MR23A-0177 1340h
The effect of temperature on the seismic anisotropy of the perovskite and post-perovskite polymorphs of MgSiO$_{3}$
Using elastic constants determined by ab initio molecular dynamics over a range of temperatures, we show that the seismic anisotropy of MgSiO$_{3}$ perovskite is significantly temperature dependent. At 90 GPa, the direction of greatest shear wave splitting changes from [001] at 0 K, to [010] at 3500 K. In addition, there is no shear wave splitting in the [100] direction at 0K, but a significant amount of splitting is exhibted at 3500 K. We have also calculated the first set of high-temperature elastic constants of the new post-perovskite phase by ab initio molecular dynamics methods. We find that, in contrast to MgSiO$_{3}$ perovskite, temperature has little effect on the acoustic anisotropy of this phase. We determine ($\partial$lnV$_{S}$/$\partial$lnV$_{P}$)$_{P}$ for the post-perovskite phase and find it to be very low at about 0.9.
http://www.es.ucl.ac.uk/research/desmond/
MR23A-0178 1340h
THE DYNAMICS OF THE POST-PEROVSKITE BOUNDARY AS PORTRAYED BY THE SHALLOW-WATER EQUATIONS
The recent discovery of the post-perovskite phase transition is indeed exciting from the perspective of fluid dynamics, because of its proximity to the core-mantle boundary (CMB). This situation raises some poignant issues about the traditional concept of a bottom thermal-boundary layer in mantle convection, because this new phase transition is, in fact, embedded inside the boundary layer itself. The steep Clapeyron slope of close to 10 MPa/K also raises the possibilities that the phase boundary may disappear altogther under regions of upwelling ,if there is a local increase of temperature by about 1000 K. Since the deflection of the phase boundary is O(50 km), as compared to the typical wavelengths of lower-mantle convection above the phase transition, we have made use of the shallow-water equation by invoking the hydrostatic ansatz and accounting only for the vertical momentum and heat-transfer. We developed a set of 2-D cartesian equations in the long-horizontal wavelength limit for the position of the phase boundary h(x,t), v(x,t) the horizontal velocity , and T(x,t), the temperature perturbation from the background temperature profile in the deep mantle, where t is time and x is a horizontal coordinate above the CMB. The set of nonlinear PDE's consisted of two initial-value nonlinear coupled partial differential equations and is an initial-boundary-value problem for T and h and one elliptic PDE for v. The time-derivative of h is the dominant coupling to both the PDE's governing T and v. There are four dimensionless parameters governing this system: S ,which governs the density change of the transition; Rq , which is a measure of the latent-heat released, D, the dissipation number and Tc, a measure of the temperature difference between the CMB and the lower mantle above the D" layer. This formalism can be extended to chemical variations in the D" layer. We can also take into account 3-D and spherical geometries, thus paving the road for an efficient computational means of matching the mantle convection solution to the core dynamics in the face of the post-perovskite phase change.
MR23A-0179 1340h
MgSiO$_{3}$ Under Conditions of the Earth's Deep Interior
MgSiO$_{3}$ phase diagram has been studied theoretically by first principles static and both {\it ab initio} and semi-empirical molecular dynamics methods. The melting curve of MgSiO$_{3}$ was obtained also by dislocation-mediated theory of melting. All methods produce a consistent phase diagram of MgSiO$_{3}$, which is calculated up to pressure of 4 Mbar. At high pressure, the diagram shows presence of three MgSiO$_{3}$ phases, namely, perovskite, so-called post-perovskite, and liquid. The diagram is in good agreement with the recent experimental data on post-perovskite phase. The MgSiO$_{3}$ melting curve is rather steep at pressures under 100 GPa while at higher pressures it has a much lower slope and lies above that of Fe by about 1000 K
MR23A-0180 1340h
The Role Played by Radiative Heat-Transfer in Earth's Thermal History
For the last 30 years mantle heat transfer was thought to be governed by convective mantle circulation, where heat-transfer is operative by means of a thermal-boundary type of law in which classical scaling works well. In the last 5 years there has been increasing evidence that radiative heat-transfer may play an important role, especially in the deep mantle (Badro et al., 2004). Consequently we have studied the role played by radiative heat-transfer in conjunction with a core-coupling thermal history model. Our model results are based on a 2-D cartesian domain geometry and do not include the effects of phase transitions, at 670 km and 2750 km. We have focussed on varying the strength of radiative thermal conductivity by means of a single parameter $f$. This prefactor $f$ is applied to the the radiative part of the Hofmeister composite conductivity model (Hofmeister, 1999). We have neglected the effects of water, grain-size and Fe on the radiative thermal conductivity. Our results show a clear impact of the scaling parameter $f$. Small values of $f$ representing models which are dominated by lattice conductivity show a significant delay of 1-2 Gyr in planetary secular cooling compared to corresponding uniform conductivity models. This appears to be due to a low conductivity zone (LCZ) produced at shallow depth by these variable temperature and pressure dependent models. Increasing $f$ from 0 to 10 produces a less pronounced LCZ. As a result the thermal resistance of the thermal boundary layer decreases and the rate of secular cooling increases with $f$. Our results dominated by the temperature and pressure sensitive LCZ illustrate the shortcomings of purely pressure dependent monotonic conductivity profiles for thermal history models. Heat flow from the core also depends strongly on the radiative conductivity in our models, including thermal coupling between mantle and core. Strong variations of some 100%, increasing with $f$, were observed in the core heat flux. The recently discovered post-perovskite phase transition with a highly positive Clapeyron slope will have a destabilizing effect and impact on core/mantle coupling. However, this would interact strongly with the radiative thermal conductivity at the D" and is likely to be stabilizing (Matyska et al., 1994). Results of ongoing modelling experiments with this phase transition included will be shown. The observed strong fluctuations in core heat output, resulting from the natural variability of the non-linearly coupled mantle and core systems, may have impacted the operation of the geodynamo through the Earth's history. Badro, J., Rueff, J-P., Vanko, G., Monaco, G., Fiquet, G., and F. Guyot, Electronic transitions in perovskite: possible nonconvecting layers in the lower mantle, Science, 305, 383-386, 2004. Hofmeister, A.M., Mantle values of thermal conductivity and the geotherm from phonon lifetimes, Science, 283, 1699-1706, 1999. Matyska, C., Moser, J. and D.A. Yuen, The potential influence of radiative heat transfer on the formation of megaplumes in the lower mantle, Earth Planetary Sci Lett., 125, 255-266, 1994.
MR23A-0181 1340h
Synthesis and equation of state of MgGeO$_3$ post-perovskite phase
After the discovery of MgSiO$_3$ post-perovskite (PPv) phase (Murakami et al., 2004), both theoretical and experimental works related to stability and elasticity of MgSiO$_3$ PPv phase have been reported (Oganov and Ono, 2004; Iitaka et al., 2004; Tsuchiya et al., 2004, Shim et al., 2004). However, due to extreme conditions needed to synthesize MgSiO$_3$ PPv phase (125 GPa, 2500 K), it is difficult to experimentally determine various physical properties, such as elasticity, of the PPv phase. Therefore, study of analogue materials could be very useful to examine the structure and physical properties of PPv phases. A good candidate is MgGeO$_3$ because the perovskite form has been synthesized at 12-14 GPa (Leinenweber et al., 1994). MgGeO$_3$ orthopyroxene mixed with 20 wt% Pt was used as a starting material. Ar or NaCl was used as a pressure medium. High-P/T in situ X-ray diffraction experiments in a diamond cell were performed at GSECARS, Argonne National Lab, using an area detector and YLF laser for double-sided heating. In both of our two runs, the PPv phase was synthesized by heating up to 1700K at 80 GPa. The phase was heated at higher pressure and compressed up to 106 GPa, but no further phase transition was observed. In the decompression process, volume data for the phase were taken down to 7 GPa, where the PPv phase was still observed. However, the phase recovered at ambient conditions was neither PPv phase, nor any known polymorph of MgGeO$_3$. By fitting the volume data using Birch-Murnaghan equation of state, both bulk modulus and zero-pressure volume of the PPv phase were determined to be 185 (10) GPa and 184.3 (1.7) $\rm{\AA^3}$, respectively. While c/a ratio is almost constant (2.48) between 6 and 106 GPa, b/a decreases from 3.32 to 3.23 between 6 and 60 GPa, and then remains constant up to 106 GPa. If we use the volume data only between 60 and 106 GPa, both bulk modulus and zero-pressure volume are calculated to be 260 (15) GPa and 174.2 (2.6) $\rm{\AA^3}$, respectively.
MR23A-0182 1340h
Synthesis of post-perovskite phase from a natural orthopyroxene
The existence of a post-perovskite phase in the end-member composition, MgSiO$_{3}$ has been reported at 125 GPa and 2500 K (Murakami et al., 2004). This has attracted much attention due to its potential relevance for the D$"$ layer at the base of the mantle. To assess the role that the post-perovskite phase may play in D$"$, the chemical and physical properties of this new discovered phase need to be investigated in great detail. In this study, a natural Fe-containing pyroxene sample was used as a starting material. The sample was confirmed to be pure pyroxene with a=18.2439$\rm{\AA}$, b=8.8368$\rm{\AA}$, c=5.1864$\rm{\AA}$. The powder sample was mixed with 10wt% of Pt that serves as a pressure standard. Argon was used both to insulate the sample from the diamonds, and to provide a quasi-hydrostatic environment. In-situ x-ray diffraction experiments were performed at 13-ID-D, GSECARS, Advanced Photon Source. A monochromatic beam ($\lambda$=0.3344$\rm{\AA}$) was focused to a beam size on the sample of 5x6$\mu$m. The in-situ x-ray diffraction patterns were collected using an imaging plate. The double-sided laser heating technique was applied in this study. The temperatures were measured in the range of 1700-1880 K. The pyroxene sample was compressed to 106 GPa and then heated. Prior to heating, only few very weak pyroxene lines were observed from the sample. After heating at 1700-1880 K for 36 mins, the post-perovskite phase was observed. The post-heating pressure was 100 GPa. The synthesis pressure for this sample is significantly lower than previously reported for end-member MgSiO$_{3}$ (Murakami et al., 2004; Oganov and Ono, 2004; Shim et al., 2004). The unit cell parameters for the post-perovskite phase at 106(1) GPa and 300 K are a =2.47(2)$\rm{\AA}$, b=8.22(9)$\rm{\AA}$, c=6.12(2)$\rm{\AA}$. The post-perovskite phase was found to coexist with the perovskite phase in our study. We also find that this post-perovskite phase can be quenched to ambient conditions, although there is some deterioration in the quality of the diffraction pattern. The unit cell for this post-perovskite phase at ambient conditions is a =2.57(8)$\rm{\AA}$, b=9.0(3)$\rm{\AA}$, c=6.8(2)$\rm{\AA}$.
MR23A-0183 1340h
Stability of Post-Perovskite Phase in Analogue Materials to MgSiO$_{3}$
Recent high-pressure experiments by Murakami et al. (2004) showed a novel phase transition from perovskite to a CaIrO$_{3}$-type post-perovskite phase (space group: {\it Cmcm}) in MgSiO$_{3}$ above 125 GPa and 2500 K. It is well known that a wide range of chemical compositions has perovskite structure at high pressures. In order to know the chemical variation that adopts CaIrO$_{3}$-type post-perovskite structure, we examined the phase transition of perovskite structure in germinates (MgGeO$_{3}$, MnGeO$_{3}$ and CdGeO$_{3}$) and titanates (MnTiO$_{3}$ and CdTiO$_{3}$) with increasing pressure at high temperature. Experiments were made at BL10XU of SPring-8 by a combination of laser-heated diamond-anvil cell (LHDAC) techniques and synchrotron X-ray diffraction measurements. Results demonstrate that both MnGeO$_{3}$ and MgGeO$_{3}$ perovskites undergo phase transition to the CaIrO$_{3}$-type post-perovskite structure similarly to the MgSiO$_{3}$ perovskite. The transition pressures are 58 GPa and 63 GPa at 1600 K, respectively, that are much lower than that in MgSiO$_{3}$. The molar volumes of these post-perovskite phases are smaller by 1.5 % than those of perovskite at equivalent pressure. In contrast, structure of CdGeO$_{3}$ perovskite becomes less distorted from ideal cubic structure with increasing pressure, and perovskite phase is stable at least to 110 GPa at 2000 K. Post-perovskite phase transition is, therefore, unlikely to occur in CdGeO$_{3}$ with further compression. Perovskite phase is stable also in MnTiO$_{3}$ and CdTiO$_{3}$ up to 50 GPa at 1700 K and 70 GPa at 2500 K, respectively. However, the structural distortion of both MnTiO$_{3}$ and CdTiO$_{3}$ perovskite increases with pressure. This observation suggests that post-perovskite phase transition may occur in both the compositions at higher pressures.
MR23A-0184 1340h
Crystallographic preferred orientation and seismic anisotropy of the Post-Perovskite phase in the D" layer
The recent discovery of the post-perovskite phase and prediction of its elastic constants using atomistic modeling has major implications for the interpretation of seismic anisotropy of the D" layer. In an effort to determine the mechanisms for crystallographic preferred orientation development for the post-perovskite phase and interpretation of the seismic anisotropy of D" layer a series of VPSC plasticity models has been conducted. For VPSC models the glide systems have been classified into easy [100](010), [001](001), moderate [100](001), [001](100) and difficult [100](001), [001](-110), [101](-101),[-101](101),[010](001) based on the type of bonds that have to be broken (Mg-Mg,Mg-O or Si-O) for dislocation glide. The VPSC models predict [100] parallel to the flow direction and [010] normal to the flow plane, resulting in an orthorhombic anisotropy pattern with the fastest Vp parallel to the flow direction and slowest normal to the flow plane. The anisotropy of the S-waves depends in a more complex way on the details of the CPO and hence on the imposed slip systems' strengths. However, in general, splitting is highly variable within the flow plane with a minimum value parallel to the lineation and the fastest S-wave is polarized in the flow direction. We also evaluate the anisotropy induced by a shape-preferred orientation of tabular post-perovskite crystals flattened parallel to [010], which is the most likely shape given the crystal structure. Orientation of [010] normal to the foliation results in a transverse isotropy pattern with the slowest Vp normal to the foliation. The S wave pattern is again complex with low splitting both parallel and normal to the foliation plane. For waves propagating within the foliation plane, the fastest S wave is polarized parallel to the flow plane. Waves propagating oblique (30-50 degrees) to the foliation show strong splitting with fast polarization directions oblique to both foliation and lineation. If the foliation is horizontal both models may explain the common observation that horizontally polarized shear waves travel faster than vertically polarized one. However, CPO-induced anisotropy will depend on the propagation azimuth whereas shape-induced anisotropy not.
MR23A-0185 1340h
Phase stability of CaSiO$_3$ perovskite at high pressure
We investigate by first-principles the structural behavior of CaSiO$_3$ perovskite throughout Earth's lower mantle pressure regime. We confirm that the cubic perovskite modification is unstable at all pressures. The structure is stabilized by SiO$_6$ octahedral rotations corresponding to unstable phonon modes in the R\{1/2 1/2 1/2\} and M\{1/2 1/2 0\} high-symmetry points of the ideal cubic perovskite structure. The freezing-in of these vibrational modes lower the symmetry to tetragonal, orthorhombic, rhombohedral, or cubic. The relative energy differences between all the investigated phases are very small. In general, the tetragonal structures are energetically preferred to the orthorhombic ones. At pressures relevant for the lower mantle, the lowest-in-energy structure has I4/mcm symmetry, followed in increasing order of energy by P$_2$/nmc, Pnma and Imma, P4/mbm, I4/mmm and Im$\overline{3}$, Pm3m, while the highest in energy structure has R$\overline{3}$c symmetry. This trend is preserved at all pressures, with the exception of the P4/mbm phase which is metastable with respect to Pm$\overline{3}$ at low pressures. All the structures have very similar densities, about 0.25 g/cm$^3$ larger than PREM's, with a relatively constant difference at all pressures. CaSiO$_3$ is characterized by bulk modulus higher than PREM bulk modulus by about 75 GPa at 80 GPa pressure and about 125-145 GPa at the base of the D'' layer, at 135 GPa pressure. If present in the lower mantle, CaSiO$_3$ perovskite, due to its larger bulk modulus may become seismically visible.
MR23A-0186 1340h
Phase Relation and Structural Variation on the Join CaIrO$_{3}$-CaTiO$_{3}$
CaTiO$_{3}$ is found in nature as perovskite and is isostructural with a major lower mantle mineral of MgSiO$_{3}$ perovskite (space group {\it Pbnm}). Recent high-pressure experiments demonstrated that MgSiO$_{3}$ perovskite undergoes first-order structural phase transition to a post-perovskite phase above 125 GPa and 2500 K. CaIrO$_{3}$ has an orthorhombic symmetry with space group {\it Cmcm} that is the same structure as that of MgSiO$_{3}$ post-perovskite phase. The structural variation on the join CaTiO$_{3}$-CaIrO$_{3}$ is, therefore, of interest as analogy to the pressure-induced phase transition from perovskite to post-perovskite phase in MgSiO$_{3}$. We examined phase equilibria on the join CaTiO$_{3}$-CaIrO$_{3}$ at 1 GPa and 1400 _E#8249;C using a piston-cylinder apparatus. Three starting materials with Ti/Ir molar ratios of 0.25, 1, and 4 were preliminarily prepared as powder mixtures of CaTiO$_{3}$ and CaIrO$_{3}$ crystals. CaIrO$_{3}$ were synthesized from CaCO$_{3}$ and IrO2 in the air at 1000 _E#8249;C. Results show that a wide range of compositions from pure CaTiO$_{3}$ at least to Ca(Ir$_{0.78}$Ti$_{0.22}$)O$_{3}$ form continuous solid solution with perovskite structure. Phase relations in more Ir-rich composition and the structural variations both of perovskite and CaIrO$_{3}$-type structures will be discussed in detail.
MR23A-0187 1340h
First principles study of aluminous hydrous perovskite and post-perovskite
The presence of hydrogen in solids has received great attention since physical properties can be substantially altered by hydration. In order to learn about the states of hydrogen in the lower mantle, we investigate aluminous hydrous magnesium silicate perovskite and post-perovskite, the main phase in the Earth's lower mantle and its new high pressure polymorph. It has been pointed out that the presence of hydrogen in connection with aluminum substitution for silicon in perovskite could produce a major reservoir of water in lower mantle with important implications for circulation of water in the Earth's interior. We investigate by first-principle the nature of these defects, likely docking sites for protons, and binding energies for these complex defects in perovskite and post-perovskite.
MR23A-0188 1340h
Post-perovskite transition in NaMgF3
We have investigated through first principles computations the pressure-induced behavior of NaMgF3. It has the same Pbnm perovskite structure as MgSiO3, the major lower mantle phase and likewise MgSiO3 it displays the same post-perovskite transition. Static LDA calculations indicate this transition should occur shortly after 35 GPa. Phonon dispersions of the post-perovskite structures confirm its mechanical stability. The existence of a post-perovskite transition at low pressures in this material makes possible studies of properties of such phase more easily accessible in a lower pressure range by various sorts of experiments. Research supported by NSF/EAR 0135533 (COMPRES)
MR23A-0189 1340h
Elasticity and stability of FeSi at high pressures
We have used both the Local Density Approximation (LDA) and the Generalized Gradient Approximation (GGA) to Density Functional Theory (DFT) to invetigate the structural and elastic behavior of FeSi throughout Earth's lower mantle pressure regime. At lowermost mantle pressures, FeSi is in the B2 (CsCl-type) structure, and has a metallic character. The B20-B2 transition occurs between 30-40 GPa in these static calculations and is associated with a density increase of 0.35 g/cm$^3$ (\~4.8%). FeSi is heavier than the mantle and lighter than the core. For this reason and because it is a possible product of the reaction between liquid Fe and MgSiO$_3$, it may accumulate at the base of the mantle, in the D" layer. Throughout the lower mantle regime, its velocities are lower than PREM's by 1.5-2 km/s for V$_p$ and 0.6-0.9 km/s for V$_s$. If present in the D'' layer, by up to a few percents in volume, the B2 phase of FeSi will contribute to decrease both V$_p$ and V$_s$.
MR23A-0190 1340h
The "African Anomaly" and the "Pacific Anomaly" in the Lower Mantle: Similarities and Differences
Seismic results have consistently shown two prominent low-velocity anomalies in the lower mantle, with one beneath southern Africa and the other beneath Pacific. For convenience, we refer them here the "African anomaly" and the "Pacific anomaly". The African anomaly was constrained mostly by the SH, ScS, SHdiff, SKS, SKKS, P, Pdiff and PcP phases recorded in three PASSCAL seismic arrays in Africa: the Tanzania array (1994 - 1995), the Kaapvaal array (1997 - 1999) and the Kenya array (2001-2002). These seismic observations indicate that the African anomaly has a very-low velocity province (VLVP) at its base, extends at least 1300 km above the core-mantle boundary with its edges in the lower mantle dipping toward its center and has a P to S velocity perturbation ratio of 1:3. The VLVP exhibits an "L-shape" changing from a north-south orientation in the South Atlantic Ocean to an east-west direction in the Indian Ocean, and has rapidly varying thicknesses from 300 km to 0 km, steeply dipping edges and a linear gradient of shear velocity reduction from -2% (top) to -9% to -12% (bottom) relative to the preliminary reference Earth model. These structural and velocity features unambiguously indicate that the VLVP, and likely the whole African anomaly, is compositionally distinct. The Pacific anomaly is studied using the ScS and SH waves recorded in the F-net in Japan, the China National Digital Seismographic Network and several dense seismic arrays in the Northern China Interior Structure Project, and the PKP precursors and SKS-SPdKS phases recorded in several WWSSN stations. Our ScS-S differential travel times confirm the early tomographic results that the the base of the Pacific anomaly is broad, but suggest presence of larger shear velocity reductions. The ScS-S differential travel times show residuals as large as 10 seconds when the ScS phases sample the eastern part of the base, which would correspond to an average shear velocity reduction of -5% for a 300-km-thick base.Our ScS-S data also provide good sampling coverage for determining the northern, western and southern boundaries beneath the western Pacific. The ScS-S travel time residuals exhibit rapid changes across the boundaries over small epicentral distances (1$^{\circ}$), suggesting that the lateral transitions of the Pacific anomaly occur over small distances (about 50 km). Different from the African anomaly which appears to lack internal small-scale heterogeneities and has relatively small magnitude of P velocity reductions, the Pacific anomaly is characterized by the presence of significant internal small-scale heterogeneities with large P-velocity reductions and length-scales from tens kilometers to hundreds kilometers. These two anomalies, although characteristically different to some extent, could represent similar compositional anomalies produced in the early Earth's history, with different length scales and different degrees of melt.
http://geophysics.geo.sunysb.edu/wen/
MR23A-0191 1340h
Post-Perovskite Phase in Al$_2$O$_3$ and Implications for the Lower Mantle
We use the local density approximation of the density functional theory to investigate several high-pressure polymorphs of Al$_2$O$_3$ and we predict a new stable polymorph at high pressures with post-perovskite structure. We find that the ambient pressure R$\overline{3}$c corundum phase transforms to the Pbcn Rh$_2$O$_3$(II) structure at about 105 GPa, (with $\Delta$V=-2.3%, $\Delta\rho$=0.1 g/cm$^3$ shifts), in agreement with previous first-principles studies. At about 156 GPa, the Rh$_2$O$_3$(II) structure transforms to the Cmcm post-perovskite structure (with $\Delta$V=-2.9%, $\Delta\rho$=0.16 g/cm$^3$ shifts). The Al$_2$O$_3$ Pbnm perovskite structure is metastable at all pressures with respect to corundum, Rh$_2$O$_3$(II) and/or post-perovskite. The metastable perovskite to post-perovskite phase transition takes place at about 122 GPa while the Rh$_2$O$_3$(II) to perovskite at about 208 GPa. We obtain similar results using the generalized gradient approximation. Our results indicate that the incorporation of Al$_2$O$_3$ in MgSiO$_3$ will contribute to the stability of the post-perovskite phase of MgSiO$_3$ with respect to perovskite. In the 90-150 GPa pressure range, the Al$_2$O$_3$ perovskite and post-perovskite structures have specific volumes about 0.37-0.22 and 0.19-0.14 $\AA^3$/molecule smaller than the corresponding structures of MgSiO$_3$, respectively, suggesting that broad Al$_2$O$_3$-MgSiO$_3$ solid solutions are possible at the lower mantle conditions and more likely for the post-perovskite than perovskite phase. We also find that Al$_2$O$_3$ will slightly reduce the elastic constants of post-perovskite MgSiO$_3$. To our knowledge, this is the first study of Al$_2$O$_3$ at high pressure where the new post-perovskite phase is considered and theoretically predicted.
MR23A-0192 1340h
Thermal Conductivity of Deep Mantle Phases: Grain-size as a Primary Control of Radiative Transfer
The assumed dependence of thermal conductivity (k) on temperature (T) strongly influences results from mantle convection models due to feedback in the temperature equation. Numerical calculations have show that the exponential dependence of viscosity on T has a lesser influence on the style of mantle convection than does a T$^{3}$ dependence of k. Several constraints can be set on k of the deepest mantle phases through comparison. The phonon component of thermal conductivity (k$_{lat}$) for minerals is provided by laser-flash measurements. For 20 silicates and oxides examined so far, k$_{lat}$ becomes independent of temperature above roughly 1200 to 1900 K. This behavior arises because discrete phonon states only exist at low frequency, and these states are all populated by about 1500 K. Invariant k$_{lat}$(T) at high T is thus universal, and expected for the perovskite (pv) and post-pv phases, regardless of chemical composition. Deep mantle behavior thus depends on diffusion of photons. The formulation for an effective thermal conductivity due to radiative transfer was recently revised to account for physical scattering and emission characteristics of a solid medium. We applied this formulation to phases with very different spectra (perovskite, garnet, olivine), with and without Fe$^{3+}$-Fe$^{2+}$ charge transfer bands, and with and without d-d transitions of Fe$^{2+}$. We find that grain-size and Fe content are key variables, whereas charge transfer and mineral structure have relatively little effect. For grain-size = 0.1 cm and Fe/(Fe+Mg) = 0.1, k$_{rad}$ is roughly 0.1377-0.000612T+6.28T$^{2}$/10$^{7}$ in W/m-K. Lowering grain size and either raising or lowering Fe content lowers k$_{rad}$. Increasing grain-size raises k$_{rad}$ at low T. The high temperature behavior for large grain-size is difficult to predict because absorptions shift and intensify with temperature, but few measurements exist. Transparent materials such as Fe-free phases and minerals with low spin Fe can have large k$_{rad}$ at high T when grain-size nears 1 cm. However, in D", phases should bear Fe, due to interactions with the core, and high spin Fe is stable, as this disordered state is promoted at high T by its large magnetic and electronic entropy (large positive Clapeyron slope). Therefore, k$_{rad}$ of the ppv phase in D" can be modeled with the above equation. The power law dependence on T weakens convection in D". The stability of this layer against convection largely depends on the concentration of Fe ions in the silicate and oxide phases. Incorporation of metal particles similarly increases opacity, making radiative transfer less efficient, and convection more vigorous and time dependent
MR23A-0193 1340h
MgO: \textit{ab initio} equation of state and its dislocation properties from molecular dynamics simulations*
The equation of state (EOS) of MgO, and its dislocation properties were investigated using {\it ab initio} quantum-mechanics techniques and classical molecular dynamics (MD) with a Morse-stretch charge-equilibrium potential, respectively. The thermodynamically complete {\it ab initio} EOS was demonstrated to be consistent with the isotherm, thermal expansivity, heat capacity and melting curve measured in static experiments, and reproduced density and temperature measurements under shock wave loading of bulk and porous periclase. The melting locus of MgO, relevant to the Earth's lower mantle pressures, was predicted to be accessible by shock wave loading of porous periclase. Preliminary MD simulations of dislocations in MgO indicated qualitative similarity to measurements of the temperature--stress curve, and revealed a qualitative understanding of the mechanism behind non-conservative motion of edge dislocations in MgO. *Work partly performed under the auspices of the US Department of Energy under contract No. W-7405-ENG-36.
MR23A-0194 1340h
High-Resolution 3-D Numerical Studies on the Interplay between Variable Thermal Conductivity and Post-Perovskite Phase Transition
Numerical models of high-resolution three-dimensional mantle convection have been developed in order to study the interplay between the perovskite to post-perovskite (pv-ppv) phase transition near the core-mantle boundary and variable thermal conductivity. A time-dependent convection in a three-dimensional rectangular box of 2000km height and aspect ratio 6$\times$6$\times$1 is considered. We employed an extended Boussinesq approximation, where the effects of latent heat release and viscous dissipation are included. The viscosity of mantle materials is assumed to be dependent on temperature and depth. Spatial mesh divisions of up to 1024$\times$1024$\times$256 (or even doubling in each direction) are utilized, by the help of newly developed algorithm for the Earth Simulator, in order to resolve the interplay between the bottom phase transition and the variations in thermal conductivity and viscosity, which will play an important role in the dynamics of plumes in the lower mantle, as much as possible. In addition to the endothermic phase transition at 660km depth, the pv-ppv transition is modeled as an exothermic phase change located at 200km above the bottom surface. We take into account the temperature-dependence of thermal conductivity, which mimics the effects of radiative heat transfer expected to be dominant in a hotter part of the mantle. The temperature at the core-mantle boundary is also systematically varied, in order to adapt the spatial variations in thermal conductivity and viscosity in the mantle. The effect of the interplay on the convective flow patterns will be further discussed, by comparing the cases with and without the variation of thermal conductivity.
MR23A-0195 1340h
The Effect of Aluminum on the Perovskite to Post-Perovskite Phase Transition and Elasticity
Seismology provides important constraints for compositional models of the earth's deep interior. These observations commonly show widespread lateral heterogeneity in the earth's lower mantle. However, the interpretation of seismic observations in terms of mantle composition and mantle dynamics relies critically on the knowledge of density and elasticity of the high pressure phases. It is thought that the earth's lower mantle phase assemblage is dominated by magnesium-rich perovskite that may contain 4-5 mol% Al$_{2}$O$_{3}$. Previous theoretical studies consistently predict that a direct substitution of 2 Al $->$ Mg + Si is favored at high pressures in Mg-perovskite. However, the effect of Al on the perovskite$->$post-perovskite phase boundary and the elasticity of the post-perovskite phase remain unknown. In order to address these issues we performed static first principle calculations for the direct substitution of Al in the post-perovskite phase. Our prelimnary results are based on Al-free and Al-bearing postperovskite with pyrope composition (25 mol% Al$_{2}$O$_{3}$). We find that the addition of Al has a large effect on the phase transition, it increases from 90 GPa for Al-free perovskite to 160 GPa for pyrope composition. Therefore even small amounts of Al may effect the phase boundary significantly and need to be included exploring the relation between the post-perovskite phase and D''. For the isotropic wave velocities we find at 120 GPa that 25 mol% Al$_{2}$O$_{3}$ reduces the compressional, shear, and bulk sound velocity, by ~2%, ~3.5%, and ~0.8%, respectively. Therefore Al seems to have only a modest effect on elasticity, however, the observed trend suggests that lateral variation in Al-content in the post-perovskite phase cannot account for the seimically observed anti-correlation between compressional and shear wave velocity in the lowermost mantle.