Detection of melting by X-ray imaging at high pressure Li Li and Donald J. Weidner Citation: Review of Scientific Instruments 85, 065104 (2014); doi: 10.1063/1.4880730 View online: http://dx.doi.org/10.1063/1.4880730 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Fabrication of large area X-ray diffraction grating for X-ray phase imaging AIP Conf. Proc. 1466, 51 (2012); 10.1063/1.4742268 Melting-solidification transition of Zn nanoparticles embedded in SiO 2 : Observation by synchrotron x-ray and ultraviolet-visible-near-infrared light J. Appl. Phys. 108, 104302 (2010); 10.1063/1.3494098 Thermal equations of state and melting of lithium deuteride under high pressure J. Appl. Phys. 103, 093513 (2008); 10.1063/1.2913059 Melting of nanostructured Sn probed by in-situ x-ray diffraction J. Chem. Phys. 118, 1400 (2003); 10.1063/1.1531074 Thermodynamic Representations for Solid/Melt Systems at High Pressure and Temperature AIP Conf. Proc. 620, 185 (2002); 10.1063/1.1483512
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 065104 (2014)
Detection of melting by X-ray imaging at high pressure Li Li and Donald J. Weidner Mineral Physics Institute, Stony Brook University, Stony Brook, New York 11794-2100, USA
(Received 23 February 2014; accepted 19 May 2014; published online 5 June 2014) The occurrence of partial melting at elevated pressure and temperature is documented in real time through measurement of volume strain induced by a fixed temperature change. Here we present the methodology for measuring volume strains to one part in 10−4 for mm3 sized samples in situ as a function of time during a step in temperature. By calibrating the system for sample thermal expansion at temperatures lower than the solidus, the onset of melting can be detected when the melting volume increase is of comparable size to the thermal expansion induced volume change. We illustrate this technique with a peridotite sample at 1.5 GPa during partial melting. The Re capsule is imaged with a CCD camera at 20 frames/s. Temperature steps of 100 K induce volume strains that triple with melting. The analysis relies on image comparison for strain determination and the thermal inertia of the sample is clearly seen in the time history of the volume strain. Coupled with a thermodynamic model of the melting, we infer that we identify melting with 2 vol.% melting. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4880730] INTRODUCTION
EXPERIMENTAL METHOD
Detection of melting and its resulting changes in a bulk material at high pressure and temperature are important to the understanding of physical properties of materials. In multicomponent systems, melting typically initiates a one temperature, the solidus, and is complete at a second temperature, the liquidus. As there may be several hundred degrees between these two temperatures, it is often difficult to detect the onset of melting in situ. Various methods have been used such as examination of recovered samples,1 monitoring electrical resistivity,2 visual observation of sphere-drop formation,3 disappearance of X-ray diffraction spectrum,4 appearance of liquid diffuse ring in fast X-ray diffraction spectrum,5 temperature vs. average laser power,6 detection of mean-square displacement of atoms using synchrotron Mossbauer spectroscopy.7 The characterization of melts can also be carried out using X-ray tomography8, 9 on previously quenched samples. These methods have their own advantages but also limitations. Quenching may alter the character of melts and does not provide an in situ signal. The signals of some methods may depend on the amount of melts produced and are not suitable for partial molten samples. Some methods are not suited for X-ray opaque sample, and some only suited for diamond anvil cell application thus not applicable for pressure at a few gigapascal. We present here a method using synchrotron X-ray imaging to monitor the variation of the volume of the sample at high pressure (2 GPa) and high temperature using multi-anvil high pressure apparatus. The occurrence of the melts produced with step heating can be captured within a few seconds. This method is based on our ability to resolve volume strain at a precision of 10−4 . For peridotite, melting induced volume change dominates thermal expansion with 2 vol.% partial melting.
Our measurement of thermal expansion builds on the technique described in previous papers,10–12 which utilize the D-DIA high pressure device and synchrotron x-ray radiation. This paper focuses on establishing the protocols which enable detection of sample volume strain through X-ray imaging and the detection of melting phenomenon in situ. Rather than a conventional cell assembly as used in Ref. 11, a rhenium capsule is used to wrap the cylindrical sample (1 mm diameter, 1.5 mm long) to serve as the lateral strain marker (Figure 1). We use a CCD camera that records images of the sample at 20 frames/s during the heating steps. The images are processed by a software that is capable of detecting sub-pixel resolution. Images are processed to define radial strain and axial strain, which together, define volume strain. Resolution of the absolute volume of the sample is limited to a few cubic μm, since the width of the foil is a few μm. However, if one uses a starting image as a reference, a correlation between this reference and another image will yield the tiny motion of the strain marker up to 10−5 resolution.10 The sample, fine grounded KLB-1 peridotite powder13 (∼5 μm grain size), was cold pressed to 1.5 GPa, then heated to subsolidus conditions (ca. 850 ◦ C) and annealed for 30 min. The thermocouple is placed outside of the capsule, yielding a measured temperature that could be 100 ◦ C lower than the sample temperature. A dense corundum rod is placed above and below the sample and serves as an internal reference. After annealing, the sample was heated in a time dependent fashion as illustrated by the thermocouple temperature in Figure 2. Over time, the median temperature was stepped from 850 ◦ C to 1300 ◦ C in 50 ◦ C steps. About each median temperature, the temperature was oscillated, first in a sinusoidal variation, then in steps as illustrated in the inset of the diagram. The oscillations and steps are used to condition the cell assembly to yield reversible temperature–volume
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065104-2
L. Li and D. J. Weidner
FIG. 1. X-ray image of cylindrical sample wrapped in Re foil at pressure and temperature. A series of images were taken at 20 frames/s as temperature is stepped up or down. Sample volume strain are derived from comparing the images as defined by the Re markers. Volume strain precisions of 10−4 are achieved with this method.
relationships with time. The images of the sample were taken during these oscillations. The last heating step is used to define the effective thermal expansion. After the last temperature increase, the sample was quenched by turning the heating power off. An example of the time dependent volume strain is illustrated by the lower right inset in Figure 2. The sample strain is illustrated in gold and the alumina reference curve is blue. The volume responds with a sharp onset of strain with a more gradual emergent increase followed by a long term relaxation of the strain increase. We interpret the sharp increase as an indication of the quick response of the electronics to increase the power flowing through the furnace. The 1–2 s lapse for the volume strain to reach the maximum value indicates the thermal inertial of the sample. The long term relaxation represents the response of the pressure media to the increase of pressure accompanying the temperature increase.
Rev. Sci. Instrum. 85, 065104 (2014)
FIG. 2. Heating history of the experiment from 850 ◦ C to 1300 o C. Temperature is as read by the thermocouple which is probably colder than the sample. At each of the eight base temperatures (labeled T1 through T8 ), the temperature is cycled, at first sinusoidally with a period of 180 s, then with a square wave function. This heating serves to condition the cell for the sudden heating event. Strain data are taken from the last heating pulse, after confirmation that the system response was reversible. The inset on the upper left is for the second heating step and illustrates the details of the heating protocol. There are two heating pulses that have the wrong sign introduced by operator error. The inset on the lower right illustrates the volume strain response of the sample (gold) and the alumina reference (blue). The increase begins suddenly, but requires 1–2 s to reach the final value. This is likely the heating time of the sample when heated by the cylindrical furnace that surrounds the sample.
V ∂F αeff ective + , (2) V melting ∂T X X where F is the melt fraction and V is the volume V melting strain associated with melting. This last term multiplied by the temperature change yields the volume change due to melting that is driven by the temperature change. The thermal expansion of olivine at the experimental pressure and temperature is about 5.5 × 10−5 K−1 , which serves as a good estimate of the thermal expansion of the peridotite. With the melting , of 0.15, a value of 3.7 × 10−4 volume change, V V melting ∂F for ∂T will yield an equal contribution to the thermal expansion for both terms on the right-hand side of Eq. (2). as a function of F Figure 3 illustrates the magnitude of ∂F ∂T 1 = V
∂V ∂T
DISCUSSION
The volume strain induced by heating is generally defined by the thermal expansion of the material, α, times the temperature change where 1 ∂V , (1) α= V ∂T X where X represents a P-T path, typically constant P but in high pressure experiments the path is defined by the pressure medium, the pressurizing method, and is generally not constant pressure but the exact path is difficult to assess. If partial melting occurs as well in response to the temperature change, then the effective thermal expansion is given by
FIG. 3. The relationship between melt fraction, F, and melt productivity, dF/dT. The curve is derived from the program MELTS14 using KLB-1 compositions. The dotted line is the value of dF/dT that yields melting volume strain equal to thermal expansion volume strain for a change in temperature.
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065104-3
L. Li and D. J. Weidner
Rev. Sci. Instrum. 85, 065104 (2014)
thermal inertia of the sample. Thus, times shorter than 1 s will be difficult to define. It will be limited on the long time by the relaxation of the cell. ACKNOWLEDGMENTS
We wish to thank Ken Baldwin, Haiyen Chen, Wei Du, William Huebsch, Matthew Whitaker, and Michael Vaughan for support for this project. This research was partially supported by COMPRES, the Consortium for Materials Properties Research in Earth Sciences under NSF Cooperative Agreement EAR 11-57758. Support from the NSLS by the U. S. DoE, under Contract No. DE-AC02_98CH10886. The authors acknowledge support by the NSF EAR1141895, EAR1045629, and EAR0968823. 1 E.
FIG. 4. Effective thermal expansion for KLB-1 sample and corundum reference sample as a function of temperature. The sudden rise in the sample effective thermal expansion is accompanied with a slight decrease in corundum thermal expansion. We conclude that partial melting of the sample is occurring here, increasing the sample volume and decreasing the corundum expansion due to increased thermal pressure.
for a peridotite that is calculated usingthe program MELTS.14 that is required for The dashed line indicates the value of ∂F ∂T the melting contribution to be equal to the thermal expansion, indicating a value of about 2 vol.% melt. Figure 4 illustrates the effective thermal expansion of the sample and the corundum reference as a function of temperature. At 1200 o C, the effective thermal expansion of the sample nearly tripled, while the expansion of the corundum decreased. We infer that this indicates the onset of partial melting, probably in the amount of about 2%. CONCLUSION
We conclude that the onset of melting has been defined by the increase in volume strain during step heating. Partial melting by 2 vol.% of a peridotite is consistent with this observation. As the precision of the strain measurement increases, we will be able to define melting with lower amplitude temperature steps. This approach will be useful to define the time dependence of melting. It will be limited on the short time by the
Takahashi and I. Kushiro, “Melting of a dry peridotite at high-pressures and basalt magma genesis,” Am. Mineral. 68(9-10), 859–879 (1983). 2 A. M. J. Schaeffer, W. B. Talmadge, S. R. Temple, and S. Deemyad, “High pressure melting of lithium,” Phys. Rev. Lett. 109(18), 185702 (2012). 3 T. Pippinger, L. Dubrovinsky, K. Glazyrin, R. Miletich, and N. Dubrovinskaia, “Detection of melting by in situ observation of spherical-drop formation in laser-heated diamond-anvil cells,” Fisica de la Tierra 23, 12 (2011). 4 V. Swamy, N. A. Dubrovinskaya, and L. S. Dubrovinsky, “Hightemperature powder x-ray diffraction of yttria to melting point,” J. Mater. Res. 14(2), 456–459 (1999). 5 S. Anzellini, A. Dewaele, M. Mezouar, P. Loubeyre, and G. Morard, “Melting of iron at Earth’s inner core boundary based on fast X-ray diffraction,” Science 340(6131), 464–466 (2013). 6 S. Deemyad and I. F. Silvera, “Melting line of hydrogen at high pressures,” Phys. Rev. Lett. 100(15), 155701 (2008). 7 J. M. Jackson, W. Sturhahn, M. Lerche, J. Y. Zhao, T. S. Toellner, E. E. Alp, S. V. Sinogeikin, J. D. Bass, C. A. Murphy, and J. K. Wicks, “Melting of compressed iron by monitoring atomic dynamics,” Earth Planet. Sci. Lett. 362, 143–150 (2013). 8 C. Y. Shi, L. Zhang, W. G. Yang, Y. J. Liu, J. Y. Wang, Y. Meng, J. C. Andrews, and W. L. Mao, “Formation of an interconnected network of iron melt at Earth’s lower mantle conditions,” Nat. Geosci. 6(11), 971–975 (2013). 9 W. L. Zhu, G. A. Gaetani, F. Fusseis, L. G. J. Montesi, and F. De Carlo, “Microtomography of partially molten rocks: Three-dimensional melt distribution in mantle peridotite,” Science 332(6025), 88–91 (2011). 10 L. Li, P. Raterron, D. Weidner, and J. Chen, “Olivine flow mechanisms at 8 GPa,” Phys. Earth Planet. Int. 138(2), 113–129 (2003). 11 L. Li and D. J. Weidner, “Energy dissipation of materials at high pressure and high temperature,” Rev. Sci. Instrum. 78(5), 053902 (2007). 12 L. Li and D. J. Weidner, “Effect of dynamic melting on acoustic velocities in a partially molten peridotite,” Phys. Earth Planet. Int. 222, 1–7 (2013). 13 E. Takahashi, “Melting of a dry peridotite Klb-1 up to 14 Gpa – Implications on the origin of peridotitic upper mantle,” J. Geophys. Res. 91(B9), 9367–9382, doi:10.1029/JB091iB09p09367 (1986). 14 P. M. Smith and P. D. Asimow, “Adiabat_1ph: A new public front-end to the MELTS, pMELTS, and pHMELTS models,” Geochem., Geophys., Geosyst. 6(1), Q02004, doi:10.1029/2004GC000816 (2005).
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 065104 (2014)
Detection of melting by X-ray imaging at high pressure Li Li and Donald J. Weidner Mineral Physics Institute, Stony Brook University, Stony Brook, New York 11794-2100, USA
(Received 23 February 2014; accepted 19 May 2014; published online 5 June 2014) The occurrence of partial melting at elevated pressure and temperature is documented in real time through measurement of volume strain induced by a fixed temperature change. Here we present the methodology for measuring volume strains to one part in 10−4 for mm3 sized samples in situ as a function of time during a step in temperature. By calibrating the system for sample thermal expansion at temperatures lower than the solidus, the onset of melting can be detected when the melting volume increase is of comparable size to the thermal expansion induced volume change. We illustrate this technique with a peridotite sample at 1.5 GPa during partial melting. The Re capsule is imaged with a CCD camera at 20 frames/s. Temperature steps of 100 K induce volume strains that triple with melting. The analysis relies on image comparison for strain determination and the thermal inertia of the sample is clearly seen in the time history of the volume strain. Coupled with a thermodynamic model of the melting, we infer that we identify melting with 2 vol.% melting. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4880730] INTRODUCTION
EXPERIMENTAL METHOD
Detection of melting and its resulting changes in a bulk material at high pressure and temperature are important to the understanding of physical properties of materials. In multicomponent systems, melting typically initiates a one temperature, the solidus, and is complete at a second temperature, the liquidus. As there may be several hundred degrees between these two temperatures, it is often difficult to detect the onset of melting in situ. Various methods have been used such as examination of recovered samples,1 monitoring electrical resistivity,2 visual observation of sphere-drop formation,3 disappearance of X-ray diffraction spectrum,4 appearance of liquid diffuse ring in fast X-ray diffraction spectrum,5 temperature vs. average laser power,6 detection of mean-square displacement of atoms using synchrotron Mossbauer spectroscopy.7 The characterization of melts can also be carried out using X-ray tomography8, 9 on previously quenched samples. These methods have their own advantages but also limitations. Quenching may alter the character of melts and does not provide an in situ signal. The signals of some methods may depend on the amount of melts produced and are not suitable for partial molten samples. Some methods are not suited for X-ray opaque sample, and some only suited for diamond anvil cell application thus not applicable for pressure at a few gigapascal. We present here a method using synchrotron X-ray imaging to monitor the variation of the volume of the sample at high pressure (2 GPa) and high temperature using multi-anvil high pressure apparatus. The occurrence of the melts produced with step heating can be captured within a few seconds. This method is based on our ability to resolve volume strain at a precision of 10−4 . For peridotite, melting induced volume change dominates thermal expansion with 2 vol.% partial melting.
Our measurement of thermal expansion builds on the technique described in previous papers,10–12 which utilize the D-DIA high pressure device and synchrotron x-ray radiation. This paper focuses on establishing the protocols which enable detection of sample volume strain through X-ray imaging and the detection of melting phenomenon in situ. Rather than a conventional cell assembly as used in Ref. 11, a rhenium capsule is used to wrap the cylindrical sample (1 mm diameter, 1.5 mm long) to serve as the lateral strain marker (Figure 1). We use a CCD camera that records images of the sample at 20 frames/s during the heating steps. The images are processed by a software that is capable of detecting sub-pixel resolution. Images are processed to define radial strain and axial strain, which together, define volume strain. Resolution of the absolute volume of the sample is limited to a few cubic μm, since the width of the foil is a few μm. However, if one uses a starting image as a reference, a correlation between this reference and another image will yield the tiny motion of the strain marker up to 10−5 resolution.10 The sample, fine grounded KLB-1 peridotite powder13 (∼5 μm grain size), was cold pressed to 1.5 GPa, then heated to subsolidus conditions (ca. 850 ◦ C) and annealed for 30 min. The thermocouple is placed outside of the capsule, yielding a measured temperature that could be 100 ◦ C lower than the sample temperature. A dense corundum rod is placed above and below the sample and serves as an internal reference. After annealing, the sample was heated in a time dependent fashion as illustrated by the thermocouple temperature in Figure 2. Over time, the median temperature was stepped from 850 ◦ C to 1300 ◦ C in 50 ◦ C steps. About each median temperature, the temperature was oscillated, first in a sinusoidal variation, then in steps as illustrated in the inset of the diagram. The oscillations and steps are used to condition the cell assembly to yield reversible temperature–volume
0034-6748/2014/85(6)/065104/3/$30.00
85, 065104-1
© 2014 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 152.3.102.242 On: Tue, 11 Nov 2014 18:10:26
065104-2
L. Li and D. J. Weidner
FIG. 1. X-ray image of cylindrical sample wrapped in Re foil at pressure and temperature. A series of images were taken at 20 frames/s as temperature is stepped up or down. Sample volume strain are derived from comparing the images as defined by the Re markers. Volume strain precisions of 10−4 are achieved with this method.
relationships with time. The images of the sample were taken during these oscillations. The last heating step is used to define the effective thermal expansion. After the last temperature increase, the sample was quenched by turning the heating power off. An example of the time dependent volume strain is illustrated by the lower right inset in Figure 2. The sample strain is illustrated in gold and the alumina reference curve is blue. The volume responds with a sharp onset of strain with a more gradual emergent increase followed by a long term relaxation of the strain increase. We interpret the sharp increase as an indication of the quick response of the electronics to increase the power flowing through the furnace. The 1–2 s lapse for the volume strain to reach the maximum value indicates the thermal inertial of the sample. The long term relaxation represents the response of the pressure media to the increase of pressure accompanying the temperature increase.
Rev. Sci. Instrum. 85, 065104 (2014)
FIG. 2. Heating history of the experiment from 850 ◦ C to 1300 o C. Temperature is as read by the thermocouple which is probably colder than the sample. At each of the eight base temperatures (labeled T1 through T8 ), the temperature is cycled, at first sinusoidally with a period of 180 s, then with a square wave function. This heating serves to condition the cell for the sudden heating event. Strain data are taken from the last heating pulse, after confirmation that the system response was reversible. The inset on the upper left is for the second heating step and illustrates the details of the heating protocol. There are two heating pulses that have the wrong sign introduced by operator error. The inset on the lower right illustrates the volume strain response of the sample (gold) and the alumina reference (blue). The increase begins suddenly, but requires 1–2 s to reach the final value. This is likely the heating time of the sample when heated by the cylindrical furnace that surrounds the sample.
V ∂F αeff ective + , (2) V melting ∂T X X where F is the melt fraction and V is the volume V melting strain associated with melting. This last term multiplied by the temperature change yields the volume change due to melting that is driven by the temperature change. The thermal expansion of olivine at the experimental pressure and temperature is about 5.5 × 10−5 K−1 , which serves as a good estimate of the thermal expansion of the peridotite. With the melting , of 0.15, a value of 3.7 × 10−4 volume change, V V melting ∂F for ∂T will yield an equal contribution to the thermal expansion for both terms on the right-hand side of Eq. (2). as a function of F Figure 3 illustrates the magnitude of ∂F ∂T 1 = V
∂V ∂T
DISCUSSION
The volume strain induced by heating is generally defined by the thermal expansion of the material, α, times the temperature change where 1 ∂V , (1) α= V ∂T X where X represents a P-T path, typically constant P but in high pressure experiments the path is defined by the pressure medium, the pressurizing method, and is generally not constant pressure but the exact path is difficult to assess. If partial melting occurs as well in response to the temperature change, then the effective thermal expansion is given by
FIG. 3. The relationship between melt fraction, F, and melt productivity, dF/dT. The curve is derived from the program MELTS14 using KLB-1 compositions. The dotted line is the value of dF/dT that yields melting volume strain equal to thermal expansion volume strain for a change in temperature.
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065104-3
L. Li and D. J. Weidner
Rev. Sci. Instrum. 85, 065104 (2014)
thermal inertia of the sample. Thus, times shorter than 1 s will be difficult to define. It will be limited on the long time by the relaxation of the cell. ACKNOWLEDGMENTS
We wish to thank Ken Baldwin, Haiyen Chen, Wei Du, William Huebsch, Matthew Whitaker, and Michael Vaughan for support for this project. This research was partially supported by COMPRES, the Consortium for Materials Properties Research in Earth Sciences under NSF Cooperative Agreement EAR 11-57758. Support from the NSLS by the U. S. DoE, under Contract No. DE-AC02_98CH10886. The authors acknowledge support by the NSF EAR1141895, EAR1045629, and EAR0968823. 1 E.
FIG. 4. Effective thermal expansion for KLB-1 sample and corundum reference sample as a function of temperature. The sudden rise in the sample effective thermal expansion is accompanied with a slight decrease in corundum thermal expansion. We conclude that partial melting of the sample is occurring here, increasing the sample volume and decreasing the corundum expansion due to increased thermal pressure.
for a peridotite that is calculated usingthe program MELTS.14 that is required for The dashed line indicates the value of ∂F ∂T the melting contribution to be equal to the thermal expansion, indicating a value of about 2 vol.% melt. Figure 4 illustrates the effective thermal expansion of the sample and the corundum reference as a function of temperature. At 1200 o C, the effective thermal expansion of the sample nearly tripled, while the expansion of the corundum decreased. We infer that this indicates the onset of partial melting, probably in the amount of about 2%. CONCLUSION
We conclude that the onset of melting has been defined by the increase in volume strain during step heating. Partial melting by 2 vol.% of a peridotite is consistent with this observation. As the precision of the strain measurement increases, we will be able to define melting with lower amplitude temperature steps. This approach will be useful to define the time dependence of melting. It will be limited on the short time by the
Takahashi and I. Kushiro, “Melting of a dry peridotite at high-pressures and basalt magma genesis,” Am. Mineral. 68(9-10), 859–879 (1983). 2 A. M. J. Schaeffer, W. B. Talmadge, S. R. Temple, and S. Deemyad, “High pressure melting of lithium,” Phys. Rev. Lett. 109(18), 185702 (2012). 3 T. Pippinger, L. Dubrovinsky, K. Glazyrin, R. Miletich, and N. Dubrovinskaia, “Detection of melting by in situ observation of spherical-drop formation in laser-heated diamond-anvil cells,” Fisica de la Tierra 23, 12 (2011). 4 V. Swamy, N. A. Dubrovinskaya, and L. S. Dubrovinsky, “Hightemperature powder x-ray diffraction of yttria to melting point,” J. Mater. Res. 14(2), 456–459 (1999). 5 S. Anzellini, A. Dewaele, M. Mezouar, P. Loubeyre, and G. Morard, “Melting of iron at Earth’s inner core boundary based on fast X-ray diffraction,” Science 340(6131), 464–466 (2013). 6 S. Deemyad and I. F. Silvera, “Melting line of hydrogen at high pressures,” Phys. Rev. Lett. 100(15), 155701 (2008). 7 J. M. Jackson, W. Sturhahn, M. Lerche, J. Y. Zhao, T. S. Toellner, E. E. Alp, S. V. Sinogeikin, J. D. Bass, C. A. Murphy, and J. K. Wicks, “Melting of compressed iron by monitoring atomic dynamics,” Earth Planet. Sci. Lett. 362, 143–150 (2013). 8 C. Y. Shi, L. Zhang, W. G. Yang, Y. J. Liu, J. Y. Wang, Y. Meng, J. C. Andrews, and W. L. Mao, “Formation of an interconnected network of iron melt at Earth’s lower mantle conditions,” Nat. Geosci. 6(11), 971–975 (2013). 9 W. L. Zhu, G. A. Gaetani, F. Fusseis, L. G. J. Montesi, and F. De Carlo, “Microtomography of partially molten rocks: Three-dimensional melt distribution in mantle peridotite,” Science 332(6025), 88–91 (2011). 10 L. Li, P. Raterron, D. Weidner, and J. Chen, “Olivine flow mechanisms at 8 GPa,” Phys. Earth Planet. Int. 138(2), 113–129 (2003). 11 L. Li and D. J. Weidner, “Energy dissipation of materials at high pressure and high temperature,” Rev. Sci. Instrum. 78(5), 053902 (2007). 12 L. Li and D. J. Weidner, “Effect of dynamic melting on acoustic velocities in a partially molten peridotite,” Phys. Earth Planet. Int. 222, 1–7 (2013). 13 E. Takahashi, “Melting of a dry peridotite Klb-1 up to 14 Gpa – Implications on the origin of peridotitic upper mantle,” J. Geophys. Res. 91(B9), 9367–9382, doi:10.1029/JB091iB09p09367 (1986). 14 P. M. Smith and P. D. Asimow, “Adiabat_1ph: A new public front-end to the MELTS, pMELTS, and pHMELTS models,” Geochem., Geophys., Geosyst. 6(1), Q02004, doi:10.1029/2004GC000816 (2005).
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