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A Proposal of an Isothermal q-EoS for Solids at High Pressures

Autores

DOI:

https://doi.org/10.13102/sscf.v20i.10804

Palavras-chave:

EoS Isotérmica, Deformação Finita, Alta Pressão, Sólidos

Resumo

Apresentamos uma nova abordagem para a equação de estado isotérmica para sólidos quando estão submetidos a altas pressões. A questão central reside no fato que um sólido submetido a altas pressões exibe um comportamento elástico não-linear. Mostramos como a conexão entre a teoria de deformação finita q-deformada e o formalismo matemático da Mecânica Estatística Não-Extensiva, proposta por Tsallis [1], nos permite alcançar uma equação de estado q-deformada. Também estabelecemos o potencial interâtomico q-deformado associado e discutimos sua relação com o parâmetro de Grüneisen.

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Biografia do Autor

Álvaro Santos Alves, Departamento de Física (UEFS)

Doutor em Física (2011) pela Universidade Federal Fluminense. Atualmente, ocupa o cargo de professor adjunto da Universidade Estadual de Feira de Santana. Tem experiência na área de Física da Matéria Condensada, com ênfase em modelagem teórico-computacional das propriedades estruturais, eletrônicas e magnéticas de magnetos moleculares. Além disso, atua também em Física Experimental e em Ensino de Física. É membro do Grupo de Pesquisa: Física no Campus (DFIS-UEFS).

Franz A. Farias, Departamento de Física (UEFS)

Doutor em Ciências (Física) (2005) pela Universidade Federal do Rio de Janeiro. Atualmente é Professor Adjunto do Departamento de Física da Universidade Estadual de Feira de Santana (DFIS-UEFS). Tem atuado na área de Física com ênfase em Teoria Geral de Partículas e Campos, Física Matemática e Física da Matéria Condensada, atuando principalmente nos temas: Formulação Hamiltoniana de Teorias de Gauge e Geometria Não Comutativa e Tópicos de Física da Matéria Condensada (Equação de Estado dos Sólidos). É membro do Grupo de Pesquisa: Física no Campus (DFIS-UEFS).

Rodrigo Neves dos Santos, PPG-Intituto de Física (UFBA)

Graduou-se em Física pela Universidade Estadual de Feira de Santana em 2017 e obteve seu mestrado em Física pela Universidade Federal da Bahia em 2019. É doutorando no Programa de Pós-Graduação do Instituto de Física da Universidade Federal da Bahia. Tem trabalhado em DFT aplicada a sistemas magnéticos com ênfase em ímãs moleculares. É membro do Grupo de pesquisa: Física no Campus (DFIS-UEFS).

Referências

C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479 (1988).

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 (1975).

F.D. Stacey, B.J. Brennan, R.D. Irvine, Finite strain theories and comparasion 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).

H.K. Mao, Y. Wu, L.C. Chen, J.F. Shu, A.P. Jephcoat, Static compression of iron to 300 GPa and Fe_{0.8}Ni_{0.2} 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 the B1-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 Matter253, (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: Condensed Matter 271, (1-4) 158 (1999).

F.D. Stacey, The K-primed approach to high-pressure equations of state. Geophys. J. Int. 143, 621 (2000).

J-P. Poirier, Introduction to the Physics of the Earth's Interior. 2nd Edition. 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, textit{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 priciples approaches and application to solids. J. Phys.: Condens. Matter 15, 1643 (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).

F.D. Stacey, High pressure equations of state and planetery interiors. Rep. Prog. Phys. 68, 341 (2005).

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 B 364, 130 (2005).

K. Fuchizaki, Murnaghan's Equation of State Revisited. J. Phys. Soc. Japan 75, (3) 034601 (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).

Quan Liu, A New Isothermal Equation of State for Solids. Z. Naturforsch. 64a, 54 (2009).

H.C. Shrivastava, Generalized pressure-volume equations mimicking the Stacey reciprocal K-prime equation of state. Physics B 404, 251 (2009).

P. Sinha, S.K. Srivastava, N. Verma, Analysis of K-prime equations of state. Physics B 406, 2488 (2011).

P.K. Vidyarthi, B.P. Singh, Analysis of the logarithm equation of state for materials at high pressures. Physica B 410, 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, Equations of State for the Deep Earth: Some Fundamental Considerations. Minerals 9, (636) 1 (2019).

R. Tomaschitz, Extension of finite-strain equations of state to ultra-high pressure. Phys. Lett A 393, 127185 (2021).

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).

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).

Lord Kelvin, A New Specifying Method for Stress and Strain in an Elastic Solid. Phil. Mag (Series 6) 3, 95 and 444 (1902).

A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity. Fourth Edition. Cambridge: Cambridge University Press (1927).

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. Sci. 30, 244 (1944).

F.D. Murnaghan, Finite Deformation of an Elastic Solid}. New York: John Wiley and Sons (1951).

A.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).

A.F. Birch Finite Elastic Strain of Cubic Crystals. Phys. Rev. 716, (11) 809 (1947).

A.F. Birch, Elasticity and Constitution of the Earth's Interior. J. Geophys. Res. 57, (2) 227 (1952).

A. Keane, An Investigation of Finite Strain in Isotropic Material Subjected to Hydrostatic Pressure and Its Seismological Applications. Australian J. Phys. 7, 323 (1954).

C. Kittel, Introduction to Solid State Physics. 8th Edition. New Jersey: John Wiley & Sons (2005).

M.D. Knudson, M.P. Desjarlais, Shock Compression of Quartz to 1.6 TPa: Redefining a Pressure Standard. Phys. Rev. Lett. 103, 225501 (2009).

S.B. Roy, P.B. Roy, An equation of state applied to solid up to 1 TPa. J. Phys.: Condens. Matter 11, 10375 (1999).

J.M. Walsh, R.H. Christian, Equation of State of Metals from Shock Wave Measurements. Phys. Rev. 97, (6) 1544 (1955).

D.E. Gray (Editor). American Institute of Physics Handbook. New York: McGraw-Hill Book Company (1972).

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).

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).

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).

J. Naudts, Generalized thermostatistics based on deformed exponential and logarithm functions. Physica A 340, 32 (2004).

A.N. Aheart, On the Direct Solution of Bernoulli's Equation. Classroom Notes. Amer. Math. Monthly 58, (10) 696 (1951).

A.E. Parker, Who solved the Bernoulli differential equation and how did they do it?. The College Mathematical Journal 44, (2) 1 (2013).

E.P. Borges, Manifestações Dinâmicas e Termodinâmicas de Sistemas Não-Extensivos. Tese de Doutorado (CBPF). Rio de Janeiro: CBPF (2004).

F.D. Stacey, P.M. Davis, Physics of the Earth. 4th Edition. Cambridge: Cambridge University Press (2008).

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, Theory of the Earth. Boston: Blackwell Scientific Publications (1989).

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).

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).

V.Y. Vashchenko, V.N. Zubarev, Concerning the Grüneisen Constant. Sov. Phys. Solid State (English Translation) 5, (3) 653 (1963).

S.B. Segletes, Further Examinations on the Thermodynamics Stability of the Mie-Grüneisen Equation of State. J. Appl. Phys. 76, (8) 4560 (1994).

D.L. Anderson, A seismic equation of state. Geophy. J. Roy. AStr. Soc. 13, 9 (1967).

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).

V. Gospodinov, Equations of state for solids at high pressures and temperatures from shock-wave data. arXiv:cond-mat/9911407v2 [cond-mat.mtrl-sci] 26 Nov (1999).

O.L. Anderson. The Grüneisen ratio for the last 30 years. Geophys. J. Int. 143, 279 (2000).

S.B. Segletes, A Concise Physical Interpretation of Several Analytical Grüneisen Formulations}. U.S. Army Research Laboratory. Report ARL-TL-3881 (2006).

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 og bulk modulus of minerals using equation of state. Indian J. Pure Appl. Phys. 47, 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).

Á.S. Alves, F.A. Farias, R.N. dos Santos, FisCampus Brief Report Nº 01/2023 (Internal Publication). July, 31 (2023).

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 04/2023 (Internal Publication). November, 27 (2023).

Publicado

21-10-2024

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Como Citar

Alves, Álvaro S., A. Farias, F., & Neves dos Santos, R. (2024). A Proposal of an Isothermal q-EoS for Solids at High Pressures. Sitientibus Série Ciências Físicas, 20, 1–14. https://doi.org/10.13102/sscf.v20i.10804

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Física da Matéria Condensada
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