Comparison of some equation-of-state theories by using experimental high-compression data

Walzer, Uwe; Ullmann, Wolfgang; Pankov, V. L.

doi:10.1016/0031-9201(79)90150-x

Cited by 17 publications

(4 citation statements)

References 23 publications

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“…This condition also applies to any other e o s formalism that relies (explicitly or implicitly) upon series truncation (Anderson 1995). Lastly, it is assumed that the EOS parameters (in this case 77, K ' and 77", which are themselves derivatives of V with respect to pressure) are continuously differentiable with respect to pressure, a requirement that is true for all EOS formalisms (Walzer et al 1979). This has the obvious and well-known corol lary that any EOS will not correctly describe the elastic properties of the material in the neighbourhood of, or through, a phase transition.…”

Section: Introductionmentioning

confidence: 99%

Compression mechanisms and equations of state

1996

Phil. Trans. R. Soc. Lond. A

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The derivations of equations of state to describe the volume-pressure variation of a solid are based upon certain assumptions about the properties of the solid. For finite strain equations of state, these assumptions include homogeneity and isotropy of the strain distribution in the sample, the continuous differentiability of the equa tion of state parameters with respect to extensive variables, and the assumption that terms involving higher-order powers of the finite strain do not contribute sig nificantly to the free energy of the material. We examine these assumptions and demonstrate that, within the experimental uncertainties, crystalline solids with no or limited degrees of internal structural freedom compress in the manner predicted by finite strain equations of state, even though in some cases the assumptions in volved in the derivation of the equation of state are demonstrably violated. In more complex structures with a larger number of degrees of structural freedom, a variety of behaviour is observed; most undergo continuous structural change with increasing pressure and the evolution of the volume with pressure again follows that predicted by the finite strain equations of state. However, a significant number of complex structures undergo changes in compression mechanism which, in some cases, result in significant deviations from the behaviour predicted by the equations of state.

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Section: Introductionmentioning

confidence: 99%

Compression mechanisms and equations of state

1996

Phil. Trans. R. Soc. Lond. A

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“…Walzer et al (1979) and Ulmann and Pan'kov (1980) Direct integration gives the relationship between K and P:…”

Section: Two-term Power Law Potentialsmentioning

confidence: 98%

Finite strain theories and comparisons with seismological data

Stacey

Brennan

Irvine

1981

Geophysical Surveys

188

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Abstract. All the finite strain equations that we are aware of that are worth considering in connection with the interior of the Earth are given, with the assumptions on which they are based and corresponding relationships for incompressibility and its pressure derivatives in terms of density. In several cases, equations which have been presented as new or independent are shown to be particular examples of more general equations that are already familiar. Relationships for deriving finite strain equations from atomic potential functions or vice versa are given and, in particular it is pointed out that the BirchMurnaghan formuIation implies a sum of power law potentials with even powers. All the equations that survive simple plausibility tests are fitted to the lower mantle and outer core data for the PEM earth model. For this purpose the model data are extrapolated to zero temperature, using the MieGrfineisen equation to subtract the thermal pressure (at fixed density) and the pressure derivative of this equation to substract the thermal component of incompressibility. Fitting of finite strain equations to such zero temperature data is less ambiguous than fitting raw earth model data and leads immediately to estimates of the low temperature zero pressure parameters of earth materials. On this basis, using the best fitting ~uations and constraining core temperature to give an extrapolated incompressibility Ko = 1.6 X 10 Pa, compatible with a plausible iron alloy, the following numerical data are obtained: However, an inconsistency is apparent between P(p) and K(p) data, indicating that, even in the PEM model, in which the lower mantle is represented by a single set of parameters, it is not perfectly homogeneous with respect to composition and phase.

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“…With a slight modification of a formula found in Refs. [12,13], the simplest parametrization of the volume dependence for crystals can be written as…”

Section: Ii2 Anharmonic Correlated Einstein Modelmentioning

confidence: 99%

Pressure Dependence of EXAFS Debye-Waller Factors in Crystals

2012

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In present article the pressure dependence of Debye-Waller factors in crystals has been investigated by using statistical moment method and anharmonic correlated Einstein model. These two methods provide similar results which indicate that the Debye-Waller factors of crystals decreases slightly under high pressure. Our numerical results for several crystals are compared to other theoretical and experimental values and showed a good agreement.

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Comparison of some equation-of-state theories by using experimental high-compression data

Cited by 17 publications

References 23 publications

Compression mechanisms and equations of state

Compression mechanisms and equations of state

Finite strain theories and comparisons with seismological data

Pressure Dependence of EXAFS Debye-Waller Factors in Crystals

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