The Grüneisen parameter and its higher order derivatives for the Earth lower mantle and core

Shanker, J.; Sunil, K.; Sharma, B. K.

doi:10.1016/j.pepi.2016.11.002

Cited by 29 publications

(11 citation statements)

References 14 publications

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“…This is consistent with the identity given by Eq. (15), and also with the result obtained earlier by Shanker et al [8].…”

Section: Methods Of Analysissupporting

confidence: 89%

“…C P and C V are specific heats at constant pressure and constant volume, respectively. The higher order Grüneisen parameters up to fourth order are defined as follows [6][7][8]…”

Section: Methods Of Analysismentioning

confidence: 99%

“…In the present study we determine expressions for the volume derivatives of γ up to n-th order at extreme compressions using the results for third and fourth order Grüneisen parameters. The basic principles of calculus [6][7][8] are used to investigate the infinite pressure behaviour of thermoelsatic properties [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

Dwivedi

2019

Can. J. Phys.

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Expressions have been obtained for the volume derivatives of the Grüneisen parameter, which is directly related to the thermal and elastic properties of materials at high temperatures and high pressures. The higher order Grüneisen parameters are expressed in terms of the volume derivatives, and evaluated in the limit of infinite pressure. The results, that at extreme compression the third-order Grüneisen parameter remains finite and the fourth-order Grüneisen parameter tends to zero, have been used to derive a fundamental theorem according to which the volume derivatives of the Grüneisen parameter of different orders, all become zero in the limit of infinite pressure. However, the ratios of these derivatives remain finite at extreme compression. The formula due to Al’tshuler and used by Dorogokupets and Oganov for interpolating the Grüneisen parameter at intermediate compressions has been found to satisfy the boundary condition at infinite pressure obtained in the present study.

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“…This is consistent with the identity given by Eq. (15), and also with the result obtained earlier by Shanker et al [8].…”

Section: Methods Of Analysissupporting

confidence: 89%

“…C P and C V are specific heats at constant pressure and constant volume, respectively. The higher order Grüneisen parameters up to fourth order are defined as follows [6][7][8]…”

Section: Methods Of Analysismentioning

confidence: 99%

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Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

Dwivedi

2019

Can. J. Phys.

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“…So far, the GP has found diverse applications in geophysics [3,4], chemical physics [5,6], high-pressure physics, and plasma physics [7][8][9]. Recently, experiments have also started to investigate the GP in heavy-fermion systems [10][11][12], in which the physical properties at low temperatures are dominated by f electrons and their antiferromagnetic exchange interaction with the conduction electrons [13].…”

Section: Introductionmentioning

confidence: 99%

Grüneisen parameters: Origin, identity, and quantum refrigeration

Zhang²,

Guan

2020

Phys. Rev. Research

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In solid-state physics, the Grüneisen parameter (GP) was first introduced to study the effect of volume change of a crystal lattice on its vibrational frequencies and has since been widely used to investigate the characteristic energy scales of systems associated with the changes of external potentials. However, the GP is less investigated in gas systems and especially strongly interacting quantum gases. Here we report on some general results on the origin of the GP, an identity, and caloric effects in ultracold quantum gases. We prove that there exists a simple identity among three different types of GPs, quantifying the caloric effect induced by variations of volume, magnetic field, and interaction, respectively. Using exact Bethe ansatz solutions, we present a rigorous study of these different GPs and the quantum refrigeration in one-dimensional Bose and Fermi gases. Based on the exact equations of states of these systems, we further obtain analytic results for singular behavior of the GPs and the caloric effects at quantum criticality. We also predict the existence of the lowest temperature for cooling near a quantum phase transition. It turns out that the interaction ramp up and down in quantum gases provide a promising protocol of quantum refrigeration in addition to the usual adiabatic demagnetization cooling in solid-state materials.

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“…So far, the GP has found diverse applications in geophysics [3,4], chemical physics [5,6], high pressure physics and plasma physics [7][8][9]. Recently, experiments also started to focus on GP in heavy-fermion systems [10][11][12], in which the physical properties at low temperatures are dominated by f -electrons and their antiferromagnetic exchange J with conduction electrons [13].…”

Section: Introductionmentioning

confidence: 99%

Grüneisen Parameters: origin, identity and quantum refrigeration

Yu,

Zhang,

Guan

2019

Preprint

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In solid state physics, the Grüneisen parameter (GP), originally introduced in the study of the effect of changing the volume of a crystal lattice on its vibrational frequency, has been widely used to investigate the characteristic energy scales of systems with respect to the changes of external potentials. On the other hand, the GP is little investigated in a strongly interacting quantum gas systems. Here we report on our general results on the origin of GP, new identity and caloric effects in quantum gases of ultracold atoms. We prove that the symmetry of the dilute quantum gas systems leads to a simple identity among three different types of GPs, quantifying caloric effect induced respectively by variations of volume, magnetic field and interaction. Using exact Bethe ansatz solutions, we present a rigorous study of these different GPs and the quantum refrigeration in one-dimensional Bose and Femi gases. Based on the exact equations of states of these systems, we obtain analytic results for the singular behaviour of the GPs and the caloric effects at quantum criticality. We also predict the existence of the lowest temperature for cooling near a quantum phase transition. It turns out that the interaction ramp-up and -down in quantum gases provides a promising protocol of quantum refrigeration in addition to the usual adiabatic demagnetization cooling in solid state materials.

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The Grüneisen parameter and its higher order derivatives for the Earth lower mantle and core

Cited by 29 publications

References 14 publications

Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

Grüneisen parameters: Origin, identity, and quantum refrigeration

Grüneisen Parameters: origin, identity and quantum refrigeration

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