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In order to examine pressure–volume–temperature (P–V–T) relations for CaSiO3 perovskite (Ca-perovskite), high-temperature compression experiments with in situ X-ray diffraction were performed in a laser-heated diamond anvil cell (DAC) to 127 GPa and 2,300 K. We also employed an external heating system in the DAC in order to obtain P–V data at a moderate temperature of 700 K up to 113 GPa, which is the reference temperature for constructing an equation of state. The P–V data at 700 K were fitted to the second-order Birch–Murnaghan equation of state, yielding K 700,1bar = 207 ± 4 GPa and V 700,1bar = 46.5 ± 0.1 A3. Thermal pressure terms were evaluated in the framework of the Mie–Gruneisen–Debye model, yielding γ 700,1bar = 2.7 ± 0.3, q 700,1bar = 1.2 ± 0.8, and θ 700,1bar = 1,300 ± 500 K. A thermodynamic thermal pressure model was also employed, yielding α700,1bar = 5.7 ± 0.5 × 10−5/K and (∂K/∂T) V = −0.010 ± 0.004 GPa/K. Computed densities along a lower mantle geotherm demonstrate that Ca-perovskite is denser than the surrounding lower mantle, suggesting that Ca-perovskite-rich rocks do not rise up through the lower mantle. One of such rocks might be a residue of partial melting of subducted mid-oceanic ridge basalt (MORB) at the base of the mantle. Since the partial melt is FeO-rich and therefore denser than the mantle, all the components of subducted MORB may not return to shallow levels.

Thermal conductivity is essential for controlling the rate of core heat loss and long-term thermal evolution of the Earth, but it has been poorly constrained at the high pressures of Earth's lowermost mantle. We measured the lattice component of thermal diffusivity, heat transport by scattering of phonons, of both MgSiO 3 perovskite (Pv) and post-perovskite (PPv) at high pressures of up to 144 GPa and at room temperature. Lattice thermal conductivity of Pv-dominant lowermost mantle assemblage obtained in this study is about 11 W/m/K, while PPv-bearing rocks exhibit ∼60% higher conductivity. Since such Pv value is comparable to the conventionally assumed lowermost mantle conductivity, our findings do not significantly alter but support the recent notion of high core–mantle boundary heat flow along with a young inner core and high temperatures in the early deep Earth.

We report the measurements of aggregate shear velocity ( V S ) of CaSiO 3 perovskite (CaPv) at high pressure ( P ) between 32 and 133 GPa and room temperature ( T ) on the basis of Brillouin spectroscopy. The sample had a tetragonal perovskite structure throughout the experiments. The measured P – V S data show the shear modulus and its pressure derivative at ambient condition to be G 0 =115.8 GPa and G '=1.20, respectively. The zero-pressure shear velocity is determined to be V S0 =5.23 km/s, in good agreement with the previous estimate inferred from the ultrasonic measurements on Ca(Si,Ti)O 3 perovskite at 1 bar. Our experimental results are broadly consistent with the earlier calculations on tetragonal CaPv but exhibit lower velocity at equivalent pressure. Such tetragonal CaPv is present in cold subducting slabs and possibly in wide areas of the lowermost mantle. While primitive mantle includes certain amount of CaPv, a depleted peridotite (former harzburgite) layer in subducted oceanic lithosphere is deficient in CaPv and enriched in ferropericlase in the lower mantle. Such harzburgite exhibits 0.9% faster V S and 0.7% slower bulk sound velocity ( V Φ ) at the lowermost mantle P – T conditions if CaPv is present in the tetragonal form in the surrounding mantle. The observed fast V S and slow V Φ anomalies in the D” layer underneath the circum-Pacific region might be attributed in large part in the presence of subducted harzburgitic materials.

We consider the problem of selecting variables in factor analysis models. The regularization procedure is introduced to perform an automatic variable selection. In the factor analysis model, each variable is controlled by multiple factors when there are more than one underlying factor. We treat parameters corresponding to the multiple factors as grouped parameters, and then apply the group lasso. Furthermore, the weight of the group lasso penalty is modified to obtain appropriate estimates and improve the performance of variable selection. Crucial issues in this modeling procedure include the selection of the number of factors and a regularization parameter. Choosing these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating the factor analysis model via the weighted group lasso. Monte Carlo simulations are conducted to investigate the effectiveness of the proposed procedure. A real data example is also given to illustrate our procedure. The Canadian Journal of Statistics 40: 345–361; 2012 © 2012 Statistical Society of Canada Nous nous interessons a la selection de variables dans un modele d'analyse factorielle. Nous introduisons la procedure de regularisation pour faire une selection de variables de facon automatique. Dans un modele d'analyse factorielle, chaque variable est controlee par plusieurs facteurs lorsqu'il y a plus d'un facteur sous-jacent. Nous considerons les parametres correspondant a plusieurs facteurs comme des parametres groupes et nous appliquons un lasso de groupes. De plus, le poids de la fonction de penalisation du lasso de groupes est modifie afin d'obtenir des estimations appropriees et d'ameliorer la performance de la selection de variables. Des questions sur le choix du nombre de facteurs et sur le parametre de regularisation sont cruciales pour cette procedure. Le choix de ces parametres peut etre considere comme la selection d'un modele et un probleme d'evaluation. Nous obtenons un critere pour la selection de modeles pour l'evaluation d'un modele d'analyse factorielle en utilisant un lasso de groupes ponderes. L'efficacite de cette procedure est evaluee a l'aide de simulations de Monte-Carlo. Nous illustrons notre procedure a l'aide d'un vrai jeu de donnees. La revue canadienne de statistique 40: 345–361; 2012 © 2012 Societe statistique du Canada

The phase transition boundary between the face-centered cubic (fcc) structure and hexagonal close-packed (hcp) structure in an Fe–Ni alloy was determined at pressures from 25 to 107 GPa by using an internally resistive-heated diamond anvil cell (DAC), combined with in situ synchrotron X-ray diffraction measurements. The fcc–hcp phase transition boundary in Fe–9.7 wt% Ni is located at slightly lower temperatures than that in pure Fe, confirming the previous understanding that the addition of Ni expands the stability field of the fcc phase. The dP/dT slope of the boundary was determined to be 0.0426 GPa/K, which is slightly larger than that of pure Fe. The pressure interval of the two-phase region is about 6 GPa at a constant temperature, implying that the previous estimates by laser-heated DAC experiments of 10–20 GPa were overestimated. The two-phase region of fcc + hcp would be limited to a pressure of about 120 GPa even in Fe–15 wt%Ni, excluding the possibility of the existence of the fcc phase in the inner core if the simple linear extrapolation of the two-phase region is applied. The pressure and temperature dependences of the c/a axial ratio of the hcp phase in Fe–9.7 wt% Ni are generally consistent with those in pure Fe, suggesting that Ni has minor effects on the c/a ratio.

X-ray diffraction experiments on postperovskite (ppv) with compositions (Mg 0.9 Fe 0.1 )SiO 3 and (Mg 0.6 Fe 0.4 )SiO 3 at Earth core-mantle boundary pressures reveal different crystal structures. The former adopts the CaIrO 3 -type structure with space group Cmcm , whereas the latter crystallizes in a structure with the Pmcm ( Pmma ) space group. The latter has a significantly higher density ( ρ = 6.119(1) g/cm 3 ) than the former ( ρ = 5.694(8) g/cm 3 ) due to both the larger amount of iron and the smaller ionic radius of Fe 2+ as a result of an electronic spin transition observed by X-ray emission spectroscopy (XES). The smaller ionic radius for low-spin compared to high-spin Fe 2+ also leads to an ordered cation distribution in the M1 and M2 crystallographic sites of the higher density ppv structure. Rietveld structure refinement indicates that approximately 70% of the total Fe 2+ in that phase occupies the M2 site. XES results indicate a loss of 70% of the unpaired electronic spins consistent with a low spin M2 site and high spin M1 site. First-principles calculations of the magnetic ordering confirm that Pmcm with a two-site model is energetically more favorable at high pressure, and predict that the ordered structure is anisotropic in its electrical and elastic properties. These results suggest that interpretations of seismic structure in the deep mantle need to treat a broader range of mineral structures than previously considered.

To investigate the physical property of Fe7C3, we carried out in situ X-ray diffraction experiments using a Kawai-type multi-anvil apparatus and a diamond anvil cell up to 71.5 GPa and 1973 K. The carbide was found to be stable under these experimental conditions. However, we found anomalous behavior in its isothermal compression and thermal expansivity. These anomalies could be due to the magnetic phase transition in Fe7C3 from a ferromagnetic ( fm ) to a paramagnetic ( pm ) phase. The Curie temperature of 523 K at 1 bar (Tsuzuki et al. 1984) decreases with pressure, and the pressure-induced magnetic transition is estimated to occur at ~18 GPa and 300 K. The pressure-volume-temperature ( P - V - T ) data set for the pm -Fe7C3 was fitted by the Mie-Gruneisen-Debye (MGD) equation of state (EOS) and the following parameters were obtained: unit-cell volume V = 184.2 ± 0.3 A3, bulk modulus K = 253 ± 7 GPa, the pressure derivative of bulk modulus K ′ = 3.6 ± 0.2, Gruneisen parameter γ = 2.57 ± 0.05, Debye temperature 𝛉 = 920 ± 140 K, and q = 2.2 ± 0.5, respectively, at zero pressure. The calculated density for Fe7C3 provides a good explanation for the density of the Earth’s inner core obtained from seismological observations.

The relative densities of melt and solid in the deep mantle have important implications for the chemical evolution of our planet. Recent theoretical calculations suggested that a density crossover may occur in the deepest mantle, but the important effect of the melt–solid partitioning of iron has been examined only at relatively low pressures (less than 25 gigapascals). Nomura et al. extend measurements of iron partitioning between (Mg,Fe)SiO3 perovskite and melt over the entire mantle pressure range, and find that a precipitous change occurs at about 76 GPa, resulting in stronger iron enrichment in melts at higher pressures. These results imply that liquid (Mg,Fe)SiO3 becomes more dense than coexisting solid at a depth of about 1,800 kilometres in the mantle. A melt has greater volume than a silicate solid of the same composition. But this difference diminishes at high pressure, and the possibility that a melt sufficiently enriched in the heavy element iron might then become more dense than solids at the pressures in the interior of the Earth (and other terrestrial bodies) has long been a source of considerable speculation1,2. The occurrence of such dense silicate melts in the Earth's lowermost mantle would carry important consequences for its physical and chemical evolution and could provide a unifying model for explaining a variety of observed features in the core–mantle boundary region3. Recent theoretical calculations4 combined with estimates of iron partitioning between (Mg,Fe)SiO3 perovskite and melt at shallower mantle conditions5,6,7 suggest that melt is more dense than solids at pressures in the Earth's deepest mantle, consistent with analysis of shockwave experiments8. Here we extend measurements of iron partitioning over the entire mantle pressure range, and find a precipitous change at pressures greater than ∼76 GPa, resulting in strong iron enrichment in melts. Additional X-ray emission spectroscopy measurements on (Mg0.95Fe0.05)SiO3 glass indicate a spin collapse around 70 GPa, suggesting that the observed change in iron partitioning could be explained by a spin crossover of iron (from high-spin to low-spin) in silicate melt. These results imply that (Mg,Fe)SiO3 liquid becomes more dense than coexisting solid at ∼1,800 km depth in the lower mantle. Soon after the Earth's formation, the heat dissipated by accretion and internal differentiation could have produced a dense melt layer up to ∼1,000 km in thickness underneath the solid mantle. We also infer that (Mg,Fe)SiO3 perovskite is on the liquidus at deep mantle conditions, and predict that fractional crystallization of dense magma would have evolved towards an iron-rich and silicon-poor composition, consistent with seismic inferences of structures in the core–mantle boundary region.

The equation of state and pressure-induced structural evolution of pyrite-type SiO2 have been investigated based on synchrotron X-ray diffraction measurements in a diamond-anvil cell. The Rietveld refinement revealed that the oxygen coordinate x of pyrite-type SiO2 increases with increasing pressure. The SiO6 coordination polyhedra of pyrite-type SiO2 is less compressible than the unit cell, and the increase in x induces a rotation of the SiO6 coordination polyhedra to fill the blank space in the unit cell. Thus, the volume reduction in pyrite-type SiO2 is achieved mainly by the rotation of the SiO6 polyhedra, rather than by the compression of the SiO6 polyhedra. In addition, the increase in x with increasing pressure enhances a distortion of the coordination polyhedra of pyrite-type SiO2, implying that pyrite-type SiO2 is not likely to transform into a fluorite-type structure at higher pressures.

Stabilities of hexagonal new aluminous (NAL) phase and Ca-ferrite-type (CF) phase were investigated on the join NaAlSiO4-MgAl2O4 in a pressure range from 23 to 58 GPa at approximately constant temperature of 1,850 K, on the basis of in situ synchrotron X-ray diffraction measurements in a laser-heated diamond-anvil cell. The results show that NAL is formed as a single phase up to 34 GPa, NAL + CF between 34 and 43 GPa, and only CF at higher pressures in 40%NaAlSiO4-60%MgAl2O4 bulk composition. On the other hand, both NAL and CF coexist below 38 and 36 GPa, and only CF was obtained at higher pressures in 60%NaAlSiO4-40%MgAl2O4 and 20%NaAlSiO4-80%MgAl2O4 composition, respectively. These results indicate that NAL appears only up to 46 GPa at 1,850 K, and CF forms continuous solid solution at higher pressures on the join NaAlSiO4-MgAl2O4. NAL has limited stability in subducted mid-oceanic ridge basalt crust in the Earth’s lower mantle and undergoes a phase transition to CF in deeper levels.

Acoustic velocities in polycrystalline H 2 O ice have been measured at room temperature in a pressure range 6–60 GPa by a Brillouin scattering method. Synchrotron X-ray diffraction measurements were also conducted simultaneously with the Brillouin scattering measurements in a pressure range 40–60 GPa. The obtained elastic moduli of high-pressure ice indicate that bcc-structured ice undergoes two transitions related to a change in the hydrogen bonding state at approximately 40 GPa and 58 GPa, i.e. transitions of ice VII to the pre-transitional state of ice VII at 40 GPa and to the dynamically disordered ice X at 58 GPa, respectively. This observation is consistent with previous spectroscopic studies and X-ray diffraction studies. Pressure dependencies of adiabatic elastic moduli and specific heat for ice VII and its high-pressure polymorphs were obtained from the acoustic velocity and volume data measured in this study. Isothermal compression data were obtained from previous studies. The relationships between pressure and adiabatic elastic moduli for ice VII were obtained as follows: K s = 4.0(2) + 8.51(4) × P − 0.081(2) × P 2 + 5.2(4) × 10 − 4 × P 3 ; μ s = 14(2) + 1.7(3) × P − 0.04(2) × P 2 + 5(3) × 10 − 4 × P 3 . An empirical relationship between specific heat and pressure at room temperature was obtained for ice VII as follows: C p = 3.3(2) + 22.1(1) × e − 0.058(2) P . This result implies that the transition from ice VII to the dynamically disordered ice X is accompanied with a discontinuous change in several thermodynamic properties of ice. The elasticity difference between ice VII and the dynamically disordered ice X may affect the dynamics of cold subducting slabs in Earth's lower mantle and the interiors of icy planets. The thermoelastic properties of high-pressure polymorphs of ice obtained in this study could contribute to clarifying the dynamics and the evolution of Earth and icy planets and satellites.

The phase transition boundary between stishovite and CaCl2-type structure in pure SiO2 was investigated at 45–75 GPa and 300–2490 K based on the in situ X-ray diffraction measurements in a laser-heated diamond-anvil cell (LHDAC). Results show that the boundary has a positive dP/dT slope of 11.1 MPa/K and the transition occurs about 70 GPa at 2200 K along the typical mantle geotherm. This corresponds to a depth of 1700 km, somewhat shallower than the previous estimate. Seismic heterogeneities have been found in a wide depth range from 800 to 1850 km in the upper to middle layers of the lower mantle. The post-stishovite phase transition is known to be ferroelastic-type, which causes a considerable reduction in shear modulus, leading to a large slow shear velocity anomaly. The almost pure SiO2 phase included in subducted crustal materials may be therefore responsible for the relatively deep mid-lower mantle seismic heterogeneities. The shallow lower mantle anomalies are possibly caused by the similar phase transition in SiO2 phase containing Al2O3 and H2O or by the phase transition in Al-bearing CaSiO3 perovskite from cubic to tetragonal structure.

High-temperature compression experiments with in situ X-ray diffraction of ferropericlase (Fp) with a composition of (Mg 0.81 Fe 0.19 )O were made in a laser-heated diamond anvil cell to pressures ( P ) of 116 GPa at a constant temperature ( T ) of 1600–1900 K. Room-temperature experiments with a laser annealing technique were also carried out on the same material. Anomalous unit-cell volume reductions that can be explained by the spin transition of ferrous iron were observed at P = 63–96 GPa and 45–63 GPa at T = 1600–1900 K and 300 K, respectively, indicating that the spin transition pressure interval expands with increasing temperature. The observed density changes across this spin transition at T = 1600–1900 K and 300 K are about 1.6% and 1.0%, respectively, indicating that the spin transition pressure interval expands with increasing temperature. The thermal expansivity of Fp is large in the mid-lower mantle due to the effect of the spin transition. In a peridotitic composition, the spin transition in Fp increases the rock density by 0.35% at the lowermost mantle conditions. Calculated densities show that both perovskitic and peridotitic mantle models may explain the PREM lower mantle density. However, the peridotitic lower mantle model requires less assumption to satisfy the PREM density and is more self-consistent.

The electrical conductivities of natural pyrolitic mantle and MORB materials were measured at high pressure and temperature covering the entire lower mantle conditions up to 133 GPa and 2650 K. In contrast to the previous laboratory-based models, our data demonstrate that the conductivity of pyrolite does not increase monotonically but varies dramatically with depth in the lower mantle; it drops due to high-spin to low-spin transition of iron in both perovskite and ferropericlase in the mid-lower mantle and increases sharply across the perovskite to post-perovskite phase transition at the D″ layer. We also found that the MORB exhibits much higher conductivity than pyrolite. The depth–conductivity profile measured for pyrolite does not match the geomagnetic field data below about 1500-km depth, possibly suggesting the existence of large quantities of subducted MORB crust in the deep lower mantle. The observations of geomagnetic jerks suggest that the electrical conductivity may be laterally heterogeneous in the lowermost mantle with high anomaly underneath Africa and the Pacific, the same regions as large low shear-wave velocity provinces. Such conductivity and shear-wave speed anomalies are also possibly caused by the deep subduction and accumulation of dense MORB crust above the core–mantle boundary.

We extended the pressure range of sound velocity measurements for liquid water to 25 GPa and 900 K along the melting curve using a laser heated diamond anvil cell with a combined system of Brillouin scattering and synchrotron X-ray diffraction. Experimental pressure and temperature were obtained by solving simultaneous equations: the melting curve of ice and the equation of state for gold. The sound velocities obtained in liquid water at high pressures and melting temperatures were converted to density using Murnaghan's equation of state by fitting a parameter of the pressure derivative of bulk modulus at 1 GPa. The results are in good agreement with the values predicted by a previously reported equation of state for water based on sound velocity measurements. The equation of state for water obtained in this study could be applicable to water released by dehydration reactions of dense hydrous magnesium silicate phases in cold subducting slabs at lower mantle conditions, although the validity of Murnaghan's equation of state for water should be evaluated in a wider pressure and temperature ranges. The present velocity data provides the basis for future improvement of the accurate thermodynamic model for water at high pressures.

We have determined the phase transition boundary between NaCl-type (B1) and NiAs-type (B8) structures of FeO up to 208 GPa and 3800 K on the basis of synchrotron X-ray diffraction (XRD) measurements in situ at high pressure and temperature using a laser-heated diamond-anvil cell (DAC). The boundary is located at 200 GPa and 3200 K with positive Clapeyron slope. These results show that B1 phase of FeO is stable along the whole mantle geotherm, whereas B8 phase is stabilized at the inner core condition. Additionally, FeO coexisted with metallic Fe in the present experiments. We found that hexagonal close-packed (hcp) iron is stable over the entire present experimental conditions. Moreover, the direct chemical analyses of the recovered sample demonstrated that solid iron did not contain any detectable oxygen. While extensive solid solution between Fe and FeO has been speculated above 60–80 GPa, the present results strongly suggest that the system Fe–FeO is simple eutectic at least to 200 GPa pressure range.

Structural distortion and the phase transition of CaSnO3 perovskite were examined in situ at high-pressure and -temperature on the basis of synchrotron X-ray diffraction measurement in a laser-heated diamond-anvil cell. The results show that CaSnO3 perovskite transforms into a CaIrO3-type post-perovskite phase above 40 GPa and 2000 K with a high positive Clapeyron slope. It is noted that CaSnO3 post-perovskite is quenchable to ambient condition. Combined with available compression data on other perovskite-type materials, we discuss a mechanism of perovskite to post-perovskite phase transition under pressure. The perovskites, which are distorted largely from the ideal cubic perovskite structure already at ambient condition, become more deformed with increasing pressure. This eventually results in the post-perovskite phase transition at a critical angle of octahedral rotation.

In this article, room-temperature pressure scales of MgO, Au, Pt, NaCl(B2), and Ar are compared using reported volume-volume measurements up to 198 GPa with laser-annealing method. MgO: Speziale et al. 2001, Au: Hirose et al. 2008, Pt: Holmes et al. 1989, NaCl(B2): Sata et al. 2002 (MgO calibration, mBM3), and Ar: Jephcoat 1998 are consistent each other. Simultaneous volume measurements of Au and Pt using He medium are not consistent with the laser-annealed data.

We have measured the electrical resistance of (Mg0.9Fe0.1)SiO3 perovskite with increasing pressure in a diamond-anvil cell (DAC). Results demonstrate that the electrical conductivity increased with pressure to about 70 GPa, then conversely decreased to around 85 GPa, and again increased mildly to 135 GPa. As inferred from the previous studies of (Mg,Fe)O ferropericlase, the observed reduction in the conductivity of perovskite at 70–85 GPa is most likely due to the high-spin to low-spin transition of iron; it decreases the number of unpaired electrons and therefore diminishes the conduction by electron hopping between the ferric and ferrous iron sites. Present conductivity data provide valuable implications for the pressure range of spin transition in (Mg,Fe)SiO3 perovskite, which has been highly controversial. The relatively abrupt reduction in the electrical conductivity above 70 GPa is reconciled with the spin-pairing transition in ferric iron, which may occur rather sharply at this pressure range.

We report in-situ petrological evidence of deep mantle origin from podiform chromitites in the Luobusa ophiolite, southern Tibet. Analytical transmission electron microscopy measurements reveal that chromites in podiform chromitites from the Luobusa ophiolite have numerous exsolution lamellae of diopsidic clinopyroxene and coesite, which indicate an ultrahigh-pressure origin of over 3 GPa (> 100 km deep). The presence of these lamellae, coupled with abundant micro-inclusions of clinopyroxene, requires high solubility of SiO2 and CaO in the host chromite, and suggests a precursor of chromite, a CaFe2O4-structured high-pressure polymorph, stable at pressures over 12.5 GPa (> 380 km deep). These nano-scale observations and geological occurrence indicate that the mantle peridotite under the Tibetan mid-ocean ridge was transported from the deep mantle (at least 100 km, probably more than 380 km deep) by the mantle convection. It implies that the root of mantle upwelling has a much deeper origin than previously believed.

Seismic wave velocity profiles in the Earth provide one of the strongest constraints on structure, mineralogy and elastic properties of the Earth's deep interior. Accurate sound velocity data of deep Earth materials under relevant high-pressure and high-temperature conditions, therefore, are essential for interpretation of seismic data. Such information can be directly obtained from Brillouin scattering measurement. Here we describe an in situ Brillouin scattering system for measurements at high pressure and high temperature using a laser heated diamond anvil cell and synchrotron radiation for sample characterization. The system has been used with single-crystal and polycrystalline materials, and with glass and fluid phase. It provided high quality sound velocity and elastic data with X-ray diffraction data at high pressure and/or high temperature. Those combined techniques can potentially offer the essential information for resolving many remaining issues in mineral physics.

The phase relations of Fe-6.4 wt% Si and Fe-9.9 wt% Si have been investigated up to 130 GPa and 2,600 K based on in situ synchrotron X-ray diffraction measurements in a laser-heated diamond-anvil cell along with chemical analysis of the quenched samples using a field-emission electron probe microanalyzer. We found that the maximum solubility of silicon in solid hcp-iron increases with increasing pressure. Linear extrapolation of the phase boundary between hcp + B2 and hcp phases for Fe-9.9 wt% Si suggests that the solid hcp-iron can include more than 9.9 wt% Si at the Earth’s inner-core conditions. If silicon is a major light element in the outer core, a substantial amount of silicon may be incorporated into the inner core during inner-core solidification.

Partitioning of oxygen and silicon between molten iron and (Mg,Fe)SiO3 perovskite was investigated by a combination of laser-heated diamond-anvil cell (LHDAC) and analytical transmission electron microscope (TEM) to 146 GPa and 3,500 K. The chemical compositions of co-existing quenched molten iron and perovskite were determined quantitatively with energy-dispersive X-ray spectrometry (EDS) and electron energy loss spectroscopy (EELS). The results demonstrate that the quenched liquid iron in contact with perovskite contained substantial amounts of oxygen and silicon at such high pressure and temperature (P–T). The chemical equilibrium between perovskite, ferropericlase, and molten iron at the P–T conditions of the core–mantle boundary (CMB) was calculated in Mg–Fe–Si–O system from these experimental results and previous data on partitioning of oxygen between molten iron and ferropericlase. We found that molten iron should include oxygen and silicon more than required to account for the core density deficit (

The aggregate shear wave velocities of MgO (periclase) have been determined throughout Earth's lower mantle pressure regime approaching 130 GPa using Brillouin spectroscopy in conjunction with synchrotron X-ray diffraction technique in a diamond anvil cell apparatus. We found that the extrapolations of the high-pressure shear wave velocities and shear moduli to ambient pressure are highly consistent with earlier studies. However, the measurements over a wide pressure range revealed that the pressure derivative of the shear modulus (d G /d P = G 0 ′) of MgO is 1.92(2), which is distinctly lower than that of previous lower-pressure experiments. Compared with the previous results on (Mg,Fe)O ferropericlase, there is no clear correlation between iron content and G 0 ′. We calculate that the shear wave velocity profile of lower mantle along the adiabatic geotherm applied by the lower G 0 ′ value of periclase can remarkably well reproduce the global seismological 1-D velocity profile model with uniform composition model. The best-fitting result indicates the possibility of a lower mantle mineralogy with ~ 92 vol.% silicate perovskite phase, implying that the bulk composition of lower mantle is likely not to be pyrolitic but more chondritic. The present acoustic measurements performed over the large pressure range have thus led us to a better understanding of compositional model of the Earth's lower mantle.

We have determined the post-perovskite phase transition boundary in MgSiO3 in a wide temperature range from 1640 to 4380 K at 119–171 GPa on the basis of synchrotron X-ray diffraction measurements in-situ at high-pressure and -temperature in a laser-heated diamond-anvil cell (LHDAC). The results show a considerably high positive Clapeyron slope of + 13.3 ± 1.0 MPa/K and a transition temperature of about 3520 ± 70 K at the core–mantle boundary (CMB) pressure. The thermal structure in D″ layer can be tightly constrained from precisely determined post-perovskite phase transition boundary and the depths of paired seismic discontinuities. These suggest that temperature at the CMB may be around 3700 K, somewhat lower than previously thought. A minimum bound on the global heat flow from the core is estimated to be 6.6 ± 0.5 TW.

Factor analysis is one of the most popular methods of multivariate statistical analysis. This technique has been widely used in the social and behavioral sciences to explore the covariance structure among observed variables in terms of a few unobservable variables. In maximum likelihood factor analysis, we often face a problem that the estimates of unique variances turn out to be zero or negative, which is called improper solutions. In order to overcome this difficulty, we employ a Bayesian approach by specifying a prior distribution for model parameters. A crucial issue in Bayesian factor analysis model is the choice of adjusted parameters including hyper-parameters for a prior distribution and also the number of factors. The selection of these parameters can be viewed as a model selection and evaluation problem. We derive an information criterion for evaluating a Bayesian factor analysis model. Our proposed procedure may be used for preventing the occurrence of improper solutions and also for choosing the appropriate number of factors. Monte Carlo simulations are conducted to investigate the efficiency of the proposed procedures.

The effect of iron on the post-perovskite phase transition has been controversial. We have performed direct chemical analyses of co-existing perovskite and post-perovskite that were synthesized from an (Mg{sub 0.91}Fe{sub 0.09})SiO{sub 3} bulk composition using a laser-heated diamond anvil cell at pressures above 100 GPa and temperatures of 1700-1800 K. Analysis on quenched samples was carried out using the transmission electron microscope (TEM). The results demonstrate that crystalline perovskite grains are enriched in iron compared to adjacent amorphous parts presumably converted from post-perovskite. This indicates that ferrous iron stabilizes perovskite to higher pressures. The ferrous and ferric irons are likely to have competing effects on the post-perovskite phase transition, and therefore the effect of iron may be controlled by aluminum.

We have investigated the phase relations of iron and iron–nickel alloys with 18 to 50 wt.% Ni up to over 300 GPa using a laser-heated diamond-anvil cell. The synchrotron X-ray diffraction measurements show the wide stability of hcp-iron up to 301 GPa and 2000 K and 319 GPa and 300 K without phase transition to dhcp, orthorhombic, or bcc phases. On the other hand, the incorporation of nickel has a remarkable effect on expanding the stability field of fcc phase. The geometry of the temperature–composition phase diagram of iron–nickel alloys suggests that the hcp–fcc–liquid triple point is located at 10 to 20 wt.% Ni at the pressure of the inner core boundary. The fcc phase could crystallize depending on the nickel and silicon contents in the Earth's core, both of which are fcc stabilizer.

Beamline BL10XU at SPring-8, designed for X-ray diffraction experiments using diamond anvil cells at high pressure and low/high temperature, is continuously upgraded. The X-ray source, optics, and attractive experimental equipment such as simultaneous measurement systems have been optimized over the past years. The high energy and high intensity monochromatic X-ray beams emitted by an undulator source, focused using a characteristic X-ray refractive lens, have enabled us to obtain excellent counting statistics and high-resolution X-ray diffraction data even from a highly compressed sample under multi-megabar pressure. At BL10XU, low- and high-temperature conditions are achieved using a cryostat (10–300 K) and double-sided laser-heating system (1000–4000 K), respectively. Numerous results have been obtained in the fields of high-pressure materials science and mineral physics: for instance, the structural information on novel materials under pressure, including new pressure-induced structural phase transiti...

A phase transition of MgSiO3 perovskite, the most abundant component of the lower mantle, to a higher-pressure form called post-perovskite was recently discovered for pressure and temperature conditions in the vicinity of the Earth's core-mantle boundary. This discovery has profound implications for the chemical, thermal, and dynamical structure of the lowermost mantle called the D” region. Several major seismological characteristics of the D” region can now be explained by the presence of post-perovskite, and the specific properties of the phase transition provide the first direct constraints on absolute temperature and temperature gradients in the lowermost mantle. Here we discuss the current understanding of the core-mantle boundary region.

We have determined the unit-cell volumes of Au and MgO by synchrotron X-ray diffraction (XRD) measurements at pressures between 11 and 140 GPa and temperatures from 300 to 2330 K in a diamond-anvil cell (DAC). Since the MgO pressure scale appears the most practical at present, it is useful to obtain the P – V – T equation of state of Au that is consistent with the MgO scale. Here we present the new Au pressure scale based on the simultaneously measured volume data of Au and MgO in this study and in Fei et al. [Fei, Y., Li, J., Hirose, K., Minarik, W., Van Orman, J., Sanloup, C., Westrenen, W.V., Komabayashi, T., Funakoshi, K., 2004. A critical evaluation of pressure scales at high temperatures by in situ X-ray diffraction measurements. Phys. Earth Planet. Inter. 143–144, 515–526] using MgO as a reference pressure scale. The new scale predicts larger thermal pressure than previously proposed thermal equations of state of Au and therefore gives higher pressure above 1500 K in a pressure range exceeding 35 GPa.

Subduction of mid-oceanic ridge basalt (MORB) gives rise to strong chemical heterogeneities in the Earth's mantle, possibly extending down to the core–mantle boundary. Phase relations in both pyrolite and MORB compositions are precisely determined at high pressures and temperatures corresponding to lowermost mantle conditions. The results demonstrate that the post-perovskite phase transition occurs in pyrolite between 116 and 121 GPa at 2500 K, while post-perovskite and SiO2 phase transitions occur in MORB at ∼ 4 GPa lower pressure at the same temperature. Theory predicts that these phase changes in pyrolite and MORB cause shear wave velocity increase and decrease, respectively. Near the northern margin of the large low shear velocity province in the lowermost mantle beneath the Pacific, reflections from a negative shear velocity jump near 2520-km depth are followed by reflections from a positive velocity jump 135 to 155-km deeper. These negative and positive velocity changes are consistent with the expected phase transitions in a dense pile containing a mixture of MORB and pyrolitic material. This may be a direct demonstration of the presence of accumulations of subducted MORB crust in the deep mantle.

The high-pressure stability limit of calcium aluminosilicate (CAS) phase has been examined in its end-member CaAl4Si2O11 composition at 18–39 GPa and 1,670–2,300 K in a laser-heated diamond-anvil cell (LHDAC). The in-situ synchrotron X-ray diffraction measurements revealed that the CAS phase decomposes into three-phase assemblage of cubic Al-bearing CaSiO3 perovskite, Al2O3 corundum, and SiO2 stishovite above 30 GPa and 2,000 K with a positive pressure–temperature slope. Present results have important implications for the subsolidus mineral assemblage of subducted sediment and the melting phase relation of basalt in the lower mantle.

Simultaneous volume measurements of MgSiO 3 post-perovskite (PPv) and perovskite (Pv) were performed in a diamond anvil cell (DAC) combined with synchrotron X-rays. An externally-heated DAC was used in addition to a laser-heated DAC for the volume measurement experiment at high temperatures. The volume data were collected in the stability field of post-perovskite from 115 to 130 GPa. The temperature generated in the externally-heated and the laser-heated DACs for the volume measurement were up to 832 and 2330 K, respectively. Using two different but complementary heating techniques, we collected the data at a wide temperature range from 300 to 2330 K. The obtained P-V-T data for PPv and Pv were fitted to a third-ordered Birch-Murnaghan equation of state (EOS). For a precise comparison of the volume between the two phases, the EOSs were constructed based on the same pressure scale of MgO. The simultaneous volume measurements and the volumes calculated from the determined EOSs demonstrate that the volume difference between PPv and Pv of about 1.5% is almost constant with increasing temperature to 4000 K at the transition. At the base of the mantle, this density difference corresponds to a temperature anomaly of 1300 K without the phase transition due to the very small thermal expansivity of minerals, which has a significant effect on mantle dynamics. The thermal expansivity contrast between the top and the bottom of the mantle is a factor of 3.6. From a mantle convection study, this value suggests that huge and hot plumes are formed at the core–mantle boundary.

The discovery of a post-perovskite phase transition in MgSiO 3 has significant implications for seismological observations in the D ″ region at the bottom of Earth's mantle. The D ″ discontinuity, which is manifested as a sharp positive seismic-wave velocity jump 200–300 km above the core–mantle boundary (at pressure of 119∼ 125 GPa), is one of the most enigmatic seismic features in this region. Whether this velocity increase may be due to the formation of a post-perovskite phase at the D ″ discontinuity has not, however, been directly addressed by experiments. Here we present the results of aggregate sound velocity measurements of the MgSiO 3 post-perovskite phase by Brillouin spectroscopy in the diamond anvil cell (DAC) up to a pressure of 172 GPa, in combination with infrared laser annealing of the sample. Based on these results and our recent high-pressure velocity measurements on perovskite, the aggregate shear wave velocity contrast across the perovskite to post-perovskite phase transition is at most 0.5%. This contrast is much smaller than typically observed across the D ″ discontinuity, indicating that the formation of an isotropic aggregate of the post-perovskite phase provides an insufficient velocity increase to explain the D ″ discontinuity. Lattice preferred orientation (LPO) of post-perovskite is likely to be crucial for explaining the D ″ discontinuity.

A new polymorph of FeS has been observed at pressures above 30 GPa at 1,300 K by in situ synchrotron X-ray diffraction measurements in a laser-heated diamond anvil cell. It is stable up to, at least, 170 GPa at 1,300 K. The new phase (here called FeS VI) has an orthorhombic unit cell with lattice parameters a = 4.8322 (17) A, b = 3.0321 (6) A, and c = 5.0209 (8) A at 85 GPa and 300 K. Its topological framework is based on the NiAs-type structure as is the case for the other reported polymorphs (FeS I-V). The unit cell of FeS VI is, however, more distorted (contracted) along the [010] direction of the original NiAs-type cell. For example, the c/b axial ratio is ∼1.66 at 85 GPa and 300 K, which is considerably smaller than that of orthorhombic FeS II (∼1.72) and NiAs-type hexagonal FeS V (=√3 ≈ 1.73). The phase boundary between FeS IV and VI is expected to be located around 30 GPa at 1,300 K. The phase transition is accompanied by gradual and continuous changes in volume and axial ratios and may be second order. At room temperature, FeS VI becomes stable over FeS III at pressures above 36 GPa. It is, therefore, suggested that the phase boundary of FeS III–VI and/or FeS IV–VI has negative pressure dependence.

Phase relations in Mg 0.5 Fe 0.5 SiO 3 and Mg 0.25 Fe 0.75 SiO 3 were investigated in a pressure range from 72 to 123 GPa on the basis of synchrotron X-ray diffraction measurements in situ at high-pressure and -temperature in a laser-heated diamond-anvil cell (LHDAC). Results demonstrate that Mg 0.5 Fe 0.5 SiO 3 perovskite is formed as a single phase at 85–108 GPa and 1800–2330 K, indicating a high solubility of FeO in (Mg,Fe)SiO 3 perovskite at high pressures. Post-perovskite appears coexisting with perovskite in Mg 0.5 Fe 0.5 SiO 3 above 106 GPa at 1410 K, the condition very close to the post-perovskite phase transition boundary in pure MgSiO 3 . The coexistence of perovskite and post-perovskite was observed to 123 GPa. In addition, post-perovskite was formed coexisting with perovskite also in Mg 0.25 Fe 0.75 SiO 3 bulk composition at 106–123 GPa. In contrast to earlier experimental and theoretical studies, these results show that incorporation of FeO stabilizes perovskite at higher pressures. This could be due to a larger ionic radius of Fe 2+ ion, which is incompatible with a small Mg 2+ site in the post-perovskite phase.

Processes that operated in the early Earth have largely been erased or overprinted by subsequent evolution. However, some traces may persist in the deep Earth as imaged by seismology. Large‐scale features with reduced seismic velocities are simply explained as variations of composition, and small‐scale ultra‐low velocity zones are explained by the presence of Fe‐rich material that may be partially molten. Both can originate from fractional crystallization of an originally thick basal magma ocean (BMO). Many questions are raised by this scenario regarding properties of melts with various compositions, in particular the partition coefficients between melt and crystals of various elements and their relative densities. After reviewing recent progress on both the structure of the lower mantle and the mineral physics associated with partial melting/freezing of silicates at high pressure, we discuss several ways in which a BMO can be produced. We argue that, in most cases, independently of whether a melt of composition similar to that of the bulk mantle is more or less dense than crystals in equilibrium, the compositional evolution of both the magma and the solid should lead to the formation of a dense, Fe‐rich BMO whose subsequent slow evolution would explain some features of the present lower mantle. 1 Laboratoire de geologie de Lyon, ENS de Lyon, Universite Lyon-1, CNRS, Lyon, France 2 Earth‐Life Science Institute, Tokyo Institute of Technology, Meguro, Tokyo, Japan c07.indd 123 8/24/2015 4:02:55 PM

Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a high-dimensional graphical model. However, the penalized maximum likelihood procedure is sensitive to outliers. To overcome this problem, we introduce a robust estimation procedure based on the $\gamma$-divergence. The proposed method has a redescending property, which is known as a desirable property in robust statistics. The parameter estimation procedure is constructed using the Majorize-Minimization algorithm, which guarantees that the objective function monotonically decreases at each iteration. Extensive simulation studies showed that our procedure performed much better than the existing methods, in particular, when the contamination ratio was large. Two real data analyses were carried out to illustrate the usefulness of our proposed procedure., Comment: 27 pages

Lakshtanov et al. (2007) showed that incorporation of aluminum and some water into SiO2 significantly reduces the post-stishovite transition pressure in SiO2. This discovery suggested that the ferroelastic post-stishovite transition in subducted MORB crust could be the source of reflectors/scatterers with low shear velocities observed in the mid to upper lower mantle. A few years later, a similar effect was observed in anhydrous Al-bearing silica. In this paper, we show by first principles static calculations and by molecular dynamics using inter-atomic potentials that hydrogen bonds and hydrogen mobility play a crucial role in lowering the post-stishovite transition pressure. A cooperative redistribution of hydrogen atoms is the main mechanism responsible for the transition pressure reduction in hydrous aluminous stishovite. The effect is enhanced by increasing hydrogen concentration. This perspective suggests a potential relationship between the depth of seismic scatterers and the water content in stishovite.

The phase equilibria, structures, and properties of a high-pressure polymorph of silicate perovskite, called post-perovskite, are discussed. This phase was discovered in 2004 and provides a viable candidate for a deep mantle phase transition in the primary lower mantle mineral, silicate perovskite. Post-perovskite may exist in regions of the lowermost mantle at temperatures below about 3,000 K, and the phase transition from perovskite to post-perovskite may explain observations of a velocity discontinuity in seismic S waves and relatively strong anisotropy of the lower most mantle D″ region. The phase transition has important dynamical consequences for heat transport and boundary layer instabilities.

Using the laser-heated diamond anvil cell, we investigate the stability and equation of state of the postperovskite (ppv, CaIrO 3 -type) phase synthesized from a natural pyroxene composition with 9 mol.% FeSiO 3 . Our measured pressure-volume data from 12–106 GPa for the ppv phase yield a bulk modulus of 219( 5 ) GPa and a zero-pressure volume of 164.9( 6 ) Å 3 when K ′ 0 = 4. The bulk modulus of ppv is 575( 15 ) GPa at a pressure of 100 GPa. The transition pressure is lowered by the presence of Fe. Our x-ray diffraction data indicate the ppv phase can be formed at P > 109( 4 ) GPa and 2,400(400) K, corresponding to ≈400–550 km above the core-mantle boundary. Direct comparison of volumes of coexisting perovskite and CaIrO 3 -type phases at 80–106 GPa demonstrates that the ppv phase has a smaller volume than perovskite by 1.1( 2 )%. Using measured volumes together with the bulk modulus calculated from equation of state fits, we find that the bulk sound velocity decreases by 2.3(2.1)% across this transition at 120 GPa. Upon decompression without further heating, it was found that the ppv phase could still be observed at pressures as low at 12 GPa, and evidence for at least partial persistence to ambient conditions is also reported.

The stability and high-pressure behavior of perovskite structure in MnGeO3 and CdGeO3 were examined on the basis of in situ synchrotron X-ray diffraction measurements at high pressure and temperature in a laser-heated diamond-anvil cell. Results demonstrate that the structural distortion of orthorhombic MnGeO3 perovskite is enhanced with increasing pressure and it undergoes phase transition to a CaIrO3-type post-perovskite structure above 60 GPa at 1,800 K. A molar volume of the post-perovskite phase is smaller by 1.6% than that of perovskite at equivalent pressure. In contrast, the structure of CdGeO3 perovskite becomes less distorted from the ideal cubic perovskite structure with increasing pressure, and it is stable even at 110 GPa and 2,000 K. These results suggest that the phase transition to post-perovskite is induced by a large distortion of perovskite structure with increasing pressure.

Here, we precisely determined the low-pressure stability limit of phase A in the Mg-end-member antigorite bulk composition defined as the reaction forsterite + water = phase A + enstatite (“water-line” or “water-storage line”) in a multi-anvil apparatus. Pressures were determined by in situ synchrotron X-ray diffraction measurements using NaCl as an internal pressure standard. Results demonstrate that the water-line is located at 800 °C and 8.5 GPa and at 550 °C and 5.1 GPa with a Clapeyron slope of 13.6 MPa/°C. We also examined the conditions for the formation of phase A by the decomposition of antigorite on the basis of the phase relations in the systems MgO–SiO 2 –H 2 O (MSH) and MgO–Al 2 O 3 –SiO 2 –H 2 O (MASH). A descending slab peridotite retains water in phase A beyond the stability of antigorite only when temperature in the slab is lower than 550 or 660 °C at 5.1 GPa (corresponding to 160 km depth), in the system MSH or MASH, respectively. The double seismic planes observed within the slabs may be caused by the dehydration reaction of antigorite or chlorite. Their merging depths, which could represent the high-pressure stability limit of antigorite or chlorite, are 160 km or deeper beneath northeast Japan, Aleutian, Kamchatka and Kuril. Water included in hydrous slab peridotite is transported into the transition zone and deeper mantle in these areas but recycled to the surface in other subduction zones.

The interior of the Earth is under high-pressure and high-temperature conditions. High-pressure and -temperature experiments have been conducted by using the multi-anvil press and laser-heated diamond-anvil cell in order to determine the physical properties of minerals that constitute interior of the Earth. Since the sample volume in the high-pressure apparatus is very small, strong X-rays at synchrotron facilities are necessary for diffraction and imaging experiments. Here I introduce the recent studies on high-pressure and -temperature crystallography of the Earth and planetary materials.

Phase relations, mineral chemistry, and density of a natural mid-oceanic ridge basalt (MORB) composition were investigated up to 134 GPa and 2300 K by a combination of in-situ X-ray diffraction measurements and chemical analyses using transmission electron microscope (TEM). Results demonstrate that the MORB composition consists of MgSiO 3 -rich perovskite, stishovite, CaSiO 3 perovskite, and CaFe 2 O 4 -type Al-phase in the upper part of the lower mantle. The most abundant mineral of MgSiO 3 -rich perovskite undergoes phase transition to a CaIrO 3 -type post-perovskite phase above 110 GPa and 2500 K. Post-perovskite phase is similar in composition to perovskite except considerably high Na 2 O content. Stishovite transforms to CaCl 2 -type SiO 2 phase above 62 GPa and 2000 K and further to α-PbO 2 -type phase above 110 GPa. α-PbO 2 -type SiO 2 phase includes large amount of Al 2 O 3 , which significantly expands its stability relative to CaCl 2 -type phase. Phase transition of CaSiO 3 perovskite from tetragonal to cubic was also observed with increasing temperature. CaFe 2 O 4 -type Al-phase is stable to the bottom of the mantle. The density of MORB crust was calculated using volume data, combining with measured chemical compositions and calculated mineral proportions. The former MORB crust is denser than the average lower mantle at all depths greater than ∼ 720 km, contrary to earlier predictions. The subducted basaltic crust may have accumulated at the base of the mantle.

We investigated the phase transitions of FeO at high pressure and high temperature up to 87 GPa and 1730 K by in situ synchrotron X-ray diffraction measurements in a laser-heated diamond anvil cell (DAC). The results demonstrated that the NaCl-type (B1) structure of FeO undergoes transition to the NiAs-type (B8) structure above 70 GPa at 1600 K. The density increase across this transition is about 2%. Present B1–B8 transition pressure is consistent with the previous shock-induced transition pressure. The relative intensities of diffraction peaks of the B8 phase may suggest a polytype normal/inverse NiAs structure, which has a metallic nature that could promote the oxygen incorporation into the iron-rich core. Transition to the metallic B8 phase above 70 GPa is also consistent with the earlier electrical resistance measurements. The hexagonal close-packed (hcp) e-phase of Fe coexisted with FeO both at room temperature and high temperatures above 44–87 GPa.