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Effect of Fe-enrichment on seismic properties of perovskite and post-perovskite in the deep lower mantle


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Recent experimental measurements of the equation of state of perovskites and post-perovskites in the (Mg,Fe)SiO3 and (Mg,Fe,Al)(Fe,Al,Si)O3 systems over a wide range of iron contents are used to constrain the effects of Fe and Al on density and bulk modulus of these phases at deep mantle pressures. The density of Fe-bearing perovskite follows a linear relationship with Fe-content at a representative mid-mantle depth of 1850 km (80 GPa): ρ80 (g cm- 3) = 5.054(1) + 1.270(3)XFe. The bulk modulus of silicate perovskite is not sensitive to Fe-content and follows the relationship, K80 (GPa) = 546(2) + 12(25)XFe. The velocity heterogeneity parameter, ∂ln VB/∂XFe, determined by experimental values for the bulk sound speed is 0.10(1), in agreement with theory and the behaviour of other Fe-bearing silicates. Near the core-mantle boundary, Fe-rich post-perovskite is observed to be more compressible than the Mg-end-member, in contrast to theoretical predictions. From experimental data, the densities of perovskite and post-perovskite at 125 GPa (2700 km depth) are ρ125,Pv (g cm-3) = 5.426(11) + 1.38(4)XFe and ρ125,pPv (g cm-3) = 5.548(1) + 1.41(3)XFe. The density contrast across the post-perovskite transition is ̃2 per cent, irrespective of Fe-content, but the contrast in bulk sound speed increases with Fe-content. Al-rich silicates exhibit no significant differences in density or compressibility relative to Al-free silicates, but may be responsible for seismic heterogeneities due to differences in the depth and width of the post-perovskite transition. Observations of increased densities in large low shear velocity provinces and ultra-low-velocity zones may be consistent with local iron enrichment from Mg#90 to Mg# 78-88 and Mg# <50, respectively.
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Geophysical Journal International
Geophys. J. Int. (2014) doi: 10.1093/gji/ggu045
GJI Mineral physics, rheology, heat flow and volcanology
Effect of Fe-enrichment on seismic properties of perovskite
and post-perovskite in the deep lower mantle
S.M. Dorfman1and T.S. Duffy2
1Earth and Planetary Science Laboratory, Ecole polytechnique f´
erale de Lausanne, Station 3,CH-1015 Lausanne, Switzerland.
2Department of Geosciences, Princeton University, Princeton, NJ 08544, USA
Accepted 2014 February 3. Received 2014 January 27; in original form 2013 October 22
Recent experimental measurements of the equation of state of perovskites and post-perovskites
in the (Mg,Fe)SiO3and (Mg,Fe,Al)(Fe,Al,Si)O3systems over a wide range of iron contents
are used to constrain the effects of Fe and Al on density and bulk modulus of these phases
at deep mantle pressures. The density of Fe-bearing perovskite follows a linear relationship
with Fe-content at a representative mid-mantle depth of 1850 km (80 GPa): ρ80 (g cm3)=
5.054(1) +1.270(3)XFe . The bulk modulus of silicate perovskite is not sensitive to Fe-content
and follows the relationship, K80 (GPa) =546(2) +12(25)XFe . The velocity heterogeneity
parameter, ln VB/∂ XFe, determined by experimental values for the bulk sound speed is
0.10(1), in agreement with theory and the behaviour of other Fe-bearing silicates. Near the
core–mantle boundary, Fe-rich post-perovskite is observed to be more compressible than the
Mg-end-member, in contrast to theoretical predictions. From experimental data, the densities of
perovskite and post-perovskite at 125 GPa (2700 km depth) are ρ125,Pv (g cm3)=5.426(11) +
1.38(4)XFe and ρ125,pPv (g cm3)=5.548(1) +1.41(3)XFe . The density contrast across the
post-perovskite transition is 2 per cent, irrespective of Fe-content, but the contrast in bulk
sound speed increases with Fe-content. Al-rich silicates exhibit no significant differences in
density or compressibility relative to Al-free silicates, but may be responsible for seismic
heterogeneities due to differences in the depth and width of the post-perovskite transition.
Observations of increased densities in large low shear velocity provinces and ultra-low-velocity
zones may be consistent with local iron enrichment from Mg#90 to Mg# 78–88 and Mg# <50,
Key words: Composition of the mantle; Equations of state; High-pressure behaviour.
Chemical heterogeneity in the deep lower mantle has been con-
strained by geophysical observations and dynamic simulations
(Stixrude & Lithgow-Bertelloni 2012). Thermal variation alone
cannot explain observations of anticorrelated bulk and shear wave
speeds in the deep mantle (e.g. Masters et al. 2000). In addition,
seismic images of large (1500 km) low shear velocity provinces
(LLSVPs) beneath the Pacific and Africa have features such as
sharp lateral gradients at their edges that are suggestive of com-
positional heterogeneity (McNamara & Zhong 2004,2005). From
normal mode data, Ishii & Tromp (1999) reported that regions of
high density were associated with low velocities in the two plume
provinces. LLSVPs could represent hot dense piles of composi-
tionally distinct material or buoyant thermal superplumes and these
models would be expected to have different degrees of chemical
heterogeneity and distinct density structures.
The Earth’s core–mantle boundary region (D) also exhibits
highly-variable localized structure and is therefore also likely to be
chemically heterogeneous (Garnero 2000). Heterogeneities could
possibly form due to accumulations of subducted crust (Dobson
& Brodholt 2005;Hutkoet al. 2006), remnant primordial material
(Labrosse et al. 2007) or core–mantle interaction (Knittle & Jeanloz
1989,1991). Waveform modelling has led to the identification
of ultra-low velocity zones (ULVZs) just above the core–mantle
boundary (Garnero & Helmberger 1995). These ULVZs tend to
be distributed at the margins of LLSVPs and exhibit strong re-
ductions (>10 per cent) in P-andS-wave velocities. ULVZs are
thin and typically localized (5–40 km thick and 100 km wide)
with a large increase in density (10 per cent) compared with sur-
rounding material (Rost & Garnero 2006). These properties could
possibly be signatures of dense melts (Williams & Garnero 1996)
or iron-enriched solid mantle phases (Mao et al. 2006;Wicks
et al. 2010). The role of iron is thus one of the major factors
The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society. 1
Geophysical Journal International Advance Access published February 27, 2014
by guest on April 9, 2014 from
2S.M. Dorfman and T.S. Duffy
to consider in assessing compositional heterogeneity in the lower
Determining the behaviour of iron in the lower mantle’s dominant
phase, (Mg,Fe,Al)(Fe,Al,Si)O3perovskite, is complex because Fe
can occupy different structural sites with different valence and spin
states, which may differently affect seismic properties (e.g. Caracas
2010a). In addition, Fe has been observed to affect the depth and
breadth of the transition of mantle perovskite to the post-perovskite
structure, with important implications for the phase assemblage near
the core–mantle boundary (Murakami et al. 2004;Oganov&Ono
2004;Maoet al. 2004,2005). Partitioning of Fe between multiple
Fe-bearing mantle phases is also important to phase transforma-
tions and physical properties (Grocholski et al. 2012). However,
modelling of the effect of Fe on mantle phases has generally been
simplified in studies to date. For example, Trampert et al. (2001)and
Mattern et al. (2005) constructed lower-mantle mineral models in
which Fe affects the thermoelastic properties of silicate perovskite
only through its effect on the molar volume at ambient pressure,
which is far from thermodynamic stability and so can exhibit con-
siderable scatter among experimental determinations (Kiefer et al.
2002; Tange et al. 2009). Recent experimental data on Fe-bearing
mantle silicates at mantle pressures has allowed improved modelling
of the complexity of Fe-dependence of elastic properties (Nakagawa
et al. 2012).
Compression studies using X-ray diffraction as a probe provide
many of the existing experimental constraints on elasticity of lower-
mantle materials. In this work, we synthesize experimental equation
of state measurements on perovskites and post-perovskites with a
wide range of compositions and compare with theoretical calcula-
tions to assess the current understanding of the equation of state
of deep mantle silicates. We discuss the dependence of density and
seismic wave velocity on Fe- and Al-content in perovskite and post-
perovskite. We investigate the implications of these chemical effects
for deep lower-mantle heterogeneities.
A number of recent studies have carried out 300-K equation of
state measurements on perovskite and post-perovskite phases syn-
thesized in the (Mg,Fe)SiO3and (Mg,Fe,Al)(Fe,Al,Si)O3systems
(Walter et al. 2004; Guignot et al. 2007; Lundin et al. 2008; Nishio-
Hamane et al. 2008;Shimet al. 2008; Nishio-Hamane & Yagi 2009;
Catalli et al. 2010b,2011;Shiehet al. 2011; Boffa Ballaran et al.
2012; Zhang et al. 2012; Dorfman et al. 2012b,2013). These stud-
ies used synchrotron X-ray diffraction in the laser-heated diamond
anvil cell (Duffy 2005) to synthesize the high-pressure phases and
to measure their unit cell volumes as a function of pressure. The
compositions studied involve a variety of cation substitutions and
possible cation site occupancies. In particular, a number of these
recent studies have focused on Fe- and Al-rich samples, thereby
allowing compositional trends to be better constrained. The Fe frac-
tion (XFe =2Fe/[Mg+Fe +Al +Si]) over the combined Aand B
sites of the ABO3stoichiometries ranged from 0 to 0.75. In addition,
compositions with Al2O3contents as high as 25 mole per cent have
been studied (Walter et al. 2004;Shiehet al. 2011; Boffa Ballaran
et al. 2012; Dorfman et al. 2012b).
In most of these studies, the valence state of Fe in synthe-
sized perovskites and post-perovskites was not measured directly.
In-situ M¨
ossbauer spectroscopy and ex-situ electron energy loss
spectroscopy measurements of Fe3+/Fe ratios in perovskites and
post-perovskites synthesized from Al-free, Fe2+-bearing starting
materials range from 0.08 to 0.5, with a median value of 0.16 (Mc-
Cammon 1997; Frost & Langenhorst 2002;Liet al. 2004; Jack-
son et al. 2005; Sinmyo et al. 2008;Maoet al. 2011b; Sinmyo
et al. 2011). Al-content is well-known to promote higher Fe3+/Fe
in perovskite, typically 0.5–0.8 (McCammon 1997;Frost&
Langenhorst 2002; Sinmyo et al. 2011). However, crystallo-
graphic differences observed between perovskites synthesized from
(Mg,Fe2+,Al)(Al,Si)O3and (Mg,Fe3+)(Al,Si)O3-bearing composi-
tions may indicate that ferrous iron can be preserved in aluminous
perovskites (Dorfman et al. 2012b). The Fe3+/Feratioinpost-
perovskite has been observed to be close to that of the starting
material (Sinmyo et al. 2011). When discussing ferrous or ferric
iron content in this work, we refer to measured compositions of
starting materials.
In comparison of experimental studies at deep mantle conditions,
a concern involves the consistency of pressure determination and
hydrostatic stress conditions among different works (Fei et al. 2007;
Dorfman et al. 2012a). The studies under consideration here all used
an internal pressure standard for which the equation of state was
determined with reference to shock compression or other data. Most
of the studies (Lundin et al. 2008; Nishio-Hamane et al. 2008;
Nishio-Hamane & Yagi 2009; Catalli et al. 2010b,2011;Shieh
et al. 2011; Dorfman et al. 2013,2012b)usedAuasaninternal
pressure standard; for the scales chosen in these studies (Tsuchiya
2003; Dewaele et al. 2004;Feiet al. 2007), errors due to pressure
calibration differences are expected to be minimal (<1.5 GPa). In
other studies, use of KCl, NaCl, MgO or Pt may lead to systematic
differences in pressure determination. At Mbar pressures, the Pt and
NaCl scales were observed to give pressures up to 5–10 GPa lower
than Au (Dorfman et al. 2012a). As a result, studies using these
other calibrants measured perovskite and post-perovskite volumes,
V, systematically lower by up to 1.5 per cent. Differences in bulk
modulus, K, due to pressure calibration are negligible with respect
to other uncertainties. Systematic differences may also be observed
in calibrant and sample volumes due to non-hydrostatic stress in
the diamond anvil cell. Most of the studies considered here used
soft media such as Ne and laser annealing, which minimize non-
hydrostatic stress (Dorfman et al. 2012a).
Pressure–volume data were fit to the Birch–Murnaghan equation
(Birch 1947) to allow interpolation of volumes to common refer-
ence pressures. Densities, ρ, were calculated from volumes using
the known chemical compositions of the samples. The isothermal
bulk modulus, K=−V(P/∂ V)T, was obtained at reference pres-
sures from differentiation of the Birch–Murnaghan equation with
respect to volume (Jackson 1998). The bulk sound velocity was
calculated from Kand ρ:VB=K. The difference between the
adiabatic and isothermal bulk modulus is small relative to experi-
mental uncertainties and was neglected. The corresponding expres-
sions for the compressional (VP) and shear (VS) wave velocities
are VP=(K+4G/3)and VS=G,whereGis the shear
2.1 Perovskite
The pressure range of experimental volume compression data
for (Mg,Fe)SiO3compositions was 0–100 GPa (Lundin et al.
2008; Dorfman et al. 2013) and for (Mg,Fe)3Al2Si3O12 was
0–150 GPa (Walter et al. 2004; Dorfman et al. 2012b) com-
positions (Fig. 1). (Mg,Fe)3Al2Si3O12 is the pyrope–almandine
garnet system which transforms to single-phase perovskites
((Mg,Fe)0.75Al0.25)(Al0.25 Si0.75 )O3above 40–70 GPa (Irifune et al.
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Effect of Fe-enrichment on the deep lower mantle 3
Figure 1. Volumedifferences between Fe- or Fe, Al-bearing perovskites and
MgSiO3perovskite (Lundin et al. 2008). Fe-bearing perovskite with FeSiO3
(Fs) from 9–74 per cent is shown in circles (Lundin et al. 2008; Dorfman
et al. 2013). Perovskites synthesized from pyrope–almandine (Alm) compo-
sitions with 54 and 100 per cent Alm are displayed with diamonds (Dorfman
et al. 2012b). Ten per cent FeAlO3composition (Catalli et al. 2011)isshown
in triangles. Curves shown are from Birch–Murnaghan equation of state fits.
1996; Walter et al. 2004; Dorfman et al. 2012b). Relative to the Mg
end-member, (Mg,Fe)SiO3perovskite unit cell volumes increase
approximately linearly with Fe-content independent of pressure. In-
corporation of Al increases the unit cell volume of perovskite more
at low pressure (Yagi et al. 2004;Saikiaet al. 2009) than at deep
lower-mantle pressures (Walter et al. 2004; Catalli et al. 2011).
This difference may be the result of a change of mechanism of Al-
incorporation from vacancy to coupled substitution (Brodholt 2000;
Andrault et al. 2007).
To allow direct comparison between different studies, 80 GPa
was chosen as a reference pressure (corresponding to 1850 km
depth in Earth’s mantle) and the equation of state was used to
calculate the density and bulk modulus at this pressure for each
measured composition. The density of silicate perovskite increases
with Fe-content, and the majority of the experimental data are
well-described by a linear relationship (Fig. 2). For (Mg,Fe)SiO3
perovskites at 80 GPa, the least-squares fit to the densities is
ρ80 (g cm3)=5.054(1) +1.270(3)XFe . Recent experimental data
on Fe-rich compositions (Boffa Ballaran et al. 2012; Dorfman
et al. 2012b,2013) have enabled us to provide tight constraints
on the density trend to much higher iron contents than previously
The density of Al-bearing perovskites for a given Fe-content is
similar or slightly lower than Al-free perovskites. The linear fit to
densities of Fe, Al-bearing compositions is within uncertainty of the
above equation for Fe-bearing, Al-free compositions. The equation
of state of Fe3+, Al-bearing perovskite measured by Nishio-Hamane
et al. (2008) gives density and compressibility in good agreement
with studies on Fe2+-bearing compositions, despite the differences
in chemistry. Fe3+-bearing perovskites with densities 2 per cent
lower than comparable Fe2+-bearing compositions were observed
by Catalli et al. (2010b) and Boffa Ballaran et al. (2012), possibly
due to Fe-content in the perovskite B-site.
Additional constraints on effects of Fe- and/or Al-incorporation
on elastic properties of silicate perovskite have been provided
by ab initio calculations (Karki et al. 2001; Kiefer et al. 2002;
Wentzcovitch et al. 2004; Caracas & Cohen 2005;Liet al. 2005;
Stackhouse et al. 2006; Tsuchiya & Tsuchiya 2006; Zhang &
Oganov 2006; Bengtson et al. 2007; Caracas et al. 2010; Caracas
2010a,b;Hsuet al. 2010; Umemoto et al. 2010;Hsuet al. 2011a;
Huang & Pan 2012; Metsue & Tsuchiya 2012;Tsuchiya&Wang
2013). Density functional theory is not limited by experimentally
accessible conditions and can provide values for both bulk and
shear properties but results can depend on the choice of exchange-
correlation functional. For silicates, the general gradient approxima-
tion (GGA) can suffer from underbinding leading to underestimated
elastic constants and overestimated volumes, while the local den-
sity approximation (LDA) tends to produce the reverse situation
(Kiefer et al. 2002). Some density functional theory work has also
included the potential effects of Fe spin transitions on elastic prop-
erties (Bengtson et al. 2007; Caracas et al. 2010; Caracas 2010a,b;
Hsu et al. 2010,2011a; Huang & Pan 2012; Metsue & Tsuchiya
2012;Tsuchiya&Wang2013). The most recent of these studies
employ a Hubbard correction (LSDA+U), thought to produce more
accurate results for iron-bearing minerals at high pressure (Hsu et al.
2011b; Metsue & Tsuchiya 2012).
Ab initio calculations for MgSiO3perovskite predict densities
that agree with experimental measurements to within 3 per cent
(Fig. 2; Kiefer et al. 2002; Caracas & Cohen 2005; Umemoto et al.
2010; Metsue & Tsuchiya 2012). For Fe-bearing perovskite, the
increase in ρwith Fe-content predicted by the LDA method is
similar to experimental measurements but systematically offset to
higher density, consistent with volume underestimated by LDA.
However, the densities calculated for (Mg0.5Fe0.5 )SiO3and FeSiO3
compositions by Caracas & Cohen (2005) with the GGA method
are significantly lower than experimental measurements.
The bulk modulus obtained from the Birch–Murnaghan equation
fits to experimental volume data is insensitive to Fe-content or in-
creases weakly (Fig. 2). A linear fit of bulk modulus at 80 GPa to
composition, K80 (GPa) =546(2) +12(25)XFe , exhibits a stiffening
of 2±4 per cent in Kfrom XFe =0 to 100. These experimental data
are consistent with the slope predicted by theoretical calculations
(Kiefer et al. 2002; Caracas & Cohen 2005; Umemoto et al. 2010;
Metsue & Tsuchiya 2012). Generally, in mantle silicates and ox-
ides at ambient conditions, Mg,Fe-substitution only weakly affects
the bulk modulus (Speziale et al. 2005). The adiabatic bulk moduli
in the olivine–fayalite, enstatite–ferrosilite, pyrope–almandine and
ustite systems show less than a 7 per cent difference
between the Fe end-member and the Mg end-member. More limited
data on high-pressure silicates (wadsleyite, ringwoodite) also show
a weak effect of Fe-substitution on bulk modulus (Mao et al. 2011a).
Our results suggest that perovskites behave in a similar manner to
other silicates.
The possible effect of an Fe spin transition on the equation of state
and compressibility of perovskite has attracted much interest (Lin
et al. 2013). Both Fe2+-andFe
3+-bearing perovskite samples have
been observed by X-ray emission and M¨
ossbauer spectroscopy tech-
niques to undergo a transition to from high spin to low spin (Badro
et al. 2004; Jackson et al. 2005; Catalli et al. 2010b; McCammon
et al. 2010;Maoet al. 2011b) or intermediate spin (Lin et al. 2008;
McCammon et al. 2008). A spin transition in perovskite has been
observed to be associated with higher Kfor Fe-bearing perovskite
(Fig. 2; Catalli et al. 2010b,2011;Maoet al. 2011b). However,
density functional theory calculations predict that any spin transi-
tion would have a small effect on the density and bulk modulus of
by guest on April 9, 2014 from
4S.M. Dorfman and T.S. Duffy
Figure 2. (a) At 80 GPa and 300 K, density, bulk modulus and seismic wave propagation speeds for perovskites with varying Fe, Al-content determined from
experimental data (Walter et al. 2004; Murakami et al. 2007b; Lundin et al. 2008; Nishio-Hamane et al. 2008;Shimet al. 2008; Catalli et al. 2010b,2011;Mao
et al. 2011b; Boffa Ballaran et al. 2012; Dorfman et al. 2012b; Murakami et al. 2012; Dorfman et al. 2013). Bold green line fits are shown to Fe2+-bearing
compositions. (b) Density functional theory results at 80 GPa and 0 K for (Mg,Fe)SiO3perovskites from LDA (Kiefer et al. 2002; Umemoto et al. 2010;
Metsue & Tsuchiya 2012) and GGA (Caracas & Cohen 2005).
perovskite (Fig. 2; Umemoto et al. 2010;Hsuet al. 2011a;Metsue
& Tsuchiya 2012).
Fe3+-bearing compositions (Mg0.9 Fe0.1 Al0.1 Si0.9)O3and
(Mg0.9Fe0.2Si0.9 )O3may exhibit a high-to-low spin transition
at 55–70 GPa (Catalli et al. 2010b,2011). The transition was
associated with a loss of spin moment observed by X-ray emis-
sion spectroscopy, a change in M¨
ossbauer parameters, volume
collapse and decrease in compressibility at higher pressures. Other
experiments showed no difference in compressibility between
MgSiO3and (Mg0.85Fe0.15Al0.15 Si0.85 )O3perovskites (Nishio-
Hamane et al. 2008), and no discontinuities in the compression of
0.38Si0.62 Al0.36)O3perovskite single crystals (Boffa
Ballaran et al. 2012). Some differences between these observations
may be explained by site occupancy of Fe and Al (Caracas 2010a).
The spin transition in Fe3+is expected to occur only in the Pv
B-site (Hsu et al. 2011a), and site exchange between Fe and Al
may occur only at high temperature.
In another recent experimental study, X-ray emission spectra
for (Mg0.75Fe0.25)SiO3perovskite at 80–135 GPa were typical of
a mixture of high- and low-spin Fe (Mao et al. 2011b). This
Fe2+-rich perovskite was observed to be much less compressible
than MgSiO3perovskite (Fig. 2). A possible explanation for ele-
vated values of the bulk modulus seen for some studies in Fig. 2
may be incomplete relaxation of differential stress. The bulk of
the experimental and theoretical data suggest that spin transitions
in either Fe2+-orFe
3+-bearing perovskite are unlikely to cause
observable anomalies in density or bulk modulus in the lower
by guest on April 9, 2014 from
Effect of Fe-enrichment on the deep lower mantle 5
Experimentally derived values for the bulk sound speed, VB,at80
GPa are shown in Fig. 2. Theoretical and most experimental studies
report decreasing VBwith Fe-content. The fit to experimental data
is VB(km s1)=10.32(5) 1.0(1) XFe. The velocity heterogeneity
parameter, ln VB/∂ XFe (Karato & Karki 2001), from experimen-
tal data is 0.10(1), in agreement with theory (0.10, Kiefer et al.
2002) and at the lower end of values reported for other mantle sil-
icates (Speziale et al. 2005). A slightly greater decrease in VBis
observed for Fe, Al-rich compositions, but the difference is within
the uncertainty. While some studies (Catalli et al. 2010b;Maoet al.
2011b) have suggested spin transitions as a possible explanation for
anticorrelation of bulk and shear velocities in the deep mantle, the
trends observed in most of the experimental data for Fe-bearing Pv
do not support this (Fig. 2).
Ab initio theoretical studies (Kiefer et al. 2002; Caracas & Cohen
2005) predict the effect of Fe incorporation on both bulk and shear
moduli of perovskite, allowing the seismic velocities VPand VS
to be determined, but involve inherent approximations. The con-
sistency between theory and experiment in bulk sound speed for
(Mg,Fe)SiO3perovskite (Fig. 2) confirms the reliability of theoret-
ical calculations of sound velocities at deep mantle pressures. This
establishes more confidence in the application of theoretical values
for not only VB,butalsoVPand VS.
2.2 Post-perovskite
Volume compression data for (Mg,Fe)SiO3post-perovskite have
been reported from X-ray diffraction experiments at 110–155 GPa
in several studies (Fig. 3;Shiehet al. 2006; Guignot et al. 2007;
Shim et al. 2008; Nishio-Hamane & Yagi 2009; Zhang et al. 2012;
Dorfman et al. 2013). For (Mg,Fe,Al)(Fe,Al,Si)O3post-perovskites,
data were measured from 95 to 175 GPa by Nishio-Hamane & Yagi
Figure 3. Volume differences between Fe- or Fe, Al-bearing post-
perovskites and MgSiO3perovskite (Guignot et al. 2007). Fe-bearing post-
perovskite with FeSiO3(Fs) from 10–74 per cent are shown in circles
(Nishio-Hamane & Yagi 2009; Zhang et al. 2012; Dorfman et al. 2013).
Post-perovskites synthesized from pyrope–almandine (Alm) composition
with 54 per cent Alm are displayed with diamonds (Shieh et al. 2011). Fif-
teen per cent FeAlO3composition (Nishio-Hamane & Yagi 2009)isshown
in triangles. Curves shown are from Birch–Murnaghan equation of state fits.
(2009), Catalli et al. (2010a), Shieh et al. (2011) and Dorfman et al.
(2012b). Following a similar procedure, these data were fit to equa-
tions of state to determine ρand Kand interpolated to a common
reference pressure for comparison. In addition, equation of state
data for perovskite compositions were extrapolated (for Fe, Al-rich
perovskite, interpolated) to compare density and compressibility of
these two phases. The reference pressure, 125 GPa, is near the post-
perovskite transition pressure for MgSiO3(Murakami et al. 2004)
and corresponds to 2700 km depth, near the D discontinuity.
At 125 GPa, ρis also observed to increase linearly with
Fe-content in post-perovskites (Fig. 4). Post-perovskite densi-
ties are fit to the following relationship: ρ125,pPv (g cm3)=
5.548(1) +1.41(3)XFe . At this pressure, the perovskite phase is
less dense, but the effect of Fe-content is similar: ρ125,Pv (g cm3)
=5.426(11) +1.38(4)XFe . The density difference across the post-
perovskite transition, ρ, was measured to be 1.5 per cent (±0.1–
0.7 per cent) at 125 GPa for both MgSiO3(Komabayashi et al. 2008)
and Alm54 compositions (Shieh et al. 2011; Dorfman et al. 2012b).
A comparable difference of 2.2 per cent is observed between the
linear fits of the densities of perovskite and post-perovskite across
the (Mg,Fe)SiO3join at 125 GPa (Fig. 4).
Theoretical calculations have also explored the behaviour of
(Mg,Fe,Al)(Fe,Al,Si)O3post-perovskite at deep lower-mantle con-
ditions (Iitaka et al. 2004; Caracas & Cohen 2005; Stackhouse
et al. 2005; Wookey et al. 2005; Stackhouse et al. 2006; Tsuchiya
& Tsuchiya 2006; Zhang & Oganov 2006; Caracas & Cohen 2007,
2008; Caracas 2010a,b;Hsuet al. 2012;Yuet al. 2012). These
predictions have used LDA and GGA methods, and more recently,
Hubbard Ucorrections to better model the electronic spin state
of Fe. Calculated densities for the perovskite and post-perovskite
phases at 125–136 GPa are in good agreement with experimen-
tal measurements at 125 GPa, though they yield a lower density
contrast between the two phases for Fe-rich compositions: ρ
is 1.4 per cent for MgSiO3but only 0.5–1.1 per cent for FeSiO3
(Caracas & Cohen 2005; Wookey et al. 2005; Stackhouse et al.
2006). The slope of increase in ρ125 with XFe from LDA calculations
is in better agreement with experimental data than GGA, which un-
derestimates the effect of Fe. No significant difference was predicted
between the densities of Fe2+-andFe
3+-bearing post-perovskite (Yu
et al. 2012).
The bulk modulus of the post-perovskite phase was found to be
more compressible with higher Fe-content(Zhang et al. 2012, Fig. 4)
and this can be described by: K125,pPv (GPa) =665(3) 81(16)XFe .
In contrast, data for the perovskite phase at this pressure show
no significant change in bulk modulus with Fe-content. The fit
to K125,Pv for perovskites is 692(7) GPa +30(52) GPa ×XFe.
Experimental trends thus show increasing contrast in VBbetween
Pv and pPv with Fe-content (Fig. 4). From XFe =0 to 40, the con-
trast in bulk sound speed between perovskite and post-perovskite
phases more than doubles, from 3.1 to 6.4 per cent. This increase
in contrast in VB,PvVB,pPvis not reported in theoretical stud-
ies, which predict only a slight effect of Fe-content on K125,pPv
(Fig. 4).
Volume compression data observed by Shieh et al. (2011)for
((Mg,Fe)0.75Al0.25)(Al0.25 Si0.75 )O3post-perovskites suggest a strong
increase in bulk modulus for more Fe-rich post-perovskite, but addi-
tional data are needed to confirm this (Shieh et al. 2011). Although
data for Fe#74 post-perovskite observed by Dorfman et al. (2013)
are insufficient to determine bulk modulus, they also indicate higher
volumes than predicted by the trend in Zhang et al. (2012). Possible
mechanisms for an increase in bulk modulus for compositions with
Fe#>40 could include a spin transition (e.g. Lin et al. 2008)ora
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6S.M. Dorfman and T.S. Duffy
Figure 4. (a) At 125 GPa and 300 K, density, bulk modulus and seismic wave propagation speeds for perovskites and post-perovskites with varying Fe,
Al-content determined from experimental data (Mao et al. 2006; Shieh et al. 2006; Guignot et al. 2007; Murakami et al. 2007b,2007a; Lundin et al. 2008;
Shim et al. 2008; Nishio-Hamane & Yagi 2009; Catalli et al. 2010a;Maoet al. 2011b; Shieh et al. 2011; Boffa Ballaran et al. 2012; Dorfman et al. 2012b;
Zhang et al. 2012; Dorfman et al. 2013). Colors of symbols have same meanings as in Fig. 2. Bold green line fits are shown to Fe2+-bearing compositions
(solid =perovskite, dashed =post-perovskite). (b) Density functional theory results at 125 GPa and 0 K for (Mg,Fe)SiO3perovskites and post-perovskites
from LDA (Kiefer et al. 2002;Yuet al. 2012) and GGA (Caracas & Cohen 2005,2008). Perovskite calculations are shown in solid black. Post-perovskite
results are dotted and shown in green for Fe2+-bearing compositions, while dotted red represent Fe3+-bearing compositions.
modification of the post-perovskite structure in Fe-rich composi-
tions (Yamanaka et al. 2010).
A large decrease in shear modulus with Fe-content in post-
perovskite was observed in a nuclear resonant inelastic X-ray scat-
tering experiment by Mao et al. (2006). Based on measured partial
phonon density of states of Fe and volume compression data, this
experiment determined velocities VPand VSof an (Mg0.6Fe0.4 )SiO3
pPv lower than those of MgSiO3pPv by 11 and 38 per cent, respec-
tively (Fig. 4). However, this technique is sensitive to the extrap-
olation from the partial phonon density of states which may lead
to underestimation of velocities (Sturhahn & Jackson 2007). This
has been the only experimental determination of bulk elastic wave
velocities of an Fe-bearing silicate at deep mantle pressures.
Theoretical studies do not predict any stiffening of the bulk mod-
ulus or large decrease in elastic wave velocities at high Fe-content.
A spin transition in post-perovskite was not predicted to occur at
Earth-relevant pressures (Caracas & Cohen 2008). Overall, given
the higher required experimental pressures and more limited data,
it is perhaps not surprising that the observed variation in pPv prop-
erties with Fe-content is more uncertain and less consistent with
theory. Further compression experiments on Fe-rich pPv are needed
at deep lower-mantle pressures.
by guest on April 9, 2014 from
Effect of Fe-enrichment on the deep lower mantle 7
The volume or density is the property most precisely constrained
by the experiments discussed above and is the driver of thermo-
chemical convection in the mantle. The style of convection will de-
pend on the relative contributions of chemical and thermal anoma-
lies (Davaille 1999; Deschamps & Tackley 2008). A fundamental
question is whether dense chemical heterogeneities are entrained
in mantle convection or sequestered at the core–mantle boundary.
To remain at the core–mantle boundary, chemical heterogeneities
must be enriched enough in heavy elements (Fe) to offset thermal
buoyancy. Assuming thermal and chemical effects are independent
(Anderson & Hama 1999), for a hot, dense heterogeneity with neu-
tral buoyancy, the thermal and chemical effects are equal:
XFe .(1)
Using the experimental results discussed above, we can calcu-
late the Fe-enrichment necessary to balance thermal anomalies.
The variation of thermal expansivity, α, with pressure and tem-
perature for MgSiO3was estimated from density functional theory
calculations (Wentzcovitch et al. 2004) yielding αρ =7.63 ×105
3/K for MgSiO3perovskite at 80 GPa and 2000 K. The differ-
ence in density due to temperature relative to that of end-member
MgSiO3perovskite at 2000 K and 80 GPa was calculated for tem-
perature anomalies of 200, 500 and 800 K (Fig. 5a). Based on the
effect of Fe-content on density at this pressure (Fig. 2), a chemical
heterogeneity with Mg# (Mg/(Mg+Fe)) =87 would be neutrally
buoyant in a Mg# 90 mantle if it is also 500 K hotter than the sur-
rounding rock (Fig. 5b). This is consistent with long-term stability
of dense heterogeneities in the deep mantle estimated by probabilis-
tic tomography to be enriched in Fe by 2 per cent and warmer by
300 K (Trampert et al. 2004).
Based on current experimental data, the density contrast be-
tween perovskite and post-perovskite phases appears to be insen-
sitive to temperature (Komabayashi et al. 2008) and Fe-content.
Komabayashi et al. (2008) observed that the 1.5 percent density
contrast across the post-perovskite transition would be equivalent
to the contrast due to a 1300 K difference in temperature. The
2.2 per cent density contrast shown by our (Mg,Fe)SiO3perovskite
and post-perovskite data set may imply an even greater impact of
the post-perovskite transition on buoyancy (equivalent to a 1900 K
thermal difference). This density contrast could also be produced in
either silicate phase at 125 GPa by a XFe of 9 Mg# (Mg# 81, rel-
ative to Mg#90, see Fig. 4). However, both Fe and Al contents have
strong effects on the pressure and width of the post-perovskite tran-
sition, so the depth at which this density difference is observed and
its sharpness will depend on composition. In Fe-rich compositions,
a broad post-perovskite transition has been observed with a mix-
ture of very Fe-rich post-perovskite and Fe-poor perovskite (Mao
et al. 2004,2005; Dorfman et al. 2013). A two-phase loop with
difference in Fe-content between post-perovskite and perovskite
XFe,pPvXFe,Pvas high as 0.6 (Dorfman et al. 2013) would have
a high contrast in properties between these two phases at the base
of the lower mantle: ρ between adjacent perovskite and post-
perovskite grains could be up to 0.8 g cm3, or 13 per cent. This
contrast could have important implications for the rheology of the
D phase assemblage (Ammann et al. 2010).
The effect of Fe-incorporation on density of perovskite and post-
perovskite can be used to determine composition of heterogeneities.
Recent studies have suggested that observed lower-mantle densi-
Figure 5. (a) Effect of 200, 500 and 800 K thermal anomalies on density
of perovskite from Wentzcovitch et al. (2004). (b) From density data for
Fe-rich and Fe, Al-rich perovskites, amount of Fe-enrichment necessary to
balance buoyancy due to temperature.
ties (Ricolleau et al. 2009) and shear wave velocities (Murakami
et al. 2012) are consistent with a Si-enriched composition, at least
93 per cent perovskite. Assuming a perovskitic lower mantle, den-
sity contrasts may be dominated by differences in Fe-content in
perovskite or post-perovskite. Based on the trend in Fig. 2,an
LLSVP with density up to 2–5 per cent greater than a Mg/(Mg+Fe)
90 per cent bulk mantle would be consistent with Mg/(Mg+Fe) of
as low as 78–88 per cent in perovskite. A ULVZ at the core–mantle
boundary 10 per cent denser than Mg#90 post-perovskite could be
composed of Mg#50 post-perovskite. Based on theoretical (Wookey
et al. 2005; Stackhouse et al. 2006; Caracas & Cohen 2008)and
experimental (Mao et al. 2006) constraints on VP, Mg#50 post-
perovskite would propagate Pwaves 6–20 per cent slower than
Mg#90 post-perovskite, similar to the 4–19 per cent VPreduction
observed by Rost & Garnero (2006). A FeSiO3post-perovskite
would be 22 per cent denser than Mg#90. If regions are observed
with greater density than this (e.g. Rost & Garnero 2006), they
by guest on April 9, 2014 from
8S.M. Dorfman and T.S. Duffy
must be both richer in Fe and poorer in Si, that is, enriched in
denser (Mg,Fe)O or Fe metal.
For compositions with more (Mg,Fe)O or other Si- or Al-rich
phases, we must also consider the effects of these phases on chem-
ical partitioning and phase equilibria. Ricolleau et al. (2009) ob-
served that the partitioning of Fe between (Mg,Fe)O and silicate
phases has a negligible effect on the density of the mantle. Similar
modelling with our data set shows that varying the partitioning co-
efficient, KD, of Fe between perovskite and magnesiow¨
ustite over
the range of experimental values (e.g. Auzende et al. 2008; Sakai
et al. 2009) results in density differences of 0.1 per cent. Exchange
of Fe with (Mg,Fe)O may have more important effects on the depth
and sharpness of the post-perovskite transition (Grocholski et al.
2012). In the (Mg,Fe)SiO3system, Fe-incorporation was observed
to produce a shallower and broader phase transition (e.g. Dorfman
et al. 2013), but partitioning of Fe into the oxide phase sharp-
ens the transition. Al incorporation has been observed to deepen
and broaden the post-perovskite transition such that Al-rich post-
perovskite would not be observed in the lower mantle (Tateno et al.
2005; Dorfman et al. 2012b). Stabilization of perovskite in Fe,
Al-rich heterogeneities could possibly produce anticorrelated VB
and VSdue to the 3–7 per cent higher VBobserved in perovskite rela-
tive to post-perovskite of the same composition (at 125 GPa, Fig. 4).
However, in compositions with sufficiently high Si, Al-content such
as MORB, the presence of separate Si- and Al-bearing phases
erased this effect on the post-perovskite transition (Grocholski
et al. 2012).
In summary, experimentaland theoretical data are compiled to de-
termine the effects of Fe and/or Al incorporation on the elastic prop-
erties of (Mg,Fe,Al)(Fe,Al,Si)O3perovskite and post-perovskite at
representative mantle depths. Using recent volume compression
data on perovskites with up to 75 per cent FeSiO3, we provide con-
straints on the density, bulk modulus and bulk sound speed of Fe-
bearing perovskites. Experimental compression data for perovskite
are in good agreement with density functional theory calculations,
showing a weak increase in the bulk modulus with Fe-content. For
post-perovskite, experimental studies have observed a decrease in
bulk modulus with Fe-content, in contrast to theory. Electronic spin
transitions and differences in valence state of Fe in perovskite and
post-perovskite phases are not expected to produce observable dif-
ferences in seismic velocities in the lower mantle. Across the post-
perovskite transition, the experimental data show a density increase
of 2 per cent and an increasing contrast in bulk compressibility
with Fe-content. The density contrast across the phase transition is
comparable to the contrast due to decreasing Mg# by 9 or decreasing
temperature by 1900 K. Al may increase the density of Fe-bearing
perovskite by allowing paired substitution for Mg and Si, but can
stabilize perovskite over post-perovskite.
The National Science Foundation and Carnegie-Department of
Energy Alliance Center provided support for this research.
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... Iron-enrichment has been suggested to explain seismic observations of dense regions in the deep lower mantle such as large low shear velocity provinces (LLSVPs) (e.g., [1]) and ultra-low velocity zones (ULVZs) (e.g., [2,3]). For LLSVPs, the difference in Fe/(Mg + Fe), or Fe#, relative to the surrounding mantle is inferred to be as much as 7% based on estimated chemical density differences up to 2% [4]. ULVZs may be more dramatically enriched in Fe to generate density differences of 10% or more. ...
... Model compositions for variable Fe#, mol% SiO 2 and pressure are combined with measurements of physical properties of bridgmanite and magnesiowüstite to determine the observable seismic properties of mantle heterogeneities. Recent experimental equation of state measurements over a wide range of compositions have confirmed that the densities of bridgmanite and post-perovskite vary linearly with Fe 2+ -content (Supplementary Figure S11) [4]. The Fe#-and pressure-dependence of density of ferropericlase/magnesiowüstite requires a more complex model due to the composition-dependent spin transition. ...
... Heterogeneous mantle SiO 2 -content may also explain enigmatic differences in seismic velocities V S and V P in LLSVPs [56]. The deep lower mantle has been noted for anticorrelation of V S and V P , which neither thermal differences nor iron content alone can explain [4]. However, differences in Fe-content in combination with SiO 2 -content produce complex effects on density and compressibility. ...
Full-text available
Both seismic observations of dense low shear velocity regions and models of magma ocean crystallization and mantle dynamics support enrichment of iron in Earth’s lowermost mantle. Physical properties of iron-rich lower mantle heterogeneities in the modern Earth depend on distribution of iron between coexisting lower mantle phases (Mg,Fe)O magnesiowüstite, (Mg,Fe)SiO3 bridgmanite, and (Mg,Fe)SiO3 post-perovskite. The partitioning of iron between these phases was investigated in synthetic ferrous-iron-rich olivine compositions (Mg0.55Fe0.45)2SiO4 and (Mg0.28Fe0.72)2SiO4 at lower mantle conditions ranging from 33–128 GPa and 1900–3000 K in the laser-heated diamond anvil cell. The resulting phase assemblages were characterized by a combination of in situ X-ray diffraction and ex situ transmission electron microscopy. The exchange coefficient between bridgmanite and magnesiowüstite decreases with pressure and bulk Fe# and increases with temperature. Thermodynamic modeling determines that incorporation and partitioning of iron in bridgmanite are explained well by excess volume associated with Mg-Fe exchange. Partitioning results are used to model compositions and densities of mantle phase assemblages as a function of pressure, FeO-content and SiO2-content. Unlike average mantle compositions, iron-rich compositions in the mantle exhibit negative dependence of density on SiO2-content at all mantle depths, an important finding for interpretation of deep lower mantle structures.
... While the effect of ferrous iron on bridgmanite elasticities is straightforward (e.g. Dorfman and Duffy (2014) and Shukla et al. (2015b)), the effect of ferric iron on the elasticities of bridgmanite is more complex. Some studies have found that ferric iron increases the bulk modulus (K) (Andrault et al., 2001;Dorfman and Duffy, 2014;Nishiyama et al., 2007;Nishio-Hamane et al., 2008), while others have found the opposite and that K decreases with ferric iron concentration (Ballaran et al., 2012;Li et al., 2005;Saikia et al., 2009;Liu et al., 2018). ...
... Dorfman and Duffy (2014) and Shukla et al. (2015b)), the effect of ferric iron on the elasticities of bridgmanite is more complex. Some studies have found that ferric iron increases the bulk modulus (K) (Andrault et al., 2001;Dorfman and Duffy, 2014;Nishiyama et al., 2007;Nishio-Hamane et al., 2008), while others have found the opposite and that K decreases with ferric iron concentration (Ballaran et al., 2012;Li et al., 2005;Saikia et al., 2009;Liu et al., 2018). Some of this discrepancy can be explained due to differences in both how ferric iron is present and how the spin transition is treated. ...
... There has been considerable debate on the exact position of this transition as it is heavily dependent upon the background chemistry in which it occurs (Grocholski et al., 2012) with both Fe and Al having large effects on this transition. Ferrous iron has been seen to lower the onset pressure of ppv formation and broaden the transition (Sun et al., 2018;Caracas and Cohen, 2005;Dorfman and Duffy, 2014;Mao et al., 2004) but in the presence of ferropericlase it can raise this pressure (and sharpen the transition) due to partitioning effects (Catalli et al., 2009;Grocholski et al., 2012). FeeAl pairs deepen the transition while also greatly broadening it (Grocholski et al., 2012;Sun et al., 2018;Akber-Knutson et al., 2005;Nishio-Hamane et al., 2007;Andrault et al., 2010;Catalli et al., 2009;Tateno et al., 2005). ...
The seismic velocities of ferric iron-enriched bridgmanite under core-mantle boundary (CMB) conditions were calculated using GGA + U ab initio molecular dynamics to probe whether ferric iron enriched mantle can explain the properties of ultra-low velocity zones (ULVZ). Under these conditions ferric iron demonstrated some unusual properties. The effect of ferric iron on the 0 K transition pressure of the bridgmanite (bdg) to postperovskite (ppv) transition with GGA + U has some dependence upon the value of Ueff that is set for B site ferric iron which is in contrast to most substances where Ueff has little effect on the properties. We find that ferric iron can both stabilise and destabilise the bdg phase relative to the ppv phase depending upon the value of U. This is due to the spin state transition of B-site ferric iron and was not seen in ferrous or aluminous ferric bridgmanite which lack such a transition at mantle conditions. Due to the similar energies and pressure derivatives of the bdg and ppv phases very subtle energy changes (such as that of iron clustering or different theoretical or experimental setups) can have large effects on the relative phase stabilities at different pressures. The spin state of ferric iron in bdg demonstrates some novel behaviours. With large iron enrichment the spin state of the B site has a non-linear dependence on concentration and depends upon the local arrangement of iron. At typical lower mantle pressures, ferric iron is expected to be high spin in the A site and low spin at the B site but at the temperatures of the CMB thermal spreading of the electrons causes ferric iron at the B site to become high spin. This is not a typical “spin transition” however as it involves no structural rearrangement of the unit cell and is predicted to have no effect on the elasticity and thus the seismicity of the crystal. Our elasticity results show that at the CMB ferric iron-enriched bridgmanite has nearly identical Vp and Vs to ferrous iron-bearing bridgmanite, and thus bridgmanite containing large amounts of Fe²⁺ or Fe³⁺ can both explain ULVZ properties when mixed with ferropericlase. We find, however, that mixing of both ferric and ferrous iron in bridgmanite causes a large (up to 1 km/s) non-ideal decrease in Vp when there is middling amounts of ferric iron. This non-linear mixing should have significant effects throughout the lower mantle whenever such amounts of ferric iron are present though such a ferrous:ferric ratio would typically require an increase of the natural ferrous:ferric ratio (for example through very high oxidation fugacities or chemical doping). In the case of ULVZs this non-linear mixing significantly impairs the fitting to some ULVZ data sets (those with a dlnVs/dlnVp ~ 3), but greatly improves the fitting to other ULVZ data sets (those with a dlnVs/dlnVp ~ 1). The oxidation state of highly enriched iron in bridgmanite at CMB conditions has, therefore, a large effect on the ability of mantle mixtures that are highly enriched in iron to replicate ULVZ properties.
... High-pressure is a tool that enabled important contributions to the science and the industry, benefiting to many areas such as physics, Earth sciences, biology, food sciences, pharmaceutical research and biotechnology [1][2][3][4][5]. For instance, the study of particular substances submitted to high pressure and high temperature can help to the understanding of the Earth's interior composition [1,2]. ...
... High-pressure is a tool that enabled important contributions to the science and the industry, benefiting to many areas such as physics, Earth sciences, biology, food sciences, pharmaceutical research and biotechnology [1][2][3][4][5]. For instance, the study of particular substances submitted to high pressure and high temperature can help to the understanding of the Earth's interior composition [1,2]. The effect of compression and decompression on inactivation of microorganisms has also been studied [3]. ...
... GPa is presented in the Fig. 5a. In this spectral region, we find modes related to units as CO 2 ), splits in two weak bands at 4.8 GPa and gain intensity when 12.4 GPa is reached. The phase transitions effects also can be seen by discontinuities in the wavenumber versus pressure plot in Fig. 5b, confirming the main results established through the previous analysis of the lattice modes spectral region. ...
DL-glutamic acid monohydrate crystal was synthesized from an aqueous solution by slow evaporation technique. The crystal was submitted to high-pressure (1 atm-14.3 GPa) to investigate its vibrational behavior and the occurrence of phase transitions. We performed Raman spectroscopy as probe and through the analysis of the spectra we discovered three structural phase transitions. The first one occurs around 0.9 GPa. In this phase transition, glutamic acid molecules suffer modifications in their conformations while water molecules are less affected. The second phase transition at 4.8 GPa involves conformational changes related to CO2-, NH3+ units and the water molecules, while the third one, between 10.9 and 12.4 GPa, involves motions of several parts of the glutamic acid as well as the water molecules. Considering the dynamic of high pressure, the second phase of DL-glutamic acid monohydrate crystal presented a better stability compared with the second phase of its polymorphs α and β L-glutamic acid. In addition, water molecules seem to play important role on this structural stability. All changes are reversible.
... We have updated the parameters of several species, including the elasticity and/or equation of state of wadsleyite (Wang et al. 2014), diopside (Sang & Bass 2014), hedenbergite , akimotoite (Zhou et al. 2014), corundum (Dewaele & Torrent 2013), Na-majorite (Dymshits et al. 2013), coesite (Chen et al. 2015), stishovite (Wang et al. 2012), bridgmanite (Dorfman et al. 2013;Zhang et al. 2013;Dorfman & Duffy 2014), post-perovskite (Sakai et al. 2016), NAL and calcium-ferrite phases (Imada et al. 2012;Dai et al. 2013;Kojitani et al. 2011;Pamato et al. 2014;Mookherjee et al. 2012) and regular solution parameters of the Calcium-Ferrite (cf) phase to better describe cf-nal phase relations (Ono et al. 2009;Imada et al. 2011). We have also updated phase equilibria, for example by including experimental data that build on more recent developments in pressure calibration such as the study of the ri=bg+fp transition by Ye et al. (2017). ...
Full-text available
We derive exact expressions for the thermal expansivity, heat capacity, and bulk modulus for assemblages with arbitrarily large numbers of components and phases, including the influence of phase transformations and chemical exchange. We illustrate results in simple two-component, two-phase systems, including Mg-Fe olivine-wadsleyite and Ca-Mg clinopyroxene-orthopyroxene, and for a multi-compontent model of mantle composition in the form of pyrolite. For the latter we show results for the thermal expansivity and heat capacity over the entire mantle pressure-temperature regime to 40 GPa, or a depth of 1000 km. From the thermal expansivity, we derive a new expression for the phase buoyancy parameter that is valid for arbitrarily large numbers of phases and components and which is defined at every point in pressure-temperature space. Results reveal regions of the mantle where the magnitude of the phase buoyancy parameter is larger in magnitude than for those phase transitions that are most commonly included in mantle convection simulations. These regions include the wadsleyite to garnet and ferropericlase transition, which is encountered along hot isentropes (e.g. 2000 K potential temperature) in the transition zone, and the ferropericlase and stishovite to bridgmanite transition, which is encountered along cold isentropes (e.g. 1000 K potential temperature) in the shallow lower mantle. We also show the bulk modulus along a typical mantle isentrope and relate it to the Bullen inhomogeneity parameter. All results are computed with our code HeFESTo, updates and improvements to which we discuss, including the implementation of the exact expressions for the thermal expansivity, heat capacity, and bulk modulus, generalization to allow for pressure dependence of non-ideal solution parameters, and an improved numerical scheme for minimizing the Gibbs free energy. Finally we present the the results of a new global inversion of parameters updated to incorporate more recent results from experiment and first principles theory, as well as a new phase (nal phase), and new species: Na-majorite and the NaAlO2 end-member of ferropericlase.
... The incorporation of Fe resulted in an increase in density from 2.60 gcm −3 of Fe-free verity [40] to 2.761 gcm −3 in our sample, which represented a 6% increase in density at ambient conditions. While the incorporation of Fe affected both elastic moduli and the density, it has been shown that the increase in density due to the increase in Fe contents was responsible for the observed low velocities in Fe-bearing minerals compared to their Fe-free varieties [46]. ...
Full-text available
Dehydration and fluid circulation are integral parts of subduction tectonics that govern the dynamics of the wedge mantle. The knowledge of the elastic behavior of aqueous fluid is crucial to understand the fluid–rock interactions in the mantle through velocity profiles. In this study, we investigated the elastic wave velocities of chlorite at high pressure beyond its dehydrating temperature, simulating the progressive dehydration of hydrous minerals in subduction zones. The dehydration resulted in an 8% increase in compressional (Vp) and a 5% decrease in shear wave (Vs) velocities at 950 K. The increase in Vp can be attributed to the stiffening of the sample due to the formation of secondary mineral phases followed by the dehydration of chlorite. The fluid-bearing samples exhibited Vp/Vs of 2.45 at 950 K. These seismic parameters are notably different from the major mantle minerals or hydrous silicate melts and provide unique seismic criteria for detecting mantle fluids through seismic tomography.
... Owing to its strong effect on density (Irifune et al., 2010;Dorfman and Duffy, 2014), hence mass and moment of inertia, the Fe content of the lower mantle is thought to be relatively well-constrained at~8% by weight (e.g., McDonough and Sun, 1995). However, the partitioning of Fe between phases is poorly constrained (Lin et al., 2013). ...
Constraining Earth's bulk composition is fundamental to understanding our planet's formation and evolution. While the lower mantle accounts for a majority of the bulk silicate Earth, it is also the least accessible. As experimental and theoretical mineral physics constraints on mineral elasticity at lower mantle temperatures and pressures have improved, comparisons between predicted seismic velocity and density profiles for hypothesized bulk compositions and 1D seismic models have become commonplace. However, the degree to which a given composition is a better or worse fit than another composition is not always reported, nor are the influences of the assumed temperature profile and other uncertainties discussed. Here we compare seismic velocities and densities for perovskitite, pyrolite, and harzburgite bulk compositions calculated using advanced ab initio techniques to explore the extent to which the associated uncertainties affect our ability to distinguish between candidate compositions. We find that predicted differences between model compositions are often smaller than the influence of temperature uncertainties and therefore these comparisons lack discriminatory power. The inability to distinguish between compositions is largely due to the high sensitivity of seismic properties to temperature accompanied by uncertainties in the mantle geotherm, coupled with diminished sensitivity of seismic velocity to composition toward the base of the mantle. An important exception is the spin transition in (Mg,Fe)O-ferropericlase, which is predicted to give a distinct variation in compressional wave velocity that should distinguish between relatively ferro-magnesian and silica-rich compositions. However, the absence of an apparent spin transition signature in global 1D seismic profiles is a significant unresolved issue in geophysics, and it has important geochemical implications. The approach we present here for establishing discriminatory power for such comparisons can be applied to any estimate of seismic velocities and associated uncertainties, and offers a straightforward tool to evaluate the robustness of model comparisons.
In this study, we investigate the seismic structure of the D′′ layer beneath the Indian Ocean by modeling the ScS-S and PcP-P differential travel time residuals corrected for the velocity structure above it. These times, representative of the anomalies in the D′′ layer, vary from -9.58 to 5.06 s for the shear wave (ScS-S) and -4.54 to 3.14 s for the compressional wave (PcP-P). Modeling of the residuals using a grid search approach reveals velocity perturbations in the range of -3.06% to 5.72% for the shear and -4.81% to 5.47% for the compressional waves, in the D′′ layer. Interestingly, the perturbations are positive below the Indian Ocean Geoid Low (IOGL) and negative below the adjoining region. The results clearly reveal presence of high velocity material atop the Core Mantle Boundary (CMB) beneath the IOGL, representing dehydrated Tethyan subducted slabs. Further, the low RSP values in the lowermost mantle beneath the western part of IOGL, calculated using the P and S velocity estimates from this study, mostly lie between 0.01 and 2.7. This implies that the anomalies may be thermal in origin, owing to the heterogeneities resulting from cold lithospheric slabs at the CMB.
Context. The discovery of low density exoplanets in the super-Earth mass regime suggests that ocean planets could be abundant in the galaxy. Understanding the chemical interactions between water and Mg-silicates or iron is essential for constraining the interiors of water-rich planets. Hydration effects have, however, been mostly neglected by the astrophysics community so far. As such effects are unlikely to have major impacts on theoretical mass-radius relations, this is justified as long as the measurement uncertainties are large. However, upcoming missions, such as the PLATO mission (scheduled launch 2026), are envisaged to reach a precision of up to ≈3 and ≈10% for radii and masses, respectively. As a result, we may soon enter an area in exoplanetary research where various physical and chemical effects such as hydration can no longer be ignored. Aims. Our goal is to construct interior models for planets that include reliable prescriptions for hydration of the cores and mantles. These models can be used to refine previous results for which hydration has been neglected and to guide future characterization of observed exoplanets. Methods. We have developed numerical tools to solve for the structure of multi-layered planets with variable boundary conditions and compositions. Here we consider three types of planets: dry interiors, hydrated interiors, and dry interiors plus surface ocean, where the ocean mass fraction corresponds to the mass fraction of the H 2 O equivalent in the hydrated case. Results. We find H and OH storage capacities in the hydrated planets equivalent to 0−6 wt% H 2 O corresponding to up to ≈800 km deep ocean layers. In the mass range 0.1 ≤ M ∕ M ⊕ ≤ 3, the effect of hydration on the total radius is found to be ≤2.5%, whereas the effect of separation into an isolated surface ocean is ≤5%. Furthermore, we find that our results are very sensitive to the bulk composition.
Significance Iron-bearing bridgmanite is the most abundant mineral in the Earth’s interior. We overcome the experimental challenge of measuring iron-bearing materials by using Brillouin scattering techniques optimized for extreme pressure conditions in combination of diamond-anvil cell. By using such techniques, results of acoustic wave velocities in the pressure range of the entire mantle are reported here. Based on our results, we show that the greater part of the lower mantle is Fe ²⁺ -rich because the gradient of our model gives excellent fit to that of Preliminary Reference Earth Model for almost all the pressure range of the lower mantle with an Fe ³⁺ /ΣFe of 0.2. Our lower-mantle model also shows a distinctive Si-enriched composition with Mg/Si of 1.14 relative to the upper mantle.
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Electronic states of iron in the lower mantle's dominant mineral, (Mg,Fe,Al)(Fe,Al,Si)O3 bridgmanite, control physical properties of the mantle including density, elasticity, and electrical and thermal conductivity. However, the determination of electronic states of iron has been controversial, in part due to different interpretations of Mössbauer spectroscopy results used to identify spin state, valence state, and site occupancy of iron. We applied energy-domain Mössbauer spectroscopy to a set of four bridgmanite samples spanning a wide range of compositions: 10–50% Fe/total cations, 0–25% Al/total cations, 12–100% Fe3+/total Fe. Measurements performed in the diamond-anvil cell at pressures up to 76 GPa below and above the high to low spin transition in Fe3+ provide a Mössbauer reference library for bridgmanite and demonstrate the effects of pressure and composition on electronic states of iron. Results indicate that although the spin transition in Fe3+ in the bridgmanite B-site occurs as predicted, it does not strongly affect the observed quadrupole splitting of 1.4 mm/s, and only decreases center shift for this site to 0 mm/s at ~70 GPa. Thus center shift can easily distinguish Fe3+ from Fe2+ at high pressure, which exhibits two distinct Mössbauer sites with center shift ~1 mm/s and quadrupole splitting 2.4–3.1 and 3.9 mm/s at ~70 GPa. Correct quantification of Fe3+/total Fe in bridgmanite is required to constrain the effects of composition and redox states in experimental measurements of seismic properties of bridgmanite. In Fe-rich, mixed-valence bridgmanite at deep-mantle-relevant pressures, up to ~20% of the Fe may be a Fe2.5+ charge transfer component, which should enhance electrical and thermal conductivity in Fe-rich heterogeneities at the base of Earth's mantle.
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Using single-crystal elasticity data we constrain the effect of chemical substitutions on the elastic properties of mantle minerals and estimate the consequences for the seismic properties of mantle rocks. At ambient conditions the calculated relative variation of compressional and shear velocities ∂lnvp/∂XFe and ∂lnvs/∂XFe due to Fe-Mg substitution, range between -0.05 and -0.46 and between -0.08 and -0.74 respectively in the main mantle minerals. The corresponding heterogeneity ratios R = ∂lnvs/∂lnvp for Fe-Mg substitution range between 0.9 and 1.7 suggesting that the effect of this substitution is very different in different solid solutions systems. More limited experimental results for Ca-Mg substitution and Al enrichment in pyroxenes and garnets were also evaluated. Only Ca-Mg substitution in garnets is found to produce large (>2.0) values of R. Heterogeneity parameters at upper mantle and transition zone conditions can be substantially different from ambient P-T values in some cases. Using a first-order approximation of the effect of Fe-Mg substitution on the elastic properties of the most relevant upper mantle rocks, we find that the sensitivities of seismic velocities to Fe enrichment can vary as much as 2-3 times between the different rock types. We estimate that in the upper mantle the value of ∂lnvs/∂lnvp for pyrolite, piclogite and harzburgite decreases from 1.5 to 1.0 at the base of the transition zone, while it only decreases from 1.5 to 1.3 in mid ocean ridge basalt eclogite, which is enriched in garnet. We also estimate that the seismic effect of lateral changes in lithology from average mantle to subducted slab rocks decreases in intensity at upper mantle and transition zone depths, in agreement with seismic tomographic models. Information about the effects of Ca and Al enrichment are still too incomplete to make predictions of their effects on whole rocks, but they could be relevant based on our limited information.
The elastic constants and acoustic velocities of MgSiOs perovskite, the most abundant mineral of the earth's lower mantle (LM), were discussed. Earth model indicated that the top of the LM behaved as typical aggregate of pyrolitic composition. The elastic constants were used to predict acoustic velocity of LM mineral aggregates. Results show that the values of the predicted properties were independent of the order used in the finite strain expansion of the free energy.
The electronic environment of the Fe nuclei in two silicate perovskite samples, Fe0.05Mg0.95SiO3 (Pv05) and Fe0.1Mg0.9SiO3 (Pv10), have been measured to 120 GPa and 75 GPa, respectively, at room temperature using diamond anvil cells and synchrotron Mossbauer spectroscopy (SMS). Such investigations of extremely small and dilute 57 Fe-bearing samples have become possible through the development of SMS. Our results are explained in the framework of the “three-doublet” model, which assumes two Fe2+ -like sites and one Fe 3+ -like site that are well distinguishable by the hyperÞ ne Þ elds at the location of the Fe nuclei. At low pressures, Fe3+ /ΣFe is about 0.40 for both samples. Our results show that at pressures extending into the lowermost mantle the fraction of Fe3+ remains essentially unchanged, indicating that pressure alone does not alter the valence states of iron in (Mg,Fe)SiO3 perovskite. The quadrupole splittings of all Fe sites Þ rst increase with increasing pressure, which suggests an increasingly distorted (noncubic) local iron environment. Above pressures of 40 GPa for Pv10 and 80 GPa for Pv05, the quadrupole splittings are relatively constant, suggesting an increasing resistance of the lattice against further distortion. Around 70 GPa, a change in the volume dependence of the isomer shift could be indicative of the endpoint of a continuous transition of Fe3+ from a highspin to a low-spin state.
[1] Using first-principles calculations we predict the effects of composition on the perovskite to post-perovskite phase transition. The transition is predicted at 107 GPa for pure MgSiO3. The addition of Al2O3 slightly increases this transition pressure, and the addition of Fe2+ considerably reduces it; the FeSiO3 end-member term is stable in the post-perovskite modification with respect to perovskite at all pressures. We also determine the static equations of state, densities, elasticity and seismic wave velocities. At the transition Vp increases slightly, and Vs increases significantly, consistent with the seismic observations for D″. The addition of both Fe2+ and Al2O3 decrease the seismic wave velocities.
[1] We have critically reviewed and discussed currently available information regarding the spin and valence states of iron in lower mantle minerals and the associated effects of the spin transitions on physical, chemical, and transport properties of the deep Earth. A high-spin to low-spin crossover of Fe2+ in ferropericlase has been observed to occur at pressure-temperature conditions corresponding to the middle part of the lower mantle. In contrast, recent studies consistently show that Fe2+ predominantly exhibits extremely high quadrupole splitting values in the pseudo-dodecahedral site (A site) of perovskite and post-perovskite, indicative of a strong lattice distortion. Fe3+ in the A site of these structures likely remains in the high-spin state, while a high-spin to low-spin transition of Fe3+ in the octahedral site of perovskite occurs at pressures of 15–50 GPa. In post-perovskite, the octahedral-site Fe3+ remains in the low-spin state at the pressure conditions of the lowermost mantle. These changes in the spin and valence states of iron as a function of pressure and temperature have been reported to affect physical, chemical, rheological, and transport properties of the lower mantle minerals. The spin crossover of Fe2+ in ferropericlase has been documented to affect these properties and is discussed in depth here, whereas the effects of the spin transition of iron in perovskite and post-perovskite are much more complex and remain debated. The consequences of the transitions are evaluated in terms of their implications to deep Earth geophysics, geochemistry, and geodynamics including elasticity, element partitioning, fractionation and diffusion, and rheological and transport properties.
We use density functional theory to study the effect of Fe and Al on properties of MgSiO3 perovskite and post-perovskite. The addition of Fe increases the compressibility and density of MgSiO3 and considerably decreases the transition pressure between the two phases. MgSiO3 perovskite transforms to post-perovskite at about 112 GPa. FeSiO3 is stable as post-perovskite at all pressures relative to perovskite. We find ferrous iron to be in a high spin state over the whole mantle pressure range, and it partitions preferentially into the post-perovskite structure. Ferrous iron in MgSiO3 decreases the seismic wave velocities and slightly decreases the seismic anisotropy. At 120 GPa, FeSiO3 post-perovskite has Vp = 12.4 km/s and Vs = 6.3 km/s and MgSiO3 post-perovskite has Vp = 14.2 km/s and Vs = 7.9 km/s. The seismic anisotropy of post-perovskite MgSiO3 is 15% for Vp and 26% for Vs. Aluminum slightly decreases the density and increases the transition pressure. Pure alumina transforms from perovskite to post-perovskite at 120 GPa. Al2O3 also increases the compressibility of perovskite and decreases that of post-perovskite. Al decreases the seismic wave velocities and considerably increases the seismic anisotropy of post-perovskite. At 120 GPa, post-perovskite Al2O3 has Vp = 13.8 km/s and Vs = 7.4 km/s and seismic anisotropy of 18% for Vp and 43% for Vs. For proposed mantle compositions such as pyrolite the changes in seismic wave velocities due to the transition from perovskite to post-perovskite, that is positive jumps in both Vp and Vs, can explain those observed at the top of the D″ layer.
Despite immense progress in imaging seismic velocity anomalies in the mantle over the past 15 years, we still know relatively little about their physical cause. One way to shed some light on this problem is to investigate the relative amplitudes of compressional and shear velocity anomalies in the mantle. Unfortunately, the amplitudes of velocity anomalies can be quite sensitive to the data sets and imaging techniques employed. It is therefore usually meaningless to take two models from the literature and do a simple comparison. In this paper, we consider joint modeling of P and S data sets and compare with some recent results from the literature. Some robust patterns are beginning to emerge which allow us to identify regions of the lower mantle which are anomalous. Such regions seem to be associated with large-scale upwelling in the mantle and may indicate chemical interaction with the core.
A generalized inverse method is applied to infer the radial lower mantle composition and temperature profile from seismological models of density and bulk sound velocity. The computations are performed for a five-component system, MgO-FeO-CaO-Al2O3-SiO2 and three phases: (Mg,Fe,Al)(Si,Al)O3 perovskite, (Mg,Fe)O magnesiowustite, and CaSiO3 perovskite. A detailed review of the elasticity data set used to compute the elastic properties of mineral assemblages is given. We consider three different a priori compositional models-pyrolite, chondritic and a model based on cosmic abundances of elements-as a priori knowledge for the inversions in order to investigate the sensitivity of any given best-fit solution to the assumed initial composition. Consistent features in all inversions, independent of the a priori model, are a total iron content of XFe~= 0.10 +/- 0.06 and a subadiabatic temperature gradient over most of the lower mantle depth range. A peculiar correlated behaviour of the two most sensitive parameters (iron content and temperature) is found below the 660 km discontinuity: over the depth range from 660 km down to 1300 km. Significantly, we find that the bulk composition inferred from any given inversion is strongly dependent on the choice of a priori model. Equally satisfactory fits to the lower mantle bulk sound velocity and density profiles can be obtained using any of the a priori models. However, the thermal structure associated with these compositional models differs significantly. Pyrolite yields a relatively cool geotherm (T660~= 1800 K and XPv~= 0.64), while perovskite-rich models such as chondritic or cosmic models yield hot geotherms (T660~= 2500 K and XPv~= 0.84 for the latter), but all of the geotherms are subadiabatic. The results of inversions are virtually unaffected by the partitioning of iron between perovskite and magnesiowustite. Out of the five oxide components considered in our models, the bulk Al2O3 and CaO contents of the mineral assemblages are least well constrained from our inversions. Our results show that a major shortcoming of lower mantle compositional and thermal models based on inversions of bulk sound velocity and density is the strong dependence of the final solution on the a priori model. That is, a wide variety of best-fit compositional and thermal models can be obtained, all of which provide satisfactory fits to global average seismic models. It is, in fact, this non-uniqueness that dominates the resulting a posteriori uncertainties and prevents a clear discrimination between different compositional models. Independent constraints on the thermal structure or on the shear properties of lower mantle assemblages are needed to infer lower mantle composition with a higher degree of certainty.
The most abundant mineral on Earth has a perovskite crystal structure and a chemistry that is dominated by MgSiO 3 with the next most abundant cations probably being aluminum and ferric iron. The dearth of experimental elasticity data for this chemically complex mineral limits our ability to calculate model seismic velocities for the lower mantle. We have calculated the single crystal elastic moduli ( cij) for (Mg, Fe 3 +)(Si, Al)O 3 perovskite using density functional theory in order to investigate the effect of chemical variations and spin state transitions of the Fe 3+ ions. Considering the favored coupled substitution of Mg 2+-Si 4 + by Fe 3+-Al 3+, we find that the effect of ferric iron on seismic properties is comparable with the same amount of ferrous iron. Ferric iron lowers the elastic moduli relative to the Al charge-coupled substitution. Substitution of Fe 3+ for Al 3+, giving rise to an Fe/Mg ratio of 6%, causes 1.8% lower longitudinal velocity and 2.5% lower shear velocity at ambient pressure and 1.1% lower longitudinal velocity and 1.8% lower shear velocity at 142 GPa. The spin state of the iron for this composition has a relatively small effect (< 0.5% variation) on both bulk modulus and shear modulus.