Nomura et al. Progress in Earth and Planetary Science (2017) 4:34
DOI 10.1186/s40645-017-0149-2

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open Access

Melting phase relations in the
MgSiO3–CaSiO3 system at 24 GPa
Ryuichi Nomura1* , Youmo Zhou1* and Tetsuo Irifune1,2

Abstract
The Earth’s lower mantle is composed of bridgmanite, ferropericlase, and CaSiO3-rich perovskite. The melting phaserelations between each component are key to understanding the melting of the Earth’s lower mantle and the
crystallization of the deep magma ocean. In this study, melting phase relations in the MgSiO3–CaSiO3 systemwere investigated at 24 GPa using a multi-anvil apparatus. The eutectic composition is (Mg,Ca)SiO3 with 81–86 mol%
MgSiO3. The solidus temperature is 2600–2620 K. The solubility of CaSiO3 component into bridgmanite increases withtemperature, reaching a maximum of 3–6 mol% at the solidus, and then decreases with temperature. The same trend
was observed for the solubility of MgSiO3 component into CaSiO3-rich perovskite, with a maximum of 14–16 mol% at
the solidus. The asymmetric regular solutions between bridgmanite and CaSiO3-rich perovskite and between MgSiO3
and CaSiO3 liquid components well reproduce the melting phase relations constrained experimentally.
Keywords: Bridgmanite, CaSiO3-rich perovskite, Melting phase relations, Multi-anvil experiments, High pressure andhigh temperature, Thermodynamics

Introduction
Determining melting phase relations in natural rockforming, multi-component systems at high pressures isessential to understand the origin and consequences ofthe deep mantle melting (e.g., Williams and Garnero
1996) and the crystallization of the deep magma oceanof the early Earth (e.g., Ito et al. 2004). Although numerous melting experiments have been performed for these
purposes, the range of parameter space (pressure (P),temperature (T), and compositions (X)) studied is limited for tracing the crystallization of the magma ocean
and for a comprehensive investigation into the origin of
the deep mantle melting. Indeed, it is not practical tocover the vast P–T–X space relevant to deep Earthevents based on experiments alone. In contrast, experiments in simpler systems combined with thermodynamic models provide a powerful tool to understandthe melting chemistry in the multi-component system.
Such comprehensive datasets and thermodynamic
models have been constructed for pressures up to thoseof the mantle transition zone (Gasparik 2003).
* Correspondence: nomura@sci.ehime-u.ac.jp; youmo@sci.ehime-u.ac.jp
1
Geodynamics Research Center, Ehime University, 2-5 Bunkyo, Matsuyama,
Ehime 790-8577, Japan
Full list of author information is available at the end of the article

In addition, the occurrence of a certain degree oftemperature gradient is inevitable in melting experiments using laser-heated diamond anvil cells or multianvil apparatuses, especially under the high pressures ofthe lower mantle. The temperature gradient obscuresthe melting chemistry in multi-component systems because phase segregation changes the bulk compositionsof interest. In these cases, only limited information, suchas phase equilibria and element partitioning between thephases in contact, can be extracted by assuming local
chemical equilibrium. This problem could be overcome
by experiments in simple binary systems.
The lower mantle is composed of bridgmanite, ferropericlase, and CaSiO3-rich perovskite (Irifune 1994).
Normal mid-ocean ridge basalt has a mineral assemblageof bridgmanite, CaSiO3-rich perovskite, a SiO2 phase,and an aluminous phase in the lower mantle (Hirose etal. 1999). Therefore, the binary melting phase relations
between each mineral-constituting component are important in understanding the melting behaviors of thelower mantle. Previously, the MgO–MgSiO3 system wasinvestigated at the lower-mantle pressures using a multianvil press (Liebske and Frost 2012), but little is known
about the other systems.

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
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Nomura et al. Progress in Earth and Planetary Science (2017) 4:34

This paper is aimed at establishing the melting phaserelations in the MgSiO3–CaSiO3 system at 24 GPa,
avoiding ambiguous implications for Earth science that
require other melting phase relations such as MgO–
CaSiO3. The eutectic composition, solidus temperature,and solubility between the two endmembers were investigated experimentally at 24 GPa. Although Gasparik(1996) has performed a melting experiment on the same
system at 22.4 GPa, it is difficult to confirm melting
from the backscattered electron image presented in his
paper. In the present work, we re-investigate the system
to find the interaction parameters between the MgSiO3
and CaSiO3 components by thermodynamic analysis in
the framework for the endmembers (de Koker andStixrude 2009; Stixrude and Lithgow-Bertelloni 2011;
Bajgain et al. 2015) consistent with a previous work in
the MgO-MgSiO3 system (Liebske and Frost 2012).

Methods/experimental
Starting materials

We used three starting compositions, i.e., Mg0.90Ca0.10SiO3 (Mg90), Mg0.75Ca0.25SiO3 (Mg75), and Mg0.50Ca0.50SiO3 (Mg50). Bubble-free, chemically homogenous glasses
were synthesized for Mg0.75Ca0.25SiO3 and Mg0.50Ca0.50SiO3 in Pt crucibles at 2023 K using chemical mixtures of
SiO2 (99.9%, Kojundo Chemical Laboratory Co., Ltd.),
MgO (> 99.99%, Kojundo Chemical Laboratory Co., Ltd.),
and CaCO3 (> 98.0%, Kanto Chemical Co., Inc.), after decarbonation at 1273 K for 16 h. The starting material witha bulk composition of Mg0.90Ca0.10SiO3 was not vitrifiedcompletely, which is likely because of its high Mg content.
We crushed and ground it to fine particles. The bulk composition of the latter starting material was confirmed via
electron microprobe analysis after a subsolidus highpressure and high-temperature experiment. Table 1 lists
the bulk compositions of the starting materials. The starting materials were stored in a furnace at 383 K before use.
High-pressure melting experiments

High-pressure and high-temperature experiments were
performed at 24 GPa and 2600–3000 K in a Kawai-type
multi-anvil apparatus (Orange 2000, Geodynamics Research Center, Ehime University). A 10/4 (octahedronedge length/truncation edge length) cell assembly waschosen for pressure generation. The pressure of 24 GPa
was calibrated based on the coexistence and dissociationof wadsleyite into bridgmanite and periclase at 2273 K
in the Mg2SiO4 system (Fei et al. 2004), in addition toother phase transitions at room temperature, 1873 and2273 K, as described in Zhou et al. (2017). The pressure
calibration (Additional file 1: Figure S1) suggests thatpressure does not vary with temperature above 1873 K.
This is also evidenced by the recovery of bridgmanitefrom 2620 K (OS3099) since the pressure drop of lessPage 2 of 11

than 2 GPa is needed to be within the stability field ofbridgmanite at that temperature (Gasparik 1996; Fei et al.
2004). A LaCrO3 heater was chosen for temperature generation. The temperature was monitored with a W97Re3W75Re25 thermocouple. No correction was applied for thepressure effect on the electromotive force of the thermocouple. The junction of the thermocouple was positioned
at the center of the heater and between two Re capsules.
The cell assembly used in this study is identical to that of
Zhang et al. (1993) with respect to the octahedron dimension (edge length, 10 mm), the heater material (LaCrO3),
and the capsule material (Re). However, we used capsuleswith much smaller dimensions in both length and diameter and adopted a longer sleeve heater with a muchsmaller diameter to reduce the thermal gradient. Zhang etal. (1993) reported a temperature drop of ~ 50 K at a distance of ~ 0.5 mm from the hot spot axially. In this study,
the center of the sample (~ 0.2 mm thick) is ~ 0.5 mm
away axially from the thermocouple junction. Therefore,
the uncertainty of the sample temperature caused by thetemperature gradient is much less than 50 K. Indeed, we
confirmed drastic changes of the melting phase relations
within 100 K in a series of experiments. In addition, theobtained electron microprobe images of the recovered
samples suggest that the thermal gradient in the axial direction was negligible and it was not the dominant factorof temperature uncertainty (i.e., no systematic error).
Therefore, small, non-systematic changes in the geometry
and temperature profile caused by the differences in
the geometry of components (heater shape and size, thedegree of cell deformation during heating, and so on)in each run lead to uncertainties in temperature. We
adopted the variations in the heating powertemperature relationships (Additional file 1: Figure S2)
as temperature uncertainties, although they represent
the variations not only in the thermocouple-sample
geometry and temperature profile but also in other factors not related to the temperature uncertainty but tothe heating efficiency. Therefore, uncertainties would
be overestimated. However, this is the best way to express the uncertainties in experimental temperatures(Table 2). The high-pressure samples were quenched by
cutting off the power supply at the target temperatures
after heating for 5–20 min. The experimental conditions and results are summarized in Table 2.
Phase identification and chemical analysis

The recovered samples were embedded in epoxy resinand finely polished for subsequent analyses. Phase identification was conducted with a microfocus X-ray diffraction (XRD) apparatus (Rigaku MicroMax-007HF) using
Cu Kα radiation. The sample surface was coated withcarbon and analyzed using a field emission-type scanning electron microscope (FE-SEM; JEOL JSM7000F).

Nomura et al. Progress in Earth and Planetary Science (2017) 4:34

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Table 1 Chemical compositions of starting materials
Name

Phasea

MgO

CaO

SiO2

Total (wt.%)

Mg

Ca

Si

∑Cationb

Mg/(Mg + Ca)

Mg90

Mixture35.63(22)5.30(45)

58.87(54)99.79(33)0.903(1)0.097(9)1.001(4)2.000(4)0.904(8)Mg75

Glass (29)28.99(22)

13.67(10)57.12(42)99.78(50)0.753(5)0.255(2)1.004(2)2.004(3)0.747(2)

Mg50

Glass (26)

18.53(16)25.65(15)54.89(36)99.07(59)0.503(3)0.500(2)0.999(2)2.001(2)0.501(2)aNumber of electron microprobe analyses is shown in parentheses. Mg90 is a mixture of glass and oxides; see the main text for detailsb
Number of oxygen is 3

Chemical compositions were measured using an energydispersive X-ray spectrometer with a silicon-drift detector(EDS; Oxford Instruments X-MaxN) attached to the FESEM at 15 kV and 1 nA with collection times of ~ 30 s.
Mg2SiO4 forsterite was used as the compositional standard for Mg and Si, while CaSiO3 wollastonite was used for
Ca. The grains of bridgmanite, CaSiO3-rich perovskite
were analyzed in a focused mode with a beam size of lessthan 1 μm. The quenched melt was analyzed in a scanningmode larger than the spatial scale of heterogeneity.
Thermodynamic modeling

Among many available thermodynamic approaches thatcan describe the melting behavior in a multi-component
system, we followed that of Liebske and Frost (2012) tomaintain consistency with the results for the MgO–
MgSiO3 system, which has been studied extensively athigh pressures, including lower-mantle pressures. Liebske
and Frost (2012) used the chemical potentials given by
Lithgow-Bertelloni and Stixrude (2005) and Stixrude andLithgow-Bertelloni (2011) for the solid phases and by deKoker and Stixrude (2009) for the liquid phases; these
papers constructed an internally consistent thermodynamic model, although the equations, parameterization,and parameter set differ slightly from those of Liebske andFrost (2012). For solids, we used the thermodynamic descriptions and parameter sets of Lithgow-Bertelloni andStixrude (2005) and Stixrude and Lithgow-Bertelloni(2011) based on usability and consistency with other components. For liquids, we followed Liebske and Frost (2012)
to maintain consistency with the MgO–MgSiO3 system.
We describe all of these equations below for clarification.

Chemical equilibrium is attained when the chemical
potentials (μ) of the components become equal between
the liquid and solid phases:
liquidμsolid
¼ μY
Y

;

ð1Þ

represents the chemical potential of compowhere μphaseYnent Y, i.e., MgSiO3 or CaSiO3, in the assigned phase.
The chemical potentials of solids and liquid are
expressed as follows:¼ μo;phaseþ RTln aphase;
μphase
Y
Y
Y




phase
o;phasephase¼ μY
þ RTln X Y
μYþ RTln γ phase;Yð2Þ
where μoY , aY, XY, and γY are the chemical potentials of
the endmember, activity, molar concentration, and activity coefficient of component Y, respectively. The activity
coefficients of solid and liquid are described by theasymmetric regular solution expressions

 h

 i
2
phase
phase
¼
A
1−X
RTln γ phase
−A
1−4X
;
o
1
MgSiO3
MgSiO3
MgSiO3

ð3Þ

 h

 i
2
phase
phase
¼
A
1−X
RTln γ phase
þ
A
1−4X
;
o
1
CaSiO3
CaSiO3
CaSiO3

ð4Þ
where A0 and A1 are expressed as follows:

Table 2 Experimental summary
Run no.

T (K)Duration (min)SMaPhase assemblage

2600(36)

20

Mg90

Bdg + CaPv

Mg75

Bdg + CaPv

Mg90[HT] Melt + Bdg, [LT] Bdg + CaPv

Mg75

[HT] CaPv, [LT] Bdg + CaPv

Mg90

Melt

Mg75

Melt + CaPv

Mg50

Melt + CaPv

P = 24 GPa
OS3097OS3099OS3095OS31502620(38)

2700(41)

3000(46)

15

10

5

SM starting material, Bdg, bridgmanite, CaPv CaSiO3-rich perovskite, HT high-temperature region, LT low-temperature regiona
See Table 1 for details

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
phase
A0 ¼ W phase
CaSiO3 ‐MgSiO3 þ W MgSiO3 ‐CaSiO3 =2;

ð5Þ



phase
A1 ¼ W phase−W
CaSiO3 ‐MgSiO3
MgSiO3 ‐CaSiO3 =2;

ð6Þ

where WY − Z is an interaction parameter between components Y and Z.
Once the chemical potentials of the liquid and solid
endmembers are evaluated, we can determine the interaction parameter W by fitting the experimental data to
the above equations.
The Gibbs free energy (G) of solid endmembers were
determined from the Helmholtz free energy (F) as given
by Lithgow-Bertelloni and Stixrude (2005) and Stixrude
and Lithgow-Bertelloni (2011):
GðP; T Þ ¼ F ðV ; T Þ þ PV ;

ð7ÞF ðV ; T Þ ¼ F 0 ðV 0 ; T 0 Þ þ F cmp ðV ; T 0 Þþ ½F th ðV ; T Þ−F th ðV ; T 0 Þ;ð8ÞPðV ; T Þ ¼ P cmp ðV ; T 0 Þ þ Pth ðV ; T Þ;

ð9ÞFig. 1 Melting temperatures of CaSiO3. The black line represents themelting temperatures calculated in this study, the crosses represent
the experimental data by Gasparik et al. (1994), the blue circles byShen and Lazor (1995), the orange squares by Zerr et al. (1997), andthe dark gray dashed line represents the molecular dynamics simulation
by Liu et al. (2010). The gray region is the stability region of CaSiO3
perovskite at the melting temperatures (Gasparik et al. 1994)

where F is composed of a standard-state term (F0), a
compression term (Fcmp), and a thermal term (Fth). Pressure (P) is composed of a compression term (Pcmp) and athermal term (Pth). The compression term is expressedby the following third-order finite-strain (f ) model:
9
F cmp ðV ; T 0 Þ ¼ V 0 K T 0 f 22
9þ V 0 K T 0 K T 0′ −4 f 3
2





 2 1=21
2;
θ ¼ θ0 1 þ 6γ 0 f þ −12γ 0 þ 36γ 0 −18q0 γ 0 f
2

ð10Þ

ð17Þ





9
P cmp ðV ; T 0 Þ ¼ ð1 þ 2f Þ5=2 3K T 0 f þ K T 0 K T 0 ′ −4 f 2 ;
2

"
1 V0
f ¼
2
V

2=3

#
−1 ;

ð11Þ
ð12Þ

where V0, KT0, and K′T0 are the volume at a reference
state, the bulk modulus, and the first derivative of thebulk modulus, respectively. The thermal term is derived
from the Debye model:

θ
;
ð13Þ
F th ðV ; T Þ ¼ 9nRTD
TDðxÞ ¼ x−3Z x

lnð1− expð−t ÞÞt 2 dt;

ð14Þ

0

γ
ðE th ðV ; T Þ−E th ðV ; T 0 ÞÞ;V −3 Z θ 3
T
θ
t
dt;
E th ðV ; T Þ ¼ 9nRTt
T
0 e −1

Pth ðV ; T Þ ¼

ð15Þ
ð16Þ

γ ¼ γ0ð1 þ 2f Þ;
ð1 þ 6γ 0 f Þ

ð18Þ

where the parameters F(V0, T0), V0, KT0, K′T0, θ0, γ0,and q0 were given by Stixrude and Lithgow-Bertelloni(2011).
Table 3 Thermodynamic properties of liquids
MgSiO3

CaSiO3MgO

T0 (K)

1773

3000

3000

V0 (cm3/mol)

37.20(6)45.1(12)16.46(1)KT0 (GPa)27.3(2)22.2(30)34.0(1)KT0′

5.7(5)

4.60(17)4.50(5)γ00.60(2)0.73

0.96(2)γ′− 1.24(5)− 1.18(5)− 0.37(5)Cv (J/K/mol)

173(2)

146(6)56(3)S0 (J/K/mol)

333(3)

425(3)

173.5(20)F0 (kJ/mol)− 1709.09

2282.25− 845.22

Reference

LF2012

B2015

LF2012

Italicized values were constrained in this study. The others are from literature:
LF2012, Liebske and Frost (2012); B2015, Bajgain et al. (2015)

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Table 4 Thermodynamic properties of solids
Bdg

CaPv

Pc

T0 (K)

300

300

300

V0 (cm3/mol)

24.45

27.45

11.24

KT0 (GPa)

251(3)

236(4)

161(3)

KT0′

4.1(1)

3.9(2)

3.8(2)

γ01.57(5)

1.89(7)1.36(5)q0

1.1(3)

0.9(16)

1.7(2)

θ0 (K)

905(5)

796(44)767(9)F0 (kJ/mol)− 1368(1)− 1463(8)− 569

The parameters are from Stixrude and Lithgow-Bertelloni (2011)
Bdg bridgmanite, CaPv CaSiO3-rich perovskite, Pc periclase

For liquids, we followed Liebske and Frost (2012) tomaintain consistency. The expressions of the solid compression terms Fcmp and Pcmp were also applied to liquids, Fcmp and Pcmp. The thermal part is expressed asfollows:TF th ðV ; T Þ ¼ −S 0 ðT −T 0 Þ−C v T ln−ðT −T 0 Þ
T0







V
þ γ−γ 0 ;−C v ðT −T 0 Þ γ 0 −γ ′ ln
V0

ð19Þ
γ
Pth ðV ; T Þ ¼ C v ðT −T 0 Þ;
V

′ V
−1 ;
γ ¼ γ0 þ γ
V0Fig. 2 Melting temperatures of MgSiO3. The black line represents themelting temperatures calculated in this study, the crosses by Di Paolaand Brodholt (2016), and the dashed gray line by de Koker and Stixrude(2009). The melting temperatures determined by high-pressure
experiments are also plotted: orange squares, Zerr and Boehler(1993); blue circles, Shen and Lazor (1995)

Results and discussion
X-ray diffraction and phase identification

ð20Þ
ð21Þ

where the parameters of MgSiO3 liquid are from Liebske
and Frost (2012), except for F0. For the liquid propertiesof the CaSiO3 endmember, we used the result of abinitio calculations by Bajgain et al. (2015) by fitting theirdataset to the above equations. The F0 and S0 of the
CaSiO3 liquid were determined by fitting the melting
temperatures measured by Zerr et al. (1997), which
are consistent with the results of molecular dynamics
simulations by Liu et al. (2010) (Fig. 1). The thermodynamic parameters used in this study are summarized in Tables 3 and 4.
The previous study fitted F0 for standard melting
points: MgO, 3070 K at 1 bar; MgSiO3, 2900 K at
25 GPa. We found that the F0 fitted using the equations
defined in the aforementioned methods is slightly different from those reported by previous studies.
Nevertheless, we confirmed that we could reproduce
the melting temperatures of MgO and MgSiO3 andthe MgO–MgSiO3 melting phase relations using theparameters obtained in this study (Fig. 2, Additional file 1:
Figures S3 and S4).

Additional file 1: Figure S5 shows the XRD patterns of therun products. Intense peaks from Re were unavoidably observed in all the patterns due to the small sample sizes inthis study. Peaks from bridgmanite were evidently observed in OS3097 and OS3099, indicating that the experiments were performed outside of the garnet stability
region, which is consistent with a previous study that reported the phase transformation of a MgSiO3-rich composition from garnet to bridgmanite at 22.4 GPa(Gasparik 1996). Some weak peaks, presumably indexed
to bridgmanite, were observed in OS3095 and OS3150(e.g., Additional file 1: Figure S5e). The bridgmanite isinterpreted as quench crystals from melt in the corresponding SEM images as shown later. CaSiO3-rich perovskite was not identified in all the samples since itshould be amorphized at the ambient pressure.
Electron microscopic observation and compositional
analysis

Figures 3, 4, 5, and 6 show the backscattered electron
images of the recovered samples. At 2600 K, the subsolidus phase assemblage of bridgmanite plus CaSiO3rich perovskite was obtained in both starting compositions (Fig. 3). Bridgmanite contains 5–6 mol% CaSiO3
component, which is higher than that reported by Irifune et al. (2000) at 1773–2173 K, suggesting a positive

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Fig. 3 Backscattered electron images for the samples recovered from high pressure and high temperature (Run No. OS3097). The subsolidus
phase assemblage of bridgmanite (Bdg) plus CaSiO3-rich perovskite (CaPv) was observed in both Mg90 and Mg75. T.C., thermocouple

temperature effect on solubility. We did not determine
the solubility of MgSiO3 component in CaSiO3-richperovskite because of its small grain size. At 2620 K,
the sample OS3099-Mg90 had a quenched melt with
quench textures surrounded by bridgmanite, which isinterpreted as the liquidus phase, at the side part of thecapsule (Fig. 4). At the central part, the subsolidus

phase assemblage of bridgmanite plus CaSiO3-rich perovskite was found. This observation suggests that theaxial thermal gradient in the heater has been effectively
reduced so that the radial thermal gradient mainly influenced the phase distribution in this sample. In thesample OS3099-Mg75, we observed a segregation of
CaSiO3-rich perovskite at the hot side part of theFig. 4 Backscattered electron images for the samples recovered from high pressure and high temperature (Run No. OS3099). In Mg90, a quenchedmelt was found at the hottest region surrounded by bridgmanite (Bdg), which is interpreted as the liquidus phase. In contrast, CaSiO3-rich perovskite(CaPv) was found to be segregated in Mg75. We failed to find the melt. The subsolidus phase assemblage was observed at the central (cold) part ofboth samples

Nomura et al. Progress in Earth and Planetary Science (2017) 4:34

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Fig. 5 Backscattered electron images for the samples recovered from high pressure and high temperature (Run No. OS3095). Quenched melts were
found at most of the sample areas. In Mg75, the liquidus phase, CaSiO3-rich perovskite (CaPv), was found at the coldest part

capsule (Fig. 4). This CaSiO3-perovskite is interpreted
as the liquidus phase, although we failed to find thequenched melt. At 2700 K, the samples were extensively molten, as clearly evidenced by the textures
shown in Fig. 5. Both quenched melts exhibited textures similar to that of metal casting: fine grains attached to the mold wall; columnar grains arranged
closely in parallel with the direction of cooling heat flow;
and granular grains accumulated at the center. The

sample OS3095-Mg90 had a bulk composition identical tothat of the starting material, supporting a complete
melting. In the sample OS3095-Mg75, CaSiO3-richperovskite, interpreted as the liquidus phase, was observedat the coldest part of the capsule. At 3000 K, the sample
OS3150-Mg50 yielded a phase assemblage of CaSiO3-richperovskite plus melt (Fig. 6), identical to the sample
OS3095-Mg75 (Fig. 5). The results of the chemical
analyses are summarized in Table 5.

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Fig. 6 Backscattered electron images for the sample recovered from high pressure and high temperature (Run No. OS3150-Mg50). A quenchedmelt was found at the hottest region surrounded by CaSiO3-rich perovskite (CaPv), which is interpreted as the liquidus phase

Melting phase relations in the MgSiO3–CaSiO3 system

The phase relations are summarized in Fig. 7. The
solubility of MgSiO3 component into CaSiO3-rich perovskite is much higher than that predicted by theoretical calculations (Jung and Schmidt 2011). This isbecause Jung and Schmidt (2011) considered a tetragonal structure (I4/mcm) for CaSiO3 perovskite, in
addition to their use of oversimplified assumptions, as
commented in their paper. Indeed, Komabayashi et al.
(2007) showed that CaSiO3 perovskite undergoes aphase transition from tetragonal to cubic above ~500 K at ~ 24 GPa. We determined the interaction
parameter Wsolid by fitting our experimental data together with the dataset of Irifune et al. (2000) to thefollowing equations:
W solid
MgSiO3 ‐CaSiO3 ½kJ=mol ¼ 108ð11Þ−0:024ð5Þ  T ½K;W solid
CaSiO3 ‐MgSiO3 ½kJ=mol ¼ 52ð8Þ þ 0:010ð4Þ  T ½K:The eutectic point was found to be located at 81–
86 mol% MgSiO3 and 2600–2620 K. The interaction
parameter Wliquid was determined by fitting our experimental data to the following equations:
W liquid
MgSiO3 ‐CaSiO3 ½kJ=mol ¼ 1839ð741Þ−0:59ð26Þ  T ½K;W liquid
CaSiO3 ‐MgSiO3 ½kJ=mol ¼ −1170ð167Þ þ 0:39ð6Þ  T ½K:The parameters were estimated using a linear leastsquares method weighted by the compositional uncertainty. Therefore, the standard error of the fitting parameter, shown in parenthesis, does not include
temperature uncertainty since the dataset from theTable 5 Chemical compositions of phases in run products
Run no.

SMa

Phaseb

MgO

CaO

SiO2

Total (wt.%)

Mg

Ca

Si

∑Cationc

Mg/(Mg + Ca)

OS3097

Mg90

S-Bdg (48)37.56(101)3.07(121)

62.12(76)102.74(112)0.915(19)0.054(21)1.016(4)1.984(4)0.945(22)Mg75

S-Bdg (32)36.45(93)3.35(86)

61.46(72)101.25(130)0.901(16)0.060(15)1.020(4)1.980(4)0.938(16)OS3099Mg90

Melt (9)33.57(42)8.49(28)

57.33(86)99.39(86)0.864(12)0.157(6)0.990(6)2.010(6)0.846(5)L-Bdg (44)38.25(106)2.12(79)

61.04(100)101.42(171)0.943(15)0.038(14)1.010(3)1.990(3)0.962(14)S-Bdg (34)38.26(100)1.99(60)

60.84(106)101.09(181)0.946(13)0.035(11)1.009(4)1.991(4)0.964(11)Mg75

OS3095OS3150S-CaPv (28)

4.89(63)

40.58(67)52.85(67)98.32(85)0.140(18)0.834(17)1.013(5)1.987(5)0.143(17)

L-CaPv (29)5.34(75)

40.30(83)52.72(84)98.36(97)0.153(22)0.827(17)1.010(8)1.990(8)0.155(21)S-CaPv (33)

5.68(57)

39.90(78)52.97(64)

98.55(87)0.161(16)0.816(16)1.011(7)1.989(7)0.165(16)S-Bdg (44)39.05(66)1.80(31)61.89(74)102.74(121)0.949(8)0.031(6)1.010(3)1.990(3)0.968(6)Mg90

Melt (13)35.49(38)5.29(13)58.47(44)99.24(84)0.904(4)0.097(2)0.999(2)2.000(2)0.903(2)Mg75

Melt (15)31.47(46)10.35(16)57.63(57)

99.46(112)0.812(4)0.192(2)0.998(2)2.002(2)0.809(2)L-CaPv (31)4.39(36)42.59(58)53.01(65)100.00(81)0.124(10)0.865(13)1.005(4)1.995(4)0.125(10)Mg50

Melt (21)28.27(72)

14.57(90)56.85(40)99.70(67)0.737(16)0.273(18)0.995(2)2.005(2)0.730(17)

L-CaPv (37)3.42(43)43.32(59)53.52(31)100.25(48)0.096(12)0.878(13)1.013(3)1.987(3)0.099(12)SM starting material, S- subsolidus, L- liquidus, Bdg bridgmanite, CaPv CaSiO3-rich perovskitea
See Table 1 for detailsb
Number of electron microprobe analyses is shown in parenthesescNumber of oxygen is 3

Nomura et al. Progress in Earth and Planetary Science (2017) 4:34

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Fig. 7 Melting phase diagram in the MgSiO3–CaSiO3 system at 24 GPa. The filled red circle represents the composition of liquid above liquidus, thefilled and open orange squares represent the liquid and coexisting bridgmanite (Bdg), the filled and open blue squares represent the liquid andcoexisting CaSiO3-rich perovskite (CaPv), the open diamonds represent the subsolidus phases, the cross symbols represent the subsolidus phases at 25
and 27 GPa reported in Irifune et al. (2000), and the dashed gray line represents the subsolidus phases at 25 GPa reported in Jung and Schmidt (2011)

literature did not describe how the temperature uncertainty was determined. The experimental data suggest thatthe interaction parameters approach to zero at high temperatures, suggesting an ideal behavior. These empirical(linear) fitting equations should not be extrapolated out
from the experimental range. Figure 7 shows the resulting
phase diagram from the thermodynamic calculations together with the experimental data. In prohibiting the extrapolation, the uncertainty of the thermodynamic model
is described by the deviations from the experimental data
(Figs. 1 and 7, Additional file 1: Figure S4).

Conclusions
Melting phase relations in the system MgSiO3–CaSiO3
were determined experimentally at 24 GPa. A thermodynamic model was constructed to reproduce the experimental data. The experimental dataset and thethermodynamic parameters derived in this study serveas the basis for understanding the complicated melting
behaviors of the Earth’s lower mantle.
The advantage of establishing a thermodynamic modelis that the degree of melting can be calculated at a certain P-T in a multi-component system. The seismic observations suggested a degree of melting of < 5–30% in

ultra-low velocity zones at the base of the lower
mantle (Williams and Garnero 1996). The estimationof the degree of melting depends on the wetting
property and the elastic properties of the melt; conversely, these properties depend on the compositionsof the melt; thus, they depend on the degree of melting. The degree of melting is also an important parameter in understanding the chemical differentiation
during magma ocean crystallization. The melt-solid
separation by rheological transition occurs at a crystal
fraction of approximately 60% (e.g., Abe 1995). Therefore, it is of great importance to understand thephase relations together with the knowledge of thedegree of melting at relevant pressures and temperatures. However, there are some difficulties in obtaining the degree of melting by high-pressure melting
experiments under thermal gradients because the observed degree of melting arises from the thermal gradients, not from the phase equilibrium.
Figure 8 shows the eutectic temperatures of the
MgO–MgSiO3 system calculated using interaction
parameters constrained from the chemical analysesof the recovered diamond anvil cell (DAC) samples(Ohnishi et al. 2017) and those measured directly byNomura et al. Progress in Earth and Planetary Science (2017) 4:34

Page 10 of 11

Additional fileFig. 8 Eutectic temperatures of the MgO–MgSiO3 system calculatedusing interaction parameters constrained from chemical analyses of
the recovered DAC samples (Ohnishi et al. 2017) and those measured
directly by pyrometry in DAC experiments (Baron et al. 2017)

pyrometry in DAC experiments (Baron et al. 2017).
As shown in Fig. 8, there is a deviation between
these two studies with systematically lower temperatures in Baron et al. (2017). The deviation may havebeen caused by the inaccuracy of the temperature
measurements by the pyrometer, the uncertain
wavelength-dependent emissivity of the sample, andthe effect of integrated radiation along the thermal
gradients in an axial direction. The latter would beserious when transparent materials are used as asample and pressure medium, resulting in an underestimation of the temperature. Indeed, the melting
temperatures of endmembers show large discrepancies among DAC studies even if similar melting criteria were used. On the other hand, chemical
analyses of the liquid and solid phases in contact(Ohnishi et al. 2017) present a much more reliabledataset because only an assumption of the local
equilibrium is necessary without the information ontemperature (it is noted that chemical equilibrium isassumed implicitly when melting temperatures aremeasured directly). Therefore, constructing thethermodynamic model using the Gibbs free energiesof the endmembers by ab initio calculations andphase relations constrained by multi-anvil and DAC
experiments combined with chemical analysis should
be a promising approach to understand the mineralogy of deep mantle melting and comparisons withobservations; however, this approach requires a stepby-step accumulation of relevant phase diagrams.

Additional file 1: Figure S1. Pressure calibrations at room temperature(RT) and high temperatures. Fo, Mg2SiO4, forsterite; Wd, Mg2SiO4 wadsleyite;
Rw, Mg2SiO4 ringwoodite; Ak, MgSiO3 akimotoite; Bdg, MgSiO3 bridgmanite;Pc, MgO periclase. Pressures of the phase transitions at high temperatures
were taken from Morishima et al. (1994), Suzuki et al. (2000), and Fei et al.
(2004). The red point at 790 ton, 23 GPa, and 2273 K is 0.55 GPa away fromthe green curve of 1873 K, which is comparable to the standard deviationof the fitting curves, 0.4 GPa. Figure S2: Heating power-temperature
relationships. Figure S3: Melting temperatures of MgO. The black line
represents the melting temperatures calculated in this study, and thedashed gray line represents those by de Koker and Stixrude (2009).
The melting temperatures determined by high-pressure experiments
and ab initio calculations are also plotted: orange squares, Zerr and
Boehler (1994); green triangles, Alfe (2005); blue circles, Zhang andFei (2008); purple squares, Du and Lee (2014); and red squares, Kimura et al.
(2017). Figure S4: Melting phase diagram in the MgO–MgSiO3 system at
24 GPa. The black line represents the phase boundary calculated in thisstudy, and the gray line represents that by Liebske and Frost (2012). The
experimental data by Liebske and Frost (2012) are also plotted, where thered circle represents the composition of liquid above liquidus, the green
squares represent liquid coexisting with periclase (Pc), the orange squares
represent liquid coexisting with bridgmanite (Bdg), and the diamonds
represent subsolidus phases. Interaction parameter updated by Ohnishi et al.
(2017) was used to calculate the phase relations. Figure S5: X-ray diffraction
patterns of the run products. The black short bars beneath the curves denotethe peak positions of bridgmanite (Bdg) and rhenium (Re). (PDF 1046 kb)
Acknowledgements
We thank Takashi Taniuchi (Ehime Univ.) for discussions and Dr. Toru Shinmei(Ehime Univ.), Dr. Takeshi Arimoto (Ehime Univ.), Dr. Wei Sun (Ehime Univ.), and
Dr. Steeve Gréaux (Ehime Univ.) for their assistance in our experiments. We
thank the editor and the anonymous reviewers for their constructive
comments and suggestions. We thank Dr. Hideharu Kuwahara (Ehime
Univ.) and Dr. Chie Kato (Tokyo Tech.) for their assistance in the compositional
analyses.
Funding
This work was supported by JSPS KAKENHI Grant Numbers JP15H05470,
JP15H05830, and JP25220712.
Authors’ contributions
RN and YZ designed the project. YZ and TI designed the experiments. YZ
carried out the melting experiments and the chemical analysis. RN analyzed
the data. RN and YZ wrote the manuscript. All authors read and approved
the final manuscript.
Competing interests
The authors declare that they have no competing interests.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in publishedmaps and institutional affiliations.
Author details
1
Geodynamics Research Center, Ehime University, 2-5 Bunkyo, Matsuyama,
Ehime 790-8577, Japan. 2Earth-Life Science Institute, Tokyo Institute ofTechnology, 2-12-1 Ookayama, Meguro, Tokyo 152-8550, Japan.
Received: 13 July 2017 Accepted: 14 November 2017

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