A Three Parameter q-EoS for Solids under High Pressures
DOI:
https://doi.org/10.13102/sscf.v20i.11252Palavras-chave:
EoS Isotérmica, Três parâmetros, Alta pressão, SólidosResumo
Generalizamos aqui o principal resultado do trabalho anterior [1], a q-EoS, para uma ordem arbitrária n de um sólido submetido a altas pressões. É a conexão entre a deformação finita e o parâmetro q, este último no contexto da formulação matemática da Mecânica Estatística Não-Extensiva, como postulada por C. Tsallis [2], que permite desenvolver esta abordagem. Seguindo as linhas do trabalho anterior, determinamos a relação com o potencial interatômico q-deformado em ordem n. Também discutimos a conexão com o parâmetro de Grüneisen.
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Á.S. Alves, F.A. Farias, R.N. dos Santos, A Proposal of an Isothermal q-EoS for Solids at High Pressures. Sititentibus Ser. Cien. Fis. 20, 1 (2024).
C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479 (1988).
C. Tsallis, Nonextensive Statistics: Theoretical, Experimental and Computational Evidences and Connections. Braz. J. Phys. 29, (1) 1(1999).
J. Naudts, Deformed exponential and logarithms in generalized thermostatistics. Physica A 316, 323 (2002).
J. Naudts, Generalized thermostatistics based on deformed exponential and logarithm functions. Physica A 340, 32 (2004).
E.P. Borges, Manifestações Dinâmicas e Termodinâmicas de Sistemas Não-Extensivos. Tese de Doutorado (CBPF). Rio de Janeiro: CBPF (2004).
C. Tsallis, Introduction to Nonextensive Statistical Mechanics. New York: Springer-Verlag (2009).
C. Tsallis, Mecânica estatística de sistemas complexos. Rev. Bras. Ens. Fis. 43, Suppl. (1) e20200384 (2021).
F. D. Murnaghan, Finite Deformations of an Elastic Solid. Amer. J. Phys. 59, (20) 235 (1937).
F. D. Murnaghan, The Compressibility of Media under Extreme Pressures. Proc. Nat. Acad. 731 Sci. 30, 244 (1944).
F. D. Murnaghan, Finite Deformation of an Elastic Solid. New York: John Wiley and Sons (1951).
F. Birch, The Effect of Pressure Upon the Elastic Parameters of Isotropic Solids, According to Murnaghan’s Theory of Finite Strain. J. Appl. Phys. 9, 279 (1938).
F. Birch Finite Elastic Strain of Cubic Crystals. Phys. Rev. 716, (11) 809 (1947).
F. Birch, Elasticity and Constitution of the Earth’s Interior. J. Geophys. Res. 57, (2) 227 (1952).
F. D. Stacey, High pressure equations of state and planetary interiors. Rep. Prog. Phys. 68, 530 341 (2005).
F. D. Stacey, Equations of State for the Deep Earth: Some Fundamental Considerations. Minerals 9, (636) 1 (2019).
F. D. Stacey, The K-primed approach to high pressure equations of state. Geophys. J. Int. 143, 621 (2000).
L. V. Al’tshuler, S. E. Brusnikin, E. A. Kuz’menkov, Isotherms and Grüneisen functions for 25 metals. J. Appl. Mech. Tech. Phys. 28, 129 (1987).
A. Keane, An Investigation of Finite Strain in Isotropic Material Subjected to Hydrostatic Pressure and Its Seismological Applications. Australian J. Phys. 7, 323 (1954).
J. M. Walsh, R.H. Christian, Equation of State of Metals from Shock Wave Measurements. Phys. Rev. 97, (6) 1544 (1955).
L. Knopoff, The theory of finite strain and compressibility of solids. J. Geophys. Res. 68, 2929 (1963).
L. Knopoff, Equations of state of solids at moderately high pressures. New York: Academic Press (1965).
D. L. Anderson, A seismic equation of state. Geophys. J. Roy. Astro. Soc. 13, 9 (1967).
O. L. Anderson, On the Use of Ultrasonic and Shock Wave Data to Estimate the Compressions at Extremely High Pressures. Phys. Earth Planet. Int. 1, 169 (1968).
R. D. Irvine, F. D. Stacey, Pressure Dependence of the Thermal Grüneisen Parameter, with Application to the Earth’s Lower Mantle and Outer Core. Phys. Earth Planet. Int. 11, 157 564 (1975).
F. D. Stacey, B.J. Brennan, R. D. Irvine, Finite strain theories and comparison with seismological data. Geophys. Surv. 4, 189 (1981).
Y. Sato-Sorensen, Phase transitions and equations of state for the sodium halides: NaF, NaCl, NaBr, and NaI. J. Geophys. Res. 88, 3543 (1983).
H. S. Kim, E.K. Graham, D. E. Voigt, Elastic constants of single crystal wustite (FeO) and their pressure and temperature derivatives. Trans. Am. Geophys. Union (EOS) 69, 1407 (1988).
P. Vinet, J. H. Rose, J. Ferrante, J.R. Smith, Universal features of the equation of state of solids. J. Phys.: Condens. Matter 1, 1941 (1989).
D. L. Anderson, Theory of the Earth. Boston: Blackwell Scientific Publications (1989).
H. K. Mao, Y. Wu, L. C. Chen, J. F. Shu, A. P. Jephcoat, Static compression of iron to 300 GPa and Fe0.8Ni0.2 alloy to 260 GPa: Implications for composition of the core. J. Geophys. Res. 95, (B13) 21737 (1990).
O. L. Anderson, Equations of State of Solids for Geophysics and Ceramic Science. Oxford: Oxford University Press (1995).
T. J. Ahrens (Editor), Mineral Physics and Crystallography: a Handbook of Physical Constants. Washington: American Geophysical Union (1995).
F. D. Stacey, Theory of thermal and elastic properties of the lower mantle and core. Phys. Earth Planet. Int. 89, (3-4) 219 (1995).
M. Kumar, High pressure equation of state for solids. Physica B 212, 391 (1995).
W. B. Holzapfel, Physics of solids under strong compression. Rep. Prog. Phys. 59, 29 (1996).
J. Hama, K. Suito, The search for a universal equation of state correct up to very high pressures. J. Phys: Condens. Matter 8, (1) 67 (1996).
M. Taravillo, V. G. Baonza, J. Núñez, M. Cáceres, Simple equation of state for solids under compression. Phys. Rev. B 54, (10) 7034 (1996).
J. Shanker, B. Singh. S. S. Kushwah, On the high-pressure equation of state for solids. Physica B: Condensed Matter 229, (3-4) 419 (1997).
J. Shanker, S. S. Kushwah, P. Kumar, Equation of state and pressure derivatives of bulk modulus for NaCl crystal. Physics B 239, 337 (1997).
A. M. Hofmeister, IR spectroscopy of alkali halides at very high pressures: Calculation of equations of state and of the response of bulk moduli to theB1-B2 phase transition. Phys. Rev.B56,5835(1997).
J. -P. Poirier, A. Tarantola, A logarithmic equation of state. Phys. Earth Planet. Int. 109, (1-2)1(1998).
S. S. Kushwah, J. Shanker, A comparative study of equations of state for MgO. Physica B: Condensed Matter 253, (1-2) 90 (1998).
J. Shanker, S. S. Kushwah, M. P. Sharma. On the universality of phenomenological isothermal equations of state for solids. Physica B: CondensedMatter271, (1-4)158(1999).
J-P. Poirier, Introduction to the Physics of the Earth’s Interior. 2ndEdition. Cambridge: Cambridge University Press (2000).
P. B. Roy, S. B. Roy, An Isothermal Equation of State of Solid. Phys. Stat. Sol. B 226, (1)125 (2001).
F. D. Stacey, Finite Strain, thermodynamics and the earth’s core. Phys. Earth Planet. Int. 128, 179 (2001).
S. Gaurav, B. S. Sharma, S. B. Sharma, S. C. Upadhyaya, Analysis of equations of state for solids under high compressions. Physica B: Condensed Matter 322, (3-4) 328 (2002).
P. B. Roy, S. B. Roy, Applicability of three parameter equation of state of solids: compatibility with first principles approaches and application to solids. J. Phys.: Condens.Matter15, 643 (2003).
K. Sushil, K. Arunesh, P. K. Singh, B.S. Sharma, Analysis of finite-strain equations of state for solids under high pressures. Physica B 352,134 (2004).
F. D. Stacey, P. M. Davis, High pressure equations of state with applications to the lower mantle and core. Phys. Earth Planet. Int. 142, 137 (2004).
C. A. Perottoni, J. A. H. da Jornada, Artigo de Revisão: Física de Altas Pressões e a Câmara de Bigornas de Diamante. Rev. Fis. Aplicada e Instrumentação 17, (2) 39 (2004).
P. B. Roy, S. B. Roy, Applicability of isothermal three-parameter equations of state of solids- a reappraisal. J. Phys. Condens. Matter 17, 6193 (2005).
K. Arunesh, K. Dharmendra, Analysis of the generalised Rydberg equation of state. Physica B364,130(2005).
K. Fuchizaki, Murnaghan’s Equation of State Revisited. J. Phys. Soc. Japan 75, (3) 034601 672 (2006).
S. Speziale, S.R. Shieh, T.S. Duffy, High pressures elasticity of calcium oxide: A comparison between Brillouin spectroscopy and radial X-ray Diffraction. J. Geophys. Research 111,B02203 (2006).
F. D. Stacey, P. M. Davis, Physics of the Earth. 4th Edition. Cambridge: Cambridge University Press (2008).
Quan Liu, A New Isothermal Equation of State for Solids. Z. Naturforsch. 64a, 54 (2009).
H. C. Shrivastava, A Generalized pressure-volume equations mimicking the Stacey reciprocal K-prime equation of state. Physics B404, 251 (2009).
P. Sinha, S. K. Srivastava, N. Verma, Analysis of K-prime equations of state. Physics B406, 689 2488 (2011).
P. K. Vidyarthi, B. P. Singh, Analysis of the logarithm equation of state for materials at high pressures. Physica B410, 259 (2013).
G. L. Brovko, A Generalized Theory of Stress and Strain Measures in the Classical Continuum Mechanics. Moscow University Bulletin 73, (5) 117 (2018).
T. Katsura, Y. Tange, A Simple Derivation of the Birch-Murnaghan Equations of State (EOSs) and Comparison with EOSs Derived from Other Definitions of Finite Strain. Minerals 9, (745) 1 (2019).
F. D. Stacey, J. H. Hodgkinson, Thermodynamics with the Grüneisen parameter: Fundamentals and applications to high pressure physics and geophysics. Phys. Earth Planet. Inter. 286, 42 (2019).
R. Tomaschitz, Extension of finite-strain equations of state to ultra-high pressure. Phys. Lett 709 A393,127185 (2021).
S. P. Singh, J. Ram, Y. Kumar, A. Kumar, A. S. Guatam, A New Formulation of Generalized Equation of State (GEOs) based on Finite Strain Theory and Comparision with other Equations of State (EOSs). Indian Journal of Science and Technology 16, (12) 862 (2023).
M. Frost, D. Smith, E. E. McBride, J. S. Smith, S.H.Glenzer, The equations of state of statically compressed palladium and rhodium. J. Appl. Phys. 134, 035901 (2023).
E. Grüneisen, The State of a Solid Body. Translation from “Zustand des festen Körpers” by S. Reiss. Handbuch der Phys. 10, 1 (1926). Republication RE 2-18-59W. Washington: NASA (1959).
V. Y. Vashchenko, V. N. Zubarev, Concerning the Grüneisen Constant. Sov. Phys. Solid State (English Translation) 5, (3) 653 (1963).
J. C. Slater, Introduction to Chemical Physics. New York: McGraw-Hill, International Series in Physics (1939).
J. S. Dugdale, D. K. C. MacDonald, The Thermal Expansion of Solids. Phys. Rev. 89, (4) 832 (1953).
M. H. Rice, R. G. McQueen, J. M. Walsh, Compression of Solids by Strong Shock Waves. Solid State Phys. 6, 1 (1958).
D. L. Anderson, A seismic equation of state. Geophy. J. Roy. AStr. Soc. 13, 9 (1967).
V. N. Zharkov, V. A. Kalinin, Equations of State for Solids under High Pressures and Temperatures. Translated from Russian by A. Tybulewicz. New York: Springer Science+Business Media (1971).
M. A. Barton, F. D. Stacey, The Grüneisen parameter at high pressure: a molecular dynamical study. Phys. Earth Planet. Int. 39, 167 (1985).
O. L. Anderson, D. G. Isaak, The Dependence of the Anderson-Grüneisen parameter upon compression at extreme conditions. J. Phys. Chem. Solids 54, 221 (1993).
S.B. Segletes, Further Examinations on the Thermodynamics Stability of the Mie-Grüneisen Equation of State. J. Appl. Phys. 6, (8) 4560 (1994).
V. Gospodinov, Equations of state for solids at high pressures and temperatures from shockwave data. arXiv:cond-mat/9911407v2 [condmat.mtrl - sci] 26 Nov (1999).
O.L. Anderson. The Grüneisen ratio for the last 30 years. Geophys. J. Int. 143, 279 (2000).
J. Shanker, S. S. Kushwah, K. Jitendra, Analysis of thermal expansivity of solids at extreme compression. Condensed Matt. Phys. 11, 681 (2008).
G. Nand, M. Kumar, Temperature dependence of bulk modulus of minerals using equation of state. Indian J. Pure Appl. Phys. 47, (12) 867 (2009).
V. Gospodinov, Volume dependence of the Grüneisen ratio for shock-wave equation of state studies. arXiv:cond-mat/1404.1041v1 [cond-mat.mtrl-sci] 6 Jan (2014).
S. Rekha, K. Sunil, B. S. Sharma, Equations of state, thermal expansivity, and Grüneisen parameter for MgO at high temperatures and high pressures. High Temperatures–High Pressures 46, (6) 449 (2017).
J. Shanker, K. Sunil, B. S. Sharma, The Grüneisen parameter and its higher order derivatives for the Earth lower mantle and core. Phys. Earth Planet. Int. 262, 41 (2017).
F. D. Stacey, J. H. Hodgkinson, Thermodynamics with the Grüneisen parameter: Fundamentals and applications to high pressure physics and geophysics. Phys. Earth Planet. Int. 286, 42 (2019).
D. E. Gray (Editor). American Institute of Physics Handbook. New York: McGraw-Hill Book Company (1972).
R. J. Hemley (Editor), Ultrahigh-Pressure Mineralogy – Physics and Chemistry of the Earth’s Deep Interior. Review in Mineralogy, vol. 37. Washington: The Mineralogical Society of America (1998).
C. Kittel, Introduction to Solid State Physics. 8th Edition. New Jersey: John Wiley & Sons (2005).
Á.S. Alves, F.A. Farias, R.N.dos Santos, FisCampus Brief Report Nº 01/2024 (Internal Publication). March, 11 (2024).
Á.S. Alves, F.A. Farias, R.N.dos Santos, FisCampus Brief Report Nº 05/2023 (Internal Publication). December, 11 (2023).
Á.S. Alves, F.A. Farias, R.N.dos Santos, FisCampus Brief Report Nº 02/2024 (Internal Publication). Jun, 24 (2024).
Á.S. Alves, F.A. Farias, R.N.dos Santos, FisCampus Brief Report Nº 04/2024 (Internal Publication). To be released.
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Copyright (c) 2024 Álvaro Santos Alves, Franz A. Farias, Rodrigo Neves dos Santos

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