An Isothermal Equation of State of Solid

Roy, Papiya Bose; Roy, Sushil Bose

doi:10.1002/1521-3951(200107)226:1<125::aid-pssb125>3.0.co;2-1

Cited by 11 publications

(2 citation statements)

References 32 publications

(59 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solid black line is the present calculation, the green dotted line is the EOS of Vinet (Vinet et al 1987(Vinet et al , 1989, the pink dashed line is the third order EOS of Birch-Murnaghan Birch (1947). We also present the EOS of Stacey 2000 (blue dash -dot fixing the infinite dB dP at 2) and the EOS of Roy-Roy (Roy & Roy 2001 is depicted by a purple long dash -dot. A recent density functional theory (DFT) developed for molecular hydrogen (Geng et al 2012) in red.…”

Section: Using the Pressure Derivative Of The Bulk Modulus As The Equmentioning

confidence: 99%

See 1 more Smart Citation

A variable polytrope index applied to planet and material models

Weppner¹,

McKelvey²,

Thielen³

et al. 2015

Mon. Not. R. Astron. Soc.

View full text Add to dashboard Cite

We introduce a new approach to a century old assumption which enhances not only planetary interior calculations but also high pressure material physics. We show that the polytropic index is the derivative of the bulk modulus with respect to pressure. We then augment the traditional polytrope theory by including a variable polytrope index within the confines of the Lane-Emden differential equation. To investigate the possibilities of this method we create a high quality universal equation of state, transforming the traditional polytrope method to a tool with the potential for excellent predictive power. The theoretical foundation of our equation of state is the same elastic observable which we found equivalent to the polytrope index, the derivative of the bulk modulus with respect to pressure. We calculate the density-pressure of six common materials up to 10 18 Pa, mass-radius relationships for the same materials, and produce plausible density-radius models for the rocky planets of our solar system. We argue that the bulk modulus and its derivatives have been under utilized in previous planet formation methods. We constrain the material surface observables for the inner core, outer core, and mantle of planet Earth in a systematic way including pressure, bulk modulus, and the polytrope index in the analysis. We believe this variable polytrope method has the necessary apparatus to be extended further to gas giants and stars. As supplemental material we provide computer code to calculate multi-layered planets.

show abstract

Section: Using the Pressure Derivative Of The Bulk Modulus As The Equmentioning

confidence: 99%

“…The one we depict in Fig. 6 and Appendix D has a physical asymptotic form and has B ′ ∞ = 5/3 (Roy & Roy 2001.…”

mentioning

confidence: 99%

A variable polytrope index applied to planet and material models

Weppner¹,

McKelvey²,

Thielen³

et al. 2015

Mon. Not. R. Astron. Soc.

View full text Add to dashboard Cite

show abstract

On the pressure (volume) dependence of Grüneisen parameter, Debye temperature and thermal expansivity in ε‐Fe

Liu¹,

Chen

2004

Physica Status Solidi (b)

View full text Add to dashboard Cite

show abstract

Inverted equations of state for solids under high pressures

2011

View full text Add to dashboard Cite

In the present communication we have reviewed some inverted type equations of state for solids under high pressures. An inverted equation of state (EOS) gives volume as a function of pressure for a solid under isothermal conditions. We have considered various equations of state proposed by earlier workers which express volume as a function of pressure. Expressions for bulk modulus and its pressure derivatives based on such EOSs are obtained and reported here. It is emphasized here that the high pressure derivative properties are very sensitive to the forms of equations of state representing volume-pressure relationships. We have also studied the thermoelastic properties of solids based on pressure derivatives of bulk modulus. Applications have been extended in the present review article to the solids which are metals as well as non-metals including geophysical minerals present in the lower mantle and core of the Earth.

show abstract

An Isothermal Equation of State of Solid

Cited by 11 publications

References 32 publications

A variable polytrope index applied to planet and material models

A variable polytrope index applied to planet and material models

On the pressure (volume) dependence of Grüneisen parameter, Debye temperature and thermal expansivity in ε‐Fe

Inverted equations of state for solids under high pressures

Contact Info

Product

Resources

About