Supplementary Information for
High-pressure melting of MgO from (Mg,Fe)O solid solutions
Zhixue Du and Kanani K.M. Lee
(Department of Geology and Geophysics, Yale University, New Haven, CT)
Geophysical Research Letters, 2014
Introduction
This data set contains all the measurements of temperatures, pressures and elemental
compositions of ferropericlase melting experimental runs. Supplementary figure captions
for S1-S6, and supplemental table captions (Table S1-S3) are included “text01”.
Compilation of EPMA data is in ts01. Direct measurements of temperatures, pressures,
estimated melt fraction and calculated average post-melting composition are in ts02. Best
fit thermodynamic parameters are given in ts03. Figures are listed as Figs. S1-6, which
describes schematic of laser ramp-heating experiments (S1), the programmable laserheating systems (S2), input and output module signals (S3), recovery sample procedure
(S4), BSE image of melt showing dendritic texture (S5), scanning electron microscopy
(SEM) image of a quenched ferropericlase sample using Ar as a pressure medium (S6),
respectively.
1.1. Melting at high pressure and temperature measurement
Prior to the melting heating duration, the laser-heated diamond-anvil cell (DAC)
(Fig. S1) sample was annealed from one side at ~1200 K for 10 minutes to minimize
differential stress while not introducing severe chemical heterogeneity due to Soret
diffusion [Sinmyo and Hirose, 2010]. In preliminary experiments, we found that during
flash-heating [Du et al., 2013; Yang et al., 2012] ferropericlase often results in unsteady,
sometimes runaway, heating. This tendency to “run away” when laser heating is likely
due to a change in the absorption of the laser by the sample [Jeanloz and Kavner, 1996],
thus results in an unsuccessful temperature measurement. Additionally, the long
recognized Soret diffusion of iron also dictates that care be exercised when laser heating.
In order to ensure steady heating of our samples, we designed a programmable laserheating system (Fig. S2) which implements synchronization of ramped laser heating and
multispectral temperature measurement [Du et al., 2013]. This revised laser-heating
system includes the following new features:
a) A mechanical shutter (MS in Fig. S2) to precisely control the timing of the
temperature measurement (C3 in Fig. S2).
b) Compact RIO system programmed with LabVIEW (National Instruments) to
externally synchronize and control the heating NIR laser (100 W 1070 nm watercooled fiber laser) and the mechanical shutter described above.
We found that a short duration heating (~1s) that includes a short ramp up of the laser
power and then held steady at a single laser power before an immediate quench, allowed
for even heating and consequent melting of the sample. We used a predefined laser
pulse to melt the sample (Fig. S1, Bottom): the laser is set at a low power for 2 seconds
(Fig. S1, a) and then linearly ramped up to peak power every 20ms within 1 second (Fig.
S1, b-c) and kept at the peak power for 0.5-1 second before turned off (Fig. S1, d-e). A
mechanical shutter is opened 20-40 ms before the laser is quenched to allow temperature
measurement of the sample at peak power. Laser power and the sample’s thermal
emission are also monitored every 1 ms with photodiodes PD1 and PD2 respectively
during laser heating (Fig. S3), to ensure that the peak laser power corresponds to the peak
temperature and to ensure that a runaway of the temperature did not occur. By
synchronizing the shutter with the laser, it allows the temperature to be measured right
before quenching (Fig. S3). With these new features, we are able to melt the sample at
short duration (<1s), while still allowing 2-D temperature map of the sample during
melting which had not been achieved in previous studies [Campbell, 2008; Nomura et al.,
2011; Yang et al., 2012].
1.2. Thermal pressure
Pressures in our experiments are measured before and after melting, as listed in Table S1.
However the pressures at high temperature during melting are not measured. Therefore
the corrections for thermal pressures are considered as followed. Generally, thermal
pressures are negligible when a soft pressure medium is used, such as Ar [Fischer et al.,
2013; Zerr and Boehler, 1994], KCl [Anzellini et al., 2013], KBr or NaCl [Fischer et al.,
2013]. However significant pressure increases upon heating are expected and observed
[Andrault et al., 1998; Goncharov et al., 2010; Heinz, 1990]: Pth=~0.5 αKΔT, where α,
KT, ΔT are the coefficient of thermal expansivity, bulk modulus and temperature
increase, respectively for subsolidus experiments. In addition, a sharp pressure drop due
to relaxation of deviatoric stress is reported in [Kavner and Duffy, 2001]. The thermal
pressures in our experiments are unknown and are assumed to be similarly insignificant
as [Fischer et al., 2013; Tateno et al., 2010] given the relaxation of the pressure medium
(i.e., itself) at high temperature under melt conditions. As such we report only the before
and after melting pressures and assume that the effect of laser heating above the sample
solidus does not yield a large increase in pressure due to thermal effects while under the
extreme high temperatures since at those high temperatures, much of the sample is either
above solidus or near solidus temperatures, thus comparatively soft.
1.3. Chemical analysis of recovered samples
Samples recovered from high-pressure, high-temperature DAC experiments are usually
held tightly within the Re gasket after decompression. In order to get a cross section of
melt region for electron probe microanalysis (EPMA), the Re gasket is first cut in half
just outside the sample region using a micro-Electrical Discharge Machine (µEDM)
equipped with a flat blade (Fig. S4a). Subsequently another cut is made by Focused Ion
Beam (FIB) with 30 KeV, 20 nA current to expose the heated regions (Fig. S4b).
Decreasing current values from 9 nA, 3 nA, 0.9 nA, 0.1 nA, 0.05 nA are used to polish
the cross section of the heated region for further EPMA. The processed samples are then
mounted upright and analyzed by a field-emission-gun scanning electron microprobe
(Phillips XL30ESEM-FEG) and an electron probe micro-analyzer with a wavelength
dispersive system (JEOL JXA-8600 or JSM-7600F). Chemical analysis was performed
using an accelerating voltage of 10 KeV and a beam current of 6.5 nA, with spatial
resolution of ~1µm in diameter [Kanaya and Okayama, 1972]. The totals of oxide weight
range percents are mostly within the range of 97-103%. This indicates good quality of
EPMA analysis and low ferric concentration in all regions of our samples.
1.4. Attainment of chemical equilibrium
At our experimental conditions, the Fe-Mg interdiffusion coefficient for the solidus phase
is estimated to be >10-10 m2/s [Yamazaki and Irifune, 2003]. So the diffusion length scale
is > 10 µm for 1s of heating, which is greater than the thickness (<5 µm) of the solidus
phase. For the liquidus phase, the corresponding Mg self-diffusion coefficient is ~10-8
m2/s ([Karki et al., 2013]), which leads to diffusion length scale >100 µm, much greater
than the thickness (2-3 µm) of the melt pocket in our experiments. This implies that at
these conditions, diffusion is fast and thus equilibrium can be attained quickly.
To further verify the chemical equilibrium between the liquidus phase (region I in
Fig.1) and solidus phase (region II in Fig. 1), we measured the composition across the
hotspot and found nearly homogeneous compositions within the melt region and
coexisting solid region. The level of homogeneity, as measured by EPMA is < 2% (Fig.
2c), at the limit of spatial resolution for our samples (~1 µm) [Kanaya and Okayama,
1972]. This level of homogeneity suggests that equilibrium, at least between regions I
and II have been achieved.
In addition, we examine the Soret effect by mass balance calculation for iron.
We calculated the “average post-melting composition (Mg#)” (Table S2), which is the
average iron content of region I and II after melting, noted as Cp.
Cp=Cm⋅ϕ+Cs⋅(1-ϕ)
Where Cm, Cs are composition of melt, coexisting solid, respectively and given in Table
S1. ϕ is the melt fraction.
We estimated ϕ from the area of region I (melt), region II (coexisting solid) from optical
images, e.g. Fig. 1a, and thickness of each region from FIB cross sections e.g. Fig. 2a.
Assuming axial symmetry for region I and region II, we calculate the volumes for each
region. The calculated Cp and ϕ are listed in Table S2. As shown, Cp and the starting
compositions are equal to within experimental uncertainties. This is a validation for our
method using programmed laser heating to minimize the Soret effect.
1.5. Comparison with pervious static measurements
In contrast to our high melting curve, the first DAC experiment reported a low
melting curve of MgO [Zerr and Boehler, 1994]. To resolve this discrepancy, several
possibilities have been proposed: macroscopic flow under high pressure prior to melting
[Belonoshko et al., 2000]; and substantial increase of laser absorption of MgO under high
pressure and high temperature [Adebayo et al., 2009]. In order to investigate other
possibilities, we conducted experiments on (Mg,Fe)O using argon as a pressure medium,
similar to [Zerr and Boehler, 1994]. We found, upon ex-situ determination of
composition by EDS of the quenched sample, Ar present in the melted regions while
absent from the regions where textures appeared rough and unaffected by melting (Fig.
S5). Thus we infer that Ar may have reacted with the sample at high pressures and
temperatures, resulting in a lower melting temperature [Zerr and Boehler, 1994]. In order
to confirm this effect, quantitative measurement of Ar concentration in the quenched melt
and coexisting solid are highly desirable. However, such measurements demand much
more sophisticated analytical tools, e.g., LA-ICP-MS or SIMS, which is beyond the
scope of this study.
In addition, compared to our results, recent multi-anvil experiments report a
steeper and higher melting curve up to 7 GPa [Zhang and Fei, 2008]. This discrepancy is
likely due to the indirect temperature measurements beyond the limit of thermocouples
(typically 2300 K), therefore is reliant on the extrapolation of a linear temperature and
power relationship for the heater which may be an invalid assumption at extreme
temperatures like those reported in their study [Zhang and Fei, 2008].
Fig. S1. Schematic of ramp heating experiment (Top) Schematics of sample
assembly; (a) Sample after annealing; (b-c) Sample after ramp heating to peak power,
Soret diffusion is expected [Sinmyo and Hirose, 2010]. (c) Right before melting, sample
is slight depleted around central region due to Soret diffusion; (d) Onset of melting, iron
preferably partitions into melt during melting; (d-e) Steady state is reached at melting,
liquidus and solidus phases are coexisting and in equilibrium; (Bottom) Programmed
laser power curve consisting of low power annealing, ramp and steady, peak power at
melting.
Fig. S2. Programmable laser-heating system. DAC: Diamond-Anvil Cell; Laser: SPI
100 W water-cooled fiber laser; PCB: CVI Laser PCB-25.4-51.5-C-1064 concave lens,
PXB: CVI Laser PXB-25.4-65.4-C-1064 Achromat convex lens; L1: Mitutoyo NIR 5X
Objectives; L2: Thorlabs AC254-200-B Achromat NIR Lens 200 mm; L3: Thorlabs
AC508-750-B Achromat NIR Lens 750 mm; M1: Newport 10QM20HM.15 Laser
Mirrors; M2: Thorlabs PF10-03-P01 Silver Mirrors; F1: Edmund NT86-123 Notch Filter;
F2: Thorlabs Neutral Density Filters NEK01; F3: Thorlabs FGS 900 Glass Filter; BS1:
Thorlabs BP145B2 Pellicle Beam Splitter (removed during heating and calibration); BS2:
OptoSigma 039-0265 Cube Beam Splitters; PH: Iris diaphragm used as adjustable pin
hole (Thorlabs ID25); PD1: Thorlabs photodiode DET36A; PD2: Thorlabs photodiode
PDA36A; C1: Hitachi CCD; The removable M2 mirror is mounted on a magnetic
kinematic mount to ensure ease of use and alignment when switching between cameras.
4-color box: 2-D temperature measurement as fully described in [Du et al., 2013]. MS:
Thorlabs SH1 mechanical shutter and SC10 shutter controller. Synchronization Unit:
National Instruments CompactRIO system cRIO-9076, with Input module NI-9215,
Output module NI 9269 and Labview software. Output CH 1 and 2 control laser power
and shutter, respectively. Input CH 1, 2, 3 track the laser intensity, thermal emission and
shutter, respectively.
Fig. S3. Laser power, sample light intensity, shutter status monitored by the input
module in the Synchronization Unit every millisecond. Black solid line: laser power
measured by PD1, showing linear ramp up before reaching peak power. Red solid line:
sample’s thermal emission measured by PD2, showing sample is heated to steady peak
temperature at ~1.4 seconds. Dash blue curve: status of mechanical shutter (MS). Sample
light is collected by a CCD camera inside the 4-color box [Du et al., 2013], indicated by
high voltage when MS is open.
Fig. S4. Recovered sample processing using EDM and FIB. (a) Primary EDM cut is to
remove majority of Re gasket material in order to shorten the FIB time. (b) FIB cuts with
multiple currents are used to expose and finely polish the heated region and takes ~12
hours to polish. Dashed line represents approximate EDM and FIB cutting locations.
Fig. S5. BSE (back-scattered electron) image of region I (melt) showing dendritic texture,
magnified from Fig. 2a.
Fig. S6. A BSE image of quenched sample of (Mg0.91Fe0.09)O at 30 GPa after flash
heating (Δt = 5 ms) using Ar as a pressure medium with EDS transect drawn in red (top
left). Corresponding Fe/Mg ratio of their Kα peaks as collected by the red EDS transect
with starting and ending points A and B. The relative intensities give a measure of the
iron abundance. (top right) Remaining panels show the compositional maps for Mg, Fe,
Ar and O. Region I shows enrichment in iron. Regions I and II show enrichment in Ar,
whereas Region III show depletion in both Fe and Ar. Region IV (the starting material) is
used as a reference. Two large white grains in melted region are dust particles.
Table S1. Results of electron microprobe analysis. Weight abundances of Fe, Mg, O, Si
are given for starting material, region I (melt), region II (coexisting solid). Standard
deviations of multiple measurements at each region are shown in parentheses.
Mg#=100 × Mg/(Mg+Fe) by mol.
Table S2. The solidus and liquidus compositions at corresponding pressures and
temperatures are listed. Uncertainty determinations as in [Du et al., 2013] and given in
parentheses.
Table S3. Best fit model parameters (ΔHMgO and ΔHFeO) assuming ideal solid solution
for (Mg,Fe)O and projected MgO melting temperatures (TMgO). Melting temperature of
FeO (TFeO) are estimated from [Fischer and Campbell, 2010].
References
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models for MgO-SiO2 melt system at high temperature, Geophys. Res. Lett., 40(1), 9499.
Kavner, A., and T. S. Duffy (2001), Pressure-volume-temperature paths in the laserheated diamond anvil cell, J. Appl. Phys., 89(3), 1907-1914.
Nomura, R., H. Ozawa, S. Tateno, K. Hirose, J. Hernlund, S. Muto, H. Ishii, and N.
Hiraoka (2011), Spin crossover and iron-rich silicate melt in the Earth's deep mantle,
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Phys. Earth Planet. Inter., 180, 172-178.
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Inner Core, Science, 330(6002), 359-361.
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84(10).
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Fig. S6.
Experimental
run no.
Fe
Mg
O
Si
total
Mg#
starting
material
11.7(0.6)
36.9(0.5)
49.5(0.8)
NA
98.2(1.2)
90.7(0.5)
Fe
Mg
O
Si
total
Mg#
Fe
Mg
O
Si
total
Mg#
Fe
Mg
O
Si
total
Mg#
140506_3G
14-0409-91
starting
melt
28.9(1.7)
31.4(0.3)
33.2(0.2)
1.9(0.06)
95.5(1.3)
71.4(1.4)
coexisting
solid
10.1(0.7)
51.4(0.7)
38.1(0.4)
NA
99.6(0.6)
92.2(0.4)
24.1(0.6)
43.6(0.5)
35.3(0.8)
NA
102.9(1.3)
80.6(0.5)
53.8(1.6)
18(0.3)
27.2(0.5)
0.41(0.05)
99.4(1.9)
43.4(0.9)
coexisting
solid
19.5(1.4)
48.8(0.6)
37.3(0.7)
NA
105.6(1.5)
86.7(0.8)
12
39.2
51.4
NA
102.7
90.8
14-0416
27.7(0.8)
35.7(1)
36.2(1)
NA
99.7(2.2)
74.7(2.3)
9.7(1)
54.1(0.9)
38.8(0.6)
NA
102.6(1.3)
93.3(0.7)
26.2(0.7)
42.3(0.7)
34.9(0.3)
NA
103.4(0.4)
78.7(0.7)
13-1118
42.7(0.9)
26.1(0.9)
31.2(0.6)
0.13(0.03)
100.1(1.5)
58.4(0.7)
16.0(0.5)
49.0(0.9)
37.2(0.6)
NA
102.5(1.1)
87.6(0.5)
12.1(0.8)
52.2(0.6)
37.5(0.5)
NA
101.8(1.1)
90.7(0.5)
13-0814
29.8(1.2)
35(0.4)
33.4(0.8)
0.9(0.1)
99.1(2.2)
73(0.8)
11.3(0.7)
49.9(1)
37.1(0.7)
NA
98.2(1.7)
91.1(0.5)
14-0610
30.4(1.2)
28.4(0.8)
30.4(1.8)
0.63(0.05)
89.8(2.3)
68.2(1.2)
6.6(2.3)
54.7(3.3)
39.0(1.4)
NA
100.3(2.7)
94.9(2)
12.8(0.7)
49.4(1.1)
39.8(0.5)
0.07(0.04)
102.0(1.5)
89.9(0.5)
140506_45G
36.3(1.1)
32(1.1)
34.5(0.7)
0.28(0.03)
103.1(0.7)
66.9(1.4)
12.5(0.9)
49.0(0.8)
37.9(0.6)
NA
99.3(1.9)
90.0(0.6)
14-0426
45.51(1)
24.3(0.3)
30.5(0.4)
2.1(0.2)
102.4(1)
55.1(0.7)
10.2(1)
53.6(0.5)
39.4(0.3)
NA
103.2(1.2)
92.4(0.7)
Table S1.
melt
8.5(0.4)
54.9(1)
38.3(0.6)
NA
101.6(1.4)
93.7(0.4)
8.9(0.9)
52.6(0.9)
41.1(0.5)
0.04(0.02)
102.7(1.2)
93.1(0.7)
Experiment
Run No.
Starting
composition
(Mg#)
Melt
(liquidus)
composition
(Mg#)
Coexisting solid
Melt
(solidus)
fraction
composition
(%)
(Mg#)
Average
Post-melting
Composition
(Mg#)
14-0409-91
91 (1)
71(2)
92(1)
6
91(2)
14-0506_3G
81 (1)
43 (1)
87 (1)
9
14-0416
91 (1)
75(2)
93(1)
13-1118
79(1)
58(1)
13-0814
91 (1)
14-0610
Ppre-
Ppost-melting
(GPa)
T (K)
3 (1)
3 (1)
3050
(200)
83(2)
3 (1)
3 (1)
2650
(200)
14
91(2)
13 (1)
11 (1)
3350
(250)
88(1)
24
81(2)
13 (1)
11 (1)
3100
(200)
73(1)
94(1)
11
92(2)
30 (1)
27 (1)
4300
(300)
91 (1)
68 (1)
95 (2)
19
90(2)
30 (1)
27 (1)
3650
(250)
140506_45G
90 (1)
67 (1)
93 (1)
7
91(2)
43 (1)
38 (1)
5000
(350)
14-0426
90 (1)
55(2)
92 (1)
8
89(2)
45 (1)
40 (1)
4200
(300)
Table S2.
heating
(GPa)
Table S3.
Pressure (GPa)
3
11
27
40
ΔHMgO (kJ/mol)
66
67
70
70
ΔHFeO (kJ/mol)
56
67
114
110
TFeO (K)
1700
(100)
2100
(100)
2500
(150)
2700
(150)
TMgO (K)
3450
(250)
3700
(250)
4750
(350)
5800
(400)