John P. Brodholt

Efficacy of the post-perovskite phase as an explanation for lowermost-mantle seismic properties

Constraining the chemical, rheological and electromagnetic properties of the lowermost mantle (D″) is important to understand the formation and dynamics of the Earths mantle and core. To explain the origin of the variety of characteristics of this layer observed with seismology, a number of theories have been proposed, including core–mantle interaction, the presence of remnants of subducted material and that D″ is the site of a mineral phase transformation. This final possibility has been rejuvenated by recent evidence for a phase change in MgSiO3 perovskite (thought to be the most prevalent phase in the lower mantle) at near core–mantle boundary temperature and pressure conditions. Here we explore the efficacy of this ‘post-perovskite’ phase to explain the seismic properties of the lowermost mantle through coupled ab initio and seismic modelling of perovskite and post-perovskite polymorphs of MgSiO3, performed at lowermost-mantle temperatures and pressures. We show that a post-perovskite model can explain the topography and location of the D″ discontinuity, apparent differences in compressional- and shear-wave models and the observation of a deeper, weaker discontinuity. Furthermore, our calculations show that the regional variations in lower-mantle shear-wave anisotropy are consistent with the proposed phase change in MgSiO3 perovskite.

Possible thermal and chemical stabilization of body-centred-cubic iron in the Earth's core

The nature of the stable phase of iron in the Earths solid inner core is still highly controversial. Laboratory experiments suggest the possibility of an uncharacterized phase transformation in iron at core conditions and seismological observations have indicated the possible presence of complex, inner-core layering. Theoretical studies currently suggest that the hexagonal close packed (h.c.p.) phase of iron is stable at core pressures and that the body centred cubic (b.c.c.) phase of iron becomes elastically unstable at high pressure. In other h.c.p. metals, however, a high-pressure b.c.c. form has been found to become stabilized at high temperature. We report here a quantum mechanical study of b.c.c.-iron able to model its behaviour at core temperatures as well as pressures, using ab initio molecular dynamics free-energy calculations. We find that b.c.c.-iron indeed becomes entropically stabilized at core temperatures, but in its pure state h.c.p.-iron still remains thermodynamically more favourable. The inner core, however, is not pure iron, and our calculations indicate that the b.c.c. phase will be stabilized with respect to the h.c.p. phase by sulphur or silicon impurities in the core. Consequently, a b.c.c.-structured alloy may be a strong candidate for explaining the observed seismic complexity of the inner core.

First-principles constraints on diffusion in lower-mantle minerals and a weak D′′ layer

Post-perovskite MgSiO3 is believed to be present in the D′′ region of the Earth’s lowermost mantle. Its existence has been used to explain a number of seismic observations, such as the D′′ reflector and the high degree of seismic anisotropy within the D′′ layer. Ionic diffusion in post-perovskite controls its viscosity, which in turn controls the thermal and chemical coupling between the core and the mantle, the development of plumes and the stability of deep chemical reservoirs. Here we report the use of first-principles methods to calculate absolute diffusion rates in post-perovskite under the conditions found in the Earth’s lower mantle. We find that the diffusion of Mg2+ and Si4+ in post-perovskite is extremely anisotropic, with almost eight orders of magnitude difference between the fast and slow directions. If post-perovskite in the D′′ layer shows significant lattice-preferred orientation, the fast diffusion direction will render post-perovskite up to four orders of magnitude weaker than perovskite. The presence of weak post-perovskite strongly increases the heat flux across the core–mantle boundary and alters the geotherm. It also provides an explanation for laterally varying viscosity in the lowermost mantle, as required by long-period geoid models. Moreover, the behaviour of very weak post-perovskite can reconcile seismic observation of a D′′ reflector with recent experiments showing that the width of the perovskite-to-post-perovskite transition is too wide to cause sharp reflectors. We suggest that the observed sharp D′′ reflector is caused by a rapid change in seismic anisotropy. Once sufficient perovskite has transformed into post-perovskite, post-perovskite becomes interconnected and strain is partitioned into this weaker phase. At this point, the weaker post-perovskite will start to deform rapidly, thereby developing a strong crystallographic texture. We show that the expected seismic contrast between the deformed perovskite-plus-post-perovskite assemblage and the overlying isotropic perovskite-plus-post-perovskite assemblage is consistent with seismic observations.

Thermal expansion and crystal structure of cementite, Fe3C, between 4 and 600 K determined by time-of-flight neutron powder diffraction

The cementite phase of Fe3C has been studied by high-resolution neutron powder diffraction at 4.2 K and at 20 K intervals between 20 and 600 K. The crystal structure remains orthorhombic (Pnma) throughout, with the fractional coordinates of all atoms varying only slightly (the magnetic structure of the ferromagnetic phase could not be determined). The ferromagnetic phase transition, with Tc ≃ 480 K, greatly affects the thermal expansion coefficient of the material. The average volumetric coefficient of thermal expansion above Tc was found to be 4.1 (1) × 10−5 K−1; below Tc it is considerably lower (< 1.8 × 10−5 K−1) and varies greatly with temperature. The behaviour of the volume over the full temperature range of the experiment may be modelled by a third-order Gruneisen approximation to the zero-pressure equation of state, combined with a magnetostrictive correction based on mean-field theory.

Pressure-induced changes in the compression mechanism of aluminous perovskite in the Earth's mantle

Although aluminium is the fifth most abundant element in the Earths mantle, its effect on the physical properties of perovskite, the main mineral phase in the lower mantle, has largely been ignored. It is becoming clear, however, that many properties of MgSiO3 perovskites are remarkably sensitive to small amounts of aluminium. In particular, perovskite with only 5 wt% Al2O3 has a bulk modulus 10% lower than that of the pure magnesian end-member. The increased compressibility may be due to the high concentrations of oxygen vacancies required to balance the charge of the aluminium; if so, this would have important consequences for the mantle, as aluminous perovskites could be weaker, have lower seismic velocities and be hosts for water. To test whether oxygen vacancies exist in aluminous perovskites, I have calculated the compressibility of end-member defect-bearing perovskites using ab initio methods. The results show that perovskites with oxygen vacancies do have significantly greater compressibilities than those without such vacancies. But the results also suggest that oxygen vacancies become unfavourable at high pressures, in which case only the physical properties of the shallow lower mantle would be affected by aluminium—with the deeper mantle retaining properties similar to those of aluminium-free perovskite.

Ab initio elasticity and thermal equation of state of MgSiO3 perovskite

We have used high-temperature ab initio molecular dynamic simulations to study the equation of state of orthorhombic MgSiO3 perovskite under lower mantle pressure^temperature conditions. We have determined the Gru « neisen parameter, Q, as a function of volume. Our state-of-the-art simulations, accurate to within 10%, resolve the long-standing controversy on thermal expansion (K) and Gru « neisen parameter of MgSiO3 perovskite. Under ambient conditions we find the values for K and Q of 1.86U10 35 K 31 and 1.51, respectively, in excellent agreement with the latest experimental studies. Calculated elastic constants and the static equation of state at 0 K agree well with previous simulations. We have found no evidence for the high-temperature phase transitions of orthorhombic MgSiO3 perovskite to cubic or tetragonal phases at mantle temperatures. fl 2001 Elsevier Science B.V. All rights reserved.

Analysis of the hydrogen-bonded structure of water from ambient to supercritical conditions

The structure of water has been analyzed at eight different thermodynamic states from ambient to supercritical conditions both by molecular dynamics (MD) and Reverse Monte Carlo (RMC) simulation. MD simulations have been carried out with two different potential models, a polarizable potential and one of the most successful nonpolarizable models, i.e., the well known Simple Point Charge potential in its revised version labeled by E (SPC/E). It has been found that, although the polarizable model can reproduce the experimental partial pair correlation functions at the high temperature states better than the nonpolarizable one, it still cannot account for all the features of the measured functions. The experimental partial pair correlation functions have been well reproduced by the RMC simulations at every state point. The resulting structures have been analyzed in detail. It has been found that the tetrahedral orientation of the hydrogen bonded neighbors is already lost at 423k, whereas the hydrogen bonds th...

Subducted banded iron formations as a source of ultralow-velocity zones at the core–mantle boundary

Ultralow-velocity zones (ULVZs) are regions of the Earths core–mantle boundary about 1–10 kilometres thick exhibiting seismic velocities that are lower than radial-Earth reference models by about 10–20 per cent for compressional waves and 10–30 per cent for shear waves. It is also thought that such regions have an increased density of about 0–20 per cent (ref. 1). A number of origins for ULVZs have been proposed, such as ponding of dense silicate melt, core–mantle reaction zones or underside sedimentation from the core. Here we suggest that ULVZs might instead be relics of banded iron formations subducted to the core–mantle boundary between 2.8 and 1.8 billion years ago. Consisting mainly of interbedded iron oxides and silica, such banded iron formations were deposited in the worlds oceans during the late Archaean and early Proterozoic eras. We argue that these layers, as part of the ocean floor, would be recycled into the Earths interior by subduction, sink to the bottom of the mantle and may explain all of the observed features of ULVZs.

Parameterizing a polarizable intermolecular potential for water

The parameterization of a polarizable intermolecular potential for water is attempted starting from a simple model of three permanent charges, a Lennard-Jones centre on the oxygen, and a single polarizable site on the centre of mass. It is found that the position of the negative charge is a surprisingly critical variable in parameterizing a successful model. The only model that reproduces 1·0 g cm-3 water properties reasonably well has the negative charge displaced 0·2 A away from the oxygen along the molecular bisector. This model reproduces the correct energy, pressure, diffusion coefficient, and structure of normal water. At supercritical conditions, however, the model, as with non-polarizable models, does not reproduce these properties satisfactorily; the pressure is too high and the diffusion coefficients are too low. In addition, a comparison with published pair distribution functions shows too much OH structure at the lowest density, whereas at the highest density the opposite is true. There are, h...

A seismologically consistent compositional model of Earth"s core

Significance It is well known that Earth’s core is made primarily of iron, alloyed with ∼5% nickel and some lighter elements, such as carbon, oxygen, silicon, or sulfur. The amount as well as the chemistry of the light elements is poorly known and still a matter of considerable debate. In this paper we calculate the seismic signature of iron-rich light-element alloys and compare them to the seismic properties of Earth’s core. We find that oxygen is required as a major light element in the core, whereas silicon, sulfur, and carbon are not required. We also find that silicon concentration in the core cannot be higher than 4.5%, and sulfur concentration cannot be higher than 2.4%. Earth’s core is less dense than iron, and therefore it must contain “light elements,” such as S, Si, O, or C. We use ab initio molecular dynamics to calculate the density and bulk sound velocity in liquid metal alloys at the pressure and temperature conditions of Earths outer core. We compare the velocity and density for any composition in the (Fe–Ni, C, O, Si, S) system to radial seismological models and find a range of compositional models that fit the seismological data. We find no oxygen-free composition that fits the seismological data, and therefore our results indicate that oxygen is always required in the outer core. An oxygen-rich core is a strong indication of high-pressure and high-temperature conditions of core differentiation in a deep magma ocean with an FeO concentration (oxygen fugacity) higher than that of the present-day mantle.