Applicability of isothermal three-parameter equations of state of solids—a reappraisal

Roy, Papiya Bose; Roy, Sushil Bose

doi:10.1088/0953-8984/17/39/007

Cited by 19 publications

(17 citation statements)

References 55 publications

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“…One of the most important issues in condensed matter sciences, particularly, in geology and geophysics, is to accurately predict the structural and physical properties of solids under high pressure and temperature1234567. In general, a solid-state material under high pressure and temperature can exhibit properties quite different from those found at ambient conditions.…”

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confidence: 99%

Condensed-matter equation of states covering a wide region of pressure studied experimentally

Gordon¹,

Juergen²,

Whangbo³

2016

Sci Rep

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The relationships among the pressure P, volume V, and temperature T of solid-state materials are described by their equations of state (EOSs), which are often derived from the consideration of the finite-strain energy or the interatomic potential. These EOSs consist of typically three parameters to determine from experimental P-V-T data by fitting analyses. In the empirical approach to EOSs, one either refines such fitting parameters or improves the mathematical functions to better simulate the experimental data. Despite over seven decades of studies on EOSs, none has been found to be accurate for all types of solids over the whole temperature and pressure ranges studied experimentally. Here we show that the simple empirical EOS, P = α1(PV) + α2(PV)2 + α3(PV)3, in which the pressure P is indirectly related to the volume V through a cubic polynomial of the energy term PV with three fitting parameters α1–α3, provides accurate descriptions for the P-vs-V data of condensed matter in a wide region of pressure studied experimentally even in the presence of phase transitions.

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confidence: 99%

Condensed-matter equation of states covering a wide region of pressure studied experimentally

Gordon¹,

Juergen²,

Whangbo³

2016

Sci Rep

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“…To have a working hypothesis for a dynamic polytrope index EOS we examined previous equations of state (Roy & Roy 2005 and pressure-density relationships (Seager et al 2007;Swift et al 2012) for an empirical function form for the changing polytrope index. To be consistent we developed our own EOS which uses the informed polytrope index as the function of reference in place of the more common pressure EOS like the Birch-Murnaghan (Birch 1947;Poirier 2000) or Vinet (Vinet et al 1987(Vinet et al , 1989Poirier 2000).…”

Section: Our Equation Of Statementioning

confidence: 99%

“…4. This EOS was cultivated by examining the functional form of dB dP for the Vinet and Birch-Murnaghan EOS (Birch 1947;Poirier 2000) and also analyzing pressure-density relationships found in previous work (Roy & Roy 2005Seager et al 2007;Swift et al 2012) including first principle calculations (French et al 2009;Hermann et al 2011;Geng et al 2012) and acquired numerical second derivatives. This was instrumental in developing the intermediate pressure ranges (10 11 − 10 13 P a) which older EOS often do not fit well.…”

Section: Comparisons Of Db Dpmentioning

confidence: 99%

A variable polytrope index applied to planet and material models

Weppner¹,

McKelvey²,

Thielen³

et al. 2015

Mon. Not. R. Astron. Soc.

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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.

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“…[1][2][3] Despite over a century of theoretical development and experimental testing of EOS for solids, 4,5 there is still a lack of consensus on the most appropriate EOS under various conditions or even the metric to evaluate appropriateness. Previous attempts 6,7 have focused on comparison with the experimental data, which limits the range of the accessible data. By contrast, computational studies can span chemical and structural space in a consistent and methodical manner, and are often able to probe extreme conditions beyond the range of current experimental techniques.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of thermodynamic equations of state across chemistry and structure in the materials project

et al. 2018

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Thermodynamic equations of state (EOS) for crystalline solids describe material behaviors under changes in pressure, volume, entropy and temperature, making them fundamental to scientific research in a wide range of fields including geophysics, energy storage and development of novel materials. Despite over a century of theoretical development and experimental testing of energy-volume (E-V) EOS for solids, there is still a lack of consensus with regard to which equation is indeed optimal, as well as to what metric is most appropriate for making this judgment. In this study, several metrics were used to evaluate quality of fit for 8 different EOS across 87 elements and over 100 compounds which appear in the literature. Our findings do not indicate a clear "best" EOS, but we identify three which consistently perform well relative to the rest of the set. Furthermore, we find that for the aggregate data set, the RMSrD is not strongly correlated with the nature of the compound, e.g., whether it is a metal, insulator, or semiconductor, nor the bulk modulus for any of the EOS, indicating that a single equation can be used across a broad range of classes of materials.

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Applicability of isothermal three-parameter equations of state of solids—a reappraisal

Cited by 19 publications

References 55 publications

Condensed-matter equation of states covering a wide region of pressure studied experimentally

Condensed-matter equation of states covering a wide region of pressure studied experimentally

A variable polytrope index applied to planet and material models

Evaluation of thermodynamic equations of state across chemistry and structure in the materials project

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