Rose-Vinet (Universal) equation of state - Revision history

98.3.20.28: /* Vinet */

2021-02-19T06:08:28Z

Vinet

← Older revision		Revision as of 08:08, 19 February 2021
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	Note: there is a possibility that this equation of state was originally proposed in 1981 by Stacey et al. <ref>[http://dx.doi.org/10.1007/BF01449185 F. D. Stacey, B. J. Brennan and R. D. Irvine "Finite strain theories and comparisons with seismological data", Surveys in Geophysics '''4''' pp. 189-232 (1981)]</ref>.		Note: there is a possibility that this equation of state was originally proposed in 1981 by Stacey et al. <ref>[http://dx.doi.org/10.1007/BF01449185 F. D. Stacey, B. J. Brennan and R. D. Irvine "Finite strain theories and comparisons with seismological data", Surveys in Geophysics '''4''' pp. 189-232 (1981)]</ref>.

	==Rose-Vinet==		==Rose-Vinet==

Carl McBride: Slight tidy.

2012-09-27T10:29:28Z

Slight tidy.

← Older revision		Revision as of 12:29, 27 September 2012
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	==Vinet==		==Vinet==
			In order to rectify the excessive stiffness of the [[Murnaghan equation of state]] as well as represent the exponential dependence of the repulsion as solid undergoes strong compression, Vinet proposed an equation of state, known as either the '''Vinet equation of state''' or '''Universal equation of state'''<ref>[http://dx.doi.org/10.1103/PhysRevB.35.1945 Pascal Vinet, John R. Smith, John Ferrante and James H. Rose "Temperature effects on the universal equation of state of solids", Physical Review B '''35''' pp. 1945-1953 (1987)]</ref>. The equation of state was formulated so that one form could represent all solids over a reasonably wide range of [[pressure]]s, depending only on data for the calibration point. Using the shorthand for the cube root specific volume:
	In order to rectify the excessive stiffness of the [[Murnaghan equation of state]] as well as represent the exponential dependence of the repulsion as solid undergoes strong compression, Vinet proposed an equation of state ~~(without mentioning that it had been used previously for instance by F. D. Stacey~~, ~~B. J. Brennan and R. D. Irvine in "Finite strain theores and comparison with seismological data", Geophysical Surveys, 4, 189-232 (1989))~~ as either the '''Vinet equation of state''' or '''Universal equation of state'''<ref>[http://dx.doi.org/10.1103/PhysRevB.35.1945 Pascal Vinet, John R. Smith, John Ferrante and James H. Rose "Temperature effects on the universal equation of state of solids", Physical Review B '''35''' pp. 1945-1953 (1987)]</ref>. The equation of state was formulated so that one form could represent all solids in reasonably wide ~~ranches~~ of pressure, depending only on data for the calibration point. Using the shorthand for the cube root specific volume:

	:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math>		:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math>
Line 9:		Line 8:
	:<math>p=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)}</math>		:<math>p=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)}</math>

			Note: there is a possibility that this equation of state was originally proposed in 1981 by Stacey et al. <ref>[http://dx.doi.org/10.1007/BF01449185 F. D. Stacey, B. J. Brennan and R. D. Irvine "Finite strain theories and comparisons with seismological data", Surveys in Geophysics '''4''' pp. 189-232 (1981)]</ref>.
	==Rose-Vinet==		==Rose-Vinet==

	==References==		==References==
	<references/>		<references/>

	[[category: equations of state]]		[[category: equations of state]]

84.163.45.92 at 13:57, 21 September 2012

2012-09-21T13:57:17Z

← Older revision		Revision as of 15:57, 21 September 2012
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	==Vinet==		==Vinet==

	In order to rectify the excessive stiffness of the [[Murnaghan equation of state]] as well as represent the exponential dependence of the repulsion as solid undergoes strong compression, Vinet proposed an equation of state (without mentioning that it had been used for instance by F. D. Stacey, B. J. Brennan and R. D. Irvine in "Finite strain theores and comparison with seismological data", Geophysical Surveys, 4, 189-232 (1989)~~previously~~ as either the '''Vinet equation of state''' or '''Universal equation of state'''<ref>[http://dx.doi.org/10.1103/PhysRevB.35.1945 Pascal Vinet, John R. Smith, John Ferrante and James H. Rose "Temperature effects on the universal equation of state of solids", Physical Review B '''35''' pp. 1945-1953 (1987)]</ref>. The equation of state was formulated so that one form could represent all solids in reasonably wide ~~rqanches~~ of pressure, depending only on data for the calibration point. Using the shorthand for the cube root specific volume:		In order to rectify the excessive stiffness of the [[Murnaghan equation of state]] as well as represent the exponential dependence of the repulsion as solid undergoes strong compression, Vinet proposed an equation of state (without mentioning that it had been used previously for instance by F. D. Stacey, B. J. Brennan and R. D. Irvine in "Finite strain theores and comparison with seismological data", Geophysical Surveys, 4, 189-232 (1989)) as either the '''Vinet equation of state''' or '''Universal equation of state'''<ref>[http://dx.doi.org/10.1103/PhysRevB.35.1945 Pascal Vinet, John R. Smith, John Ferrante and James H. Rose "Temperature effects on the universal equation of state of solids", Physical Review B '''35''' pp. 1945-1953 (1987)]</ref>. The equation of state was formulated so that one form could represent all solids in reasonably wide ranches of pressure, depending only on data for the calibration point. Using the shorthand for the cube root specific volume:

	:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math>		:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math>

84.163.45.92 at 13:53, 21 September 2012

2012-09-21T13:53:09Z

← Older revision		Revision as of 15:53, 21 September 2012
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	==Vinet==		==Vinet==

	In order to rectify the excessive stiffness of the [[Murnaghan equation of state]] as well as represent the exponential dependence of the repulsion as solid undergoes ~~infinite~~ compression, Vinet proposed an equation of state that ~~has widely~~ as either the '''Vinet equation of state''' or '''Universal equation of state'''<ref>[http://dx.doi.org/10.1103/PhysRevB.35.1945 Pascal Vinet, John R. Smith, John Ferrante and James H. Rose "Temperature effects on the universal equation of state of solids", Physical Review B '''35''' pp. 1945-1953 (1987)]</ref>. The ~~latter due to the fact that the~~ equation of state was formulated so that one form could represent all solids, depending only on the calibration point. Using the shorthand for the cube root specific volume:		In order to rectify the excessive stiffness of the [[Murnaghan equation of state]] as well as represent the exponential dependence of the repulsion as solid undergoes strong compression, Vinet proposed an equation of state (without mentioning that it had been used for instance by F. D. Stacey, B. J. Brennan and R. D. Irvine in "Finite strain theores and comparison with seismological data", Geophysical Surveys, 4, 189-232 (1989)previously as either the '''Vinet equation of state''' or '''Universal equation of state'''<ref>[http://dx.doi.org/10.1103/PhysRevB.35.1945 Pascal Vinet, John R. Smith, John Ferrante and James H. Rose "Temperature effects on the universal equation of state of solids", Physical Review B '''35''' pp. 1945-1953 (1987)]</ref>. The equation of state was formulated so that one form could represent all solids in reasonably wide rqanches of pressure, depending only on data for the calibration point. Using the shorthand for the cube root specific volume:

	:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math>		:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math>

Carl McBride: Added DOI for the reference

2011-11-07T12:13:15Z

Added DOI for the reference

← Older revision		Revision as of 14:13, 7 November 2011
Line 1:		Line 1:
	==Vinet==		==Vinet==

	In order to rectify the excessive stiffness of the [[Murnaghan equation of state]] as well as represent the exponential dependence of the repulsion as solid undergoes infinite compression, Vinet proposed an equation of state that has widely as either the '''Vinet equation of state''' or '''Universal equation of state'''<ref>P.Vinet, J.R. Smith, J. Ferrante, and J.H. Rose. Temperature effects on the universal equation of state of solids. ''~~Phys. Rev. B~~''~~, 35:~~1945,1987</ref>. The latter due to the fact that the equation of state was formulated so that one form could represent all solids, depending only on the calibration point. Using the shorthand for the cube root specific volume:		In order to rectify the excessive stiffness of the [[Murnaghan equation of state]] as well as represent the exponential dependence of the repulsion as solid undergoes infinite compression, Vinet proposed an equation of state that has widely as either the '''Vinet equation of state''' or '''Universal equation of state'''<ref>[http://dx.doi.org/10.1103/PhysRevB.35.1945 Pascal Vinet, John R. Smith, John Ferrante and James H. Rose "Temperature effects on the universal equation of state of solids", Physical Review B '''35''' pp. 1945-1953 (1987)]</ref>. The latter due to the fact that the equation of state was formulated so that one form could represent all solids, depending only on the calibration point. Using the shorthand for the cube root specific volume:

	:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math>		:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math>

	the equation of state is:		the equation of state is (Eq. 4.1):

	:<math>p=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)}</math>		:<math>p=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)}</math>

Josephrpeterson at 03:33, 7 November 2011

2011-11-07T03:33:38Z

← Older revision		Revision as of 05:33, 7 November 2011
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	==References==		==References==
	<references/>		<references/>

			[[category: equations of state]]

Josephrpeterson: Created page with "==Vinet== In order to rectify the excessive stiffness of the Murnaghan equation of state as well as represent the exponential dependence of the repulsion as solid undergoes ..."

2011-11-07T03:32:37Z

Created page with "==Vinet== In order to rectify the excessive stiffness of the Murnaghan equation of state as well as represent the exponential dependence of the repulsion as solid undergoes ..."

New page

==Vinet==

In order to rectify the excessive stiffness of the [[Murnaghan equation of state]] as well as represent the exponential dependence of the repulsion as solid undergoes infinite compression, Vinet proposed an equation of state that has widely as either the '''Vinet equation of state''' or '''Universal equation of state'''<ref>P.Vinet, J.R. Smith, J. Ferrante, and J.H. Rose. Temperature effects on the universal equation of state of solids. ''Phys. Rev. B'', 35:1945,1987</ref>. The latter due to the fact that the equation of state was formulated so that one form could represent all solids, depending only on the calibration point. Using the shorthand for the cube root specific volume:

:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math>

the equation of state is:

:<math>p=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)}</math>

==Rose-Vinet==

==References==
<references/>