Clapeyron Slope Research Articles

Slab stagnation due to a reduced viscosity layer beneath the mantle transition zone

The linear structures of seismically fast anomalies, often interpreted as subducted slabs, in the southern Asia and circum-Pacific lower mantle provided strong evidence for the whole mantle convection model. However, recent seismic studies have consistently shown that subducted slabs are deflected horizontally for large distances in mantle transition zone in the western Pacific and other subduction zones, suggesting that the slabs meet significant resistance to their descending motion and become stagnant in the transition zone. This poses challenges to the whole mantle convection model and also brings the origin of stagnant slabs into question. Here, using a global mantle convection model with realistic spine–post-spinel phase change (−2 MPa K−1 Clapeyron slope) and plate motion history, we demonstrate that the observed stagnant slabs in the transition zone and other slab structures in the lower mantle can be explained by the presence of a thin, weak layer at the phase change boundary that was suggested by mineral physics and geoid modelling studies. Our study also shows that the stagnant slabs mostly result from subduction in the past 20–30 million years, confirming the transient nature of slab stagnation and phase change dynamics on timescales of tens of millions of years from previous studies. Slab stagnation in the transition zone is explained by a thin, weak layer and is transient on timescales of tens of millions of years, according to a global mantle convection model that includes phase changes and plate motion history.

Equation of State of SiC at Extreme Conditions: New Insight Into the Interior of Carbon‐Rich Exoplanets

AbstractThere is a direct relation between the composition of a host star and that of the planets orbiting around it. As such, the recent discovery of stars with unusual chemical composition, notably enriched in carbon instead of oxygen, supports the existence of exoplanets with a chemistry dominated by carbides instead of oxides. Accordingly, several studies have been recently conducted on the Si–C binary system at high pressure and temperature. Nonetheless, the properties of carbides at the pressure‐temperature conditions of exoplanets interiors are still inadequately constrained, effectively hampering reliable planetary modeling. Here we present an in situ X‐ray diffraction study of the Si–C binary system up to 200 GPa and 3,500 K, significantly enlarging the pressure range explored by previous experimental studies. The large amount of collected data allows us to properly investigate the phase diagram and to refine the Clapeyron slope of the transition line from the zinc blende to the rock salt structure. Furthermore, the pressure‐volume‐temperature equation of state is provided for the high‐pressure phase, characterized by low compressibility and thermal expansion. Our results are used to model idealized C‐rich exoplanets of end‐members composition. In particular, we derived mass‐radius relations and performed numerical simulations defining rheological parameters and initial conditions which lead to onset of convection in such SiC planets. We demonstrate that if restrained to silicate‐rich mantle compositions, the interpretation of mass‐radius relations may underestimate the interior diversity of exoplanets.

Penetrative Convection in Super‐Earth Planets: Consequences of MgSiO3 Postperovskite Dissociation Transition and Implications for Super‐Earth GJ 876 d

AbstractTheoretical studies suggest that MgSiO3 postperovskite dissociates into MgO and MgSi2O5 at 0.9 TPa, and MgSi2O5 dissociates into MgO and SiO2 at 2.1 TPa, both with negative Clapeyron slopes. In addition, unlike a conventional view, the viscosity in super‐Earth planets is proposed to decrease with pressure when pressure exceeds ~0.1 TPa. Employing 2‐D‐axisymmtric and 3‐D‐spherical control volume compressible models, we perform an investigation on the impact of deep mantle dissociation of postperovskite into oxides, in conjunction with variations of the mantle viscosity, on the degree of the deep mantle layering, and the consequences of this layering on cooling of the rocky planets similar to super‐Earth GJ 876 d. Small‐scale convection in a layer of thickness ~500 km from which penetrative plumes originate, develops above the core‐mantle boundary (CMB) in the models for which the viscosity at the dissociation transition depth and below is less than ~1023 Pa·s. Due to the buffering effect of this deep mantle layering, while the mean mantle temperature above the layer decreases, resulting in a viscosity increase above the layer, it increases in the layered region above the CMB. This leads to a further reduction in viscosity at the bottom of the mantle. The effect is enhanced with increasing the CMB temperature and the contrast in thermal expansivity. The cooling rate of the planet decreases in the layered models due to the buffering effect of this deep mantle transition, as well as the influence of the viscosity increase above transition depth.

Stability and Reactions of CaCO3 Polymorphs in the Earth's Deep Mantle

AbstractAs an important component of carbonates in the mantle, CaCO3 is a major carrier of carbon from the surface to the deep interiors. In recent years, new varieties of CaCO3 polymorphs have been continuously predicted by first principles simulations and verified by experiments. The findings of these polymorphs open the possibility of stabilizing CaCO3 component in the lowermost mantle. Here, through extensive first principles simulations, we inspect the stability and reactions of high‐pressure CaCO3 polymorphs at high temperatures. Systematic errors from approximations to the exchange‐correlation functional in density functional theory have been essentially eliminated with a generalized rescaling method to increase the predictability of the simulations. We find temperature has important effects on the stabilities and the reactions of CaCO3 polymorphs with mantle minerals. In particular, the tetrahedrally structured CaCO3‐polymorph (space group P21/c) is found to be sensitive to temperature with a positive Clapeyron slope of 15.81(6) MPa/K. Reacting with MgSiO3, CaCO3 is shown to be less stable than MgCO3 over the whole mantle pressures (to ~136 GPa) above ~1500 K. And CaCO3 is demonstrated to readily react with SiO2 even in the cold subduction slabs. Thus, high temperature greatly increases the tendency of partitioning calcium into the silicates, and CaCO3 is not likely to be the major host of carbon in the Earth's deep mantle.

Melting curve of Si by means of the Z-method

The melting curve of silicon is investigated through classical molecular dynamics simulations. We explore pressures from 0 to 20 GPa using the EDIP, Stillinger-Weber, and Tersoff interactomic potentials. Using the Z method, we demonstrate that the predicted melting temperature Tm can be significantly overestimated, depending on the potential chosen. Our results show that none of the potentials explored is able to reproduce the experimental melting curve of silicon by means of the Z-method. However, the EDIP potential does predict the change in the Clapeyron slope, associated with the diamond to β-tin phase transition.

The combined effects of post-spinel and post-garnet phase transitions on mantle plume dynamics

Mineralogical studies indicate that two major phase transitions occur near the depth of 660 km in the Earth's pyrolitic mantle: the ringwoodite (Rw) to perovskite (Pv) + magnesiowüstite (Mw) and the majorite (Mj) to perovskite (Pv) phase transitions. Seismological results also show a complicated phase boundary structure at this depth in plume regions. However, previous geodynamical modeling has mainly focused on the effects of the Rw–Pv+Mw phase transition on plume dynamics and has largely neglected the effects of the Mj–Pv phase transition. Here, we develop a 3-D regional spherical geodynamic model to study the combined influence of these two phase transitions on plume dynamics. Our results show the following: (1) A double phase boundary occurs in the high-temperature center of the plume, corresponding to the double reflections in seismic observations. Other plume regions feature a single, flat uplifted phase boundary, causing a gap of high seismic velocity anomalies. (2) Large amounts of relatively low-temperature plume materials can be trapped in the transition zone due to the combined effects of phase transitions, forming a complex truncated cone shape. (3) The Mj–Pv phase transition greatly enhances the plume penetration capability through 660-km phase boundary, which has a significant influence on the plume dynamics. Our results provide new insights which can be used to better constrain the 660-km discontinuity variations, seismic wave velocity structure and plume dynamics in the mantle transition zone. The model can also help to estimate the mantle temperature and Clapeyron slopes at the 660 km phase boundary.

The melting points of MgO up to 4 TPa predicted based on ab initio thermodynamic integration molecular dynamics

The melting curve of MgO is extended up to 4 TPa, corresponding to the Jovian core pressure, based on the one-step thermodynamic integration method implemented on ab initio molecular dynamics. The calculated melting temperatures are 3100 and 16 000 K at 0 and 500 GPa, respectively, which are consistent with previous experimental results, and 20 600 K at 3900 GPa, which is inconsistent with a recent experimental extrapolation, which implies the molten Jovian core. A quite small Clapeyron slope () of is found at 3900 GPa due to comparable densities of the liquid and B2 phases under extreme compression. The Mg–O coordination number in the liquid phase is saturated at around 7.5 above 1 TPa and remains smaller than that in the B2 phase (8) even at 4 TPa, suggesting no density crossover between liquid and crystal and thus no further denser crystalline phases. Dynamical properties (atomic diffusivity and viscosity) are also investigated along the melting curve to understand these behaviors in greater detail.

New High‐Pressure Phase of CaCO3 at the Topmost Lower Mantle: Implication for the Deep‐Mantle Carbon Transportation

AbstractIn this study, we have investigated the stability of CaCO3 at high pressures and temperatures using synchrotron X‐ray diffraction in laser‐heated diamond anvil cells. Our experimental results have shown that CaCO3 in the aragonite structure transforms into CaCO3‐VII (P21/c) at 27 GPa and 1,500 K with a negative Clapeyron slope of −4.3(9) MPa/K. CaCO3‐VII is stable between 23 and 38 GPa at 2,300 K and transforms into post‐aragonite at 42 GPa and 1,400 K. Furthermore, it reacts with stishovite, an abundant form of SiO2 in subducted oceanic crust, forming CaSiO3‐perovskite. The occurrence of CaSiO3‐perovskite via the reaction of CaCO3‐VII and stishovite provides an explanation for the observation of the high concentrations of CaSiO3‐perovskite and some amount of CaCO3 in deep‐mantle inclusions. CaCO3‐VII is thus an important carbon‐bearing phase at the topmost lower mantle and may provide necessary carbon to produce deep‐mantle diamonds.

Elasticity of Corundum at High Pressures and Temperatures: Implications for Pyrope Decomposition and Al‐Content Effect on Elastic Properties of Bridgmanite

AbstractThe thermodynamic and elastic properties of corundum at high pressures and temperatures are calculated based on density functional theory within the local density approximation. The calculated results agree well with the available experimental results and provide reliable data up to 80 GPa and 2,500 K. Our results confirm that C14 should be positive at ambient conditions. Elastic moduli of corundum, especially its shear modulus, exhibit noticeable nonlinear dependences with pressure and thereby result in the nonlinear pressure dependences of wave velocities. The decomposition of pyrope into the assemblage of bridgmanite and corundum is also investigated within the generalized gradient approximation. The calculated phase boundary is comparable to experimental results and has a positive Clapeyron slope of +2.1 MPa/K. Pyrope decomposition can result in VP, VS, and density jumps of 12.4%, 20%, and 9.8%, respectively. A small amount of pyrope dissociation can cause a large impendence contrast and may partially account for the observed discontinuities below 660 km at the subduction zone. Combining our calculations with results from the previous study, we suggest that the incorporation of Al into bridgmanite shows no discernable effect on its elastic moduli and wave velocities. This may impede the detection of Al content in bridgmanite through seismological methods.

On the Melting Curve of Sulfur Hexafluoride

A previous correlation for the melting curve of sulfur hexafluoride (SF6) is inconsistent with the thermodynamic slope at the triple point derived from the Clapeyron equation. It is shown that this is probably due to the previous authors combining an accurate measurement of the triple point with melting-curve data that were distorted by impurities. A new equation is proposed that is consistent with the Clapeyron slope.

Phase transition in SiC from zinc-blende to rock-salt structure and implications for carbon-rich extrasolar planets

We have investigated the phase transition in SiC between the zinc-blende and rock-salt structures at high pressure and temperature in a laser-heated diamond-anvil cell. Results demonstrate that the transition occurs at 74 GPa and 2100 K with a 21% density increase, reflecting the coordination number rising from four to six. In addition, our ab initio calculations show that the boundary has a negative Clapeyron slope of −4.0 MPa/K at 2000 K. The experimentally determined phase boundary is located between those predicted by GGA and B3LYP functional. This transition may take place inside carbon-rich extrasolar planets, forming a boundary with a large density jump. Since SiC is rigid and highly thermally conductive, thermal convection in an SiC-dominant layer is not likely to occur. Nevertheless, the convection may be possible if planet interiors include both silicon carbide and silicate, and in this case the phase transition could affect the style of thermal convection.

Phase relations and mineral chemistry in pyrolitic mantle at 1600–2200 °C under pressures up to the uppermost lower mantle: Phase transitions around the 660-km discontinuity and dynamics of upwelling hot plumes

We determined phase relations of pyrolite at 12–28 GPa and 1600–2200 °C using a 6–8 Kawai-type multianvil apparatus. A large number of high pressure and high temperature experiments were conducted to constrain the phase relations especially around 660-km depth, compared with previous studies. The phase relations drastically change between 19 and 23 GPa with temperature as follows. At 19–22 GPa, a phase transition of ringwoodite (Rw) to garnet (Gt) + magnesiowüstite (Mw) occurs at 1800 °C, and no Rw is observed at 2200 °C. The mineral proportion of Gt increases with increasing temperature due to this decomposition reaction and becomes larger than that of Rw above 1800 °C. At 23 GPa, pyrolite crystallizes to a mineral assemblage of bridgmanite (Bm) + Mw + Gt + calcium perovskite by the post-spinel (pSp) transition at 1600–2000 °C and the post-garnet (pGt) transition at 2100–2200 °C, the latter of which is defined as a phase transition of a part of Gt to Bm. Clapeyron slopes of the pSp transition and the pGt transition are determined to be −1 and 5 MPa/°C, respectively, in this study. Gt is stable at any temperatures around the 660-km discontinuity (D660), and Gt-disappearance reaction occurs at 25 GPa with no temperature dependence. Densities of pyrolite were calculated in various pressure and temperature conditions by using the mineral proportions and available data of equations of state. The density at 1600 °C is higher than that at 1800–2200 °C at any pressure-temperature conditions in this study. In particular, the drastic density drop occurs at 19–24 GPa between 1600 and 1800–2200 °C because of increase of Gt proportion with increasing temperature. These suggest that upwelling hot plumes composed of pyrolite from the lower mantle do not stagnate and their ascent is promoted across D660. The mineral proportions and the density changes also suggest that the phase transition which causes D660 changes around 1800 °C from the pSp to the pGt transitions because of the mineral proportion inversion between Rw and Gt.

First Principles Thermodynamics of Minerals at HP–HT Conditions: MgO as a Prototypical Material

Ab initio thermodynamic properties, equation of state and phase stability of periclase (MgO, B1-type structure) have been investigated in a broad P–T range (0–160 GPa; 0–3000 K) in order to set a model reference system for phase equilibria simulations under deep Earth conditions. Phonon dispersion calculations performed on large supercells using the finite displacement method and in the framework of quasi-harmonic approximation highlight the performance of the Becke three-parameter Lee-Yang-Parr (B3LYP) hybrid density functional in predicting accurate thermodynamic functions (heat capacity, entropy, thermal expansivity, isothermal bulk modulus) and phase reaction boundaries at high pressure and temperature. A first principles Mie–Grüneisen equation of state based on lattice vibrations directly provides a physically-consistent description of thermal pressure and P–V–T relations without any need to rely on empirical parameters or other phenomenological formalisms that could give spurious anomalies or uncontrolled extrapolations at HP–HT. The post-spinel phase transformation, Mg2SiO4 (ringwoodite) = MgO (periclase) + MgSiO3 (bridgmanite), is taken as a computational example to illustrate how first principles theory combined with the use of hybrid functionals is able to provide sound results on the Clapeyron slope, density change and P–T location of equilibrium mineral reactions relevant to mantle dynamics.

Phase boundary between cubic B1 and rhombohedral structures in (Mg,Fe)O magnesiowüstite determined by in situ X-ray diffraction measurements

The phase relations and equation of state of (Mg0.08Fe0.92)O magnesiowustite (Mw92) have been studied using the Kawai-type high-pressure apparatus coupled with synchrotron radiation. To determine the phase boundary between the NaCl-type cubic (B1) and rhombohedral (rB1) structures in Mw92, in situ X-ray observations were carried out at pressures of 0–35 GPa and temperatures of 300–1473 K. Au and MgO were used as the internal pressure markers and metallic Fe as oxygen fugacity buffer. The phase boundary between B1 and rB1 structures was described by a linear equation P (GPa) = 1.6 + 0.033 × T (K). The Clapeyron slope (dP/dT) determined in this study is close to that obtained at pressures above 70 GPa but steeper than that obtained for FeO. An addition of MgO to FeO structure expands the stability field of the rB1 phase to lower pressures and higher temperatures. Thus, the rB1 phase may be stabilized with respect to the B1 phase at a lower pressures. The pressure–volume–temperature equation of state of B1-Mw92 was determined up to 30 GPa and 1473 K. Fitting the hydrostatic compression data up to 30 GPa with the Birch–Murnaghan equation of state (EoS) yielded: unit cell volume (V 0,T0), 79.23 ± 4 A3; bulk modulus (K 0,T0), 183 ± 4 GPa; its pressure derivative (K′ T ), 4.1 ± 0.4; (∂K 0,T /∂T) = −0.029 ± 0.005 GPa K‒1; a = 3.70 ± 0.27 × 10−5 K−1 and b = 0.47 ± 0.49 × 10−8 K−2, where α0,T = a + bT is the volumetric thermal expansion coefficient. The obtained bulk modulus of Mw92 is very close to the value expected for stoichiometric iron-rich (Mg,Fe)O. This result confirms the idea that the bulk modulus of (Mg,Fe)O is greatly affected by the actual defect structure, caused by either Mg2+ or vacancies.

Subduction-transition zone interaction: A review

AbstractAs subducting plates reach the base of the upper mantle, some appear to flatten and stagnate, while others seemingly go through unimpeded. This variable resistance to slab sinking has been proposed to affect long-term thermal and chemical mantle circulation. A review of observational constraints and dynamic models highlights that neither the increase in viscosity between upper and lower mantle (likely by a factor 20–50) nor the coincident endothermic phase transition in the main mantle silicates (with a likely Clapeyron slope of –1 to –2 MPa/K) suffice to stagnate slabs. However, together the two provide enough resistance to temporarily stagnate subducting plates, if they subduct accompanied by significant trench retreat. Older, stronger plates are more capable of inducing trench retreat, explaining why backarc spreading and flat slabs tend to be associated with old-plate subduction. Slab viscosities that are ∼2 orders of magnitude higher than background mantle (effective yield stresses of 100–300 MPa) lead to similar styles of deformation as those revealed by seismic tomography and slab earthquakes. None of the current transition-zone slabs seem to have stagnated there more than 60 m.y. Since modeled slab destabilization takes more than 100 m.y., lower-mantle entry is apparently usually triggered (e.g., by changes in plate buoyancy). Many of the complex morphologies of lower-mantle slabs can be the result of sinking and subsequent deformation of originally stagnated slabs, which can retain flat morphologies in the top of the lower mantle, fold as they sink deeper, and eventually form bulky shapes in the deep mantle.

Intercomparison of the gold, platinum, and MgO pressure scales up to 140 GPa and 2500 K

AbstractIn order to intercalibrate the equations of state (EOSs) of the three widely used pressure standards, gold, platinum, and MgO, we have measured their unit cell volumes together in the laser‐heated diamond anvil cell up to 140 GPa and 2500 K. At 300 K, three standards agree with each other within ±2.5 GPa to 135 GPa if the EOSs measured in quasi‐hydrostatic media are used. We further refined the EOSs at 300 K, making them consistent with each other within ±1 GPa up to 135 GPa. At high temperature (T), the three standards match the best within ±1 GPa between 40 and 140 GPa, when we use the scales by Dorogokupets and Dewaele (2007). However, a 2–3 GPa discrepancy remains at 20–40 GPa and 1500–2000 K, with gold yielding the highest pressure (P). The pressure discrepancy is likely related to steep decreases in the Grüneisen parameter, the anharmonicity, and/or the electronic effects for the standards at the P‐T conditions. Because gold melts near the temperatures expected for the mantle transition zone, severe anharmonic effects expected under premelting conditions make gold unsuitable for determining the phase boundaries in the region. The pressure scales by Dorogokupets and Dewaele (2007) provide tighter constrains on the Clapeyron slopes of the postspinel boundary to −2.0 to −2.7 MPa/K and the postperovskite boundary to 7–10 MPa/K. The data and refined EOSs presented here allow for reliable comparisons among experiments with different pressure standards for the entire P‐T conditions expected for the Earth's lower mantle.

Zinc-blende to rocksalt transition in SiC in a laser-heated diamond-anvil cell

We explore the stability of the ambient pressure zinc-blende polymorph (B3) structure of silicon carbide (SiC) at high pressures and temperatures where it transforms to the rocksalt (B1) structure. We find that the transition occurs \ensuremath{\sim}40 GPa lower than previously measured when heated to moderately high temperatures. A lower transition pressure is consistent with the transition pressures predicted in numerous ab initio computations. We find a large volume decrease across the transition of \ensuremath{\sim}17%, with the volume drop increasing at higher formation pressures, suggesting this transition is volume driven yielding a nearly pressure-independent Clapeyron slope. Such a dramatic density increase occurring at pressure is important to consider in applications where SiC is exposed to extreme conditions, such as in industrial applications or planetary interiors.

Premelting hcp to bcc Transition in Beryllium.

Beryllium (Be) is an important material with wide applications ranging from aerospace components to x-ray equipment. Yet a precise understanding of its phase diagram remains elusive. We have investigated the phase stability of Be using a recently developed hybrid free energy computation method that accounts for anharmonic effects by invoking phonon quasiparticles. We find that the hcp → bcc transition occurs near the melting curve at 0<P<11 GPa with a positive Clapeyron slope of 41±4 K/GPa, which is more consistent with recent experimental measurements. This work also demonstrates the validity of this theoretical framework based on the phonon quasiparticle to study the structural stability and phase transitions in strongly anharmonic materials.

Thermodynamics and Equations of State of Iron to 350\u2009GPa and 6000\u2009K

The equations of state for solid (with bcc, fcc, and hcp structures) and liquid phases of Fe were defined via simultaneous optimization of the heat capacity, bulk moduli, thermal expansion, and volume at room and higher temperatures. The calculated triple points at the phase diagram have the following parameters: bcc–fcc–hcp is located at 7.3 GPa and 820 K, bcc–fcc–liquid at 5.2 GPa and 1998 K, and fcc–hcp–liquid at 106.5 GPa and 3787 K. At conditions near the fcc–hcp–liquid triple point, the Clapeyron slope of the fcc–liquid curve is dT/dP = 12.8 K/GPa while the slope of the hcp–liquid curve is higher (dT/dP = 13.7 K/GPa). Therefore, the hcp–liquid curve overlaps the metastable fcc–liquid curve at pressures of about 160 GPa. At high-pressure conditions, the metastable bcc–hcp curve is located inside the fcc-Fe or liquid stability field. The density, adiabatic bulk modulus and P-wave velocity of liquid Fe calculated up to 328.9 GPa at adiabatic temperature conditions started from 5882 K (outer/inner core boundary) were compared to the PREM seismological model. We determined the density deficit of hcp-Fe at the inner core boundary (T = 5882 K and P = 328.9 GPa) to be 4.4%.

High-temperature ab initio calculations on FeSi and NiSi at conditions relevant to small planetary cores

The Fe–Ni–Si system is potentially a very important component of terrestrial planetary cores. However, at present, even the behaviour of the FeSi and NiSi end members is poorly understood, especially at low to moderate pressures—the data for FeSi are contradictory and NiSi has been little studied. For FeSi, there is general agreement that there is a phase transition from the ε-FeSi to the CsCl structure with increasing pressure, but, in experiments, there is disagreement as to the position and slope of the phase boundary and the range of coexistence of the two phases. In this paper we have used ab initio lattice dynamics calculations to determine the phase boundary between the ε-FeSi and CsCl structures as a function of pressure and temperature in both FeSi and NiSi. For FeSi, we find that the transition pressure at zero Kelvin is ~11 GPa and that the boundary between the ε-FeSi and CsCl phases varies little with temperature, having a slight negative Clapeyron slope, going from ~11 GPa at 300 K to ~3 GPa at 2000 K. For NiSi, there is much greater variation of the transition pressure with temperature, with a much shallower negative Clapeyron slope, going from ~156 GPa at 300 K to ~94 GPa at 2000 K.