and M. Singh, Russ. J. Earth Sci., 22: 2 (2022).
P. Vinet, J. Ferrante, J. H. Rose, and J. R. Smith, J. Geophys. Res.: Solid Earth, 92, No. B9: 9319 (1987).
S. Gaurav, B. S. Sharma, S. B. Sharma, and S. C. Upadhyaya, Phys. B, 322, No. 3: 328 (2002).
R. Rydberg, Zeitschrift für Physik, 73: 376 (2013).
J. Shanker, B. Singh, and S. S. Kushwah, Phys. B, 229, Nos. 3–4: 419 (1997).
M. Born and K. Huang, Am. J. Phys., 23, No. 7: 474 (2005).
J. Hama and K. Suito, J. Phys.: Condens. Matter, 8, No. 1: 67, (1996).
J. Shanker, S. S. Kushwah, and M. P. Sharma, Phys. B, 271, Nos. 1–4: 158 (1999).
J. Shanker, B. P. Singh, and K. Jitendra, Condens. Matter. Phys., 11, No. 4: 681 (2008).
S. Rekha, K. Sunil and B. S. Sharma, High Temperatures – High Pressures, 46, Iss. 6: 449 (2017).
F. D. Stacey, J. Phys.: Condens. Matter, 11, No. 2: 575 (1999).
F. D. Stacey, Geophys. J. Int., 143, No. 3: 621 (2000).
T. S. Sokolova, P. I. Dorogokupets, K. D. Litasov, B. S. Danilov, and A. M. Dymshits, High Pressure Res., 38, No. 3: 193 (2018).
P. I. Dorogokupets, A. M. Dymshits, K. D. Litasov, and T. S. Sokolova, Sci. Rep., 7: 1 (2017).
K. Sunil, P. K. Singh, and B. S. Sharma, Mod. Phys. Lett. B, 26, No. 22: (2012).
J. Shanker, K. Sunil, and B. S. Sharma, Phys. B, 407, No. 12: 2082 (2012).
F. D. Stacey and P. M. Davis, Phys. Earth Planet. Inter., 142, Nos. 3–4: 137 (2004).
F. D. Stacey, Rep. Prog. Phys., 68: 341 (2005).
J. Shanker, K. Sunil, and B. S. Sharma, Phys. Earth Planet. Inter., 262: 41 (2016).
L. Knopoff, J. Geophys. Res., 68: 2929 (1963).
S. Gaurav, S. Shankar, Arvind Mishra, and S. P. Singh, Metallofiz. Noveishie Tekhnol., 45, No. 10: 1151 (2023).