铁高压熔化线研究
摘要
近年来，在地球深部物质物性研究领域出现的一个重要课题是：用冲击波法测量的铁的
高压熔化线（p_H＞200GPa范围）比用金刚石压砧装置测得的数据（p＜200GPa范围）系统地偏
高（在同一压力下，温度偏高）。由于这些数据对界定地核的热结构至关重要，因而引起了
广泛关注。本文试图利用多孔材料冲击温度高于密实材料冲击温度（在相同的冲击压力下）
的特性，直接测量较低压力下铁的熔化温度，以进一步验证上述的系统偏离程度，并结合新
近发展的固体熔化理论，以求对上述系统偏离现象作出澄清和解释。
通过研究和分析，取得以下新数据和新认识：
（1）对冲击温度测量数据处理中涉及到的重要问题—界面温度解，本文作了较为系统
的讨论和评述。目前常用的解是Gover和Urtiew从傅立叶热传导模型出发导出的，
有较好的近似性和适用性。但也存在两个问题：一是物理上的不自洽性（热波速度
无限大和击波速度远大于热传导速度）；二是求解中需要用到的一个目前无法实测
的在高温高压条件下的介质的热导率数据。为此，我们回顾了非傅立叶热传导模型
解、热阻模型解及汤文辉等人提出的由金属透光性（光学厚度）引起界面温度初期
表观热辐射峰状结构问题。尽管这三个模型的物理本质不一样，但它们的界面温度
解都有一个共同点—界面温度解中有一个初始温度峰值，只是，大约经过10ns后，
它要弛豫到由傅立叶热传导模型导出的界面温度。这个结果正是傅立叶热传导模型
近似性的所在，在目前用于测量界面温度的辐射高温计系统的时间分辨率约为10—
20ns的情况下，上述的初始峰值难以被记录下来，因而傅立叶热传导解的近似性被
视为是可以“容忍”的，并得以广泛应用。“坏事可以变为好事”，后三个模型为
我们带来了新机遇，即记录中的辐射峰值对应着金属的卸载温度（误差约5%）。如
果它能被记录下来，就可以免去难以精确测定高温高压下介质热导率数据的烦恼，
因为这个数据是傅立叶热传导模型中从界面温度计算卸载温度时必不可少的。显然，
实现这个新希望的关键技术是要把高温计系统的时间分辨率提高到1ns。
（2）测量铁高压熔化线的技术基础是冲击温度的测量。冲击温度测量实验中，数据处
理要用到另一个重要的材料参数是Grüneisen系数γ。为此，我们对多孔铁（ρ_00=6.904
g/cm~3，以后不再注明）的Hugoniot物态方程作了精密测量，得到的冲击波速度关系
式：D=2.997+1.603u_p（km/s），式中D和u_p分别是冲击波速度和波后粒子速度。然后，
通过Grüneisen物态方程，得到了铁的Grüneisen系数γ，它可以用经验公式：γ/V~n=γ_0/(V~n)_0
γ_0=1.945，n=1，ρ_0=7.856g/cm~3表示，式中v为比容。本文计算γ时首次引入了多孔
铁样品熔化的修正。
（3）用光分析法测量了冲击压缩状态下多孔铁的声速。实验结果是：在p_H＜122GPa区
卜
李西军 铁高压熔化线研究2000．4
测得的是纵波声速；其经验拟合式是：c；＝5．951＋1二24！up。－0口349In‘p。，p。的
单位是＊比，c．的单位是Ms，表明在该压力区，多孔铁具有固体性质：在阶157 GPGP。
区测得的是体声速C旷 表明该压力区多孔铁己转变为液体。因此，可以把该多孔铁
的冲击熔化压力限制在122157GPa范围内。结合冲击温度计算，在THh平面上
划出了铁的一个熔化线范围，并发现，这个范围大致位于Williams等人和YOo等人
用冲击波法测得的铁的高压熔化线向低压方向的外推上。
＊）根据 Tan等人提出的金属样品发生熔化情况下的界面温度模型，用模型计算和实
验测量相结合的方法，借助多孔铁样品，确定了铁的两个熔化温度，它们分别是
（171．4GPa，5550—5730K）和（98GPa，4470－4610K）。这两个点基本落在前人用
冲击波法测得的铁的高压熔化线向低压方向的外推线上。高压声速和冲击温度测量
结果都支持了前人发表的用冲击波法测得的铁的高压熔化线的合理性。换句话说，
用冲击波方法和用金刚石压砧技术测得的铁的高压熔化线之间的系统偏差确属客观
存在。
（5）根据冲击波和金刚石压砧技术的加温加压方式和判定熔化的准则，经过分析，本
文选用表面预熔化模型修正用金刚石压砧技术测得的熔化数据，选用卢柯等人提出
的晶格过热熔化的各向同性成核灾变模型修正冲击波法的测量数据。修正后的两组
数据基本是相互吻合的。因此，物理上，真实的高压熔化线大致位于两条原始熔化
线之间。看来，我们已经找到了造成两条熔化线数据之间系统偏差的物理原因、初
步化解了一个物理疑难。下一步的工作目标应是对铁高压熔化线数据的精密化，工
作量还是很大的。
Recently, one of the hot topics on the physical property studies of the materials in the earth deep
interior is: it seems there is a gap between the melting temperatures of iron obtained by the shock
compression (SC) method, measured at the pressures of PH>200GPa and extrapolating it to the lower
pressure region, and those obtained by diamond anvil cell (DAC) method, measured at the pressure of
p<200GPa and extrapolating it to the higher pressure region. Strictly speaking, the former is higher
than the latter, and the difference can not be explained as experimental error. This is an important
issue because it constraints the thermal structure of the earth core, and therefore, influences upon the
geomagnetic field characteristics and even related to the mantle convection. In this dissertation, we
attempt to utilize the specific property of the shock temperature of porous sample is higher than that
of non-porous ones to directly measure the melting temperatures of iron by SC method in the region
of p<200GPa. And use them to testify whether the above-mentioned gap between the SC
extrapolation and the DAC measurements is true since one may doubt about the reliability of SC
extrapolation. If so. we will try to resolve this gap as the physical phenomena based on the recent
developed theories of melting of solids.
Based on experimental results and analysis, some new data and new understanding obtained in this
dissertation can be summarized as follows:
(1) A comparative systematic discussion and comment have been made on the interface temperature
solution since they are important to the data processing in shock temperature determination. In
this regard, a commonly used solution given by Grover and Urtiew from the Fourier heat
conduction model is believed to be a fairly good approximation. But there are two results in this
model: One is the physical non-consistency, i.e. infinite thermal wave velocity implicated in the
model contradicts larger shock wave speed than the heat transfer speed assumed in the model; the
other is to determine the shock temperature, one should know the thermal properties of related
materials at high pressures and high temperatures, but this quantities are not obtainable at such
extreme conditions. So, we reviewed the non-Fourier heat conduction model solution, heat
resistance model solution and apparent initial interface temperature speak solution due to the
finite optical thickness of the shocked metallic samples proposed b Tang et al.. Though the
physical essences of the three models are different with each other, these solution indicates a
initial interface temperature speak, which corresponds to the release temperature; in 10 ns or more,
it will decays to a plateau, which corresponds to the solution proposed by Grover and Urtiew. In
other words, Grover model is reasonable only if the temperature measurement system is of the
time resolution 1 0-2Ons. But according the later three models, release temperature of metals in
shock experiments can be directly obtained (within the accuracy of 95%), only if the measurement
system is of time resolution Ins.
(2) The technical basis or measuring melting temperature is the shock temperature determination. In
the shock temperature data processing, an important parameter, namely Greisen ratio y, is also
required. For this reason, we have measured the Hugoniot Equation of state (EOS) of a kind of
porous iron with average initial density Poo=6904 glcm3. The results of the shock velocity relation
can be fitted as D2.997+ 1 .603u.,, (knils), where D and u is the measured shock wave speed and
the calculate
高压熔化线（p_H＞200GPa范围）比用金刚石压砧装置测得的数据（p＜200GPa范围）系统地偏
高（在同一压力下，温度偏高）。由于这些数据对界定地核的热结构至关重要，因而引起了
广泛关注。本文试图利用多孔材料冲击温度高于密实材料冲击温度（在相同的冲击压力下）
的特性，直接测量较低压力下铁的熔化温度，以进一步验证上述的系统偏离程度，并结合新
近发展的固体熔化理论，以求对上述系统偏离现象作出澄清和解释。
通过研究和分析，取得以下新数据和新认识：
（1）对冲击温度测量数据处理中涉及到的重要问题—界面温度解，本文作了较为系统
的讨论和评述。目前常用的解是Gover和Urtiew从傅立叶热传导模型出发导出的，
有较好的近似性和适用性。但也存在两个问题：一是物理上的不自洽性（热波速度
无限大和击波速度远大于热传导速度）；二是求解中需要用到的一个目前无法实测
的在高温高压条件下的介质的热导率数据。为此，我们回顾了非傅立叶热传导模型
解、热阻模型解及汤文辉等人提出的由金属透光性（光学厚度）引起界面温度初期
表观热辐射峰状结构问题。尽管这三个模型的物理本质不一样，但它们的界面温度
解都有一个共同点—界面温度解中有一个初始温度峰值，只是，大约经过10ns后，
它要弛豫到由傅立叶热传导模型导出的界面温度。这个结果正是傅立叶热传导模型
近似性的所在，在目前用于测量界面温度的辐射高温计系统的时间分辨率约为10—
20ns的情况下，上述的初始峰值难以被记录下来，因而傅立叶热传导解的近似性被
视为是可以“容忍”的，并得以广泛应用。“坏事可以变为好事”，后三个模型为
我们带来了新机遇，即记录中的辐射峰值对应着金属的卸载温度（误差约5%）。如
果它能被记录下来，就可以免去难以精确测定高温高压下介质热导率数据的烦恼，
因为这个数据是傅立叶热传导模型中从界面温度计算卸载温度时必不可少的。显然，
实现这个新希望的关键技术是要把高温计系统的时间分辨率提高到1ns。
（2）测量铁高压熔化线的技术基础是冲击温度的测量。冲击温度测量实验中，数据处
理要用到另一个重要的材料参数是Grüneisen系数γ。为此，我们对多孔铁（ρ_00=6.904
g/cm~3，以后不再注明）的Hugoniot物态方程作了精密测量，得到的冲击波速度关系
式：D=2.997+1.603u_p（km/s），式中D和u_p分别是冲击波速度和波后粒子速度。然后，
通过Grüneisen物态方程，得到了铁的Grüneisen系数γ，它可以用经验公式：γ/V~n=γ_0/(V~n)_0
γ_0=1.945，n=1，ρ_0=7.856g/cm~3表示，式中v为比容。本文计算γ时首次引入了多孔
铁样品熔化的修正。
（3）用光分析法测量了冲击压缩状态下多孔铁的声速。实验结果是：在p_H＜122GPa区
卜
李西军 铁高压熔化线研究2000．4
测得的是纵波声速；其经验拟合式是：c；＝5．951＋1二24！up。－0口349In‘p。，p。的
单位是＊比，c．的单位是Ms，表明在该压力区，多孔铁具有固体性质：在阶157 GPGP。
区测得的是体声速C旷 表明该压力区多孔铁己转变为液体。因此，可以把该多孔铁
的冲击熔化压力限制在122157GPa范围内。结合冲击温度计算，在THh平面上
划出了铁的一个熔化线范围，并发现，这个范围大致位于Williams等人和YOo等人
用冲击波法测得的铁的高压熔化线向低压方向的外推上。
＊）根据 Tan等人提出的金属样品发生熔化情况下的界面温度模型，用模型计算和实
验测量相结合的方法，借助多孔铁样品，确定了铁的两个熔化温度，它们分别是
（171．4GPa，5550—5730K）和（98GPa，4470－4610K）。这两个点基本落在前人用
冲击波法测得的铁的高压熔化线向低压方向的外推线上。高压声速和冲击温度测量
结果都支持了前人发表的用冲击波法测得的铁的高压熔化线的合理性。换句话说，
用冲击波方法和用金刚石压砧技术测得的铁的高压熔化线之间的系统偏差确属客观
存在。
（5）根据冲击波和金刚石压砧技术的加温加压方式和判定熔化的准则，经过分析，本
文选用表面预熔化模型修正用金刚石压砧技术测得的熔化数据，选用卢柯等人提出
的晶格过热熔化的各向同性成核灾变模型修正冲击波法的测量数据。修正后的两组
数据基本是相互吻合的。因此，物理上，真实的高压熔化线大致位于两条原始熔化
线之间。看来，我们已经找到了造成两条熔化线数据之间系统偏差的物理原因、初
步化解了一个物理疑难。下一步的工作目标应是对铁高压熔化线数据的精密化，工
作量还是很大的。
Recently, one of the hot topics on the physical property studies of the materials in the earth deep
interior is: it seems there is a gap between the melting temperatures of iron obtained by the shock
compression (SC) method, measured at the pressures of PH>200GPa and extrapolating it to the lower
pressure region, and those obtained by diamond anvil cell (DAC) method, measured at the pressure of
p<200GPa and extrapolating it to the higher pressure region. Strictly speaking, the former is higher
than the latter, and the difference can not be explained as experimental error. This is an important
issue because it constraints the thermal structure of the earth core, and therefore, influences upon the
geomagnetic field characteristics and even related to the mantle convection. In this dissertation, we
attempt to utilize the specific property of the shock temperature of porous sample is higher than that
of non-porous ones to directly measure the melting temperatures of iron by SC method in the region
of p<200GPa. And use them to testify whether the above-mentioned gap between the SC
extrapolation and the DAC measurements is true since one may doubt about the reliability of SC
extrapolation. If so. we will try to resolve this gap as the physical phenomena based on the recent
developed theories of melting of solids.
Based on experimental results and analysis, some new data and new understanding obtained in this
dissertation can be summarized as follows:
(1) A comparative systematic discussion and comment have been made on the interface temperature
solution since they are important to the data processing in shock temperature determination. In
this regard, a commonly used solution given by Grover and Urtiew from the Fourier heat
conduction model is believed to be a fairly good approximation. But there are two results in this
model: One is the physical non-consistency, i.e. infinite thermal wave velocity implicated in the
model contradicts larger shock wave speed than the heat transfer speed assumed in the model; the
other is to determine the shock temperature, one should know the thermal properties of related
materials at high pressures and high temperatures, but this quantities are not obtainable at such
extreme conditions. So, we reviewed the non-Fourier heat conduction model solution, heat
resistance model solution and apparent initial interface temperature speak solution due to the
finite optical thickness of the shocked metallic samples proposed b Tang et al.. Though the
physical essences of the three models are different with each other, these solution indicates a
initial interface temperature speak, which corresponds to the release temperature; in 10 ns or more,
it will decays to a plateau, which corresponds to the solution proposed by Grover and Urtiew. In
other words, Grover model is reasonable only if the temperature measurement system is of the
time resolution 1 0-2Ons. But according the later three models, release temperature of metals in
shock experiments can be directly obtained (within the accuracy of 95%), only if the measurement
system is of time resolution Ins.
(2) The technical basis or measuring melting temperature is the shock temperature determination. In
the shock temperature data processing, an important parameter, namely Greisen ratio y, is also
required. For this reason, we have measured the Hugoniot Equation of state (EOS) of a kind of
porous iron with average initial density Poo=6904 glcm3. The results of the shock velocity relation
can be fitted as D2.997+ 1 .603u.,, (knils), where D and u is the measured shock wave speed and
the calculate
引文
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