高压下二元富氢超导体的实验研究进展

郭鉴宁; 王煜龙; 朱程程; 黄晓丽; 崔田

doi:10.11858/gywlxb.20230742

高压下二元富氢超导体的实验研究进展

doi: 10.11858/gywlxb.20230742

郭鉴宁^1,,
王煜龙¹,
朱程程¹,
黄晓丽^1,*, ,,
崔田^{1, 2}

1.
吉林大学物理学院, 吉林长春　130012
2.
宁波大学物理科学与技术学院, 浙江宁波　315211

基金项目: 国家自然科学基金（11974133，52072188）；国家重点研发计划（2022YFA1405500）；长江学者和高校创新研究团队计划（IRT_15R23）；浙江省科技创新团队（2021R01004）

详细信息

作者简介:
郭鉴宁（1998－），男，博士研究生，主要从事高压下富氢化物超导材料的实验研究. E-mail：guojn22@mails.jlu.edu.cn

通讯作者:
黄晓丽（1986－），女，博士，教授，主要从事高压下富氢化物超导材料的实验研究.E-mail：huangxiaoli@jlu.edu.cn

中图分类号: O521.2
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出版历程
- 收稿日期: 2023-09-27
- 修回日期: 2024-01-17
- 录用日期: 2024-01-17
- 网络出版日期: 2024-04-11
- 刊出日期: 2024-04-09

Progress of Experimental Research on Binary Hydride Superconductors under High Pressure

1.
College of Physics, Jilin University, Changchun 130012, Jilin, China
2.
School of Physical Science and Technology, Ningbo University, Ningbo 315211, Zhejiang, China

摘要

摘要: 自从1911年著名物理学家Onnes发现超导电性以来，人们不断努力提高超导转变温度，室温超导体是人类追逐的百年梦想。在近百年的研究历程中，铜基超导体、铁基超导体及麦克米兰极限MgB₂超导体的发现不断刷新了人们对超导领域的认知，也增强了人们进一步提高超导转变温度和挖掘高温超导机制的信心。最近，理论预测并被实验验证的新型富氢化合物显示了高温乃至室温超导电性的巨大潜力，成为室温超导体的最佳候选体系之一。值得注意的是，高压下硫氢化物和镧氢化物均具有超过200 K的超导转变温度，引领了富氢化合物的研究热潮，涌现了一些重要的理论和实验成果。本文聚焦于目前富氢化合物超导体的实验研究进展，从不同氢结构单元及氢成键特征的角度总结和归纳新型富氢化合物的晶体结构性质及超导性能。主要介绍了5种在实验上成功获得的富氢化合物超导体：间隙型、离子型、共价型、笼型及分子型。通过对比分析不同类型的富氢化合物超导体，总结出一些影响超导转变温度的普适规律，并提出目前实验上亟待解决的问题和未来主攻的实验方向。
- 高压超导 /
- 富氢化合物 /
- 金刚石对顶砧 /
- 共价型氢化物 /
- 笼型氢化物 /
- 分子型氢化物
Abstract: Since the discovery of superconductivity by the famous physicist Onnes in 1911, people have constantly tried to improve the superconducting transition temperature, and the room-temperature superconductors have also been a century-old dream of human beings. In the course of nearly a hundred years of research, it has constantly updated people’s understanding of superconductivity, enhanced people’s confidence in further improving the superconducting transition temperature and exploring the mechanism of high temperature superconductivity that scientists have discovered copper based superconductors, iron based superconductors and McMillan limit superconductors (like MgB₂). Recently, new hydrogen-rich compounds predicted theoretically and verified experimentally have shown great potential for high temperature superconductivity even room temperature superconductivity, becoming one of the best candidates for room temperature superconductors. It is worth noting that some sulfur hydrides and lanthanum hydrides have superconductivity of more than 200 K under high pressure, leading a research boom of hydrogen-rich compounds and some important theoretical and experimental results have emerged. This paper focuses on the current research progress of hydrogen-rich superconductors, summarizes the crystal structure properties and superconducting properties of new hydrogen-rich compounds from the perspective of different hydrogen structural units and hydrogen bonding characteristics. Five kinds of superconductors in hydrogen-rich compounds are introduced in this paper: interstitial type, ionic type, covalent type, cage type and molecular type, and some general rules affecting the superconducting transition temperature are summarized through comparative analysis of different types of hydrogen-rich compound superconductors. In the end, the current experimental problems to be solved and the future experimental direction are put forward.
- high-pressure superconductivity /
- hydrogen-rich compound /
- diamond anvil cell /
- covalent hydride /
- clathrate hydride /
- molecular hydride

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目前，钻爆法广泛应用于地下工程建设中，在实现经济、便捷、高效施工的同时，其产生的爆破地震效应也是公认的爆破“公害”之首^[1-2]。为保证爆破施工邻近建（构）筑物的安全正常运行，研究爆破地震波的传播规律具有重要的工程应用价值。

对于爆破地震波的传播规律，学者们已开展了大量研究工作。胡国忠^[3]运用地震波理论对监测资料进行分析，研究了地下工程爆破开挖时地面爆破的振动特性。王玉杰等^[4]研究了完整花岗岩体中爆破地震波的传播规律。董永香等^[5]通过实验和数值模拟方法，分析了不同组成的多层介质对应力波传播特性的影响。Smerzini等^[6]研究了平面和柱面水平剪切（shear horizontal，SH）波入射地下结构的动力响应特性及其对地面位移的影响。王猛等^[7]通过爆炸力学理论和数值计算方法，研究了炸药在土岩介质中爆炸的动力响应规律。王超等^[8]基于模拟、实测数据验证和量纲分析方法，研究了不同埋深隧道爆破地震波在邻近地表一定范围内的反射叠加规律和地表振动速度衰减规律。张震等^[9]、高文学等^[10]、汪平等^[11]通过数值模拟与现场监测相结合的方法，研究了浅埋隧道爆破振动的传播规律。陈学军等^[12]运用萨道夫斯基修正公式对采集的数据进行研究，探讨了不同情况下爆破振动强度的衰变规律以及振动对岩溶塌陷的影响。Jayasinghe等^[13]根据现场试验，分析了应力波在土壤和岩石中以及土壤与岩石之间的界面上的传播规律。朱斌等^[14]进行了下穿预埋燃气管道的现场爆破试验，通过应变及爆破应力波理论分析了爆破过程中爆破地震波的传播特点。高启栋等^[15]通过理论和数值模拟，对考虑爆源特征的岩石爆破诱发地震波的波形进行了研究。王秉相等^[16]使用PFC3D软件研究了应力波在散体颗粒中的传播规律和影响因素。王桂林等^[17]以重庆市某管廊甲烷爆炸案例为背景，研究了爆炸作用下地面压强与位移的响应特性。

总体来看，现今关于爆破地震波在一般地层传播规律的研究主要集中在现场监测及数值模拟方面，以现今的技术手段测定土层和岩石内部场分布仍然比较困难。考虑到研究平面SH波在一般地层的传播规律具有重要意义，本研究试图建立地面振动与土层内部振动的关系，选取爆破地震波中的平面SH波作为研究对象，基于弹性波动理论，建立半空间上层状地层的刚度矩阵及动力平衡方程组，分析土层与基岩的阻抗比、土层厚度、入射波频率和入射波角度对地表速度与土岩地层界面速度的比值的影响，以期为后续类似工程提供参考。

1. SH波入射作用下上土下岩的动力刚度矩阵建立

1.1 SH波入射作用下单层土的动力刚度矩阵

如图1所示，根据弹性波动理论，SH入射波的位移函数可写为

图 1 层状地层的局部坐标系

Figure 1. Local coordinate system for a stratified stratum

下载: 全尺寸图片幻灯片

${w^{( {\rm{i}} )}}\left( {\textit{z},x} \right) = A\exp \left[ {{\rm{i}}{k'}\left( {\textit{z}\sin \psi - x\cos \psi } \right)+{\rm{i}}\omega t} \right]$

(1)

反射SH波的位移函数可以表示为

${w^{( {\rm{f}} )}}\left( {\textit{z},x} \right) = B\exp \left[ {{\rm{i}}{k'}\left( { - \textit{z}\sin \psi - x\cos \psi } \right)+{\rm{i}}\omega t} \right]$

(2)

式中：A、B分别为入射波和反射波的幅值； ${\text{ }}{k'}$ 为波数， ${\text{ }}{k'} = \omega /{c{\rm_s}}$ ， ${\text{ }}{c{\rm_s}}$ 为波速，ω为频率；ψ为入射波传播方向与x轴的夹角，即入射角；上标“(i)”表示入射，“(f)”表示反射。

为了便于建立一般性位移场，引入 ${m_x} = \cos \psi ,{\text{ }}c = {c{\rm_s}}/{m_x},{\text{ }}\zeta = \sqrt {1/m_x^2 - 1}$ ，k=ω/c， $\omega = 2\text{π} f$ ，f为入射波频率。

根据文献[18]中构造的土层和基岩的动力刚度矩阵，土层内总位移场的表达式为

$\begin{aligned} w( {\textit{z},x} ) = \; &{w^{({\rm{i}} )}}( {\textit{z},x} )+{w^{( {\rm{f}} )}}( {\textit{z},x} ) = \left[ {A\exp \left( {{\rm{i}}\omega \frac{{\sqrt {1 - m_x^2} }}{{{c{\rm{_s}}}}}\textit{z}} \right)+B\exp \left( { - {\rm{i}}\omega \frac{{\sqrt {1 - m_x^2} }}{{{c{\rm{_s}}}}}\textit{z}} \right)} \right]\exp \left( { - {\rm{i}}\omega \frac{{{m_x}}}{{{c{\rm{_s}}}}}x+{\rm{i}}\omega t} \right) \\ {\text{ = }} & \left[ {A\exp \left( {{\rm i}k\zeta {\textit{z}}} \right)+B\exp \left( { - {\rm{i}}k\zeta \textit{z}} \right)} \right]\exp \left( { - {\rm{i}}kx+{\rm{i}}\omega t} \right){\text{ = }}u( \textit{z} )\exp \left( { - {\rm{i}}kx+{\rm{i}}\omega t} \right) \\ \end{aligned}$

(3)

由广义胡克定律可得

${\tau _{y\textit{z}}}( {\textit{z},x} ) = {{\rm{i}}}k\zeta G\left[ {A\exp \left( {{{\rm{i}}}k\zeta \textit{z}} \right) - B\exp \left( { - {{\rm{i}}}k\zeta \textit{z}} \right)} \right]\exp \left( { - {{\rm{i}}}kx+{{\rm{i}}}\omega t} \right)$

(4)

式中： ${\tau _{y\textit{z}}}\left( {\textit{z},x} \right)$ 为点(z, x)处的剪应力，G为土层的剪切模量。

土层顶面和底面的位移和应力幅值为

$\left(\begin{gathered} {w_1} \\ {\tau _{y\textit{z}1}} \end{gathered} \right) = \left(\begin{array}{*{2}{c}} 1 & 1 \\ {{\rm{i}}k\zeta G} & { -{\rm{i}}k\zeta G} \end{array}\right) \left(\begin{gathered} A \\ B \end{gathered} \right)$

(5)

$\left(\begin{gathered} {w_2} \\ {\tau _{y\textit{z}2}} \end{gathered} \right) = \left(\begin{array}{*{2}{c}} {\exp ({\rm{i}}k\zeta d)} & {\exp ({\rm{-i}}k\zeta d)} \\ {{\rm{i}}k\zeta G\exp ({\rm{i}}k\zeta d)} & -{\rm{i}}k\zeta G\exp ({\rm{-i}}k\zeta d) \end{array}\right) \left(\begin{gathered} A \\ B \end{gathered} \right)$

(6)

式中：下标1和2分别表示顶面和底面。

联立式(5)和式(6)即可得到顶底面的转换矩阵

$\left(\begin{gathered} {w_2} \\ {\tau _{y\textit{z}2}} \\ \end{gathered} \right) = \left(\begin{array}{*{2}{c}} {\cos \left({k\zeta d}\right) } & {\dfrac{1}{{k\zeta G}}\sin \left({ - k\zeta d}\right) } \\ { - k\zeta G\sin \left({k\zeta d}\right) } & {\cos \left( {k\zeta d} \right)} \end{array}\right) \left(\begin{gathered} {w_1} \\ {\tau _{y\textit{z}1}} \end{gathered} \right)$

(7)

令 ${Q_1} = - {\tau _{y\textit{z}1}}$ ， ${Q_2} = {\tau _{y\textit{z}2}}$ ， ${Q_1}$ 、 ${Q_2}$ 分别为土层上、下界面外荷载幅值，可得到该土层的动力刚度矩阵

$\left( \begin{gathered} {Q_1} \\ {Q_2} \\ \end{gathered} \right) = \frac{{k\zeta G}}{{\sin \left( {k\zeta d} \right)}} \left( \begin{array}{*{2}{c}} {\cos \left( k\zeta d \right)}&{ - 1} \\ { - 1}&{\cos \left( {k\zeta d} \right)} \end{array} \right) \left( \begin{gathered} {w_1} \\ {w_2} \\ \end{gathered} \right)$

(8)

1.2 SH波入射作用下半空间上的层状地层的动力刚度矩阵

地层往往具有上土下岩的特点，并且土层常为多层层状分布，为了进一步推广适用范围，建立了更具一般性的层状地层的动力刚度矩阵。假设n–1层土层（每层的材料参数为常数）置于基岩上（用N表示）。从土层表面至基岩顶，对各地层界面依次编号，如图2所示。

图 2 半无限基岩上层状地层示意图

Figure 2. Schematic diagram of stratified strata on semi-infinite bedrocks

下载: 全尺寸图片幻灯片

根据式(3)，第n层土层的上、下界面位移幅值可表示为

$\left( \begin{gathered} {w_{n - 1}} \\ {w_n} \\ \end{gathered} \right){\text{ = }}\left( {\begin{array}{*{20}{c}} 1&1 \\ {\exp \left( {{\text{i}}k{\zeta _n}{d_n}} \right)}&{\exp \left( {{\text{i}}k{\zeta _n}{d_n}} \right)} \end{array}} \right)\left( \begin{gathered} {A_n} \\ {B_n} \\ \end{gathered} \right)$

(9)

根据式(4)，第n层土层的上、下界面应力幅值为

$\left( \begin{gathered} {\tau _{n - 1}} \\ {\tau _n} \\ \end{gathered} \right){\text{ = }}\left( {\begin{array}{*{20}{c}} {{\text{i}}k{\zeta _n}{G_n}}&{ - {\text{i}}k{\zeta _n}{G_n}} \\ {{\text{i}}k{\zeta _n}{G_n}\exp \left( {{\text{i}}k{\zeta _n}{d_n}} \right)}&{ - {\text{i}}k{\zeta _n}{G_n}\exp \left( {{\text{i}}k{\zeta _n}{d_n}} \right)} \end{array}} \right)\left( \begin{gathered} {A_n} \\ {B_n} \\ \end{gathered} \right)$

(10)

令 ${Q_1} = - {\tau _{n - 1}}$ ， ${Q_2} = {\tau _n}$ ，由式(8)可知第n层上、下界面的力-位移关系为

$\left( \begin{gathered} {Q_{n - 1}} \\ {Q_n} \\ \end{gathered} \right){\text{ = }}\frac{{k{\zeta _n}{G_n}}}{{\sin \left( {k{\zeta _n}{d_n}} \right)}}\left( {\begin{array}{*{20}{c}} {\cos \left( {k{\zeta _n}{d_n}} \right)}&{ - 1} \\ { - 1}&{\cos \left( {k{\zeta _n}{d_n}} \right)} \end{array}} \right)\left( \begin{gathered} {w_{n - 1}} \\ {w_n} \\ \end{gathered} \right)$

(11)

土层n的刚度矩阵可写为

${{\boldsymbol K}_n^{\text{e}}} {\text{ = }}\frac{{k{\zeta _n}{G_n}}}{{\sin \left( {k{\zeta _n}{d_n}} \right)}}\left( {\begin{array}{*{20}{c}} {\cos \left( {k{\zeta _n}{d_n}} \right)}&{ - 1} \\ { - 1}&{\cos \left( {k{\zeta _n}{d_n}} \right)} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {k{\zeta _n}{G_n}\cot \left( {k{\zeta _n}{d_n}} \right)}&{ - k{\zeta _n}{G_n}\csc \left( {k{\zeta _n}{d_n}} \right)} \\ { - k{\zeta _n}{G_n}\csc \left( {k{\zeta _n}{d_n}} \right)}&{k{\zeta _n}{G_n}\cot \left( {k{\zeta _n}{d_n}} \right)} \end{array}} \right)$

(12)

在半无限基岩上表面施加荷载，只会产生去波（辐射条件），在式(4)中令A=0， ${Q_0} = - {\tau _{yz1}}$ （下标0代表半空间自由表面），消去B后得到

${Q_0} = {\rm i}k{\zeta ^{\rm R}}{G^{\rm R}}{w^{\rm R}}$

(13)

对于无阻尼体系，半空间的动力刚度系数为 ${{ K}^{\rm R}} = {\rm i}k{\zeta ^{\rm R}}{G^{\rm R}}$ 。

整体刚度矩阵组装：将各层土单元刚度矩阵 ${{\boldsymbol K}_n^{\text{e}}}$ 的子块按照该层顶底界面对号入座置于总刚度矩阵的相应位置，从而直接形成总刚度矩阵K，如图3所示。

图 3 总刚度矩阵组装过程

Figure 3. Assembly process of total stiffness matrix

下载: 全尺寸图片幻灯片

${{\boldsymbol K} = k{\zeta _1}{G_1}\left[ {\begin{array}{*{20}{c}} D_1&-Y_1&{}&{}&{}&{}&{} \\ -Y_1&{D_1+{p_2}D_2}&{ - {p_2}Y_2}&{}&{}&{}&{} \\ {}&{ - {p_2}Y_2}&{{p_2}D_2+{p_3}D_3}&{}&{}&{}&{} \\ {}&{}&{}& \ddots &{}&{}&{} \\ {}&{}&{}&{}&{{p_{N - 2}}D_{N-2}+{p_{N - 1}}D_{N-1}}&{ - {p_{N - 1}}Y_{N-1}}&{} \\ {}&{}&{}&{}&{ - {p_{N - 1}}Y_{N-1}}&{{p_{N - 1}}D_{N-1}+{p_N}D_N}&{ - {p_N}Y_N} \\ {}&{}&{}&{}&{}&{ - {p_N}Y_N}&{{p_N}D_N+{p_{\rm R}}} \end{array}} \right] }$

(14)

式中： ${p_n} = \dfrac{{{\zeta _n}{G_n}}}{{{\zeta _1}{G_1}}}$ ， ${p_{\rm R}} = \dfrac{{{\zeta ^{\rm R}}{G^{\rm R}}}}{{{\zeta _1}{G_1}}}$ ， $D_i={\cot (k{\zeta _i}{d_i})}$ ， $Y_i={\csc (k{\zeta _i}{d_i})}$ ， ${Q_n}$ 为土层界面外荷载幅值。

令 ${\boldsymbol{W}} = {\left[ {{w_0}},{{w_1}},{{w_2}}, \cdots, {{w_{N - 2}}},{{w_{N - 1}}},{{w_N}} \right]^{\rm T}}$ ， $\boldsymbol Q = \left[ {{Q_0}},{{Q_1}},{{Q_2}}, \cdots, {{Q_{N - 2}}},{{Q_{N - 1}}},{{Q_N}} \right]^{\rm T}$ ，则层状地层的动力平衡方程可写为

${\boldsymbol{KW = Q}}$

(15)

2. 上土下岩地层的波传播规律分析

2.1 SH波入射作用下上土下岩地层的动力刚度矩阵

上土下岩地层简化为无限基岩上覆盖一层厚度为d的土层，如图4所示。

图 4 上土下岩地层示意图

Figure 4. Schematic diagram of the upper soil and lower rock stratigraphy

下载: 全尺寸图片幻灯片

通过式(15)可得该模型的动力刚度矩阵

$\left( {\begin{array}{*{20}{c}} {\cos \left( {k\zeta d} \right)}&{ - 1} \\ { - 1}&{\cos \left( {k\zeta d} \right)+{\text{i}}p\sin \left( {k\zeta d} \right)} \end{array}} \right)\left( \begin{gathered} {w_1} \\ {w_2} \\ \end{gathered} \right){\text{ = }}\left( \begin{gathered} 0 \\ {Q_2} \\ \end{gathered} \right)$

(16)

式中： $p{\text{ = }}{\zeta ^{\rm R}}{G^{\rm R}}{\text{/}}(\zeta G)$ ， ${Q_2} = {\rm i}k{\zeta ^{\rm R}}{G^{\rm R}}{w^{\rm R}}$ ， ${\zeta ^{\rm R}}$ 和 ${G^{\rm R}}$ 为基岩的物理力学参数。

$\frac{{{w_1}}}{{{w^{\rm R}}}} = \frac{1}{{\cos \left( {k\zeta d} \right)+\dfrac{\rm i}{p}\sin \left( {k\zeta d} \right)}}$

(17)

$\frac{{{w_2}}}{{{w^{\rm R}}}} = \frac{1}{{1+\dfrac{\rm i}{p}\tan \left( {k\zeta d} \right)}}$

(18)

进一步得到地表速度与土岩地层界面位移的比值

$\left| {\frac{{{w_1}}}{{{w^{\rm R}}}}} \right| = \frac{1}{{\sqrt {{{\cos }^2}\left( {k\zeta d} \right)+\dfrac{{{{\sin }^2}\left( {k\zeta d} \right)}}{{{p^2}}}} }}$

(19)

$\left| {\frac{{{w_2}}}{{{w^{\rm R}}}}} \right| = \frac{1}{{\sqrt {1+\dfrac{{{{\tan }^2}\left( {k\zeta d} \right)}}{{{p^2}}}} }}$

(20)

由式(19)和式(20)得到

$\left| {\frac{{{w_1}}}{{{w_2}}}} \right| = \frac{{\sqrt {{p^2}+{{\tan }^2}\left( {k\zeta d} \right)} }}{{\sqrt {{p^2}{{\cos }^2}\left( {k\zeta d} \right)+{{\sin }^2}\left( {k\zeta d} \right)} }}$

(21)

将位移场公式（式(3)）对时间求导，可以得到地表速度与土岩地层界面速度的比值 $\left| {{u_1}{\text{/}}{u_2}} \right|$ = $\left| {{w_1}{\text{/}}{w_2}} \right|$ 。

2.2 参数分析

2.2.1 阻抗比和入射角对 $\left| {{u_1}{\text{/}}{u_2}} \right|$ 的影响

波阻抗是抗拒应力波通过的能力，也是应力波扫越一定介质的能力。为了开展更具一般性的讨论，选取入射波频率f为0～200 Hz^[19]，定义土层与基岩的阻抗比 $Z = {(\rho c)_{\rm s}}/{(\rho c)_{\rm R}}$ ，Z分别为0.10、0.50、0.70、0.90的情况下，入射角ψ为30°、45°、60°、90°时，绘制 $\left| {{u_1}{\text{/}}{u_2}} \right|$ -f曲线，如图5所示。

图 5 不同阻抗条件下入射角对

${\text{|}}{u_1}{\text{/}}{u_2}{\text{|}}$ -f曲线的影响

Figure 5. Influence of incident angles on the

${\text{|}}{u_1}{\text{/}}{u_2}{\text{|}}$ -f curves under different impedances

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由图5(a)可知：当Z比较小时， ${\text{|}}{u_1}{\text{/}}{u_2}{\text{|}}$ 的峰值随着频率的增加缓慢减小，约60 Hz时峰值由大于1向小于1转变，并且SH波的入射角对峰值几乎没有影响。由图5(a)～图5(d)可知，随着Z的增大，不同入射角下SH波对应的峰值开始慢慢地向高频分散开来，并且入射角较小的SH波向高频方向移动的速度大于入射角较大的SH波。这说明波阻抗较大的土层在高频波作用下的动力响应更加剧烈，并且速度对入射角的敏感性比峰值更强。

2.2.2 不同土层厚度下入射角对 $\left| {{u_1}{\text{/}}{u_2}} \right|$ 的影响

当土层与基层的阻抗比Z=0.19，入射波频率f为0～200 Hz，上覆土层厚度d为2、5、10、20 m，入射角为30°、45°、60°、90°时， $\left| {{u_1}} /{{u_2}} \right|$ -f曲线如图6所示。

图 6 Z=0.19时不同厚度土层下入射角对

${\text{|}}{u_1}{\text{/}}{u_2}{\text{|}}$ -f 曲线的影响

Figure 6. Effects of incident angle on the

${\text{|}}{u_1}{\text{/}}{u_2}{\text{|}}$ -f curves under different thicknesses of soil layers when Z=0.19

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对比图6(a)～图6(d)可以看出：当覆盖土层厚度不同时， $\left| {{u_1}{\text{/}}{u_2}} \right|$ 的峰值均随着入射波频率f的增大而减小，并逐渐趋于零，入射角对 $\left| {{u_1}{\text{/}}{u_2}} \right|$ 峰值的影响较小；随着覆盖土层厚度的增加，高频波对应的 $\left| {{u_1}{\text{/}}{u_2}} \right|$ 峰值逐渐向低频方向移动，随着低频波对 $\left| {{u_1}} / {{u_2}} \right|$ 峰值影响的增强，高频波的影响越来越弱。这说明覆盖的土层越厚，土层的固有频率响应峰值个数越多，且峰值越向低频集中，高频波对 $\left| {{u_1}} / {{u_2}} \right|$ 的影响程度越弱。

当土层与基层的阻抗比Z=0.70，入射波频率f为0～200 Hz，上覆土层厚度d为2、5、10、20 m，入射角为30°、45°、60°、90°时， $\left| {{u_1}} / {{u_2}} \right|$ -f曲线如图7所示。从图7可以看出：当土层厚度较小时，土层的固有频率由高频波控制，但是随着土层厚度的增加，高频固有频率对应的峰值逐渐向低频区移动，即低频固有频率对 $\left| {{u_1}{\text{/}}{u_2}} \right|$ 的影响越来越大。从波的入射角来看，当土层厚度较小时，图7(a)中4个峰值频率为130.6、144.6、163.9、196.3 Hz，不同入射角对应的 $\left| {{u_1}{\text{/}}{u_2}} \right|$ 的最大峰值频率分布范围较大，且主要处于较高的频率；随着土层厚度的增加，如图7(d)所示，4个峰值频率为12.7、12.7、16.4、19.6 Hz，不同入射角对应的 $\left| {{u_1}{\text{/}}{u_2}} \right|$ 的最大峰值频率分布范围变窄，即入射波角度的影响程度慢慢减弱。这说明：当土层与基岩的阻抗比Z较大且土层厚度较薄时，高频波和入射角对 $\left| {{u_1}{\text{/}}{u_2}} \right|$ 的影响较大；随着覆盖土层厚度的增加，不同入射角下的土层固有频率响应峰值向低频移动且相互靠近，即高频波和入射角对 $\left| {{u_1}} / {{u_2}} \right|$ 的影响程度逐渐减弱。

图 7 Z=0.70时不同厚度土层下入射角对

${\text{|}}{u_1}{\text{/}}{u_2}{\text{|}}$ -f 曲线的影响

Figure 7. Effects of incident angle on the

$\left| {{u_1}{\text{/}}{u_2}} \right|$ -f curves under different thicknesses of soil layers when Z=0.70

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3. 结　论

选取平面SH爆破地震波，基于波动理论及单层土，建立了一般状况下层状土-基岩地层的刚度矩阵和动力平衡方程组。整体而言，地表速度与土岩地层界面速度的比值 ${\text{|}}{u_1}{\text{/}}{u_2}{\text{|}}$ 的各个峰值随着入射波频率的增加而减小，且第2个峰值明显小于第1个峰值，说明实际工程中需要重点关注 ${\text{|}}{u_1}{\text{/}}{u_2}{\text{|}}$ 的第1个峰值对应的频率，即土层的一阶卓越频率。随着土层阻抗的增大，高频部分的响应越来越强烈，受入射角的影响也越来越弱。当土层较薄时， ${\text{|}}{u_1}{\text{/}}{u_2}{\text{|}}$ 的高频部分的响应比较明显，但是随着土层厚度的增加，高频部分的响应越来越弱，说明土层的高频滤波作用随着厚度的增加而增强。

图 1 典型超导体发表时间和超导转变温度^{[1, 2, 8, 12, 18–20]}

Figure 1. Emergence time and corresponding critical superconducting temperature of typical superconductors^{[1, 2, 8, 12, 18–20]}

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图 2 DAC结构示意图^[21]

Figure 2. Schematic diagram of DAC^[21]

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图 3 高压电学实验中4个电极的制备流程

Figure 3. Preparation process for four electrodesunder high-pressure

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图 4 迈斯纳效应

Figure 4. Meissner effect

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图 5 (a) 125 GPa下的SiH₄样品腔，(b) 125、192 GPa下SiH₄的电阻-温度曲线，(c) SiH₄的超导转变温度随压力的变化关系^[48]

Figure 5. (a) SiH₄ sample chamber at 125 GPa; (b) resistance-temperature curves of SiH₄ at 125 and 192 GPa;(c) dependence of critical temperature with pressure for SiH₄^[48]

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图 6 (a) 恒压退火过程中电阻与温度的关系，(b) 高压下硫化氢和硫化氘电阻与温度的关系，(c) H₃S的超导转变温度随压力的变化^[8]

Figure 6. (a) Dependence of resistance to temperature in constant pressure annealing process; (b) critical temperature of sulfur hydride and sulfur deuteride at high pressure; (c) dependence of superconducting temperature with pressure for H₃S^[8]

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图 7 不同压力下H₃S的磁化率信号^[9]

Figure 7. Susceptibility at several pressure for H₃S^[9]

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图 8 (a) 40 GPa下Zr-H样品的电阻-温度变化曲线（插图为激光加热后的样品腔），(b) 40 GPa下超导转变温度随外加磁场的变化，（c）～（d）分别用WHH与GL方程外推拟合上临界磁场^[69]

Figure 8. (a) R-T curve for Zr-H sample at 40 GPa (The sample chamber is presented in inset); (b) superconductingtemperature under applied magnetic fields at 40 GPa; (c)–(d) upper critical magnetic fieldswhich extrapolated by GL and WHH equations, respectively^[69]

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图 9 (a)立方相LaH₁₀的氢笼结构^[78]，(b) Somayazulu等^[73]合成的LaH₁₀的电阻随温度的变化，(c) Drozdov等^[12]合成的LaH₁₀的电阻随压力的变化，(d) Huang等^[76]外加磁场作用下LaH₁₀的转变温度

Figure 9. (a) Clathrate structure of LaH₁₀^[78]; (b) the superconducting critical temperature of LaH₁₀ reported by Somayazulu et al.^[73];(c) the dependence of T_c with pressure for LaH₁₀ synthesized by Drozdov et al.^[12]; (d) the critical temperature forLaH₁₀ under applied magnetic fields reported by Huang et al.^[76]

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图 10 Fm $\overline{3}$ m-CeH₁₀(a)和P6₃/mmc-CeH₉(b) 的结构，CeH₁₀在0～4 T外加磁场下的电阻随压力的变化(c)^[13]

Figure 10. Structures of Fm $\overline{3}$ m-CeH₁₀(a) and P6₃/mmc-CeH₉(b); the dependence of resistance under 0−4 T with pressure for CeH₁₀(c)^[13]

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图 11 (a) Ma等^[16]测得CaH₆的电阻随温度的变化，(b) Li等^[87]测得的CaH₆电阻随温度的变化

Figure 11. (a) Dependence of resistance with temperature for CaH₆ synthesized by Ma et al.^[16]; (b) R-T curve of CaH₆ reported by Li et al.^[87]

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图 12 (a) BaH₁₂的结构示意图，(b) BaH₁₂的电阻随温度的变化^[88]

Figure 12. (a) Structure of BaH₁₂; (b) R-T curve of BaH₁₂^[88]

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图 13 一些典型超导氢化物的超导转变宽度随磁场的变化

Figure 13. Dependence of superconducting width of typical hydrides with magnetic field

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表 1 不同课题组关于H₃S体系的超导电性研究^{[8–9, 54, 57–59]}

Table 1. Superconductivity of H₃S reported by several groups^{[8–9, 54, 57–59]}

Groups	Sample synthesis	T_c/K	Corresponding pressure/GPa	Structure of superconducting phases
Drozdov et al.^[8]	Loading H₂S gas at low temperature	203	155	Undetermined
Huang et al.^[9]	Loading H₂S gas at low temperature	183	149	Calculation: Im $\overline{3}$ m-H₃S
Einaga et al.^[55]	Loading H₂S gas at low temperature	200	150	XRD: Im $\overline{3}$ m-H₃S
Goncharov et al.^[57]	Laser heated pure S and hydrogen	Unmeasured	Unmeasured	XRD: Cccm-H₃S@50 GPa， R3m-H₃S@70 GPa， Im $\overline{3}$ m-H₃S@140 GPa
Capitani et al.^[58]	Loading H₂S gas at low temperature	200	150	Undetermined
Troyan et al.^[59]	Loading H₂S gas at low temperature	140	153	Undetermined

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表 2 实验合成的典型笼型氢化物超导体^{[12–17, 72–73]}

Table 2. Typical clathrate hydride superconductors synthesized in experiment^{[12–17, 72–73]}

Sample	Space group	Pressure/GPa	T_c/K	Mensurement method
LaH₁₀	Fm $\overline{3}$ m	170	250	XRD
ThH₁₀	Fm $\overline{3}$ m	170	161	XRD
YH₆	Im $\overline{3}$ m	183	220	XRD
YH₉	P6₃/mmc	201	243	XRD
CeH₉	P6₃/mmc	130	100	XRD
CeH₁₀	Fm $\overline{3}$ m	95	115	XRD
CaH₆	Im $\overline{3}$ m	172	215	XRD

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表 3 钇超氢化物合成条件及超导转变温度

Table 3. Superconducting critical temperature of yttrium superhydrides

Samples	Ref.	Space groups	Pressures/ GPa	T_c/K	Reactants	Synthetic methods
YH₆	Troyan et al.^[14]	Im $\overline{3}$ m	166	224	Y+NH₃BH₃	Laser heated to 2400 K at high pressure
	Kong et al.^[15]	Im $\overline {3}$ m	237	208.5	YH₃+H₂	Kept the sample for three weeks under high pressure
			183	220	Y+H₂	Laser heated to 1500 K at high pressure
			159	220	YH₃+H₂	Increased the sample to 201 GPa for one month and laser heated the sample to 2000 K
YH₉	Snider et al.^[72]	P6₃/mmc	182±8	262	Y+H₂	Pressured the Y metal wrapped by Pd film and hydrogen to over 130 GPa and laser heated the sample to 1800 K
	Kong et al.^[15]	P6₃/mmc	237	227	YH₃+H₂	Maintained the sample for three weeks
			237	237	YH₃+H₂	Maintained the sample for three weeks and laser heated sample to 700 K
			201	243	YH₃+H₂	Maintained the sample for one month and laser heated sample to 2000 K
YH₄	Shao et al.^[81]	I4/mmm	155	88	YH₂+NH₃BH₃	Increased the pressure to about 150 GPa and laser heated sample to 1500 K

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表 4 理论预测的近室温或超室温二元、三元富氢化合物超导体

Table 4. Theoretical prediction of binary and ternary polyhydrides with high-temperature superconductivity

Type	Samples	Space groups	Pressure/ GPa	T_c/K	Features
Binary hydride superconductors	AcH₁₀^[97]	R $\overline{3}$ m	200	204–251	Both are predicted to be phonon-mediated superconductors with an almost empty layer of d atoms
	AcH₁₆^[97]	P $\overline{6}$ m2	150	199–241
	TbH₉^[98]	C2/c	230	220	With a typical hydrogen cage structure, the coupling of electrons and hydrogen phonons in the Tb-4f layer plays a key role in superconductivity
	TbH₁₀^[98]	R $\overline{3}$ m	270	270
	TbH₁₀^[98]	Fm $\overline{3}$ m	230	270
	ZrH₁₀^[96]	P63/mmc	250	220	Lamellar alkene H₁₀ junction
	H₃S_0.925P_0.075^[99]	Fm $\overline{3}$ m	250	280	Doping calculation based on H₃S
	H₃S_0.96Si_0.04^[99]	Fm $\overline{3}$ m	250	274	Doping calculation based on H₃S
	SrH₆^[100]	R $\overline{3}$ m	150	220–235	Hydrogen atoms are clathratelike and form twisted chains
	SrH₁₀^[101]	Cmca	300	259	Hydrogen atoms are distributed in staggered two-dimensional honeycomb layers
	MgH₆^[102]	Im $\overline{3}$ m	300	420
	YH₁₀^{[10–11, 103]}	Im $\overline{3}$ m	250	305–326	Unique H₃₂ cagelike structure
	YH₁₀^{[10–11, 103]}	Im $\overline{3}$ m	400	303
	YH₁₀^{[10–11, 103]}	Im $\overline{3}$ m	300	310
Ternary hydride superconductors	Li₂MgH₁₆^[104]	Fd $\overline{3}$ m	250	473	Wang et al.^[105] pointed that the diffusion of protons between interstitial spaces may play a key role
	CaHfH₁₂^[104]	Pm $\overline{3}$ m	300	360	The metal skeleton material should be composed of a metal element with an effective optimal valency of 3, and the metal should occupy a volume of about 0.4 in the hydride
	CaZrH₁₂^[106]	Pm $\overline{3}$ m	200	290
	Mg_0.5Ca_0.5H₆^[107]	Im $\overline{3}$ m	200	288
	Y₃CaH₂₄^[108]	Fm $\overline{3}$ m	150	250
	Y₃LuH₂₄^[109]	Fm $\overline{3}$ m	120	283
	YLu₃H₂₄^[109]	Fm $\overline{3}$ m	110	288
	YLuH₁₂^[109]	Fd $\overline{3}$ m	140	275

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