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Ultralow-velocity zones (ULVZs) at Earth's core-mantle boundary region have important implications for the chemical composition and thermal structure of our planet, but their origin has long been debated. Hydrogen-bearing iron peroxide (FeO2Hx) in the pyrite-type crystal structure was recently found to be stable under the conditions of the lowermost mantle. Using high-pressure experiments and theoretical calculations, we find that iron peroxide with a varying amount of hydrogen has a high density and high Poisson ratio as well as extremely low sound velocities consistent with ULVZs. Here we also report a reaction between iron and water at 86 gigapascals and 2,200 kelvin that produces FeO2Hx. This would provide a mechanism for generating the observed volume occupied by ULVZs through the reaction of about one-tenth the mass of Earth's ocean water in subducted hydrous minerals with the effectively unlimited reservoir of iron in Earth's core. Unlike other candidates for the composition of ULVZs, FeO2Hx synthesized from the superoxidation of iron by water would not require an extra transportation mechanism to migrate to the core-mantle boundary. These dense FeO2Hx-rich domains would be expected to form directly in the core-mantle boundary region and their properties would provide an explanation for the many enigmatic seismic features that are observed in ULVZs.

Equilibrium fractionation factors of Ca isotopes among mantle minerals are essential for using Ca isotopes as an important tracer in mantle geochemistry. Using the vibrational frequencies obtained by the first-principles calculations based on density functional theory (DFT), we calculated equilibrium fractionation factors of Ca isotopes between two major Ca-bearing minerals, clinopyroxene (cpx) and orthopyroxene (opx). Our results show that opx has much higher 44 Ca/ 40 Ca than its co-existing cpx even at high temperatures (e.g., 1273 K), agreeing with the observations on mantle peridotites. In addition to the wellknown temperature effect, our calculations for the first time reveal that the inter-mineral Ca isotope fractionation factor between opx and cpx also has a strong dependence on the chemical composition of opx (i.e., Ca content). Specifically, it increases substantially with decreasing Ca/Mg (atomic ratio) of opx when Ca/Mgopx is lower than 1/15. Such compositional effect on inter-mineral Ca isotope fractionation provides a convincing interpretation to the different isotope fractionations between coexisting opx and cpx observed in Kilbourne Hole and San Carlos peridotites. 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t The elastic constant tensors of stishovite and the CaCl2-type silica at the Earth's mantle temperature and pressure were determined using first-principles calculations with local density approximation. The elastic properties of stishovite show not only strong pressure dependence but also temperature dependence. By increasing temperature, the shear instability of stishovite is shifted to an elevated pressure with a slope of ∼5.4 ± 1. 4M Pa /K. The softening of the shear modulus and the positive Clapeyron slope result in crossing of the sound velocities at different temperatures, which leads to the unusual positive temperature dependence of the sound velocities around the phase boundary. The transition from stishovite to the CaCl2-type silica at the lower mantle's temperature occurs at a depth far deeper than 1200 km and is accompanied by a velocity jump of ∼0.98 ± 0.08 km/ si n S wave velocity (V S) and ∼0.45 ± 0.15 km/s in P wave velocity (V P). This transition is likely related to the seismic discontinuity at the depth of ∼1670 km in the vicinity of Mariana Island. The unusual positive temperature dependence of V S of stishovite and strong anisotropy of stishovite and the CaCl2-type silica around the phase boundary

Silicon isotope fractionation factors for mantle silicate minerals, including olivine, wadsleyite, ringwoodite, pyroxenes, garnet (pyrope), majorite, and Mg-perovskite, are calculated using density functional theory. Our results show that equilibrium fractionations of Si isotopes are negligible among pyroxenes, olivine, and pyrope, but are significant between olivine and its polymorphs (wadsleyite and ringwoodite). There is also significant Si isotope fractionations between mantle minerals with different Si coordination numbers (CN), such as Mg-perovskite (CN = 6) and olivine polymorphs (CN = 4). When in equilibrium with each other, 30Si/28Si decreases in the order of olivine > pyroxenes > wadsleyite > majorite > ringwoodite > Mg-perovskite. Our calculation predicts significant Si isotope fractionation between mantle minerals, e.g., perovskite vs. ringwoodite, majorite vs. pyroxene, and olivine vs. its polymorphs even at high pressure and temperature conditions of deep mantle. The Si CN in silicate melt increases with increasing pressure, implying that Si isotope fractionation between silicate and metal could be a function of pressure. Our results suggest that Si isotopic fractionation factor between silicate and metal may decrease with increasing pressure; consequently, Si isotopic fractionation factor obtained from low pressure experiments may not be applicable to Si isotope fraction during core formation which occurred at high pressure. Finally, Si isotopes could also be fractionated between perovskite-rich mantle and residual melt during magma-ocean cooling in the lower mantle because of their different Si CNs. If such primordial signature is not destroyed and partially preserved through the Earth’s history, significant Si isotope heterogeneity could still exist between the upper and lower mantle.

X-ray grating interferometry (XGI) provides complementary information to visualize the internal structure of an object better than conventional absorption-based imaging methods, thereby having the potential for future biomedical applications. In XGI, information retrieval is critical for qualitative and quantitative research. However, information retrieval based on the phase-stepping technique usually requires that the absolute spatial translations of these phase-stepping position series lie in the range of only a few hundred nanometers, making this technique prone to mechanical instabilities and motion artifacts. In this paper, trimodal radiography using sinusoidal phase modulating interferometry is studied. The theoretical analysis of the signal retrieval algorithm using four integrating buckets is derived, and numerical experiments are demonstrated. In the proposed method, the phase modulation is generated by shifting the grating following a sinusoidal curve while the signals are retrieved from the four frames obtained by integrating the time-varying intensity over the four quarters of the modulation period. Compared with the previously proposed method, this method is easier to implement due to relaxed requirements on the phase-shifting device; high speed and continuous data averaging will greatly promote the real applications of the X-ray grating interferometer.

Equilibrium fractionation factors of Mg isotopes at high temperature and pressure are investigated for pyrope, majorite, clinopyroxene, orthopyroxene, and olivine using density functional theory. The calculated equilibrium fractionation factors are in good agreement with previous study (Schauble, 2011), suggesting that our calculations are reliable and accurate. The results reveal significant intermineral Mg isotope fractionations due to different coordination environment of Mg in minerals. Specifically, pyrope, where Mg is in eight-fold coordination, is more enriched in light Mg isotopes than olivine and pyroxene where Mg is in six-fold coordination. The calculated isotope fractionation for Mg isotopes between clinopyroxene and pyrope is consistent with observations from natural eclogites (Li et al., 2011; Wang et al., 2012). Our calculation also reveals substantial pressure effect on Mg isotope fractionations among garnet, pyroxene, and olivine. Equilibrium fractionation of Mg isotopes between pyrope and pyroxene (and olivine) could be used as a novel and independent thermometry with precision much better than the traditional garnet– clinopyroxene Fe–Mg exchange thermometry because such fractionation is significantly greater than the current uncertainties of Mg isotope analyses ( � 0.05% amu � 1 ). These Mg isotope thermometries

[1] We present first-principles results for elastic moduli (bulk, K, and shear, G) and acoustic velocities (compressional, VP, shear, VS, and bulk VΦ) of olivine (α) and wadsleyite (β) (Fex,Mg1 − x)2SiO4, at high pressure (P) and temperature (T) with varying iron content (0 ≤ x ≤ 0.125). Pressure and temperature derivatives of these properties are analyzed. We show that adding 12.5% of Fe in forsterite softens VP and VS by ∼3–6%, the same effect as raising temperature by ∼1000 K in dry olivine at 13.5 GPa—the same is true in wadsleyite. This study suggests that Fe is effective in producing seismic velocity heterogeneity at upper mantle and transition zone conditions and should be another key ingredient, in addition to temperature and water content variations, in interpreting seismic heterogeneities in the transition zone. The effect of Fe on density, elastic, and velocity contrasts across the α → β transition is also addressed at relevant conditions. We show that simultaneous changes of composition, temperature, and pressure do not affect significantly the relative density contrasts. We also find that compressional and shear impedance contrasts result primarily from velocity discontinuities rather than density discontinuity.

In this study, we used first-principles calculations based on density functional theory to investigate silicon and oxygen isotope fractionation factors among the most abundant major silicate minerals in granites, i.e., quartz and plagioclase (including albite and anorthite), and an important accessory mineral zircon. Combined with previous results of minerals commonly occurring in the crust and upper mantle (orthoenstatite, clinoenstatite, garnet, and olivine), our study reveals that the Si isotope fractionations in minerals are strongly correlated with SiO4 tetrahedron volume (or average Si–O bond length). The 30Si enrichment order follows the sequence of quartz > albite > anorthite > olivine ≈ zircon > enstatite > diopside, and the 18O enrichment follows the order of quartz > albite > anorthite > enstatite > zircon > olivine. Our calculation predicts that measurable fractionation of Si isotopes can occur among crustal silicate minerals during high-temperature geochemical processes. This work also allows us to evaluate Si isotope fractionation between minerals and silicate melts with variable compositions. Trajectory for δ30Si variation during fractional crystallization of silicate minerals was simulated with our calculated Si isotope fractionation factors between minerals and melts, suggesting the important roles of fractional crystallization to cause Si isotopic variations during magmatic differentiation. Our study also predicts that δ30Si data of ferroan anorthosites of the Moon can be explained by crystallization and aggregation of anorthite during lunar magma ocean processes. Finally, O and Si isotope fractionation factors between zircon and melts were estimated based on our calculation, which can be used to quantitatively account for O and Si isotope composition of zircons crystallized during magma differentiation.

Thermodynamic (Anderson 2005) and elastic properties (Musgrave 1970) of minerals provide the fundamental information needed to analyze seismic observations and to model Earth’s dynamic state. The connection between pressure, temperature, chemical composition, and mineralogy that produce seismic velocity gradients, heterogeneities, and discontinuities, can be established with knowledge of thermoelastic and thermodynamic equilibrium properties of single phases and their aggregates. There is a broad-based need in solid Earth geophysics for these thermoelastic properties to model the Earth. However, the materials and conditions of the Earth’s interior present several challenges. The chemical composition of the Earth’s mantle is complex with at least five major oxide components and tens of solid phases. Today, this type of challenge is more effectively addressed by a combination of experimental and computational methods. Experiments offer accurate information at lower pressures and temperatures, while computations offer more complete and detailed information at higher pressures and temperatures, where experimental uncertainties are large and conditions difficult to control in the laboratory. The overwhelming success of density functional theory (Hohenberg and Kohn 1964; Kohn and Sham 1965) combined with the quasiharmonic approximation (QHA) (Born and Huang 1956; Wallace 1972) for computations of thermodynamic properties of major mantle minerals has been reviewed in this book (Wentzcovitch et al. 2010). Although these properties were cited and compared with experiments only at ambient conditions, in general, quasiharmonic calculations perform even better at higher pressures (see references in Wentzcovitch et al. 2010). In this paper we review the extension of these calculations to high pressure and high temperature elasticity. There are important exceptions, such as CaSiO3-perovskite, whose high temperature structure is stabilized by anharmonic fluctuations (Stixrude et al. 1996). Such cases cannot be addressed using the QHA and one must resort of molecular dynamics (MD) in some form. Great progress has …

This research has been motivated by geophysics and materials physics. The objective of this research has been to advance materials theory and computations for high pressure and high temperature applications to the point that it can make a difference in our understanding of the Earth. Understanding of the mineralogy, composition, and thermal structure of the Earth evolves by close interaction of three fields: seismology, geodynamics, and mineral physics. Earth’s structure is imaged by seismology, which obtains body wave velocities and density throughout the Earth’s interior (Fig. 1⇓). Interpretation of this data relies on knowledge of aggregate properties of Earth forming materials either measured in laboratory or calculated, in many cases by both. However, the conditions of the Earth’s interior, especially at the core, may be challenging for important experiments, and materials computations have emerged to contribute decisively to this field. Earth’s evolution is simulated by geodynamics, but these simulations need as input information about rheological and thermodynamic properties of minerals, including phase transformation properties such as Clapeyron slopes. Our research has concentrated on the phases of the Earth’s mantle, particularly the deep mantle whose conditions are more challenging for experiments. The mantle accounts for ~83% of the Earth’s volume. In this article we will review the essential first-principles approach used to investigate solids at high temperatures and pressures, summarize their performance for mantle minerals (Fig. 2⇓), and point to critical results that have stirred us in the current research path. The success is remarkable, but some limitations point the way to future developments in this field. Figure 1. (a) Velocities and density profiles (Kennett et al. 1995), (b) Earth’s cross section, and (c) composition and mineralogy of Earth’s layers. Figure 2. Phases proportions versus depth and or pressure. Ol = (Mg,Fe)2SiO4 olivine, also known as α-phase; β = (Mg,Fe) …

The lower mantle is the largest layer of the Earth. Pressures and temperatures there vary from 23 GPa to 135 GPa and ~1,900 K to 4,000 K. Aluminous perovskite, Al-Mg1− x Fe x SiO3, and ferropericlase, Mg1− x Fe x O, are the most important phases of the Earth’s lower mantle, comprising ~62 vol% and ~35 vol% of this region, respectively. The remaining consists of CaSiO3-perovskite, according to the pyrolitic compositional model (Ringwood 1982). Silicate perovskite transforms into another polymorph, post-perovskite, at conditions expected to occur near the D″ discontinuity in the deep slower mantle, i.e., 2,500 K and 125 GPa (Murakami et al. 2004; Oganov and Ono 2004; Tsuchiya et al. 2004; Wentzcovitch et al. 2006). The spin-state crossover (also referred to as “spin pairing transition” or “spin(-state) transition”) of iron in ferropericlase under pressure was observed in 2003 by X-ray emission spectroscopy (XES) (Badro et al. 2003). In the following year a similar phenomenon was also identified in iron-bearing perovskite (Mg1− x Fe x SiO3) by the same technique (Badro et al. 2004). This phenomenon had been predicted for decades (Fyfe 1960; Gaffney and Anderson 1973; Ohnishi 1978; Sherman 1988, 1991; Sherman and Jansen 1995; Cohen et al. 1997) but the pressure conditions were challenging for this type of experiment and it took several decades to observe it. The implications of this phenomenon for the properties of this region, or of the entire planet, are yet to be understood. Today, theoretical studies are making decisive contributions to this problem. This article reviews the main theoretical results on the spin-state crossover in the lower mantle phases. Spin changes in strongly correlated oxides and silicates under pressure is the type of problem that …

ARTICLE I NFO Phase relations in α-β-γ Mg2SiO4 have been investigated by first principles quasi-harmonic free energy computations. The computed phase boundaries obtained using the local density approximation (LDA) and the generalizedgradientapproximation(GGA)brackettheexperimentalones,withLDA(GGA)calculationsgivingthe lowest (highest) bound, while the Clapeyron slopes are in good agreement with the experimentally determined ones. This is the same trend displayed by previous similar computations. Further analyses reveal that despite the uncertaintiesinphaseboundary determination, thecalculated discontinuitiesindensity, bulk modulus, and bulk sound velocity are quite insensitive to pressure and have small uncertainties and useful accuracy to discriminate potential sources of discontinuities in the mantle. We verify that ∼3% density discontinuity at 410-km depth can be produced primarily by the α to β transition in an aggregate with pyrolite composition, i.e. ∼60 vol.% of Mg2SiO4. However, the 1.3-2.9% density discontinuity observed in some places at 520-km depth cannot be accounted for solely by the β to γ transition but also requires changes in the coexisting pyroxene/garnet/Ca- perovskite system.

We present LDA+U calculations of high temperature elastic properties of bridgmanite with composition (Mg$_{(1-x)}$Fe$_{x}^{2+}$)SiO$_3$ for $0\le{x}\le0.125$. Results of elastic moduli and acoustic velocities for the Mg-end member (x=0) agree very well with the latest high pressure and high temperature experimental measurements. In the iron-bearing system, we focus particularly on the change in thermoelastic parameters across the state change that occurs in ferrous iron above $\sim$30 GPa, often attributed to a high-spin (HS) to intermediate spin (IS) crossover but explained by first principles calculations as a lateral displacement of substitutional iron in the perovskite cage. We show that the measured effect of this change on the equation of state of this system can be explained by the lateral displacement of substitutional iron, not by the HS to IS crossover. The calculated elastic properties of (Mg$_{0.875}$Fe$_{0.125}^{2+}$)SiO$_3$ along an adiabatic mantle geotherm, somewhat overestimate longitudinal velocities but produce densities and shear velocities quite consistent with Preliminary Reference Earth Model data throughout most of the lower mantle., Comment: Accepted for Geophysical Research Letters (DOI: 10.1002/2014GL062888)

A main characteristic of typical relaxor ferroelectrics distinguished from normal ferroelectric is the diffuse phase transition (DPT), i.e. the dielectric constant slowly varies nearby the temperature of the dielectric peak. DPT behavior can be well described by a modified Curie-Weiss formula. Dependence of the critical exponent on the tunneling frequency has been investigated with the eight-potential-well order-disorder ferroelectric model. For low tunneling frequency, the ferroelectric phase transition is of second-order and the system conforms to the Curie-Weiss law. The critical exponent departs significantly from the Curie-Weiss value of unity and increases with increasing tunneling frequency at the region of the first-order phase transition, which is a typical diffuse phase transition behavior. Our work is useful for understanding the phenomena that some normal ferroelectrics show pressure-induced crossover from normal ferroelectric to relaxor.

In X-ray grating-based phase contrast imaging, information retrieval is necessary for quantitative research, especially for phase tomography. However, numerous and repetitive processes have to be performed for tomographic reconstruction. In this paper, we report a novel information retrieval method, which enables retrieving phase and absorption information by means of a linear combination of two mutually conjugate images. Thanks to the distributive law of the multiplication as well as the commutative law and associative law of the addition, the information retrieval can be performed after tomographic reconstruction, thus simplifying the information retrieval procedure dramatically. The theoretical model of this method is established in both parallel beam geometry for Talbot interferometer and fan beam geometry for Talbot-Lau interferometer. Numerical experiments are also performed to confirm the feasibility and validity of the proposed method. In addition, we discuss its possibility in cone beam geometry ...

Deciphering the origin of seismic velocity heterogeneities in the mantle is crucial to understanding internal structures and processes at work in the Earth. The spin crossover in iron in ferropericlase (Fp), the second most abundant phase in the lower mantle, introduces unfamiliar effects on seismic velocities. First-principles calculations indicate that anticorrelation between shear velocity (VS) and bulk sound velocity (Vφ) in the mantle, usually interpreted as compositional heterogeneity, can also be produced in homogeneous aggregates containing Fp. The spin crossover also suppresses thermally induced heterogeneity in longitudinal velocity (VP) at certain depths but not in VS. This effect is observed in tomography models at conditions where the spin crossover in Fp is expected in the lower mantle. In addition, the one-of-a-kind signature of this spin crossover in the RS/P (∂ ln VS/∂ ln VP) heterogeneity ratio might be a useful fingerprint to detect the presence of Fp in the lower mantle.

Amorphous silica aerogels doped with ions (SADAs) were prepared by the sol-gel route and supercritical drying. The visible luminescence of SADAs was measured and compared with that of porous silicon (PS), pure silica aerogels (PSAs) and silica xerogels doped with ions (SXDAs). The effect of annealing on the luminescence intensity of SADAs was investigated. Results show that (1) the luminescent intensity of as-prepared SADAs is much higher than that of as-prepared PSAs and SXDAs after annealing at ; (2) after annealing at , the visible luminescence of SADAs is further substantially enhanced and becomes much higher than that of PS. However, for PSAs and SXDAs after annealing at the luminescent intensity is still kept at a very low value in comparison with that of SADAs. The strong visible luminescence appearing in SADAs is ascribed to significant amounts of the twofold coordinated Si (the (neutral) centre) in SADAs.

The discovery of a pressure induced iron-related spin crossover in Mg((1-x))Fe(x)O ferropericlase (Fp) and Mg-silicate perovskite, the major phases of Earth's lower mantle, has raised new questions about mantle properties which are of central importance to seismology. Despite extensive experimental work on the anomalous elasticity of Fp throughout the crossover, inconsistencies reported in the literature are still unexplained. Here we introduce a formulation for thermoelasticity of spin crossover systems, apply it to Fp by combining it with predictive first principles density-functional theory with on-site repulsion parameter U calculations, and contrast results with available data on samples with various iron concentrations. We explain why the shear modulus of Fp should not soften along the crossover, as observed in some experiments, predict its velocities at lower mantle conditions, and show the importance of constraining the elastic properties of minerals without extrapolations for analyses of the thermochemical state of this region.

We combine density functional theory (DFT) within the local density approximation (LDA), the quasiharmonic approximation (QHA), and a model vibrational density of states (VDoS) to calculate elastic moduli and sound velocities of gamma-[Fe_x,Mg_(1-x)]_2SiO_4 (ringwoodite), the most abundant mineral of the lower Earth's transition zone (TZ). Comparison with experimental values at room-temperature and high pressure or ambient-pressure and high temperature shows good agreement with our first-principles findings. Then, we investigate the contrasts associated with the beta-to-gamma-[Fe_x,Mg_(1-x)]_2SiO_4 transformation at pressures and temperatures relevant to the TZ. This information offers clearly defined reference values to advance the understanding of the nature of the 520 km seismic discontinuity., Comment: 29 pages, 6 figures, 2 tables. Under Review

The high quality and cm-dimension red bronze single crystal K0.33MoO3 was prepared by the EHTS method using new molar ratio. In the temperature range from 130 to 410 K, the samples have semiconductor-like temperature dependence of resistance, i.e., log R∝1/T, and the energy gap Eg is calculated to be approximately 0.4 eV.

[1] At the Rayleigh number appropriate to Earth's mantle, radial heat transport is dominated by solid state thermal convection. Because of the large number of physical properties required to determine the Rayleigh number, and because these properties are expected to be (perhaps strong) functions of pressure and temperature (P-T), laboratory measurements of them under the high pressure and temperature conditions that occur in the deep Earth are of fundamental importance. Recent experimental data demonstrate that an electronic spin transition in iron that occurs at midmantle depths results in significant changes in the physical properties of the ferropericlase component of mantle mineralogy. Additional recent results suggest that it may also exist in the dominant perovskite component. Using control volume based numerical models we investigate the impacts on mantle mixing of this spin transition through its influence on the most important subset of these physical properties, namely density, thermal expansivity, bulk modulus and heat capacity. Our numerical model results demonstrate that this electronic transition enhances mixing in the lower regions of the lower mantle by enhancing the vigor of rising plumes. The lowermost region of the mantle is slightly warmed and the upper mantle slightly cooled by spin-induced effects. However, the spin crossover in the lower mantle appears not to significantly influence mantle layering. Due to the competition that could exist between the strength of the spin-induced thermodynamic properties of ferropericlase and perovskite, cold descending thermal anomalies could stagnate at middle-to-lower mantle depths and lead to the occurrence of “mid mantle avalanches.”

First-principles quasiharmonic calculations play a very important role in mineral physics because they can predict the structural and thermodynamic properties of materials at pressure and temperature conditions of the Earth’s interior that are still challenging for experiments. They also enable calculations of thermal elastic properties by providing second-order derivatives of free energies with respect to strain. The latter are essential to interpret seismic tomography of the mantle in terms of temperature, composition, and mineralogy, in the context of geophysical processes. However, these are exceedingly demanding computations requiring up to ∼10 3 parallel jobs running on tens or more processors each. Here we introduce an analytical and computationally simpler approach that requires only calculations of static elastic constants and phonon density of states for unstrained configurations. This approach, currently implemented for crystals with up to orthorhombic symmetry, decreases the computational effort, i.e., CPU time and human labor, by up to two orders of magnitude. Results for the major mantle phases periclase (MgO) and forsterite (α-Mg2SiO4) show excellent agreement with previous first-principles results and experimental data.

We developed a method to calculate the anharmonic free energy without requiring any adjustable parameter. The requisite computations are first-principles quasiharmonic calculations plus an additional Canonical (NVT) ensemble first-principles molecular-dynamics simulation and, therefore, are affordable. The thermodynamic properties of diamond and MgO at high temperature improve substantially after including the anharmonic free energy.

[1] In the paper “Pressure‐volume‐temperature relations in MgO: An ultrahigh pressure‐temperature scale for planetary sciences applications” by Zhongqing Wu, Renata M. Wentzcovitch, Koichiro Umemoto, Baosheng Li, Kei Hirose, and Jin‐Cheng Zheng (Journal of Geophysical Research, 113, B06204, doi:10.1029/2007JB005275, 2008), on Figure 4 two theoretical melting curves by Belonoshko and Dubrovinsky [1996] and Strachan et al. [1999] are switched; that is, the dotted line is from Belonoshko and Dubrovinsky [1996] and the heavy dashed line is from Strachan et al. [1999].

A semiempirical ansatz to compute anharmonic contributions to the free energy neglected in quasiharmonic calculations is introduced. A parametrized temperature-dependent modification of the vibrational density of states designed to be used directly with the quasiharmonic free-energy expression is proposed. An approximate relationship between the modified frequencies and the renormalized frequencies is developed. This parametrization is shown to produce the correct low and high temperature behavior of the anharmonic free energy and other thermodynamics properties. It is shown that the thermodynamics properties of - and -Mg2SiO4 forsterite and wadsleyite and MgO periclase improve considerably after inclusion of anharmonic effects. Anharmonicity is shown to have a significant effect on the phase boundary of the forsterite to wadsleyite transformation. Inclusion of anharmonic effects can reconcile discrepancies between the measurements of the Clapeyron slope of this transition and the values predicted by quasiharmonic calculations.

[1] In situ crystallography based on diamond anvil cells have been extended to the multimegabar regime. Temperatures in these experiments have crossed the 2500 K mark. Yet, current high pressure-temperature (PT) standards of calibration produce uncertainties that inhibit clear conclusions about phenomena of importance to planetary processes, e.g., the postperovskite transition in Earth’s mantle. We introduce a new thermal equation of state (EOS) of MgO which appears to be predictive up to the multimegabar and thousands of kelvin range. It is obtained by combining first principles local density approximation quasi-harmonic (QHA) calculations with experimental lowpressure data. This EOS agrees exceptionally well with shock compression data. The postspinel and postperovskite phase boundaries recalculated using our EOS match seismic observations. The latter, in particular, supports the idea that postperovskite transforms back to perovskite before the core-mantle boundary. The recalculated experimental Clapeyron slope of the postperovskite transition is also more consistent with those obtained by first principles calculations. Citation: Wu, Z., R. M. Wentzcovitch, K. Umemoto, B. Li, K. Hirose, and J.-C. Zheng (2008), Pressure-volume-temperature relations in MgO: An ultrahigh pressure-temperature scale for planetary sciences applications, J. Geophys. Res., 113, B06204

[i] The vibrational properties of Mg 2 SiO 4 wadsleyite have been calculated over a wide pressure range using density functional perturbation theory (DFPT). Both the normal mode frequencies and their volume dependences are consistent with the available Raman and infrared data. We provide detailed information about vibrational properties that are still not experimentally available. The vibrational density of states (vDOS) is used to calculate the Helmholtz free energy within the quasi-harmonic approximation (QHA) and other thermodynamic quantities without further approximations. The extensive and successful comparisons with experiments demonstrate once more that the QHA combined with first principles vDOSs can provide accurate thermodynamic properties of minerals over the large pressure-temperature regime relevant for the Earth.

The ferroelectric properties of disorder $\mathrm{Pb}({\mathrm{Zr}}_{0.5}{\mathrm{Ti}}_{0.5}){\mathrm{O}}_{3}$ thin films are investigated with Monte Carlo simulations on the basis of a first-principles-derived Hamiltonian. It is found that there exists a critical thickness of about three unit cells $(\ensuremath{\sim}12\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$ below which the ferroelectricity disappears under the condition that the in-plane polarizations are suppressed by sufficient clamping effect. Above the critical thickness, periodic 180\ifmmode^\circ\else\textdegree\fi{} stripe domains with out-of-plane polarizations are formed in the systems in order to minimize the energy of the depolarizing field. The stripe period increases with increasing film thickness. The microscopic mechanism responsible for these phenomena is discussed.

Using a first-principles-based approach, we determine the ferroelectric pattern in PbZr$_{0.5}$Ti$_{0.5}$O$_3$ ultrathin film. It is found that vortex stripes are formed in the system and they are responsible for the 180$^\circ$ domains observed. When a local external field is exerted, the vortex stripe transforms into the vortex loop structure, which leads to the formation of a smaller domain with the polarization antiparallel to the field in the center of the field region. This may provide a convenient way to manipulate nanodomains in thin films., Comment: 5 pages, 3 figures

Monte Carlo simulations based on a first-principles-derived Hamiltonian are conducted to study the properties of Pb(Zr1-xTix)O3 alloys compositionally modulated along the [100] pseudocubic direction near the morphotropic phase boundary. It is shown that compositional modulation causes the polarization to continuously rotate away from the modulation direction, resulting in the unexpected triclinic and C-type monoclinic ground states and huge enhancement of electromechanical responses (the peak of piezoelectric coefficient is as high as 30,000 pC/N). The orientation dependence of dipole-dipole interaction in modulated structure is revealed as the microscopic mechanism to be responsible for these anomalies.

The effect of a defect-induced internal field on the dielectric response of relaxor ferroelectrics is investigated using a Monte Carlo simulation. It was observed that only at a small temperature range near the temperature of the dielectric maximum does the susceptibility decrease markedly due to the internal field. This temperature range increases with enhancing internal field. We found that the susceptibility is almost independent of the internal field width at low internal field width, and then decreases linearly with enhancing internal field width. This dependence of the susceptibility on the internal field width is very similar to the relation of the dielectric constant with logarithmic aging time, which probably suggests a linear dependence of the internal field on the logarithm of the aging time. The frequency dependence of the susceptibility aging is sensitive to the temperature. With increasing temperature, the curve of the susceptibility change against logarithmic frequency varies from concave to approximately linear, and then to convex, which is in agreement with the recent aging rate measurement.

Monte Carlo simulations based on a first-principles-derived Hamiltonian are conducted to study the properties of Pb(Zr1-xTix)O3 alloys compositionally modulated along the [100] pseudocubic direction near the morphotropic phase boundary. It is shown that compositional modulation causes the polarization to continuously rotate away from the modulation direction, resulting in the unexpected triclinic and C-type monoclinic ground states and huge enhancement of electromechanical responses (the peak of piezoelectric coefficient is as high as 30,000 pC/N). The orientation dependence of dipole-dipole interaction in modulated structure is revealed as the microscopic mechanism to be responsible for these anomalies.

An improved eight-potential-well order-disorder ferroelectric model with isotropic distribution of random fields has been proposed and the field-induced phase transition and polarization behavior of relaxor ferroelectrics has been investigated. It was found that the type of phase transition, first order or second order, is independent of the random field width when the random field has an isotropic distribution. By introducing tunneling frequency between the nearest-neighbor wells, we observed a distinct threshold field and a corresponding nonzero phase transition temperature for field-induced phase transition, which is in good agreement with recent field-induced polarization measurement. Three kinds of dependence of polarization under an external electric field on temperature were demonstrated.

The structural and dynamical correlations, and the equation of state of crystalline I(2)O(4), I(2)O(5), and I(2)O(6) are investigated by first-principles calculations based on the density functional theory (DFT). The lattice dynamics results reveal distinctive features in the phonon density of states among the three crystals. The frequencies of the stretch modes in I(2)O(4) and I(2)O(5) are clearly separated from those of the other (e.g., bending) modes by a gap, with all stretch modes above the gap. In contrast, the gap in I(2)O(6) separates the highest-frequency stretch modes with other stretch modes, and there is no gap between the stretch and the other modes in I(2)O(6). The motion of iodine atoms is involved in all vibrational modes in I(2)O(5), but only in low-frequency lattice modes in I(2)O(6). In I(2)O(4), iodine atoms are involved in modes with frequency below 700 cm(-1). Van der Waals correction within our DFT calculations is found to reduce the overestimation of the equilibrium volume, with its effect on structure similar to the pressure effect. Namely, both effects significantly decrease the inter-molecular distances, while slightly increasing the bond lengths within the molecules. This causes the frequencies of some vibrational modes to decrease with pressure, resulting in negative "modes Grüneisen parameters" for those modes. Thermodynamic properties, derived from the equation of state, of crystalline I(2)O(4), I(2)O(5), and I(2)O(6) are discussed within the quasi-harmonic approximation.

Thermodynamic properties of β-HMX crystal are investigated using the quasi-harmonic approximation and density functional theory within the local density approximation (LDA), generalized gradient approximation (GGA), and GGA + empirical van der Waals (vdW) correction. It is found that GGA well describes the thermal expansion coefficient and heat capacity but fails to produce correct bulk modulus and equilibrium volume. The vdW correction improves the bulk modulus and volume, but worsens the thermal expansion coefficient and heat capacity. In contrast, LDA describes all thermodynamic properties with reasonable accuracy, and overall is a good exchange-correlation functional for β-HMX molecular crystal. The results also demonstrate significant contributions of phonons to the equation of state. The static calculation of equilibrium volume for β-HMX differs from the room-temperature value incorporating lattice vibrations by over 5%. Therefore, for molecular crystals, it is essential to include phonon contributions when calculated equation of state is compared with experimental data at ambient condition.

Using a first-principles-based Monte Carlo approach, we investigate the strain–temperature phase diagram of BaTiO3 ultrathin film without any surface charge screening. Although the depolarizing field has little effect on the phase types, a unique stripe domain structure with periodic out-of-plane polarization forms in the ultrathin films to minimize the energy of the depolarizing field under the constraint of the boundary condition, which leads to an unusual characteristic of the phase diagram. As a result, the total out-of-plane polarization remains zero at any strain and temperature. The film thickness has obvious effects on the phase diagram, e.g. the Curie temperature decreases and the strain moves to more negative values when the film thickness decreases. It is found that the compressive strain plays a decisive role in the characterization of ferroelectric polarization in such films, which suppresses the in-plane polarization while supporting the out-of-plane polarization, and thus drives the polarization to rotate from the in-plane to the normal direction.

Through ab initio-based simulations of the perovskite ferroelectric ultrathin films, we find that on applying an external electric field, ferroelectric ultrathin films can form kinds of self-organization nanodomain patterns including concentric loop stripes and nanodomain lattices. The characteristic size of the domain structure can be conveniently adjusted by controlling the film thickness and field, which should be very attractive in many applications. Our results are helpful for understanding the difference between the ferroelectric ultrathin film and bulk.

Dielectric properties of the relaxor films are theoretically investigated with the Monte Carlo simulation. We find that the size effect on the dielectric susceptibility of films is neglectable while the influence of the surface layer of the film is overlooked. On the contrary, while the surface layer is explicitly considered, we observe a systematic increase of Tm (the temperature at which the dielectric susceptibility reaches the maximum) and a systematic decrease of the maximum dielectric susceptibility as the film thickness decreases. An additional broadening of the transition region around Tm and the frequency dispersion of the dielectric susceptibility above Tm are also observed. The mechanism responsible for these phenomena is presented.

The thermodynamic properties of crystals can be routinely calculated by density functional theory cal- culations combining with quasi-harmonic approximation. Based on the method developed recently by Wu and Wentzcovitch (Phys Rev B 79:104304, 2009) and Wu (Phys Rev B 81:172301, 2010), we are able to further ab initio include anharmonic effect on thermodynamic properties of crystals by one additional canonical ensemble with numbers of particle, volume and temperature fixed (NVT) molecular dynamic simulations. Our study indicates that phonon-phonon interaction causes the renormalized phonon frequencies of wadsleyite decrease with tempera- ture. This is consistent with the Raman experimental observation. The anharmonic free energy of wadsleyite is negative and its heat capacity at constant pressure can exceed the Dulong-Petit limit at high temperature. The anharmonicity still significantly affects thermodynamic properties of wadsleyite at pressure and temperature con- ditions correspond to the transition zone.