冲击压缩至兆巴压力下铁的电导率及其地球物理意义
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摘要
本文提出和研究了一种可用于兆巴压力冲击压缩下测量金属电导率的新方法——四电极垂向引线法。用二级轻气炮作为加载手段，测量了铁在终态平衡压力为101-208GPa的压力区间内的电导率。首次将铁的电导率测量的压力范围扩展到了200GPa以上，并达到了固-液混合相区。发现金属电导率的Bloch-Gr(?)neisen公式在冲击压力高达200GPa时且在铁的冲击熔化固-液混合相区仍然有效。并以此为根据计算了地核的电导率分布，提出了铁的电导率在内／外界面处发生跃变的论断。本文取得的主要结果或结论如下：
1)提出并研究了一种冲击压缩下测量金属电导率的新方法——使用刻槽单晶蓝宝石做金属样品绝缘层的四电极垂向引线法。(a)用样品嵌入带沟槽绝缘块的结构代替前人常用的“三明治”夹层(即绝缘层／样品／绝缘块)结构，解决了原样品组件构型中金属样品环氧树脂包覆层高压下导电所产生的分流效应对测量结果的影响，提高了可测量的压力上限：(b)解决了由于构型改变而引起的部件加工与组装以及实验测量中的若干技术性困难，包括研制成专用的大功率脉冲恒流源等；(c)对于新构型引起的样品增厚而提高输入电流对样品预加热的影响，本文设计了专门实验检验，并证实了这种欧姆加热可以忽略不计；(d)用一维流体力学模拟计算了冲击压缩下金属样品受压变化的时间历程，对判读和分析电导率变化的波形记录起到了指导性作用。实测结果与上述预测基本相符。
2)用二级轻气炮作为加载手段，测量了铁在终态平衡压力为101～208GPa的压力区间内的电导率，(电导率从1．45X10~4Ω~(-1)cm~(-1)变化到7．65×10~3Ω~(-1)cm~(-1)。首次将铁的电导率测量的压力范围扩展到了200GPa以上，并达到了熔化固-液混合相区。结果表明，本文的测量数据与Keeler等人测量数据之间存在系统差异，Keeler等人的数据明显偏高。分析后认为，主要是因为在Keeler的样品组装中使用的环氧树脂绝缘层在高压下导电所产生的分流效应引起的。
3)通过对铁在冲击压缩下发生α-ε相变时的退磁效应对测量信号波形影响的分析，以及对样品中的冲击波在前后蓝宝石界面上反射的分析，获得了铁的电导率数据，为今后开展这类实验测量提供了有用的技术和认识。
4)Bloch-Gr(?)neisen关系。通过对电导率测量数据的分析，发现关于金属电导率的Bloch-Gr(?)neisen公式对于铁在冲击压力高达208GPa且已进入冲击熔化固-液混合相区时仍然有效，此时的平衡温度已达5220K。为了检验Bloch-Gr(?)neisen公式
一
在兆巴压力冲击压缩下的有效性，本文取Keeler在较低压力下8相区的一个电导
率数据作为参考点，得到了81co卜Grnelsen公式关于s－铁在高温高压下电导率
。。。。。＿。。＿＿1．589exp卜刀33v“‘）x m”。。。。。。－。。。。＿＿－3／＿
的一个解析表达式：a＝一，这里，比容v的单位是cm丫g，
丁 一
温度丁的单位是 K，电导率。的单位是O－‘cm－‘。卜铁的高压电导率之所以与仅
考虑晶格散射的BlochGriineisen公式符合性好，是因为e－铁己不存在任何磁有
序结构，高温高压下Sp电子的散射主要以声子散射为主，己没有。－铁中的磁子
散射贡献，同时s－d散射亦居于次要地位。
5）地核的温度分布。本文对地核的物质成分做了详细评述，并估算了固态内地核的
杂质成分与含量。从纯铁的冲击熔化温度出发，用Lindemann定律外推到内地核
边界（ICB）条件（330GPa）下，估算出铁的熔化温度约为6200K。进一步考虑
实际地核含有杂质而导致熔化温度的降低，得到真实地核在r 处的熔化温度约
为5400K，该熔化温度即为ICB处地核的实际温度。根据绝热压缩假设，结合
PREM模型，从ICB处的温度出发分别计算了固态内核与液态外核中的温度分布，
其中得到地心的温度约为5600K，核－慢边界地核一侧的温度约为4100K。在估算
杂质对熔化温度的影响时，本文在前人工作的基础上，提出了一个同时考虑固液
两 相 中 杂 质 含 量 对 熔 化 温 度 的 影 响 的 估 算 公 式：
＿丁”rj。＿。j＼＿、I．11、、＿＿。＿，＿。，，＿、，＿＿，
凸Tin＝二l0－叫＞：In（－L＊。＞：Ino－L川，这里，丁“是纯铁在内核边界压力
illZ“””“’““‘’“”“”‘“‘’‘’“－－
下的熔化温度，O是地核结晶时所有杂质在液态外核中的配分系数，从s是第Z
种杂质在固态内核中所占的摩尔分数，X；／是第i种杂质在液态外核中所占的摩尔
分数，ATffi是杂质导致的熔化温度的降低。
6）地核的电导率分布。既然BlochGriinisen公式被证明在地核的温度、压力条件下
及铁的固－液混合相区仍然有效，对于主要成分由。－铁组成的地核，就允许用
BlochGriinisen公式并结合地核的温度结构以及PREM模型计算整个地核（包括
液态外地核与固态内地核）的电导率分布。计算结果表明，整个地核的电导率在
4300～8400口－’cm‘之间，且随压力（深度
In this dissertation, a novel method using four electrodes perpendicular to shock front was proposed to measure the electrical conductivity of metals under shock compression up to megabar pressures. The electrical conductivities of iron under shock compression in the final equilibrium pressures ranging from 101 to 208GPa were obtained by using the two-stage light gas gun techniques. The measurements for the electrical conductivity of iron were first expanded experimentally
to pressures beyond 200 GPa, entering into the solid-liquid mixed phase region of iron. The Bloch-Griineisen equation describing the high-pressure electrical conductivity of metals was found still hold true up to 200 GPa for e-iron (hep structure), even in its solid-liquid mixed phase region. By using the Bloch-Griineisen equation, the distribution of electrical conductivity in the earth's core was calculated, based on which a new model that there exists a discontinuity in the conductivity at the Inner Core Boundary (ICB) was proposed. The main results and conclusions of this dissertation are as follows:
(1) A new method by using the four electrodes perpendicular to shock front and the drilled sapphire disk with a rectangular cell as the insulated layer was proposed, which was used in measuring the electrical conductivity of metals under strong shock compression, (a) A new configuration by enclosure the sample in the rectangular cell of the sapphire disk was used to replace the "sandwich" configuration (insulated layer / sample / insulated block) previously used by the other investigators. The shunting effect in the sandwich configuration due to the electric conducting of the epoxy resin surrounding the
sample under high pressures, which will result in a high conductivity data, was eliminated. The pressure limit in the measurements was improved, (b) Several technical problems including the machining of the cell in the sapphire disk and the assembling of the experimental set-up were solved, and the high-power pulsed constant current device was developed, (c) A special experiment was designed to exam the effect of the ohm heating on the conductivity of the sample because of the large current in the experiment measurements. Results show that this effect is negligible, (d) The pressure-history of the metal
sample during the shock reverberating processes between the two sapphire disks was calculated by using the one-dimensional fluid dynamics method which is very helpful in the data analyzing. The experimental records of the conductivity signal
profile were reasonably consistent with the above model calculations.
(2) The electrical conductivities (from 1.45 x 104 Q-1cm"1 to 7.65x 103 Q-1cm-1) for iron at the final equilibrium shock compression states from 101 to 208GPa were obtained by using the two-stage light gas gun techniques. The measurement for the electrical conductivity of iron was expanded, for the first time, to the pressure range over 200 GPa, and entered the solid-liquid mixed phase region of iron. Experimental results indicated that there existed systematically differences between our results and those of Keeler's. By analyzing we find that Keeler's conductivity data were overestimated due to the shunting effect.
(3) By analyzing the reverberation of shock wave between the front- and rear- interfaces of sample and the sapphire disks, and after taking into account of the influence of the demagnetization on the signal profile resulting from the a - s phase transition of iron, the electrical conductivity of iron was finally deduced. This provides useful techniques for the similar measurements in the future.
(4) The high-pressure conductivity relation of e -iron. Our measured data strongly supports that the Bloch- Griineisen formula describing the electrical conductivity of metals under high-pressure and high-temperature holds true up to 200GPa for iron even in the solid-liquid mixed phase region (the equilibrium temperature reaches 5220K). To exam the validity of the Bloch- Griineisen formula at megabar pressures, we
1)提出并研究了一种冲击压缩下测量金属电导率的新方法——使用刻槽单晶蓝宝石做金属样品绝缘层的四电极垂向引线法。(a)用样品嵌入带沟槽绝缘块的结构代替前人常用的“三明治”夹层(即绝缘层／样品／绝缘块)结构，解决了原样品组件构型中金属样品环氧树脂包覆层高压下导电所产生的分流效应对测量结果的影响，提高了可测量的压力上限：(b)解决了由于构型改变而引起的部件加工与组装以及实验测量中的若干技术性困难，包括研制成专用的大功率脉冲恒流源等；(c)对于新构型引起的样品增厚而提高输入电流对样品预加热的影响，本文设计了专门实验检验，并证实了这种欧姆加热可以忽略不计；(d)用一维流体力学模拟计算了冲击压缩下金属样品受压变化的时间历程，对判读和分析电导率变化的波形记录起到了指导性作用。实测结果与上述预测基本相符。
2)用二级轻气炮作为加载手段，测量了铁在终态平衡压力为101～208GPa的压力区间内的电导率，(电导率从1．45X10~4Ω~(-1)cm~(-1)变化到7．65×10~3Ω~(-1)cm~(-1)。首次将铁的电导率测量的压力范围扩展到了200GPa以上，并达到了熔化固-液混合相区。结果表明，本文的测量数据与Keeler等人测量数据之间存在系统差异，Keeler等人的数据明显偏高。分析后认为，主要是因为在Keeler的样品组装中使用的环氧树脂绝缘层在高压下导电所产生的分流效应引起的。
3)通过对铁在冲击压缩下发生α-ε相变时的退磁效应对测量信号波形影响的分析，以及对样品中的冲击波在前后蓝宝石界面上反射的分析，获得了铁的电导率数据，为今后开展这类实验测量提供了有用的技术和认识。
4)Bloch-Gr(?)neisen关系。通过对电导率测量数据的分析，发现关于金属电导率的Bloch-Gr(?)neisen公式对于铁在冲击压力高达208GPa且已进入冲击熔化固-液混合相区时仍然有效，此时的平衡温度已达5220K。为了检验Bloch-Gr(?)neisen公式
一
在兆巴压力冲击压缩下的有效性，本文取Keeler在较低压力下8相区的一个电导
率数据作为参考点，得到了81co卜Grnelsen公式关于s－铁在高温高压下电导率
。。。。。＿。。＿＿1．589exp卜刀33v“‘）x m”。。。。。。－。。。。＿＿－3／＿
的一个解析表达式：a＝一，这里，比容v的单位是cm丫g，
丁 一
温度丁的单位是 K，电导率。的单位是O－‘cm－‘。卜铁的高压电导率之所以与仅
考虑晶格散射的BlochGriineisen公式符合性好，是因为e－铁己不存在任何磁有
序结构，高温高压下Sp电子的散射主要以声子散射为主，己没有。－铁中的磁子
散射贡献，同时s－d散射亦居于次要地位。
5）地核的温度分布。本文对地核的物质成分做了详细评述，并估算了固态内地核的
杂质成分与含量。从纯铁的冲击熔化温度出发，用Lindemann定律外推到内地核
边界（ICB）条件（330GPa）下，估算出铁的熔化温度约为6200K。进一步考虑
实际地核含有杂质而导致熔化温度的降低，得到真实地核在r 处的熔化温度约
为5400K，该熔化温度即为ICB处地核的实际温度。根据绝热压缩假设，结合
PREM模型，从ICB处的温度出发分别计算了固态内核与液态外核中的温度分布，
其中得到地心的温度约为5600K，核－慢边界地核一侧的温度约为4100K。在估算
杂质对熔化温度的影响时，本文在前人工作的基础上，提出了一个同时考虑固液
两 相 中 杂 质 含 量 对 熔 化 温 度 的 影 响 的 估 算 公 式：
＿丁”rj。＿。j＼＿、I．11、、＿＿。＿，＿。，，＿、，＿＿，
凸Tin＝二l0－叫＞：In（－L＊。＞：Ino－L川，这里，丁“是纯铁在内核边界压力
illZ“””“’““‘’“”“”‘“‘’‘’“－－
下的熔化温度，O是地核结晶时所有杂质在液态外核中的配分系数，从s是第Z
种杂质在固态内核中所占的摩尔分数，X；／是第i种杂质在液态外核中所占的摩尔
分数，ATffi是杂质导致的熔化温度的降低。
6）地核的电导率分布。既然BlochGriinisen公式被证明在地核的温度、压力条件下
及铁的固－液混合相区仍然有效，对于主要成分由。－铁组成的地核，就允许用
BlochGriinisen公式并结合地核的温度结构以及PREM模型计算整个地核（包括
液态外地核与固态内地核）的电导率分布。计算结果表明，整个地核的电导率在
4300～8400口－’cm‘之间，且随压力（深度
In this dissertation, a novel method using four electrodes perpendicular to shock front was proposed to measure the electrical conductivity of metals under shock compression up to megabar pressures. The electrical conductivities of iron under shock compression in the final equilibrium pressures ranging from 101 to 208GPa were obtained by using the two-stage light gas gun techniques. The measurements for the electrical conductivity of iron were first expanded experimentally
to pressures beyond 200 GPa, entering into the solid-liquid mixed phase region of iron. The Bloch-Griineisen equation describing the high-pressure electrical conductivity of metals was found still hold true up to 200 GPa for e-iron (hep structure), even in its solid-liquid mixed phase region. By using the Bloch-Griineisen equation, the distribution of electrical conductivity in the earth's core was calculated, based on which a new model that there exists a discontinuity in the conductivity at the Inner Core Boundary (ICB) was proposed. The main results and conclusions of this dissertation are as follows:
(1) A new method by using the four electrodes perpendicular to shock front and the drilled sapphire disk with a rectangular cell as the insulated layer was proposed, which was used in measuring the electrical conductivity of metals under strong shock compression, (a) A new configuration by enclosure the sample in the rectangular cell of the sapphire disk was used to replace the "sandwich" configuration (insulated layer / sample / insulated block) previously used by the other investigators. The shunting effect in the sandwich configuration due to the electric conducting of the epoxy resin surrounding the
sample under high pressures, which will result in a high conductivity data, was eliminated. The pressure limit in the measurements was improved, (b) Several technical problems including the machining of the cell in the sapphire disk and the assembling of the experimental set-up were solved, and the high-power pulsed constant current device was developed, (c) A special experiment was designed to exam the effect of the ohm heating on the conductivity of the sample because of the large current in the experiment measurements. Results show that this effect is negligible, (d) The pressure-history of the metal
sample during the shock reverberating processes between the two sapphire disks was calculated by using the one-dimensional fluid dynamics method which is very helpful in the data analyzing. The experimental records of the conductivity signal
profile were reasonably consistent with the above model calculations.
(2) The electrical conductivities (from 1.45 x 104 Q-1cm"1 to 7.65x 103 Q-1cm-1) for iron at the final equilibrium shock compression states from 101 to 208GPa were obtained by using the two-stage light gas gun techniques. The measurement for the electrical conductivity of iron was expanded, for the first time, to the pressure range over 200 GPa, and entered the solid-liquid mixed phase region of iron. Experimental results indicated that there existed systematically differences between our results and those of Keeler's. By analyzing we find that Keeler's conductivity data were overestimated due to the shunting effect.
(3) By analyzing the reverberation of shock wave between the front- and rear- interfaces of sample and the sapphire disks, and after taking into account of the influence of the demagnetization on the signal profile resulting from the a - s phase transition of iron, the electrical conductivity of iron was finally deduced. This provides useful techniques for the similar measurements in the future.
(4) The high-pressure conductivity relation of e -iron. Our measured data strongly supports that the Bloch- Griineisen formula describing the electrical conductivity of metals under high-pressure and high-temperature holds true up to 200GPa for iron even in the solid-liquid mixed phase region (the equilibrium temperature reaches 5220K). To exam the validity of the Bloch- Griineisen formula at megabar pressures, we
引文
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陈大年等，1987．爆炸与冲击，7(1)：27．
董玉斌等，1988．动态断裂过程的数值分析及LY-12铝的层裂．高压物理学报，2(4)：305-312．
李西军，2000．铁高压熔化线研究．中国工程物理研究院博士学位论文．
戴诚达，1999．铁陨石的冲击熔化特性与地核的热结构。中国工程物理研究院博士学位论文．
徐锡申，张万箱等著，1986．实用物态方程理论导引．北京；科学出版社．
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