To the Question of Validity Grüneisen Solid State Equation


The first justified theory of solid state was proposed by Grüneisen in the year 1912 and was based on the virial theorem. The forces of interaction between two atoms were assumed as changing with distance between them according to inverse power laws. But only virial theorem is insufficient to deduce the equation of state, so this author has introduced some relations, which are correct, when the forces linearly depend on displacement of atoms. But with such law of interaction the phase transitions cannot take place. Debye received Grüneisen equation in another way. He deduced the expression for thermocapacity, using Plank formula for energy of harmonic vibrator. Taking into account the dependence of atomic vibration frequency from distance between atoms, when the forces of interaction are anharmonic, he received the equation of state, which in classical limit turns to Grüneisen equation. The question, formulated by Debye is—How can we come to phase transitions, when Plank formula for harmonic vibrator was used? Debye solved this question not perfectly, because he was born to small anharmonicity. In the presented work a chain of atoms is considered, and their movement is analysed by means of relations, equivalent to virial theorem and theorem of Lucas (disappearing of mean force). Both are the results of variation principle of Hamilton. The Grüneisen equation for low temperature (not very low, where quantum expression for energy is essential) was obtained, and a family of isotherms and isobars are drown, which show the existence of spinodals, where phase transitions occur. So, Grüneisen equation is an equation of state for low temperatures.

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V. Kozlovskiy, "To the Question of Validity Grüneisen Solid State Equation," World Journal of Condensed Matter Physics, Vol. 2 No. 4, 2012, pp. 219-227. doi: 10.4236/wjcmp.2012.24038.

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[1] W. Sutherland, “A Kinetic Theory of Solids, with an Experimental Introduction,” Philosophical Magazine Series V, Vol. 32, No. 199, 1891, pp. 524-553. doi:10.1080/14786449108620220
[2] G. Mie, “To the Kinetics Theory of One-Atomic Corps,” Annals of Physics, Vol. 11, No. 8, 1903, pp. 657-697.
[3] E. Grüneisen, “To the Theory of One-Atomic Solid Corps,” Physical Magazine, Vol. 12, No. 22-23, 1911, pp. 1023-1026.
[4] E. Grüneisen, “Theory of Solid State One-Atomic Elements,” Annals of Physics, Vol. 39, No. 12, 1912, pp. 257-306.
[5] P. Debye, “To the Theory of Heat Capacities,” Annals of Physics, Vol. 39, 1912, pp. 789-839.
[6] S. Ratnowsky, “One-Atomic Solid Corps Equation of State and the Quantum Theory,” Annals of Physics, Vol. 38, 1912, pp. 637-648.
[7] K. Eisenmann, “One-atomic Solid Corps Equation of State, according to the Quantum Theory,” Annals of Physics, Vol. 39, No. 16, 1912, pp. 1165-1174.
[8] E. Grüneisen, “Molecular Theory of Solid Corps,” The Structure of the Matter, Conference of Physics, Bruxeles, October 1913.
[9] P. Debye, “Equation of State and Quantum Hypothesis,” Physical Magazine, Vol. 14, 1913, pp. 259-260.
[10] P. Debye, “The Equation of State and Quantum Hypothesis with Supplement of Heat Conduction,” Lectures on the Kinetic Theory of Matter and Electricity, Leipzig and Berlin, B. G. Teubner, 1914, pp. 19-46.
[11] V. Fock and G. Krutkow, “Remarks to the Virial Theorem of Classical Mechanic,” Physical Magazine of USSR, Vol. 1, No. 6, 1932, pp. 756-758.
[12] V. Ch. Kozlovskiy, “Dynamical Equations for Time-Averaged Coordinates at Thermal Equilibrium,” Soviet Physics Journal, Vol. 34, No. 4, 1991, pp. 353-359.
[13] W. Braunbek, “Gratings Dynamics Theory of Melting Phenomenon,” Physical Magazine, Vol. 38, No. 6-7, 1926, pp. 549-572.
[14] L. N. Syrkin, “To the Question of Temperature Dependence of Thermal Ionic Polarization,” Journal of Technical Physics, Vol. 26, No. 6, 1956, pp. 1163-1165.
[15] Ja. I. Frenkel, “Statistical Physics, Moscow,” Academy of Sciences, Leningrad, 1948.
[16] Yu. M. Goryachev, L. L. Moiseenko and E. I. Shvartsman, “Parameters of Elastodynamic State of Dodecaborides of Rare Earth Metals,” Soviet Physics Journal, Vol. 34, No. 5, 1991, pp. 455-458.
[17] D. S. Lemon and C. M. Lund, “Thermodynamics of High Temperature Mie-Grüneisen Solids,” American Journal of Physics, Vol. 67, No. 12, 1999, pp. 1105-1108. doi:10.1119/1.19091
[18] F. Lindemann, “About the Calculation of Molecular Own Frequencies,” Physical Magazine, Vol. 11, No. 14, 1910, pp. 609-612.
[19] J. J. Gilvarry, “The Lindemann and Grüneisen Laws,” Physical Review, Vol. 102, No. 2, 1956, pp. 308-316. doi:10.1103/PhysRev.102.308
[20] E. Grüneisen, “To the Theory of One-atomic Solid Corps,” Conference of German Physical Society, Vol. 13, 1911, pp. 836-847.

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