Pressure dependence of thermal transport properties

Hofmeister, Anne M.

doi:10.1073/pnas.0610734104

Cited by 122 publications

(94 citation statements)

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“…Experimental measurements are challenging and have not been attempted above 40 GPa [4]. The predictions of Debye theory are strongly model dependent with estimated values of the isothermal logarithmic density derivative a ranging from 4 to 8 [5][6][7], leading to uncertainties in the extrapolated value of the thermal conductivity at the base of the mantle of a factor of 5.…”

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confidence: 99%

Thermal Conductivity of Periclase (MgO) from First Principles

2010

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We combine first-principles calculations of forces with the direct nonequilibrium molecular dynamics method to determine the lattice thermal conductivity k of periclase (MgO) up to conditions representative of the Earth's core-mantle boundary (136 GPa, 4100 K). We predict the logarithmic density derivative a ¼ ð@ lnk=@ ln Þ T ¼ 4:6 AE 1:2 and that k ¼ 20 AE 5 Wm À1 K À1 at the core-mantle boundary, while also finding good agreement with extant experimental data at much lower pressures.

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Thermal Conductivity of Periclase (MgO) from First Principles

2010

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“…It ranges between 5 W/mK and 10 W/mK (21,22). The high value results from a linear increase throughout the mantle, but it is also suggested that the slope is proportional to the inverse of bulk modulus, leading to a flattening profile at high pressure (23). Here, we use a parabolic profile reaching 5 W/mK at the CMB.…”

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confidence: 99%

Topology of the postperovskite phase transition and mantle dynamics

Monnereau

Yuen

2007

Proc. Natl. Acad. Sci. U.S.A.

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The postperovskite (ppv) phase transition occurs in the deep mantle close to the core-mantle boundary (CMB). For this reason, we must include in the dynamical considerations both the Clapeyron slope and the temperature intercept, T int, which is the temperature of the phase transition at the CMB pressure. For a CMB temperature greater than T int, there is a double crossing of the phase boundary by the geotherms associated with the descending flow. We have found a great sensitivity of the shape of the ppv surface due to the CMB from variations of various parameters such as the amount of internal heating, the Clapeyron slope, and the temperature intercept. Three-dimensional spherical models of mantle convection that can satisfy the seismological constraints depend on the Clapeyron slope. At moderate value, 8 MPa/K, the best fit is found with a core heat flow amounting for 40% of the total heat budget (Ϸ15 TW), whereas for 10 MPa/K the agreement is for a lower core heat flow (20%, Ϸ7.5 TW). In all cases, these solutions correspond to a temperature intercept 200 K lower than the CMB temperature. These models have holes of perovskite adjacent to ppv in regions of hot upwellings. has provoked an immense interest in the earth sciences because of the close proximity of the phase change to the core-mantle boundary (CMB), unveiling a large part of the enigmatic DЉ layer. The DЉ is a seismic structure whose complexity has remained puzzling for a long time. Interpreted in terms of phase boundary undulations, it would offer the chance to provide an absolute constraint on the temperature within the thermal boundary layer of the mantle. This would have great impact on our understanding of the dynamical state and thermal history of the earth. Concerted efforts recently have been devoted to sharpening the seismic imaging of DЉ (4-6), but results remain interpreted in the framework of 1D thermal models. On the other hand, previous work (7-11) investigating mantle convection with a ppv transition has focused more on dynamical effects and the magnitude of the Clapeyron slope than on the topology of the ppv surface itself. Thus, these investigators have neglected to consider the temperature intercept of the phase transition, which matters a lot in the case of a ppv transition because it is situated so near to the lower boundary of mantle convection.This delicate location makes it necessary for one to take into account the relative magnitude between the temperature at the CMB, T CMB , and the temperature of the ppv transition at the CMB pressure of 135 GPa. This latter temperature is called the temperature intercept, T int (see Fig. 1). In Fig. 1, we show the relationship between various geotherms (cold, warm, and hot) and the phase boundary, commonly known as the Clapeyron curve (red color), which is given by the equation cast in red. We note that in the case when T CMB is greater than T int , the geotherm may cross the phase boundary at two places (known as ''double-crossing'') (4). This feature is necessarily related to the existe...

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“…However, the P − κ RT relationship cannot be explained based on these alone. To support this argument, we fitted our P − κ RT data, adapting the expression proposed by Hofmeister [34]:…”

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“…ρ and ρ 0 are mass densities at applied pressure and with no applied pressure, respectively. This model assumes the change in group velocity can be approximated by the change in bulk sound velocity [34]. For T ¼ 300 K, T=T o ¼ 1, and κ 0 ¼ 2113 W=m-K, the resulting κ RT using Eq.…”

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confidence: 99%

“…This could have important implications for the thermal conductivity of Earth mantle minerals. Hofmeister [34] noted that comparing measured mineral thermal conductivity with analytical models required fitting parameters due to the omission of the pressure dependence of phonon lifetimes. Our first principle study calculates κ directly without adjustable parameters.…”

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Polar Effects on the Thermal Conductivity of Cubic Boron Nitride under Pressure

Mukhopadhyay

Stewart

2014

Phys. Rev. Lett.

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We report the lattice thermal conductivity (κ) of cubic boron nitride (c-BN) under pressure calculated using density functional theory. Pressure was used to manipulate the c-BN phonon dispersion and study its effect on thermal conductivity. These results were compared to c-BN's mass-equivalent, nonpolar counterpart, diamond, in order to isolate the effect of polar bonds on thermal conductivity. Unlike diamond, the variation of κ at room temperature (κ RT ) with applied pressure in c-BN is nonlinear in the lowpressure regime followed by a transition to a linear regime with a distinct change in the slope at P > 114 GPa. We find that the change in κ with pressure cannot be described with power law expressions commonly used for Earth mantle materials. The nonlinearity in the low-pressure regime can be related to the nonlinear change in LO-TO gap, group velocities, and specific heat with increasing pressure. In addition, we find that, although optical branch contributions to thermal conductivity are small (∼2% at RT), the rise in κ RT for P > 114 GPa is due to (1) the decoupling of the longitudinal acoustic branch from the optical branches and (2) depopulation of the optical branches. These lead to a sharp reduction in acousticacoustic-optic (a-a-o) scattering and a discrete change in the acoustic phonon mean free paths. This study illustrates the importance of optical branches and their interactions with acoustic branches in determining the total thermal conductivity of polar materials. This finding is also relevant for current research in geologic minerals under pressure and the design of thermoelectrics. The last decade has seen a renaissance in the study and understanding of thermal conductivity (κ) in materials and nanostructures, driven largely by new ab initio Boltzmann transport approaches [1-6], large-scale molecular dynamics simulations [7][8][9][10], and novel κ measurement techniques [11][12][13]. These approaches offer an unprecedented window into the secret life of phonons, providing, for the first time, accurate estimates for (1) normal and umklapp scattering rates in crystals [2,14], (2) thermal conductivity accumulation function [11,15,16], and (3) the often underestimated role of optical phonons [17,18]. These insights have led to the prediction of new high κ materials (e.g., BAs [19]), techniques for improving thermoelectrics [20,21], and κ estimates for minerals deep in the Earth [6,22].While the thermal conductivities of numerous materials have been calculated from first principles recently, a fundamental question of how thermal transport in polar materials differs from their nonpolar counterparts is still unresolved. The answer to this question also has practical implications for fields ranging from heat flow in Earth mantle materials to thermoelectrics design. It is well known that long-range Coulomb interactions between ions in a polar system result in a nonanalytic term in the dynamical matrix that depends on the Born effective charge Z Ã and dielectric constant ε ∞ . This term leads to Lydan...

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Pressure dependence of thermal transport properties

Cited by 122 publications

References 59 publications

Thermal Conductivity of Periclase (MgO) from First Principles

Thermal Conductivity of Periclase (MgO) from First Principles

Topology of the postperovskite phase transition and mantle dynamics

Polar Effects on the Thermal Conductivity of Cubic Boron Nitride under Pressure

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