高压下铁的熔化曲线及外地核候选组分的约束性研究
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摘要
本文目的是研究地球深部物质在高温高压环境下的物性,主要限定在对地核材料的物性研究,其方法是采用凝聚态物理理论及近年发展起来的高压实验技术来研究深部地球物理问题,因而属于一种学科交叉的研究课题。研究内容由两部分构成,第一部分是高压下铁的熔化曲线,第二部分是从对外地核候选组分Fe/FeO/FeS(重量百分比为58.96/35.83/5.21)混合物的Hugoniot线、声速和熔化温度的测量出发,对外地核成分进行约束性研究。文中取得的有创新意义的结果归纳如下:
一、铁是地核的主要成分。通常认为地核又是由液态外核和固态内核组成,因而铁的高压熔化曲线是备受关注的科学问题,因为通过它可以推断出内外核界面(ICB)处(330GPa)的温度(严格讲是一级近似温度,又称锚定(anchor)温度),从而进一步推断出地核的温度剖面。但是近二十年来,在铁的高压熔化曲线的研究中还存在一个长期未能澄清的科学问题,即用冲击波方法测到的200GPa以上ε(hcp)-铁的熔化温度要比用金刚石压砧(DAC)装置测到的100GPa以下的数据呈系统性的偏高。虽然在最新的DAC实验中使用的X—射线衍射和激光双面加热技术克服了样品内温度梯度过大等技术问题,在冲击波方法中也考虑到了对过热熔化修正的影响,两者之间的偏差有所缩小,但是其间的偏差依然存在。在前人(李西军等人,见本院研究生部李西军博士毕业论文,2000年;Luo et al,Phys。Earth Planet。Inter,2004,143:369)根据Hugoniot声速数据确定了过热熔化温度后,再经过修正得到平衡熔化温度的方法中存在不确定性的基础上,本文提出了一个新的通过能量平衡原理直接计算平衡熔化温度的热力学计算方法。本文根据最新的Hugoniot声速测量结果,用这种分析方法计算了冲击压强为260GPa时铁的平衡熔化温度(5300K),并以这个点为参考点通过Lindemann熔化定律计算了ε-铁的高压熔化曲线,把它外推到低压下,发现与静高压最新的测量结果(Shen et al., Geophys Res Lett, 1998, 25: 373; Ma et al., Phys. Earth Planet. Inter., 2004, 143: 455)是一致的,从而得到了一条可以统一最新静高压和动高压熔化线测量数据的ε-铁的熔化曲线,解决了以上所说的一个科学难题。这就是本文的主要创新点。上述工作还进一步得到以下三个方面分析结果的支持。
1、基于ε相铁的OK等温状态方程和有效Gruneisen参数γ_(eff)以及比热C_v等基本物性参数,用热力学方法计算了固态、固-液混合态、液态铁的Hugoniot线。对于固态和液态铁,计算的P—V线与实验测量数据符合得很好,这也表明这种计算方法也可以很好的区分Hugoniot实验数据中固相区和液相区。但在很窄的固-液混合压力区内,由于被测样品中的冲击波分裂为两个波阵面,冲击波速度和粒子速度的实验数据有较大的分散性,因而实验数据和计算曲线之间有一些不大的区别。但是就总体而言,理论计算与实验测量数据的一致性表明了以上计算方法和所用参数值的合理性。
The purpose of this thesis is to study the physical properties of the materials in Earth's deep interior, here mainly restricting to the Earth's core ones, at high pressure and high temperature, by means of theories of condensed matter and recently developed high pressure techniques. So this work is a research topic belonging to cross disciplines. The content of it can be divided into two parts. One is the high pressure melting curve of iron, the other is a constrained investigation for the candidate Earth's outer core composition, in which a Fe-O-S system with 90.12/7.98/1.9 wt. % is chosen as the sample materials and its Hugoniot curve, Hugoniot sound velocities and melting temperature measurements are made and analyzed. Some main and /or innovative results are summarized as follows:I Iron is the main component of Earth's core. It is also acknowledged that the Earth's core could be distinguished into a liquid outer core and a solid inner core. Therefore, the high pressure melting line of iron is a much concerned scientific problem for us since from which the temperature at the inner core boundary (ICB, at 330GPa) can be inferred as an reference data with first-order approximation (also called anchor temperature), so as to further examine the temperature profile within Earth's core. But, an unresolved scientific issue has appeared and always troubled us for nearly twenty years, i.e. the melting temperatures of iron measured by the shock compression (SC) experiment above 200 GPa are higher than those measured by diamond anvil cell (DAC) technique below 100 GPa while the former is extrapolated by Lindemann law to the corresponding lower pressure region. Although recent developed accurate X-ray diffraction and double-side laser heating techniques have been introduced in DAC measurements and superheating correction methods have been introduced in SC's data analysis, the melting temperature data discrepancies between DAC and SC experiments have been reduced but not closed nowadays. For this reason, a thermodynamic way to direct calculating the equilibrium melting temperature in SC's data analysis, instead of the superheating correction methods respectively proposed by Li Xijun (Doctoral thesis, China Academic of Engineering Physics, 2000) and Luo et al (Phys. Earth Planet. Inter, 2004,143:369), is proposed in this work. Using this new data analysis technique, an equilibrium melting temperature of 5300K at 260GPa from SC measurements can be informed, from which a surprisingly well agreement between this new SC's data and new DAC data (Shen et al., Geophys Res Lett, 1998,25: 373; Ma et al., Phys. Earth Planet. Inter., 2004, 143: 455) joined by Lindemann law has been observed. This is a main achievement
made in this paper. The rationality of this method is further supported by three kinds of the following calculations.(1) According to the exiting OK isothermal equation of state and the effective Griineisen parameter yeff and specific heat Cv, the Hugoniots relevant to solid, solid-liquid mixture and liquid regions for iron have been calculated by means of this thermodynamic analysis method, respectively. In solid and liquid regions, the calculated Hugoniots are in good agreement with experiments, which also show this calculation method is an excellent tool to distinguish solid and liquid phase from the experimental Hugoniot points. This is an additional unique merit of the method. As for in the solid-liquid mixture, a slightly scattered experimental data appear when compared with the calculation Hugoniot, because of a two-wave shock structure formation in the region.(2) Along the above-mentioned calculational Hugoniot, the Hugoniot bulk sound velocities relevant to solid and liquid phases have also been computed with same thermodynamic ways. Both are in accord with experiments. Otherwise, if we use Brown's Hugoniot parameters (J. Appl. Phys, 2000, 88: 5496) i.e. without distinguishing solid and liquid state, the computed sound velocities are 3% less than the experiments for solid iron. This is one of important conclusions revealed in this work.(3) Griineisen parameter y is one of the important thermodynamic quantities since it often appears in the equation of state and melting temperature calculations. But the available data of 7 for iron along Hugoniot are not only limited, but also diverse with each other. For this reason, we make a calculation with same thermodynamic technique for the effective Griineisen parameter along Hugoniot, denoted by yeff, based on the available data of specific heat of Cv and the Griineisen parameter y from both lattice (N) and electron (e) contributions. The results demonstrated that yeff can be in good agreement with experimental yN at lower pressure and with the calculated data deduced from experimental Hugoniot bulk sound velocity at higher pressure region, showing a rational or a correct physical basis for this yeff calculations.II In the candidate Earth's outer core compositions study, ternary alloys of Fe-O-S with 90.12/7.98/1.9 by wt.% (corresponding to Fe/FeO/FeS with 58.96/35.83/5.21 by wt.%) is chosen as the sample material, based on Alfe's suggestions (Nature, 2000 ,405:172) and the PREM model (Dziewonski, Earth Planet. Interiors, 1981,25: 297) constrained by both density and sound velocity vs pressure relations. This is the first experimental investigation for a ternary alloy candidate model of Earth's outer core composition research. (1) Hugoniot curve for this Fe-O-S system with initial density p0—6.69 (±0.06) g/cm3 has
been made in the range from 50 to 210 GPa. The measured Hugoniot parameters are Q—3.97 (±0.07) km/s, X=1.58 (±0.03) , which is well agreement with the calculated data deduced from the individual Hugoniot of Fe, FeO, and FeS through the volume additive modelling, Introduction to the Experimental Equation of State, Beijing: Science, Press, 1999; Lin et al., Chin J High Press Phys.Lett, 1998, 12: 40). The calculated 0 K isothermal from the measured Hugoniot through Wu's method (Chin Phys Lett, 2002, 19: 528) is also consistent well with that calculated from the individual 0 K isotherms of the ingredients through the volume additive law. Both results indicate that the volume additive model is reasonable for this kind of mixture and no detectable chemical reactions occur among Fe, FeO and FeS during shock compression.(2) Hugoniot sound velocities measurements show that the equilibrium melting temperature of 3830K at the shock-induced completely melting point of 167GPa can be inferred based on the thermodynamic energy balance calculation, and, therefore, the melting curve relevant to this kind of mixture can be calculated according to Lindemann law. To further verifying the rationality of this calculated melting curve, The Tan-Dai- Ahrens model (High Press Res, 1990; Geophys. Res. Lett, 2000) has been used to direct measure the release melting temperatures for comparison. The results are Tm=3100K at 108GPa and Tm =2880K at 90GPa, both lie on the calculated melting curve within the experimental error range. The melting temperature of this Fe-O-S is 5400K while extrapolated to ICB at 330 GPa.(3) At ICB (330 GPa), the melting temperatures of pure iron and this Fe-O-S material are 5930 K and 5400K respectively. The contribution of O and S to the melting depression is about 600K at 33OGPa. In order to compare with PREM model, the Hugoniot density and bulk sound velocity should be corrected for the temperature difference between Hugoniot state and the Earth's outer core state calculated by this thermodynamic analysis method, with an uncertainty better than that of the previously proposed " average temperature correction coefficient". The results show that the ternary alloy candidate Earth's outer core compositions of Fe-O-S system can be basically constrained with PREM model. A small concentration adjustments for O and S elements vs core depth should be made in further, due to the need for improving the coincidence degree between the PREM model and the behavior of candidate material of Fe-O-S system.
一、铁是地核的主要成分。通常认为地核又是由液态外核和固态内核组成,因而铁的高压熔化曲线是备受关注的科学问题,因为通过它可以推断出内外核界面(ICB)处(330GPa)的温度(严格讲是一级近似温度,又称锚定(anchor)温度),从而进一步推断出地核的温度剖面。但是近二十年来,在铁的高压熔化曲线的研究中还存在一个长期未能澄清的科学问题,即用冲击波方法测到的200GPa以上ε(hcp)-铁的熔化温度要比用金刚石压砧(DAC)装置测到的100GPa以下的数据呈系统性的偏高。虽然在最新的DAC实验中使用的X—射线衍射和激光双面加热技术克服了样品内温度梯度过大等技术问题,在冲击波方法中也考虑到了对过热熔化修正的影响,两者之间的偏差有所缩小,但是其间的偏差依然存在。在前人(李西军等人,见本院研究生部李西军博士毕业论文,2000年;Luo et al,Phys。Earth Planet。Inter,2004,143:369)根据Hugoniot声速数据确定了过热熔化温度后,再经过修正得到平衡熔化温度的方法中存在不确定性的基础上,本文提出了一个新的通过能量平衡原理直接计算平衡熔化温度的热力学计算方法。本文根据最新的Hugoniot声速测量结果,用这种分析方法计算了冲击压强为260GPa时铁的平衡熔化温度(5300K),并以这个点为参考点通过Lindemann熔化定律计算了ε-铁的高压熔化曲线,把它外推到低压下,发现与静高压最新的测量结果(Shen et al., Geophys Res Lett, 1998, 25: 373; Ma et al., Phys. Earth Planet. Inter., 2004, 143: 455)是一致的,从而得到了一条可以统一最新静高压和动高压熔化线测量数据的ε-铁的熔化曲线,解决了以上所说的一个科学难题。这就是本文的主要创新点。上述工作还进一步得到以下三个方面分析结果的支持。
1、基于ε相铁的OK等温状态方程和有效Gruneisen参数γ_(eff)以及比热C_v等基本物性参数,用热力学方法计算了固态、固-液混合态、液态铁的Hugoniot线。对于固态和液态铁,计算的P—V线与实验测量数据符合得很好,这也表明这种计算方法也可以很好的区分Hugoniot实验数据中固相区和液相区。但在很窄的固-液混合压力区内,由于被测样品中的冲击波分裂为两个波阵面,冲击波速度和粒子速度的实验数据有较大的分散性,因而实验数据和计算曲线之间有一些不大的区别。但是就总体而言,理论计算与实验测量数据的一致性表明了以上计算方法和所用参数值的合理性。
The purpose of this thesis is to study the physical properties of the materials in Earth's deep interior, here mainly restricting to the Earth's core ones, at high pressure and high temperature, by means of theories of condensed matter and recently developed high pressure techniques. So this work is a research topic belonging to cross disciplines. The content of it can be divided into two parts. One is the high pressure melting curve of iron, the other is a constrained investigation for the candidate Earth's outer core composition, in which a Fe-O-S system with 90.12/7.98/1.9 wt. % is chosen as the sample materials and its Hugoniot curve, Hugoniot sound velocities and melting temperature measurements are made and analyzed. Some main and /or innovative results are summarized as follows:I Iron is the main component of Earth's core. It is also acknowledged that the Earth's core could be distinguished into a liquid outer core and a solid inner core. Therefore, the high pressure melting line of iron is a much concerned scientific problem for us since from which the temperature at the inner core boundary (ICB, at 330GPa) can be inferred as an reference data with first-order approximation (also called anchor temperature), so as to further examine the temperature profile within Earth's core. But, an unresolved scientific issue has appeared and always troubled us for nearly twenty years, i.e. the melting temperatures of iron measured by the shock compression (SC) experiment above 200 GPa are higher than those measured by diamond anvil cell (DAC) technique below 100 GPa while the former is extrapolated by Lindemann law to the corresponding lower pressure region. Although recent developed accurate X-ray diffraction and double-side laser heating techniques have been introduced in DAC measurements and superheating correction methods have been introduced in SC's data analysis, the melting temperature data discrepancies between DAC and SC experiments have been reduced but not closed nowadays. For this reason, a thermodynamic way to direct calculating the equilibrium melting temperature in SC's data analysis, instead of the superheating correction methods respectively proposed by Li Xijun (Doctoral thesis, China Academic of Engineering Physics, 2000) and Luo et al (Phys. Earth Planet. Inter, 2004,143:369), is proposed in this work. Using this new data analysis technique, an equilibrium melting temperature of 5300K at 260GPa from SC measurements can be informed, from which a surprisingly well agreement between this new SC's data and new DAC data (Shen et al., Geophys Res Lett, 1998,25: 373; Ma et al., Phys. Earth Planet. Inter., 2004, 143: 455) joined by Lindemann law has been observed. This is a main achievement
made in this paper. The rationality of this method is further supported by three kinds of the following calculations.(1) According to the exiting OK isothermal equation of state and the effective Griineisen parameter yeff and specific heat Cv, the Hugoniots relevant to solid, solid-liquid mixture and liquid regions for iron have been calculated by means of this thermodynamic analysis method, respectively. In solid and liquid regions, the calculated Hugoniots are in good agreement with experiments, which also show this calculation method is an excellent tool to distinguish solid and liquid phase from the experimental Hugoniot points. This is an additional unique merit of the method. As for in the solid-liquid mixture, a slightly scattered experimental data appear when compared with the calculation Hugoniot, because of a two-wave shock structure formation in the region.(2) Along the above-mentioned calculational Hugoniot, the Hugoniot bulk sound velocities relevant to solid and liquid phases have also been computed with same thermodynamic ways. Both are in accord with experiments. Otherwise, if we use Brown's Hugoniot parameters (J. Appl. Phys, 2000, 88: 5496) i.e. without distinguishing solid and liquid state, the computed sound velocities are 3% less than the experiments for solid iron. This is one of important conclusions revealed in this work.(3) Griineisen parameter y is one of the important thermodynamic quantities since it often appears in the equation of state and melting temperature calculations. But the available data of 7 for iron along Hugoniot are not only limited, but also diverse with each other. For this reason, we make a calculation with same thermodynamic technique for the effective Griineisen parameter along Hugoniot, denoted by yeff, based on the available data of specific heat of Cv and the Griineisen parameter y from both lattice (N) and electron (e) contributions. The results demonstrated that yeff can be in good agreement with experimental yN at lower pressure and with the calculated data deduced from experimental Hugoniot bulk sound velocity at higher pressure region, showing a rational or a correct physical basis for this yeff calculations.II In the candidate Earth's outer core compositions study, ternary alloys of Fe-O-S with 90.12/7.98/1.9 by wt.% (corresponding to Fe/FeO/FeS with 58.96/35.83/5.21 by wt.%) is chosen as the sample material, based on Alfe's suggestions (Nature, 2000 ,405:172) and the PREM model (Dziewonski, Earth Planet. Interiors, 1981,25: 297) constrained by both density and sound velocity vs pressure relations. This is the first experimental investigation for a ternary alloy candidate model of Earth's outer core composition research. (1) Hugoniot curve for this Fe-O-S system with initial density p0—6.69 (±0.06) g/cm3 has
been made in the range from 50 to 210 GPa. The measured Hugoniot parameters are Q—3.97 (±0.07) km/s, X=1.58 (±0.03) , which is well agreement with the calculated data deduced from the individual Hugoniot of Fe, FeO, and FeS through the volume additive modelling, Introduction to the Experimental Equation of State, Beijing: Science, Press, 1999; Lin et al., Chin J High Press Phys.Lett, 1998, 12: 40). The calculated 0 K isothermal from the measured Hugoniot through Wu's method (Chin Phys Lett, 2002, 19: 528) is also consistent well with that calculated from the individual 0 K isotherms of the ingredients through the volume additive law. Both results indicate that the volume additive model is reasonable for this kind of mixture and no detectable chemical reactions occur among Fe, FeO and FeS during shock compression.(2) Hugoniot sound velocities measurements show that the equilibrium melting temperature of 3830K at the shock-induced completely melting point of 167GPa can be inferred based on the thermodynamic energy balance calculation, and, therefore, the melting curve relevant to this kind of mixture can be calculated according to Lindemann law. To further verifying the rationality of this calculated melting curve, The Tan-Dai- Ahrens model (High Press Res, 1990; Geophys. Res. Lett, 2000) has been used to direct measure the release melting temperatures for comparison. The results are Tm=3100K at 108GPa and Tm =2880K at 90GPa, both lie on the calculated melting curve within the experimental error range. The melting temperature of this Fe-O-S is 5400K while extrapolated to ICB at 330 GPa.(3) At ICB (330 GPa), the melting temperatures of pure iron and this Fe-O-S material are 5930 K and 5400K respectively. The contribution of O and S to the melting depression is about 600K at 33OGPa. In order to compare with PREM model, the Hugoniot density and bulk sound velocity should be corrected for the temperature difference between Hugoniot state and the Earth's outer core state calculated by this thermodynamic analysis method, with an uncertainty better than that of the previously proposed " average temperature correction coefficient". The results show that the ternary alloy candidate Earth's outer core compositions of Fe-O-S system can be basically constrained with PREM model. A small concentration adjustments for O and S elements vs core depth should be made in further, due to the need for improving the coincidence degree between the PREM model and the behavior of candidate material of Fe-O-S system.
引文
[1] Birch F. Elasticity and constitution of the earth's interior[J]. J. Geophys. Res, 1952; 20: 227～286.
[2] Dziewonski A M, Anderson D L. Preliminary reference earth model [J]. Earth Planet. Interiors, 1981, 25: 297-356.
[3] Brown J M, McQueen, R. G. Phase transitions, Gruneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa [J]. J. Geophys. Res, 1986; 91: 7485-7494
[4] Williams Q, Jeanloz R, Bass J, Svendsen B, Ahrens T J. The melting curve of iron to 250 GPa: a constraint on temperature at earth's center[J]. Science, 1987; 236: 181-183.
[5] Boehler R. Temperature in the Earth's core from melting point measurements of iron at high static pressures[J]. Nature, 1993; 363: 534-536.
[6] Yoo C S, Akella J, Campbell A J, Mao H K, Hemley R J. The phase diagram of iron by in situ x-ray diffraction: Implications for Earth's core [J]. Science, 1995; 270, 1473-1475
[7] Shen G, Hu J, Hemley R J, Mao H. High P-T phase diagram and equation of sate of iron [A]. Eos Trans. AGU, 77(46), Fall Meet. Suppl., F696, 1996.
[8] Bass J D, Svendson B, Ahrens T. The temperature of shock compressed iron [A]. In: Manghnani, M. H., Syono, Y. (Eds), High Pressure Research in Mineral Physics, vol. 39. Geophysical Monograph Set. 39, Washington, D. C: American Geophysical Union, 1987: 393-492.
[9] Yoo C S, Holmes N C, Ross M, Webb D, Pike C. Shock temperatures and melting of iron at Earth core conditions [J]. Phys. Rev. Lett, 1993; 70: 3931-3934.
[10] Anderson O L, Duba A. Experimental melting curve of iron revised [J]. J. Geophys. Res, 1997; 102: 22659-22669.
[11] Lyzenga G A, Ahrens T J, Mitchell A C. Shock temperature of SiO2 and their geophysical implications [J]. J. Geophys. Res, 1983; 88: 2431-24444.
[12] Shen G, Mao H K, Hemley R J, Duffy T S, and Rivers M L. Melting and crystal structure of iron at high pressures and temperatures [J]. Geophysical Research Letters, 1998; 25: 373-376.
[13] Ma Y Z, Somayazulu M, Shen G., Mao H K, Shu J F, Hemley R J. In situ X-ray diffraction studies of iron to earth-core conditions [J]. Phys. Earth. Planet Inter, 2004; 143: 455-467.
[14] Li X J, Zhang D Y, Liu F S, Jing F Q. Shock Melting Temperature of Initially Porous Iron and Indication for Melting Curve of Iron at High Pressures [J]. Chin. Phys. Lett, 2004; 21: 2019-2021.
[15] Lu K, Li Y. Homogeneous nucleation catastrophe askinetic stability limit for superheated crystal [J]. Phys. Rev. Lett, 1998; 80: 4474-4477.
[16] Luo S N, Ahrens T J, Shock-induced superheating and melting curves of geophysically important minerals [J]. Phys. Earth Planet. Inter, 2004; 143: 369-386.
[17] Laio A, Bernard S, Chiarotti G L, Scandolo S, Tosatti E. Physics of iron at earth's core conditions [J]. Science, 2000; 287: 1027-1030.
[18] Belonoshko A B, Ahujia R. Embedded-atom molecular dynamic study of iron melting [J]. Phys. Earth Planet. Liter, 1997; 84: 171-184.
[19] Neumann G S, Stixrude L, Cohen R E, Gulsersen O. Elasticity of iron at the temperature of the earth's inner core [J]. Nature, 2001; 413: 57-60.
[20] Stixrude L, Wasserman E, Composition and temperature of the earth's inner core [J]. J. Geophys. Res, 1997; 102:24729-24739.
[21] Alfe D, Gillan M J, Price G D. Composition and temperature of the Earth's core constrained by combing ab initio calculation and seismic data [J]. Earth Planet Sci. Lett, 2002; 195: 91-98
[22] Jeanloz R. Properties of iron at high pressures and the state of the core [J]. J. Geophys. Res, 1979; 84: 6059-6068.
[23] Anderson O L. The Gruneisen parameter for iron at outer core conditions and the resulting conductive heat and power in the core [J]. Physics of Earth and Planetary Interiors, 1998; 109: 179-197.
[24] Li X J, Zhou X. M, Wang F H, and Jing F Q. Restudy of Gruneisen Parameter of Iron in the Pressure Range of 90-160 GPa [J]. Chin. Phys. Lett, 2001; 18: 85-87.
[25] Mao H K, Wu Y, Chen L C, Shu J F, Jephcoat A P. Static compression of iron to 300 GPa and Fe_0.8Ni_0.2 alloy to 260 GPa: Implications for composition of the core [J]. J. Geophys. Res, 1990; 95: 21737-21742.
[26] Anderson O L, Dubrovinsky L, Saxena S K, LeBinhan T. Experimental vibrational Gruneisen ratio values for -iron up to 330 GPa at 300 K [J]. Geophys. Res. Lett, 2001; 28: 399-402.
[2] Dziewonski A M, Anderson D L. Preliminary reference earth model [J]. Earth Planet. Interiors, 1981, 25: 297-356.
[3] Brown J M, McQueen, R. G. Phase transitions, Gruneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa [J]. J. Geophys. Res, 1986; 91: 7485-7494
[4] Williams Q, Jeanloz R, Bass J, Svendsen B, Ahrens T J. The melting curve of iron to 250 GPa: a constraint on temperature at earth's center[J]. Science, 1987; 236: 181-183.
[5] Boehler R. Temperature in the Earth's core from melting point measurements of iron at high static pressures[J]. Nature, 1993; 363: 534-536.
[6] Yoo C S, Akella J, Campbell A J, Mao H K, Hemley R J. The phase diagram of iron by in situ x-ray diffraction: Implications for Earth's core [J]. Science, 1995; 270, 1473-1475
[7] Shen G, Hu J, Hemley R J, Mao H. High P-T phase diagram and equation of sate of iron [A]. Eos Trans. AGU, 77(46), Fall Meet. Suppl., F696, 1996.
[8] Bass J D, Svendson B, Ahrens T. The temperature of shock compressed iron [A]. In: Manghnani, M. H., Syono, Y. (Eds), High Pressure Research in Mineral Physics, vol. 39. Geophysical Monograph Set. 39, Washington, D. C: American Geophysical Union, 1987: 393-492.
[9] Yoo C S, Holmes N C, Ross M, Webb D, Pike C. Shock temperatures and melting of iron at Earth core conditions [J]. Phys. Rev. Lett, 1993; 70: 3931-3934.
[10] Anderson O L, Duba A. Experimental melting curve of iron revised [J]. J. Geophys. Res, 1997; 102: 22659-22669.
[11] Lyzenga G A, Ahrens T J, Mitchell A C. Shock temperature of SiO2 and their geophysical implications [J]. J. Geophys. Res, 1983; 88: 2431-24444.
[12] Shen G, Mao H K, Hemley R J, Duffy T S, and Rivers M L. Melting and crystal structure of iron at high pressures and temperatures [J]. Geophysical Research Letters, 1998; 25: 373-376.
[13] Ma Y Z, Somayazulu M, Shen G., Mao H K, Shu J F, Hemley R J. In situ X-ray diffraction studies of iron to earth-core conditions [J]. Phys. Earth. Planet Inter, 2004; 143: 455-467.
[14] Li X J, Zhang D Y, Liu F S, Jing F Q. Shock Melting Temperature of Initially Porous Iron and Indication for Melting Curve of Iron at High Pressures [J]. Chin. Phys. Lett, 2004; 21: 2019-2021.
[15] Lu K, Li Y. Homogeneous nucleation catastrophe askinetic stability limit for superheated crystal [J]. Phys. Rev. Lett, 1998; 80: 4474-4477.
[16] Luo S N, Ahrens T J, Shock-induced superheating and melting curves of geophysically important minerals [J]. Phys. Earth Planet. Inter, 2004; 143: 369-386.
[17] Laio A, Bernard S, Chiarotti G L, Scandolo S, Tosatti E. Physics of iron at earth's core conditions [J]. Science, 2000; 287: 1027-1030.
[18] Belonoshko A B, Ahujia R. Embedded-atom molecular dynamic study of iron melting [J]. Phys. Earth Planet. Liter, 1997; 84: 171-184.
[19] Neumann G S, Stixrude L, Cohen R E, Gulsersen O. Elasticity of iron at the temperature of the earth's inner core [J]. Nature, 2001; 413: 57-60.
[20] Stixrude L, Wasserman E, Composition and temperature of the earth's inner core [J]. J. Geophys. Res, 1997; 102:24729-24739.
[21] Alfe D, Gillan M J, Price G D. Composition and temperature of the Earth's core constrained by combing ab initio calculation and seismic data [J]. Earth Planet Sci. Lett, 2002; 195: 91-98
[22] Jeanloz R. Properties of iron at high pressures and the state of the core [J]. J. Geophys. Res, 1979; 84: 6059-6068.
[23] Anderson O L. The Gruneisen parameter for iron at outer core conditions and the resulting conductive heat and power in the core [J]. Physics of Earth and Planetary Interiors, 1998; 109: 179-197.
[24] Li X J, Zhou X. M, Wang F H, and Jing F Q. Restudy of Gruneisen Parameter of Iron in the Pressure Range of 90-160 GPa [J]. Chin. Phys. Lett, 2001; 18: 85-87.
[25] Mao H K, Wu Y, Chen L C, Shu J F, Jephcoat A P. Static compression of iron to 300 GPa and Fe_0.8Ni_0.2 alloy to 260 GPa: Implications for composition of the core [J]. J. Geophys. Res, 1990; 95: 21737-21742.
[26] Anderson O L, Dubrovinsky L, Saxena S K, LeBinhan T. Experimental vibrational Gruneisen ratio values for -iron up to 330 GPa at 300 K [J]. Geophys. Res. Lett, 2001; 28: 399-402.