Fe高压熔化线的实验研究进展

甘波; 李俊; 蒋刚; 张友君

doi:10.11858/gywlxb.20210859

Fe高压熔化线的实验研究进展

doi: 10.11858/gywlxb.20210859

甘波^1,,
李俊²,
蒋刚¹,
张友君^1,*, ,

1.
四川大学原子与分子物理研究所，四川成都　610065
2.
中国工程物理研究院流体物理研究所，四川绵阳　621999

基金项目: 国家自然科学基金（42074098，41804082）

详细信息

作者简介:
甘　波（1994－），男，博士研究生，主要从事冲击波物理与地球物理研究.E-mail：ganbo325@stu.scu.edu.cn

通讯作者:
张友君（1986－），男，博士，副研究员，主要从事高压物理与地球物理研究.E-mail：zhangyoujun@scu.edu.cn

中图分类号: O521.2; P31
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出版历程
- 收稿日期: 2021-08-02
- 修回日期: 2021-09-12

A Review of the Experimental Determination of the Melting Curve of Iron at Ultrahigh Pressures

GAN Bo^1
,,
LI Jun²,
JIANG Gang¹,
ZHANG Youjun^{1,*
, ,}

1.
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, Sichuan, China
2.
Institute of Fluid Physics, CAEP, Mianyang 621999, Sichuan, China

摘要

摘要: 铁是典型的d电子过渡金属之一，其在高压下的熔化行为对于揭示地核的成分、热结构和热演化至关重要。在实验室中创造极端高温高压条件以及诊断和测量凝聚介质的熔化行为和熔化温度比较困难，导致长期以来不同实验之间以及实验与理论之间获得的铁的高压熔化线存在较大争议。近年来，随着高压实验技术的发展，对铁高压熔化线的认识逐渐趋于一致。本文介绍了用于研究铁在高压下熔化行为和熔化温度的动、静高压实验技术，总结了高压下诊断铁和过渡金属熔化的方法及其优缺点，并分析了不同实验之间产生差异的原因。基于目前关于铁高压熔化温度的实验和理论研究结果，铁在内外核边界压力（约330 GPa）下的熔化温度可限定为5900～6300 K。系统总结铁在高压下的熔化行为对于进一步认识熔化的物理机制、研究其他过渡金属的高压熔化行为等具有重要的指导和借鉴意义。
- 铁 /
- 高压熔化 /
- 静高压 /
- 动高压 /
- 地核温度
Abstract: Iron is one of the typical d-orbital transition metals. Its melting behavior and melting curve at high pressure are of great importance for revealing the composition, thermal structure, and thermal evolution of the Earth’s core. Creating the extreme high pressure-temperature conditions and measuring the melting temperatures of the condensed matters in the laboratory are quite challenging, resulting in a long-term controversy on the melting curves of iron at high pressures among various experiments and between experiments and theories. With the development of various experimental techniques, the results between experimental and theoretical studies are generally consistent with each other. This review presents the main static and dynamic compression techniques that have been used to study the high-pressure melting curve of iron in recent years; it also explores the advantages and disadvantages of melting diagnostics for iron and transition metals. The possible reasons for the discrepancy in the melting curves of iron are also discussed. Based on the experimental and theoretical results of the melting curve of iron, the melting temperature of iron can be anchored to 5900–6300 K at the pressure of the inner core boundary (ICB, about 330 GPa). Summarizing the current researches on the melting behaviors of iron under static and dynamic compression has an important implication for studying the melting curves of other transition metals, as well as the melting mechanism.
- iron /
- high-pressure melting /
- static compression /
- dynamic compression /
- Earth’s core temperature

HTML全文

作为各种电子装备中最典型的机电耦合器件之一，石英晶体振荡器是设备中不可或缺的高稳定频率源，是整个电子系统的关键元件，广泛地应用于各种导航、通信、测量等仪器设备中。随着科技发展与需求的增长，工业部门要求晶体振荡器（晶振）在更严苛的环境中也能够稳定可靠地工作，而晶振因其结构与材料的特点恰恰对振动冲击环境极其敏感^[1-3]，过量的冲击振动会引起晶振输出频率偏移，甚至导致组件发生物理破坏而失效^[4-5]。在一些航空航天装备中，由各种因素导致的冲击环境是很难避免的。如Moening^[6]统计分析了1963～1985年间因振动和冲击导致的航天飞行故障案例，发现由火工品爆炸冲击引起的运载火箭飞行失效比例非常高，在88起故障案例中有41起由此引起，并且其中的70%最终造成巨大损失。虽然航天器上火工品的爆炸冲击一般不会引起主结构的变形或损坏，但是对晶体、陶瓷、玻璃外壳等脆性材料而言却足够严酷，有可能导致其结构碎裂而失效。

相关研究表明，在高加速度冲击下，由于芯片内部材料与可动组件的脆弱性^[7]、缓冲材料性能不足^[8]等因素，一些电子元件很容易发生结构损伤而失效。为保证这类元件在工作中的安全，人们一方面研究元件在冲击环境下的响应特性与恰当的隔振缓冲装置^[9-10]，减弱冲击环境对元件的作用；另一方面总结冲击环境测试评估方法与规范^[11-12]，通过冲击环境测试确认元件的可靠性。为了评估冲击环境的严酷程度，Gaberson等^[13-14]指出伪速度冲击响应谱较加速度谱更有优势，并利用半正弦载荷模拟了多种类型爆炸冲击环境。Irvine^[15]总结了电子器件在冲击环境下的失效理论和试验研究结果，给出了多种结构下材料的力学常数与失效阈值。Li等^[16]根据单自由度系统的响应特点，分析了结构的损伤边界形式。上述研究为电子产品在冲击环境下的可靠性评估提供了一种可行的途径。本研究借鉴单自由度系统研究思路，改进文献[16]中损伤边界在低频段的临界参数选取方式，结合贴片晶振的典型结构，分析其易损组件的结构特点，通过施加与实际冲击信号更接近的正弦衰减信号来研究结构的动力学响应，以获得各频率的临界载荷与临界冲击谱，通过真实测得的冲击载荷验证改进后损伤边界的有效性。

1. 贴片晶振在冲击环境下的失效模式

贴片晶振是利用石英晶体的压电效应制成的一种电子器件，可为系统提供高稳定的频率源。它主要由石英晶片、基座、上盖板、导电胶、电极镀层以及内部电路构成，如图1所示。其中，石英晶片是一片按一定方位角从石英晶体上切下的薄片，在晶片的两面涂敷电极，通过导电胶固定在基座上，是晶振的核心组件。

图 1 贴片晶振的结构

Figure 1. Structure of surface mounted device (SMD) crystal oscillator

下载: 全尺寸图片幻灯片

在冲击环境下，电子器件的失效一般可分为结构失效和性能失效，其中结构失效又可根据失效机理分为材料破坏（材料的应力、应变超出其容许极限）和大位移失效（如大位移导致各组件间设计外的接触、碰撞等）。如图2所示，晶振在受到加速度冲击作用时，内部依靠导电胶支承的晶片可能会由于端部应力过大而发生断裂^[4-5]，从而导致晶振乃至整个系统的不可逆性失效。这也是晶振在冲击环境中经常发生的损伤模式。另外，在极端温度条件下，冲击载荷会导致导电胶破坏或脱胶，此种情况不在本研究讨论范围。

图 2 晶振在冲击下的断裂部位^[4]

Figure 2. Fracture position of crystal under impact loading^[4]

下载: 全尺寸图片幻灯片

2. 基于冲击响应谱的结构损伤边界

2.1 冲击响应谱中的结构应力损伤准则

在考核器件和设备在冲击环境下的可靠性时，一般用冲击响应谱^[17]表征环境的严酷度。它用载荷作用在一系列不同频率单自由度系统上的效果，即结构对冲击载荷的响应来描述冲击环境。当一个单自由度质量弹簧系统受到给定冲击激励时，其响应峰值为其固有频率的函数。由此函数绘成的图形即为冲击响应谱。按照所选用的单自由度系统响应参数，冲击响应谱可分为绝对加速度谱、伪速度谱、相对位移谱等。

对于如图3所示的无阻尼单自由度系统，受到基础加速度激励 $\ddot y(t)$ 时，若记 $z = x - y$ 为振子与基础的相对位移， $\omega = \sqrt {k/m}$ 为系统无阻尼固有圆频率（k、m分别为无阻尼单自由度系统的刚度与质量），则其运动方程可写为

图 3 单自由度质量弹簧系统

Figure 3. Single-degree-of-freedom system with mass, stiffness system

下载: 全尺寸图片幻灯片

$\ddot z + {\omega ^2}z = - \ddot y$

(1)

解得振子的相对位移、相对速度、绝对加速度分别为

$z(t) = - \frac{1}{\omega }\int_0^t {\ddot y(\tau )\sin \omega (t - \tau ){\rm{d}}\tau }$

(2)

$\dot z(t) = - \int_0^t {\ddot y(\tau )\cos \omega (t - \tau ){\rm{d}}\tau }$

(3)

$\ddot x(t) = \omega \int_0^t {\ddot y(\tau )\sin \omega (t - \tau ){\rm{d}}\tau }$

(4)

对于一系列这样的单自由度系统，所得的绝对加速度谱（a）、伪速度谱（v_p）与相对位移谱（d_r）与其所选取的响应参数分别为

$\begin{cases} {a(f) = \max (\left| {\ddot x(t)} \right|)} &\\ {{v_{\rm{p}}}(f) = \max (\left| {{\omega}z(t)} \right|)} &\\ {{d_{\rm{r}}}(f) = \max (\left| {z(t)} \right|)} \end{cases}$

(5)

式中： $f = \omega /2\text{π}$ 为单自由度系统的固有频率。它们之间有以下关系

$\frac{{a(f)}}{{2\text{π} f}} = {v_{\rm{p}}}(f) = 2\text{π} f{d_{\rm{r}}}(f)$

(6)

根据结构的应力损伤准则，当结构某处的材料应力大于其临界应力时，可以认为结构发生损坏，无法再满足正常工作需求。考虑如图3所示的单自由度系统。Li等^[16]对不同频率载荷作用下结构的应力响应特点进行了分析。当冲击载荷频率显著低于结构频率时，相当于考察一个质量块通过刚度很大的弹簧连接件施加加速度激励时的响应。这种情况下质量块的运动与激励几乎一致，作用于质量块的力主要由质量块运动导致的惯性力产生。由于惯性力与质量块的加速度一一对应，且质量块的最大加速度与激励载荷的最大加速度近似，因而作用于质量块的力的大小可以用式（4）中的绝对加速度表征，在冲击响应谱上表现为绝对加速度谱的谱值大小。结构中的最大应力（ ${\sigma _{\max }}$ ）为

${\sigma _{\max }} = \frac{m}{S}{\ddot x_{\max }} = \frac{m}{S}a$

(7)

式中：S为弹簧连接件的连接面积。当冲击载荷频率显著高于结构频率时，相当于考察一个大质量块通过刚度很小的弹簧连接件施加加速度激励时的响应。这种情况下质量块对激励的响应很小，而弹簧连接件的变形较大，作用于质量块的力主要由弹簧连接件变形导致的弹力引起。弹力的大小可以用式（2）中的相对位移表征，在冲击响应谱上表现为相对位移谱的谱值大小。结构中的最大应力为

${\sigma _{\max }} = \frac{k}{S}{z_{\max }} = \frac{k}{S}{d_{\rm{r}}}$

(8)

另一方面，在实际的微小结构中，冲击下的响应特点由3个时间尺度及其相互关系决定^[18]，即弹性波的渡越时间 ${\tau _{\rm{A}}}$ 、结构的振动周期T和冲击载荷的持续时间 ${t_{\rm{l}}}$ 。当冲击持续时间 ${t_{\rm{l}}}$ 大于弹性波渡越时间 ${\tau _{\rm{A}}}$ 及结构振动周期T时，可用准静态理论来分析结构在冲击下的响应；当冲击持续时间 ${t_{\rm{l}}}$ 小于弹性波的渡越时间 ${\tau _{\rm{A}}}$ 及结构振动周期T时，需要考虑应力波在结构中的传播，用应力波理论来分析结构响应。

因此，当冲击载荷频率大于结构频率时（即冲击载荷特征时间与结构振动周期有 ${t_{\rm{l}}} < T$ ），应用应力波理论来分析结构响应更恰当。在材料的弹性范围内，根据一维弹性波理论^[19]，材料的应力响应 $\sigma$ 和质点与基础之间的相对速度 $v$ 之间的关系为

$\sigma = \rho cv$

(9)

式中： $\rho$ 为材料的质量密度， $c$ 为材料中的弹性波速。在冲击载荷频率与结构频率相当的范围内（即图4中的振动区），考虑到不同的结构形式对应力波在结构中传播的影响，引入与结构形状有关的形状系数 $\kappa$ ，则结构中某处的最大应力响应与最大相对速度v_max的关系可写为^{[13, 20]}

图 4 相对时间尺度与结构冲击响应的分析方法^[18]

Figure 4. Relative time scale and the analysis method of structural impact response^[18]

下载: 全尺寸图片幻灯片

${\sigma _{\max }} = \kappa \rho c{v_{\max }}$

(10)

定义结构某点的最大伪速度响应与最大相对速度响应的比值为加载因子 $\lambda$

$\lambda = \frac{{{v_{\rm{p}}}}}{{{v_{\max }}}} = \frac{{\max (\left| {{\omega}z(t)} \right|)}}{{\max (\left| {\dot z(t)} \right|)}}$

(11)

则式（10）可改写为

${\sigma _{\max }} = \kappa \rho c{v_{\rm{p}}}/\lambda$

(12)

由于式（9）是式（10）的特殊形式（ $\kappa = 1$ ），因此式（12）适用于图4中的整个非准静态区（即当冲击载荷频率大于或等于结构频率时）。在式（7）、式（8）及式（12）中，若已知结构的临界应力 ${\sigma _{\rm{c}}}$ ，则可以在冲击响应谱图上确定各临界谱的谱值a_c、d_rc及v_pc

${a_{\rm{c}}} = \frac{S}{m}{\sigma _{\rm{c}}}$

(13)

${d_{{\rm{rc}}}} = \frac{S}{k}{\sigma _{\rm{c}}}$

(14)

${v_{{\rm{pc}}}} = \frac{\lambda }{{\kappa \rho c}}{\sigma _{\rm{c}}}$

(15)

根据以上讨论，当冲击载荷频率f_p小于结构频率f时，临界谱值由式（13）给出；当冲击载荷频率大于或等于结构频率时，临界谱值由式（14）与式（15）的较小值给出，即

$B(f) = \begin{cases} \displaystyle\frac{{{a_c}}}{{2\text{π} f}} & {f_{\rm{p}}} < f \\ \min (2\text{π} f{d_{{\rm{rc}}}},{v_{{\rm{pc}}}}) & {f_{\rm{p}}} \geqslant f \end{cases}$

(16)

式（16）对Li等^[16]提出的冲击响应谱损伤边界作了进一步改进。需要指出的是，在工程实际中，结构频率与冲击载荷频率并不是一个可以直接比较的值，并且结构件也不是单自由度的，而是具有多阶固有频率，同时冲击载荷信号也包含各种频率成分，其主导频率往往是一个频率范围。为了突出主要矛盾，以上提到的结构频率视为结构被冲击载荷所激起有效质量最大的模态所对应的频率，冲击载荷频率为其主导频率范围的上界。

2.2 结构的模态分析与简化

结合贴片晶振的典型结构，利用ABAQUS软件建立仿真模型，如图5所示，各组件的尺寸见表1。

图 5 晶振结构的有限元模型

Figure 5. Finite element model of SMD crystal oscillator

下载: 全尺寸图片幻灯片

表 1 模型尺寸

Table 1. Geometrical dimensions of the model

Structure module	Length/mm	Width/mm	Height/mm	Structure module	Length/mm	Width/mm	Height/mm
Crystal plate	5.0	3.2	0.08	Pad	1.4	1.1	0.05
Conductive adhesive	0.4	0.4	0.20	Lid	6.0	4.0	0.10
Electrode	2.0	1.5	0.02	Circuit block 1	4.0	2.2	0.30
Packaging base	7.0	5.0	1.80	Circuit block 2	0.3	1.2	0.50

下载: 导出CSV

| 显示表格

为了获得更高的数值精度，对晶片组件及封装结构中相关区域的网格进行细化。对于晶片网格数与总单元数分别为51200、109352的模型，若将单元数增加一倍，则相同条件下模型应力与结构基频的相对偏差均小于1%，可以认为，该有限元模型是足够准确的。为模拟材料的阻尼作用，在ABAQUS中设定线性体黏度参数为0.06，二次体黏度参数为1.2。

由于常用导电胶的玻璃态转化温度在100 ℃左右，室温下处于玻璃态，因此仿真过程中选用线弹性模型进行模拟。石英晶体的抗压屈服应力为1 GPa，而抗拉强度受拉伸形式及样品形状的影响较大，其值为40～70 MPa。以下计算中，抗拉强度取临界值40 MPa，即当晶片某处应力大于该临界值时，视为结构发生破坏而导致晶振失效。有限元模型的材料参数如表2所示。

表 2 有限元模型中的材料参数

Table 2. Material parameters in finite element model

Module	Material	Elastic modulus/GPa	Density/(g·cm⁻³)	Poisson’s ratio	Tensile strength/MPa
Crystal plate	Quartz	[C_pq]^[21]	2.65		40
Integrated circuit	Silicon	13.0	2.33	0.28
Electrode	Silver	73.2	10.53	0.38
Packaging base	Phenolic resin	2.0–2.9	1.25–1.30	0.35–0.38
Lid	Packfong	100.8	8.70	0.37
Conductive adhesive	Epoxy polymer	2.9	2.52	0.34
Pad	SnAgCu solder	41.6	8.74	0.40

下载: 导出CSV

| 显示表格

对于表2中没有确定值的参数，在有限元建模过程中均取其取值范围的中间值。石英晶体的弹性常数由以下矩阵给定

$[{C_{pq}}] = \left( {\begin{array}{*{20}{c}} {86.74}&{ - 8.25}&{27.15}&{ - 3.66}&0&0 \\ { - 8.25}&{129.77}&{ - 7.42}&{5.70}&0&0 \\ {27.15}&{ - 7.42}&{102.83}&{9.92}&0&0 \\ { - 3.66}&{5.70}&{9.92}&{38.61}&0&0 \\ 0&0&0&0&{68.81}&{2.53} \\ 0&0&0&0&{2.53}&{29.01} \end{array}} \right){\rm{GPa}}$

(17)

考虑到实际试验中载荷的频率范围以及可能的失效部件，在0.5～15 kHz频率范围内对晶片组件进行模态分析，考察其动态特性，分析晶片及相关组件的模态时，将导电胶与基座相连的表面全约束。表3列出了晶片及相关组件的前15阶模态以及各阶模态在法向（垂直于晶片所在平面的方向）激起的有效质量。若将第1阶模态激起的有效质量作为参考标准，各阶模态的有效质量与该标准的比值设为比例系数P，可见在晶片的法向，第1、3、5阶模态所激起的有效质量明显较大，而且这3阶激起的有效质量占总体的94.87%。可以认为，当该结构受到法向冲击载荷时，2.585、16.898、42.546 kHz这3阶频率的模态叠加基本反映了结构响应，并且第1阶模态的有效质量远大于其他模态，因此认为响应中结构的主要频率f₁ = 2.585 kHz。

表 3 晶片的各阶模态频率

Table 3. Modal frequencies of the crystal plate

Modal order	Natural frequency/kHz	Effective mass in normal direction/kg	P	Modal order	Natural frequency/kHz	Effective mass in normal direction/kg	P
1	2.585	3.26288 × 10⁻⁶	1.00000	9	73.438	1.13510 × 10⁻⁸	0.00348
2	12.479	7.97027 × 10⁻⁹	0.00244	10	89.044	4.91526 × 10⁻⁸	0.01506
3	16.898	8.92118 × 10⁻⁷	0.27341	11	106.386	3.74328 × 10⁻⁹	0.00115
4	36.781	1.54332 × 10⁻⁸	0.00473	12	114.336	1.38521 × 10⁻¹⁰	0.00004
5	42.546	3.24468 × 10⁻⁷	0.09944	13	120.211	2.83863 × 10⁻⁹	0.00087
6	56.597	4.45802 × 10⁻¹¹	0.00001	14	127.139	2.82303 × 10⁻⁸	0.00865
7	61.552	5.64709 × 10⁻⁹	0.00173	15	145.952	2.23781 × 10⁻¹⁰	0.00007
8	69.982	1.17592 × 10⁻⁷	0.03604

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| 显示表格

图6显示了第1、3、5阶模态的平均横向振型的相对幅值（以最大位移为参考值1）。可以看到，第1、3、5阶模态均为横向弯曲模态，与悬臂梁的前3阶振型类似。为分析晶振结构在冲击环境下的损伤边界，在后续的理论分析中将晶片组件简化为全支承悬臂梁结构，即忽略基座构件和导电胶，直接将载荷施加于全支承晶体板的固定端。需要注意的是，石英晶体板与基座实际上是通过两角点处的导电胶连接的，如图1（侧视图）和图2（俯视图）所示。若将结构视为长l = 5.0 mm、宽b = 3.2 mm、厚h = 0.08 mm的悬臂梁，容易求得其前3阶频率分别为2.777、17.405、48.793 kHz，与晶片结构法向占优势的前3阶模态十分接近，相应的振型也具有良好的一致性。可以认为，结构在法向载荷作用下所激起的响应可以近似用悬臂梁模型描述。

图 6 晶片组件第1、3、5阶模态距固支边相同距离的点的平均横向位移相对幅值

Figure 6. Average relative deflection of the points at the same distance from the fixed edge of the 1st, 3rd, and 5th order modes of the structure

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2.3 晶振结构的损伤边界计算

当冲击载荷主导频率的上界低于晶片组件（简化为悬臂梁结构）的一阶频率时，认为梁中的应力主要由梁结构随载荷运动所导致的惯性力产生，结构的损伤边界由冲击载荷的加速度谱控制。将悬臂梁固支端受到的横向加速度载荷近似为恒定加速度作用下梁所受的惯性力（见图7）。单位长度梁结构所受的惯性力F为

图 7 悬臂梁结构受均布载荷作用

Figure 7. Cantilever beam structure under uniform load

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$F = \rho bh{a_{\rm{h}}}$

(18)

式中： ${a_{\rm{h}}}$ 为原横向载荷的加速度幅值，ρ为梁材料的密度。此时梁上的最大应力响应在固支端发生，且在这种弯曲状态下梁结构最外层纤维的应力是最大的，即

$\sigma = \frac{{Mh}}{{2I}} = \frac{{\rho b{h^2}{l^2}{a_{\rm{h}}}}}{{4I}}$

(19)

式中： $M$ 为梁的最大弯矩， $I$ 为梁截面关于中性轴的惯性矩。若材料发生损伤的临界应力为 ${\sigma _{\rm{c}}}$ ，则有悬臂梁结构在低频载荷作用下的损伤边界

$\begin{aligned} \\ {a_{\rm{c}}} = \frac{{4I}}{{\rho b{h^2}{l^2}}}{\sigma _{\rm{c}}}\end{aligned}$

(20)

当冲击载荷主导频率的上界高于梁结构的一阶频率时，梁中的最大应力主要由梁受冲击部位相对位移导致的结构最大应力以及应力波在结构中的传播产生的最大应力来决定，因此结构的损伤边界由相对位移谱与伪速度谱中的较小值控制。若设 ${d_{{\rm{rc}}}}$ 线与 ${a_{\rm{c}}}$ 线在伪速度冲击谱中相交于频率 ${f_0}$ 处，由式（6）可得

$2\text{π} {f_0}{d_{{\rm{rc}}}} = {a_{\rm{c}}}/2\text{π} {f_0}$

(21)

结合式（7）、式（8），可求得交点频率 ${f_0} = \displaystyle\frac{{\sqrt {k/m} }}{{2\text{π} }}$ 恰好与结构频率相等。对于受横向载荷的悬臂梁结构，两者交点处对应的圆频率为

${\omega _1} = {({\beta _1}l)^2}\sqrt {\frac{{EI}}{{\rho bh{l^4}}}}$

(22)

式中： ${\,\beta _1}l$ 是与悬臂梁频率阶数相关的常数( ${\beta _1}l = 1.875$ )，E为梁材料的弹性模量。结合式（20）和式（22），可得结构的临界相对位移谱值

${d_{{\rm{rc}}}} = \frac{{{a_{\rm{c}}}}}{{{\omega}^2 _1}} = \frac{{4{l^2}}}{{{{({\beta _1}l)}^4}hE}}{\sigma _{\rm{c}}}$

(23)

结构的临界伪速度谱值由式（15）求得，悬臂梁结构受横向载荷的形状系数^[16] $\kappa = r/\eta$ ， $\eta {\rm{ = }}\sqrt {I/bh}$ ，其中 $r = h/2$ 为梁外层纤维距中性轴的距离，则临界伪速度谱值为

${v_{{\rm{pc}}}} = \frac{{2\sqrt {I/(bh)} }}{{\rho h\sqrt {E/\rho } }}\lambda {\sigma _{\rm{c}}} = 2{\sigma _{\rm{c}}}\sqrt {\frac{I}{{E\rho b{h^3}}}}$

(24)

当载荷频率大于或等于结构频率时， $\lambda$ = 1（见附录A）。根据表2中石英晶体的材料参数，当简化为悬臂梁模型进行分析时，其弹性模量取3个主方向的平均值，由式（20）、式（23）、式（24）求得其损伤边界的各临界参数为 ${a_{\rm{c}}} = 963{{g}}$ ， ${d_{{\rm{rc}}}} = 35.8\;{\rm{\text{μ} m}}$ ， ${v_{{\rm{pc}}}} = 1.59\;{\rm{m/s}}$ 。

3. 晶振结构冲击响应的有限元仿真验证

为了验证第2节中简化分析得到的损伤边界对于晶振结构的有效性，如图8所示，通过在晶振底部4个焊盘处施加垂直向上的冲击载荷，利用有限元模型计算晶振结构在冲击环境下的动力学响应，使用ABAQUS/Explicit求解器进行冲击动力学分析，以得到临界冲击载荷及相应的临界冲击响应谱。

图 8 在晶振焊盘处施加加速度载荷

Figure 8. Applying acceleration load to the welding pads

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为了验证求得的损伤边界在各频率载荷作用下的有效性，首先在晶振焊盘处施加与冲击载荷相近的正弦衰减信号（见图9）

图 9 正弦衰减信号

Figure 9. Attenuated sinusoidal signal

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${a_{\rm{s}}}(t) = {a_0} \cdot \sin ({\omega _{\rm{p}}}t) \cdot \exp \left( {\frac{{ - {\omega _{\rm{p}}}t}}{{10\text{π} }}} \right)\;\;\left(0 \leqslant t \leqslant \frac{{80\text{π} }}{{{\omega _{\rm{p}}}}}\right)$

(25)

对在0.5～30.0 kHz频率范围内的几组载荷，逐步增加其幅值，当晶片的最大应力响应达到其临界值时，判定结构发生失效，记录失效发生的时间，并标记从开始加载至结构破坏这一过程中的载荷信号为临界载荷，其冲击响应谱即为该频率载荷下的临界冲击响应谱。

依次施加不同频率的正弦衰减信号，得到相应的临界载荷，在图10上画出各临界冲击谱谱线。可以看到，其基本与依据悬臂梁模型推导得到的损伤边界相吻合。当载荷频率低于结构频率时，损伤边界受等加速度谱线控制；当载荷频率高于结构频率时，损伤边界受等相对位移谱线与等伪速度谱线中的较小值控制。可以注意到各临界谱谱线所形成的最低点对应的频率 $f^{\prime} _0$ 比损伤边界的交点频率 ${f_0}$ 稍小，该现象与悬臂梁模型的一阶频率为2.777 kHz而晶片组件的一阶频率为2.585 kHz的观察相吻合。由于有限元模型中晶片组件的支承方式并非全边固支，而是通过与导电胶连接的面区域支承，因此损伤边界与临界冲击谱之间仍存在一些差异。图11为晶振结构受横向冲击作用时的应力云图，晶片组件最大应力出现在与导电胶、基座连接区的附近。

图 10 损伤边界与临界正弦衰减信号的冲击谱

Figure 10. Damage boundary and SRS of critical attenuated sinusoidal signal

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图 11 晶振受横向冲击时的应力云图

Figure 11. Stress contour of crystal oscillator under lateral shock

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由于上述仿真分析所施加的冲击载荷均只包含一种频率成分，与实际工程中的冲击载荷存在一定差异，为了验证所得的损伤边界是否适用于实际冲击环境，选用一组实测冲击载荷信号来验证损伤边界的有效性。图12为一组实测冲击信号的加速度时程曲线，在晶振底部的焊盘处施加该冲击载荷，逐步调整载荷幅值，使晶片达到的最大应力响应恰好等于其临界应力，并标记达到最大应力的时间，记该时刻之前加载的冲击信号为临界冲击载荷，得到的临界冲击响应谱如图13所示。可见，其与损伤边界较好地吻合，可以认为该损伤边界在包含多个频率分量的冲击载荷作用下依然可以适用。需要指出的是，晶片结构在整个载荷时程的初期，即7.25 ms时，已达到最大值，因而所得的临界载荷的冲击响应谱并非图12中载荷的冲击响应谱。

图 12 实测冲击信号

Figure 12. Measured shock signal

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图 13 损伤边界临界冲击信号的冲击谱

Figure 13. Damage boundary and shock response spectrum of critical shock signal

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4. 结　论

借鉴单自由度系统在不同频率下响应特点的分析，根据结构的应力损伤准则，在伪速度冲击响应谱中获得了改进的损伤边界参数，并结合晶振模型验证了其有效性，得到以下结论。

（1）当冲击载荷主导频率上界低于结构主要频率时，结构的损伤边界由等加速度谱线控制；当冲击载荷主导频率上界高于结构主要频率时，结构的损伤边界由等相对位移谱线和等伪速度谱线中的较小值控制。

（2）当晶振受到垂直于晶片平面的冲击载荷时，晶片的动力学响应与悬臂梁结构类似，可以用简单的悬臂梁模型近似地分析晶片的损伤破坏机理。

（3）通过对晶振结构的有限元分析，得到了其在冲击载荷作用下大频率范围的损伤边界，验证了损伤边界各参数选取的有效性。这为以晶振为代表的一些微小高频元器件的力学失效分析以及冲击环境适应性设计提供了参考。

图 1 LH-DAC静高压实验系统示意图^[11]

Figure 1. Schematic of static compression in a LH-DAC^[11]

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图 2 二级轻气炮动高压实验装置示意图（根据文献[117]改绘）

Figure 2. Schematic diagram of dynamic shock compression using a two-stage light gas gun (modified by Ref. [117])

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图 3 金刚石压腔静高压实验中一些典型的用于研究铁高压熔化的诊断方法与标准：(a) XRD^[10]，(b) SMS^[151]， (c) XAS^[154]，(d) 电阻率^[155]，(e) 激光功率与温度的关系^[10]

Figure 3. Some typical diagnostic methods and criteria used to study the melting behavior of iron at high pressures in heated DAC experiments: (a) XRD^[10], (b) SMS^[151], (c) XAS^[154], (d) resistivity^[155], (e) relationship between laser power and temperature^[10]

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图 4 动高压实验中常用的冲击熔化诊断方法^{[40, 120, 156]}：(a) 冲击压力与Hugoniot温度关系的不连续，(b) 沿着冲击绝热线声速的不连续，(c) 冲击下hcp结构的X射线衍射峰消失^[120]

Figure 4. Typical diagnostics for the shock-induced melting in dynamic compression experiments^{[40, 120, 156]}: (a) discontinuity of the relationship between shock pressure and Hugoniot temperature, (b) discontinuity of sound velocity along the Hugoniot, (c) the disappearance of XRD peak for hcp structure under shock loading^[120]

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图 5 铁高压熔化温度的典型静高压实验研究结果^{[10, 143-155]}（绿色、红色、蓝色和洋红色图例分别表示采用直接显微观察样品表面、XRD、SMS和XAS获得的LH-DAC静高压实验结果，橙色图例表示采用电阻率作为诊断方法获得的RH-DAC静高压实验结果）

Figure 5. Typical results of the melting temperatures of iron at high pressures using static compression experiments^{[10, 143-155]} (The green, red, blue, and magenta legends represent the experimental results of LH-DAC experiments obtained by direct microscopic observation of sample surface, XRD, SMS, and XAS as diagnostic methods, respectively; the orange legends represent the experimental results of RH-DAC experiments using resistivity measurements as the diagnostic method.)

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图 6 铁高压熔化温度的典型动高压实验研究结果^{[47, 119-120, 143, 157, 161, 163-164]}（实心图例表示采用多通道瞬态辐射高温计直接测得的铁的Hugoniot温度和熔化温度，其中绿色^[143]、蓝色^[157]和洋红色^[119]图例代表使用微米厚铁膜或铁箔、4～6个波长通道的高温计测得的Hugoniot温度，红色图例^[47]代表使用毫米厚块状铁、16个波长通道的高温计测得的Hugoniot温度；空心图例表示高功率激光加载动高压实验中采用XAS和XRD测得的铁的冲击熔化，通过热力学计算得到的Hugoniot温度）

Figure 6. Typical results of the melting temperatures of iron at high pressures by dynamic compression experiments^{[47, 119-120, 143, 157, 161, 163-164]} (The solid legends show that Hugoniot temperatures and melting temperatures of iron are directly measured by a multichannel transient radiation pyrometer; the legends of green^[143], blue^[157] and magenta^[119] represent the Hugoniot temperatures of iron measured by a pyrometer with 4–6 wavelength channels using iron film (foil) sample; the red legend^[47] represent the Hugoniot temperatures of iron measured by a pyrometer with 16 wavelength channels using bulk iron sample; the open legends represent that the Hugoniot temperatures of iron are calculated through thermodynamic calculations from the shock melting measurements by XAS and XRD in the dynamic compression experiments of high power laser loading.)

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图 7 铁高压熔化温度的典型动高压和静高压实验结果对比^{[10, 47, 120, 154-155, 163]}（动高压实验结果与静高压实验结果具有良好的一致性，尤其是采用XAS^[154]和XRD^[10]作为诊断技术的LH-DAC静高压实验和改进样品靶结构并采用多通道瞬态辐射高温计^[47]的动高压实验结果之间）

Figure 7. A comparison of the typical results on the melting temperatures of iron at high pressures obtained by the static and dynamic compression experiments^{[10, 47, 120, 154–155, 163]} (The results are generally consistent with each other between dynamic and static experiments. In particular, the results of LH-DAC static experiments using XAS^[154] and XRD^[10] as diagnostic techniques are in good agreement with those of dynamic experiments using improved pyrometry^[47].)

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图 8 铁高压熔化温度的理论模拟和热力学计算结果^[129-142]（理论研究主要包括两类：基于分子动力学或第一性原理的理论模拟以及基于热力学状态参数的热力学计算）

Figure 8. Melting temperatures of iron at high pressures using theoretical simulations and thermodynamic calculations^[129-142] (Theoretical studies mainly include two categories: simulations based on molecular dynamics or first-principles and thermodynamic calculations based on thermodynamic parameters.)

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图 9 铁高压熔化线的典型研究结果^{[10, 47, 119, 129-135, 138-139, 141, 143, 145-146, 155, 157]}（20年前铁高压熔化线的实验与理论研究结果之间存在较大的差异，而目前实验与理论研究结果之间已经基本吻合）

Figure 9. Typical results of the melting curves of iron at high pressures^{[10, 47, 119, 129-135, 138-139, 141, 143, 145-146, 155, 157]} (Twenty years ago, there was a big difference in the melting curves of iron between experimental and theoretical studies, while the current studies show an overall agreement between experimental and theoretical results.)

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表 1 高压下铁的熔化温度的实验和理论研究总结

Table 1. Summary of experimental and theoretical studies on the melting temperature of iron at high pressures

Technique	Method	Melting diagnostic	Expt. and theo. conditions		T_{M, ICB}/K	Reference, year
Technique	Method	Melting diagnostic	p/GPa	T_M(T_H)/K	T_{M, ICB}/K	Reference, year
Theory	Ab initio DFT	Free energies	50–350	3020–6860	6680±600	Ref.[129], 1999
	Thermodynamics	Database	0–330	1811–5790	5790	Ref.[130], 2000
	AIMD	Free energies	60–330	2460–7100	7100	Ref.[131], 2000
	FP-MD	A single potential	100–330	2830–5400	5400±400	Ref.[132], 2000
	Ab initio DFT	Free energies	50–350	2550–6380^a	6210±600^a	Ref.[133], 2002
	Ab initio DFT	Free energies	50–350	2890–6510^b	6350±600^b	Ref.[133], 2002
	Thermodynamics	Free energy	58–462	2840–7240	6050	Ref.[134], 2003
	FP	Number of atoms	323–332	6270–6440	6370±100	Ref.[135], 2009
	Monte Carlo	Free energies	330	6900	6900±400	Ref.[136], 2009
	Thermodynamics	Database	0–353	1810–5080	4900	Ref.[137], 2010
	AIMD	Free energies	190–1500	4500–12500	6150	Ref.[138], 2013
	AIMD	Structure	0–365	1700–6740	6350	Ref.[139], 2015
	Thermodynamics	Database	107–350	3790–6020	5880	Ref.[140], 2017
	AIMD	Free energies	330	6170	6170±200	Ref.[141], 2018
	SMM	LC	0–350	1810–5720	5570	Ref.[142], 2021
Static	LH-DAC(s)	Textural	0–102	1750–4180	7600±500	Ref.[143], 1987
		Motion	16–197	2220–3860	4850±200	Ref.[144-145], 1993
		Visual bservation	0–144	1811–3530	6130±350	Ref.[146], 1994
		XRD	11–80	2100–3090		Ref.[147-148], 2004
		XRD	60–105	2750–3510	5800±200	Ref.[149], 2004
		XRD	27–130	2580–3180		Ref.[150], 2008
		SMS	20–82	2220–3030		Ref.[151], 2013
		Fast XRD	57–158	3140–4470	6230±500	Ref.[10], 2013
		XANES	75–117	2840–3090		Ref.[152], 2015
		SMS	19–60	2120–2800	5700±200	Ref.[153], 2016
		XANES	43–133	2660–4700		Ref.[154], 2018
	RH-DAC	Resistivity	6–290	1900–5360	5500±220	Ref.[155], 2019
Dynamic (shock wave)	TSLGG	SVD	40–400	655–10024^c	5800±500	Ref.[156], 1986
	TSLGG	T-p discontinuity	202–301	5500–9370^*	7600±500	Ref.[143], 1987
	TSLGG	T-p discontinuity	203–300	5200–8990^*	7800±500	Ref.[157], 1987
	TSLGG	T-p discontinuity	159–339	4460–8360^*	6830±500	Ref.[119], 1993
	TSLGG	SVD	84–171	4380–5440^e*	6000	Ref.[158-159], 2001
	PG	SVD	14–73	1820–2780^f	5300±400	Ref.[160], 2002
	TSLGG	SVD	225–260	5100–6100^d	6350±500	Ref.[40], 2004
	HP laser	SED	50–150	4000–5000^#	7800±1200	Ref.[41], 2005
	HP laser	EXAFS	90–560	1320–8160^#	6400	Ref.[161], 2013
	TSLGG	SVD	73–127	3240–3680^e	5885±500	Ref.[162], 2009
	HP laser	XANES	260–420	5680–10800^#		Ref.[163], 2015
	HP laser	EXAFS	40–500	660–17000^#		Ref.[164], 2016
	HP laser	XRD	144–273	3100–5560^#	6400	Ref.[120], 2020
	TSLGG	SVD	120–256	4250–5500^*	5950±500	Ref.[47], 2020
Note: Superscript lowercase letters “a” and “b” represent the theoretical results of ab initio molecular dynamics simulation without and with free-energy correction, respectively; “c” and “d” represent that the Hugoniot temperatures were calculated based on the measurements of sound velocities of iron and preheated iron, respectively; “e” represents the porous iron was used in shock compression experiments; “*” represents that the Hugoniot temperatures were measured by a multi-channel quasi-spectral optical pyrometer; “#” represents that the Hugoniot temperatures were calculated through thermodynamic calculations based on the results of dynamic compression experiments of high power laser loading.

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参考文献(255)

[1]	谭华. 实验冲击波物理 [M]. 北京: 国防工业出版社, 2018. TAN H. Experimental shock wave physics [M]. Beijing: National Defense Industry Press, 2018.
[2]	GORMAN M G, BRIGGS R, MCBRIDE E E, et al. Direct observation of melting in shock-compressed bismuth with femtosecond X-ray diffraction [J]. Physical Review Letters, 2015, 115(9): 095701. doi: 10.1103/PhysRevLett.115.095701
[3]	JENSEN B J, CHERNE F J, COOLEY J C, et al. Shock melting of cerium [J]. Physical Review B, 2010, 81(21): 214109. doi: 10.1103/PhysRevB.81.214109
[4]	ROSS M, YANG L H, BOEHLER R. Melting of aluminum, molybdenum, and the light actinides [J]. Physical Review B, 2004, 70(18): 184112. doi: 10.1103/PhysRevB.70.184112
[5]	ERRANDONEA D, BOEHLER R, ROSS M. Melting of the rare Earth metals and f-electron delocalization [J]. Physical Review Letters, 2000, 85(16): 3444–3447. doi: 10.1103/PhysRevLett.85.3444
[6]	PATEL N N, SUNDER M. High pressure melting curve of osmium up to 35 GPa [J]. Journal of Applied Physics, 2019, 125(5): 055902. doi: 10.1063/1.5045823
[7]	YAP C Y, CHUA C K, DONG Z L, et al. Review of selective laser melting: materials and applications [J]. Applied Physics Reviews, 2015, 2(4): 041101. doi: 10.1063/1.4935926
[8]	BOYER R R. An overview on the use of titanium in the aerospace industry [J]. Materials Science and Engineering: A, 1996, 213(1/2): 103–114. doi: 10.1016/0921-5093(96)10233-1
[9]	FISCHER R A. Melting of Fe alloys and the thermal structure of the core [M]//TERASAKI H, FISCHER R A. Deep Earth: Physics and Chemistry of the Lower Mantle and Core. Hoboken: John Wiley, 2016: 3–12.
[10]	ANZELLINI S, DEWAELE A, MEZOUAR M, et al. Melting of iron at Earth’s inner core boundary based on fast X-ray diffraction [J]. Science, 2013, 340(6131): 464–466. doi: 10.1126/science.1233514
[11]	PARISIADES P. A review of the melting curves of transition metals at high pressures using static compression techniques [J]. Crystals, 2021, 11(4): 416. doi: 10.3390/cryst11040416
[12]	PARISIADES P, COVA F, GARBARINO G. Melting curve of elemental zirconium [J]. Physical Review B, 2019, 100(5): 054102. doi: 10.1103/PhysRevB.100.054102
[13]	JAPEL S, SCHWAGER B, BOEHLER R, et al. Melting of copper and nickel at high pressure: the role of d electrons [J]. Physical Review Letters, 2005, 95(16): 167801. doi: 10.1103/PhysRevLett.95.167801
[14]	ROSS M, BOEHLER R, ERRANDONEA D. Melting of transition metals at high pressure and the influence of liquid frustration: the late metals Cu, Ni, and Fe [J]. Physical Review B, 2007, 76(18): 184117. doi: 10.1103/PhysRevB.76.184117
[15]	ALFÈ D, VOČADLO L, PRICE G D, et al. Melting curve of materials: theory versus experiments [J]. Journal of Physics: Condensed Matter, 2004, 16(14): S973–S982. doi: 10.1088/0953-8984/16/14/006
[16]	DAI C D, HU J B, TAN H. Hugoniot temperatures and melting of tantalum under shock compression determined by optical pyrometry [J]. Journal of Applied Physics, 2009, 106(4): 043519. doi: 10.1063/1.3204941
[17]	SANTAMARÍA-PÉREZ D, ROSS M, ERRANDONEA D, et al. X-ray diffraction measurements of Mo melting to 119 GPa and the high pressure phase diagram [J]. The Journal of Chemical Physics, 2009, 130(12): 124509. doi: 10.1063/1.3082030
[18]	ERRANDONEA D. Improving the understanding of the melting behaviour of Mo, Ta, and W at extreme pressures [J]. Physica B: Condensed Matter, 2005, 357(3/4): 356–364. doi: 10.1016/j.physb.2004.11.087
[19]	PIGOTT J S, VELISAVLJEVIC N, MOSS E K, et al. Experimental melting curve of zirconium metal to 37 GPa [J]. Journal of Physics: Condensed Matter, 2020, 32(35): 355402. doi: 10.1088/1361-648X/ab8cdb
[20]	ERRANDONEA D. High-pressure melting curves of the transition metals Cu, Ni, Pd, and Pt [J]. Physical Review B, 2013, 87(5): 054108. doi: 10.1103/PhysRevB.87.054108
[21]	LAZOR P, SHEN G, SAXENA S K. Laser-heated diamond anvil cell experiments at high pressure: melting curve of nickel up to 700 kbar [J]. Physics and Chemistry of Minerals, 1993, 20(2): 86–90. doi: 10.1007/BF00207200
[22]	GREGORYANZ E, DEGTYAREVA O, SOMAYAZULU M, et al. Melting of dense sodium [J]. Physical Review Letters, 2005, 94(18): 185502. doi: 10.1103/PhysRevLett.94.185502
[23]	NARYGINA O, MCBRIDE E E, STINTON G W, et al. Melting curve of potassium to 22 GPa [J]. Physical Review B, 2011, 84(5): 054111. doi: 10.1103/PhysRevB.84.054111
[24]	GUILLAUME C L, GREGORYANZ E, DEGTYAREVA O, et al. Cold melting and solid structures of dense lithium [J]. Nature Physics, 2011, 7(3): 211–214. doi: 10.1038/nphys1864
[25]	KULYAMINA E Y, ZITSERMAN V Y, FOKIN L R. Titanium melting curve: data consistency assessment, problems and achievements [J]. Technical Physics, 2018, 63(3): 369–373. doi: 10.1134/S1063784218030131
[26]	BUFFETT B A. Earth’s core and the geodynamo [J]. Science, 2000, 288(5473): 2007–2012. doi: 10.1126/science.288.5473.2007
[27]	LABROSSE S. Thermal evolution of the core with a high thermal conductivity [J]. Physics of the Earth and Planetary Interiors, 2015, 247: 36–55. doi: 10.1016/j.pepi.2015.02.002
[28]	LAY T, HERNLUND J W, BUFFETT B A. Core-mantle boundary heat flow [J]. Nature Geoscience, 2008, 1(1): 25–32. doi: 10.1038/ngeo.2007.44
[29]	ALBOUSSIÈRE T, DEGUEN R, MELZANI M. Melting-induced stratification above the Earth’s inner core due to convective translation [J]. Nature, 2010, 466(7307): 744–747. doi: 10.1038/nature09257
[30]	GUBBINS D, SREENIVASAN B, MOUND J, et al. Melting of the Earth’s inner core [J]. Nature, 2011, 473(7347): 361–363. doi: 10.1038/nature10068
[31]	BUFFETT B A. The thermal state of Earth’s core [J]. Science, 2003, 299(5613): 1675–1677. doi: 10.1126/science.1081518
[32]	NIMMO F. Energetics of the core [J]. Treatise on Geophysics, 2015, 8: 27–55. doi: 10.1016/B978-0-444-53802-4.00139-1
[33]	DEWAELE A, LOUBEYRE P, OCCELLI F, et al. Toroidal diamond anvil cell for detailed measurements under extreme static pressures [J]. Nature Communications, 2018, 9(1): 2913. doi: 10.1038/s41467-018-05294-2
[34]	DUBROVINSKAIA N, DUBROVINSKY L, SOLOPOVA N A, et al. Terapascal static pressure generation with ultrahigh yield strength nanodiamond [J]. Science Advances, 2016, 2(7): e1600341. doi: 10.1126/sciadv.1600341
[35]	DUBROVINSKY L, DUBROVINSKAIA N, PRAKAPENKA V B, et al. Implementation of micro-ball nanodiamond anvils for high-pressure studies above 6 Mbar [J]. Nature Communications, 2012, 3(1): 1163. doi: 10.1038/ncomms2160
[36]	SWIFT D C, JOHNSON R P. Quasi-isentropic compression by ablative laser loading: response of materials to dynamic loading on nanosecond time scales [J]. Physical Review E, 2005, 71(6): 066401. doi: 10.1103/PhysRevE.71.066401
[37]	KALITA P, BROWN J, SPECHT P, et al. Dynamic X-ray diffraction and nanosecond quantification of kinetics of formation of β-zirconium under shock compression [J]. Physical Review B, 2020, 102(6): 060101. doi: 10.1103/PhysRevB.102.060101
[38]	EGGERT J H, HICKS D G, CELLIERS P M, et al. Melting temperature of diamond at ultrahigh pressure [J]. Nature Physics, 2010, 6(1): 40–43. doi: 10.1038/nphys1438
[39]	DUFFY T S, SMITH R F. Ultra-high pressure dynamic compression of geological materials [J]. Frontiers in Earth Science, 2019, 7: 23. doi: 10.3389/FEART.2019.00023
[40]	NGUYEN J H, HOLMES N C. Melting of iron at the physical conditions of the Earth’s core [J]. Nature, 2004, 427(6972): 339–342. doi: 10.1038/nature02248
[41]	HUSER G, KOENIG M, BENUZZI-MOUNAIX A, et al. Temperature and melting of laser-shocked iron releasing into an LiF window [J]. Physics of Plasmas, 2005, 12(6): 060701. doi: 10.1063/1.1896375
[42]	GLENZER S H, FLETCHER L B, GALTIER E, et al. Matter under extreme conditions experiments at the Linac Coherent Light Source [J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2016, 49(9): 092001. doi: 10.1088/0953-4075/49/9/092001
[43]	NAGLER B, ARNOLD B, BOUCHARD G, et al. The matter in extreme conditions instrument at the linac coherent light source [J]. Journal of Synchrotron Radiation, 2015, 22(3): 520–525. doi: 10.1107/S1600577515004865
[44]	MASON P, BANERJEE S, SMITH J, et al. Development of a 100 J, 10 Hz laser for compression experiments at the High Energy Density instrument at the European XFEL [J]. High Power Laser Science and Engineering, 2018, 6: e65. doi: 10.1017/hpl.2018.56
[45]	ZHANG Y J, SEKINE T, LIN J F, et al. Shock compression and melting of an Fe-Ni-Si alloy: implications for the temperature profile of the Earth’s core and the heat flux across the core-mantle boundary [J]. Journal of Geophysical Research: Solid Earth, 2018, 123(2): 1314–1327. doi: 10.1002/2017JB014723
[46]	ZHANG Y J, TAN Y, GENG H Y, et al. Melting curve of vanadium up to 256 GPa: consistency between experiments and theory [J]. Physical Review B, 2020, 102(21): 214104. doi: 10.1103/PhysRevB.102.214104
[47]	LI J, WU Q, LI J B, et al. Shock melting curve of iron: a consensus on the temperature at the Earth’s inner core boundary [J]. Geophysical Research Letters, 2020, 47(15): e2020GL087758. doi: 10.1029/2020GL087758
[48]	MCMAHAN A K. Pressure-induced changes in the electronic structure of solids [J]. Physica B, 1986, 139/140: 31–41. doi: 10.1016/0378-4363(86)90519-X
[49]	POUROVSKII L V. Electronic correlations in dense iron: from moderate pressure to Earth’s core conditions [J]. Journal of Physics: Condensed Matter, 2019, 31(37): 373001. doi: 10.1088/1361-648X/ab274f
[50]	LUO S N, AHRENS T J, ÇAĞIN T, et al. Maximum superheating and undercooling: systematics, molecular dynamics simulations, and dynamic experiments [J]. Physical Review B, 2003, 68(13): 134206. doi: 10.1103/PhysRevB.68.134206
[51]	MORRIS J R, WANG C Z, HO K M, et al. Melting line of aluminum from simulations of coexisting phases [J]. Physical Review B, 1994, 49(5): 3109–3115. doi: 10.1103/PhysRevB.49.3109
[52]	BELONOSHKO A B. Molecular dynamics of MgSiO₃ perovskite at high pressures: equation of state, structure, and melting transition [J]. Geochimica et Cosmochimica Acta, 1994, 58(19): 4039–4047. doi: 10.1016/0016-7037(94)90265-8
[53]	GILLAN M J, ALFÈ D, BRODHOLT J, et al. First-principles modelling of Earth and planetary materials at high pressures and temperatures [J]. Reports on Progress in Physics, 2006, 69(8): 2365–2441. doi: 10.1088/0034-4885/69/8/R03
[54]	GENG H Y, WU Q. Predicted reentrant melting of dense hydrogen at ultra-high pressures [J]. Scientific Reports, 2016, 6(1): 36745. doi: 10.1038/srep36745
[55]	GENG H Y, WU Q, MARQUÉS M, et al. Thermodynamic anomalies and three distinct liquid-liquid transitions in warm dense liquid hydrogen [J]. Physical Review B, 2019, 100(13): 134109. doi: 10.1103/PhysRevB.100.134109
[56]	CAZORLA C, ALFÈ D, GILLAN M J. Constraints on the phase diagram of molybdenum from first-principles free-energy calculations [J]. Physical Review B, 2012, 85(6): 064113. doi: 10.1103/PhysRevB.85.064113
[57]	BELONOSHKO A B, ROSENGREN A. High-pressure melting curve of platinum from ab initio Z method [J]. Physical Review B, 2012, 85(17): 174104. doi: 10.1103/PhysRevB.85.174104
[58]	BELONOSHKO A B, DAVIS S, SKORODUMOVA N V, et al. Properties of the fcc Lennard-Jones crystal model at the limit of superheating [J]. Physical Review B, 2007, 76(6): 064121. doi: 10.1103/PhysRevB.76.064121
[59]	WANG S C, ZHANG G M, LIU H F, et al. Modified Z method to calculate melting curve by molecular dynamics [J]. The Journal of Chemical Physics, 2013, 138(13): 134101. doi: 10.1063/1.4798225
[60]	FROST D J, POE B T, TRØNNES R G, et al. A new large-volume multianvil system [J]. Physics of the Earth and Planetary Interiors, 2004, 143/144: 507–514. doi: 10.1016/J.PEPI.2004.03.003
[61]	SHCHEKA S S, WIEDENBECK M, FROST D J, et al. Carbon solubility in mantle minerals [J]. Earth and Planetary Science Letters, 2006, 245(3/4): 730–742. doi: 10.1016/j.jpgl.2006.03.036
[62]	NIETO-SANZ D, LOUBEYRE P, CRICHTON W, et al. X-ray study of the synthesis of boron oxides at high pressure: phase diagram and equation of state [J]. Physical Review B, 2004, 70(21): 214108. doi: 10.1103/PhysRevB.70.214108
[63]	HORVATH-BORDON E, RIEDEL R, ZERR A, et al. High-pressure chemistry of nitride-based materials [J]. Chemical Society Reviews, 2006, 35(10): 987–1014. doi: 10.1039/b517778m
[64]	ITO E, YAMAZAKI D, YOSHINO T, et al. Pressure generation and investigation of the post-perovskite transformation in MgGeO₃ by squeezing the Kawai-cell equipped with sintered diamond anvils [J]. Earth and Planetary Science Letters, 2010, 293(1/2): 84–89. doi: 10.1016/j.jpgl.2010.02.023
[65]	ZHOU X F, MA D J, WANG L F, et al. Large-volume cubic press produces high temperatures above 4000 Kelvin for study of the refractory materials at pressures [J]. Review of Scientific Instruments, 2020, 91(1): 015118. doi: 10.1063/1.5128190
[66]	LAZICKI A, FEI Y W, HEMLEY R J. High-pressure differential thermal analysis measurements of the melting curve of lithium [J]. Solid State Communications, 2010, 150(13/14): 625–627. doi: 10.1016/j.ssc.2009.12.029
[67]	SILBER R E, SECCO R A, YONG W J. Constant electrical resistivity of Ni along the melting boundary up to 9 GPa [J]. Journal of Geophysical Research: Solid Earth, 2017, 122(7): 5064–5081. doi: 10.1002/2017JB014259
[68]	EZENWA I C, SECCO R A. Invariant electrical resistivity of Co along the melting boundary [J]. Earth and Planetary Science Letters, 2017, 474: 120–127. doi: 10.1016/j.jpgl.2017.06.032
[69]	BERRADA M, SECCO R A, YONG W J. Decreasing electrical resistivity of gold along the melting boundary up to 5 GPa [J]. High Pressure Research, 2018, 38(4): 367–376. doi: 10.1080/08957959.2018.1493476
[70]	BRAND H, DOBSON D P, VOČADLO L, et al. Melting curve of copper measured to 16 GPa using a multi-anvil press [J]. High Pressure Research, 2006, 26(3): 185–191. doi: 10.1080/08957950600873089
[71]	MING L C, BASSETT W A. Laser heating in the diamond anvil press up to 2000 ℃ sustained and 3000 ℃ pulsed at pressures up to 260 kilobars [J]. Review of Scientific Instruments, 1974, 45(9): 1115–1118. doi: 10.1063/1.1686822
[72]	ANZELLINI S, BOCCATO S. A practical review of the laser-heated diamond anvil cell for university laboratories and synchrotron applications [J]. Crystals, 2020, 10(6): 459. doi: 10.3390/cryst10060459
[73]	LIN J F, SHU J F, MAO H K, et al. Amorphous boron gasket in diamond anvil cell research [J]. Review of Scientific Instruments, 2003, 74(11): 4732–4736. doi: 10.1063/1.1621065
[74]	FUNAMORI N, SATO T. A cubic boron nitride gasket for diamond-anvil experiments [J]. Review of Scientific Instruments, 2008, 79(5): 053903. doi: 10.1063/1.2917409
[75]	HEMLEY R J, MAO H K, SHEN G Y, et al. X-ray imaging of stress and strain of diamond, iron, and tungsten at megabar pressures [J]. Science, 1997, 276(5316): 1242–1245. doi: 10.1126/science.276.5316.1242
[76]	MAO H K, SHU J F, SHEN G Y, et al. Elasticity and rheology of iron above 220 GPa and the nature of the Earth’s inner core [J]. Nature, 1998, 396(6713): 741–743. doi: 10.1038/25506
[77]	WU T C, BASSETT W A. Deviatoric stress in a diamond anvil cell using synchrotron radiation with two diffraction geometries [J]. Pure and Applied Geophysics, 1993, 141(2): 509–519. doi: 10.1007/BF00998343
[78]	KLOTZ S, CHERVIN J C, MUNSCH P, et al. Hydrostatic limits of 11 pressure transmitting media [J]. Journal of Physics D: Applied Physics, 2009, 42(7): 075413. doi: 10.1088/0022-3727/42/7/075413
[79]	DEWAELE A, LOUBEYRE P. Pressurizing conditions in helium-pressure-transmitting medium [J]. High Pressure Research, 2007, 27(4): 419–429. doi: 10.1080/08957950701659627
[80]	MAO H K, BELL P M, SHANER J W, et al. Specific volume measurements of Cu, Mo, Pd, and Ag and calibration of the ruby R₁ fluorescence pressure gauge from 0.06 to 1 Mbar [J]. Journal of Applied Physics, 1978, 49(6): 3276–3283. doi: 10.1063/1.325277
[81]	BOSE S. Planck’s law and the light quantum hypothesis [J]. Journal of Astrophysics and Astronomy, 1994, 15(1): 3–7. doi: 10.1007/BF03010400
[82]	WEIK M H. Planck’s law [M]//WEIK M H. Computer Science and Communications Dictionary. Boston: Springer, 2000: 1284.
[83]	BENEDETTI L R, LOUBEYRE P. Temperature gradients, wavelength-dependent emissivity, and accuracy of high and very-high temperatures measured in the laser-heated diamond cell [J]. High Pressure Research, 2004, 24(4): 423–445. doi: 10.1080/08957950412331331718
[84]	BENEDETTI L R, ANTONANGELI D, FARBER D L, et al. An integrated method to determine melting temperatures in high-pressure laser-heating experiments [J]. Applied Physics Letters, 2008, 92(14): 141903. doi: 10.1063/1.2906893
[85]	DEWAELE A, TORRENT M, LOUBEYRE P, et al. Compression curves of transition metals in the Mbar range: experiments and projector augmented-wave calculations [J]. Physical Review B, 2008, 78(10): 104102. doi: 10.1103/PhysRevB.78.104102
[86]	SHEN G Y, WANG Y B, DEWAELE A, et al. Toward an international practical pressure scale: a proposal for an IPPS ruby gauge (IPPS-Ruby2020) [J]. High Pressure Research, 2020, 40(3): 299–314. doi: 10.1080/08957959.2020.1791107
[87]	DATCHI F, DEWAELE A, LOUBEYRE P, et al. Optical pressure sensors for high-pressure-high-temperature studies in a diamond anvil cell [J]. High Pressure Research, 2007, 27(4): 447–463. doi: 10.1080/08957950701659593
[88]	AKAHAMA Y, KAWAMURA H. Pressure calibration of diamond anvil Raman gauge to 410 GPa [J]. Journal of Physics: Conference Series, 2010, 215: 012195. doi: 10.1088/1742-6596/215/1/012195
[89]	DEWAELE A, BELONOSHKO A B, GARBARINO G, et al. High-pressure-high-temperature equation of state of KCl and KBr [J]. Physical Review B, 2012, 85(21): 214105. doi: 10.1103/PhysRevB.85.214105
[90]	TANGE Y, NISHIHARA Y, TSUCHIYA T. Unified analyses for P-V-T equation of state of MgO: a solution for pressure-scale problems in high P-T experiments [J]. Journal of Geophysical Research: Solid Earth, 2009, 114(B3): B03208. doi: 10.1029/2008JB005813
[91]	MATSUI M, PARKER S C, LESLIE M. The MD simulation of the equation of state of MgO: application as a pressure calibration standard at high temperature and high pressure [J]. American Mineralogist, 2000, 85(2): 312–316. doi: 10.2138/am-2000-2-308
[92]	MAO H K, BELL P M. Equations of state of MgO and ε-Fe under static pressure conditions [J]. Journal of Geophysical Research: Solid Earth, 1979, 84(B9): 4533–4536. doi: 10.1029/JB084iB09p04533
[93]	DECKER D L. High-pressure equation of state for NaCl, KCl, and CsCl [J]. Journal of Applied Physics, 1971, 42(8): 3239–3244. doi: 10.1063/1.1660714
[94]	DECKER D L. Equation of state of NaCl and its use as a pressure gauge in high-pressure research [J]. Journal of Applied Physics, 1965, 36(1): 157–161. doi: 10.1063/1.1713864
[95]	YE Y, SHIM S H, PRAKAPENKA V, et al. Equation of state of solid Ne inter-calibrated with the MgO, Au, Pt, NaCl-B2, and ruby pressure scales up to 130 GPa [J]. High Pressure Research, 2018, 38(4): 377–395. doi: 10.1080/08957959.2018.1493477
[96]	SHEELENDRA K, VIJAY A. Equation of state, thermoelastic properties and melting behavior of NaCl at high temperatures and high pressures [J]. Journal of Physics and Chemistry of Solids, 2018, 123: 364–370. doi: 10.1016/j.jpcs.2018.08.027
[97]	FAN D W, ZHOU W G, WEI S Y, et al. A simple external resistance heating diamond anvil cell and its application for synchrotron radiation X-ray diffraction [J]. Review of Scientific Instruments, 2010, 81(5): 053903. doi: 10.1063/1.3430069
[98]	JENEI Z, CYNN H, VISBECK K, et al. High-temperature experiments using a resistively heated high-pressure membrane diamond anvil cell [J]. Review of Scientific Instruments, 2013, 84(9): 095114. doi: 10.1063/1.4821622
[99]	WEIR S T, JACKSON D D, FALABELLA S, et al. An electrical microheater technique for high-pressure and high-temperature diamond anvil cell experiments [J]. Review of Scientific Instruments, 2009, 80(1): 013905. doi: 10.1063/1.3069286
[100]	PASTERNAK S, AQUILANTI G, PASCARELLI S, et al. A diamond anvil cell with resistive heating for high pressure and high temperature X-ray diffraction and absorption studies [J]. Review of Scientific Instruments, 2008, 79(8): 085103. doi: 10.1063/1.2968199
[101]	DU Z X, MIYAGI L, AMULELE G, et al. Efficient graphite ring heater suitable for diamond-anvil cells to 1300 K [J]. Review of Scientific Instruments, 2013, 84(2): 024502. doi: 10.1063/1.4792395
[102]	DUBROVINSKY L S, SAXENA S K, LAZOR P. High-pressure and high-temperature in situ X-ray diffraction study of iron and corundum to 68 GPa using an internally heated diamond anvil cell [J]. Physics and Chemistry of Minerals, 1998, 25(6): 434–441. doi: 10.1007/s002690050133
[103]	BALZARETTI N M, GONZALEZ E J, PIERMARINI G J, et al. Resistance heating of the gasket in a gem-anvil high pressure cell [J]. Review of Scientific Instruments, 1999, 70(11): 4316–4323. doi: 10.1063/1.1150095
[104]	LIERMANN H P, MERKEL S, MIYAGI L, et al. Experimental method for in situ determination of material textures at simultaneous high pressure and high temperature by means of radial diffraction in the diamond anvil cell [J]. Review of Scientific Instruments, 2009, 80(10): 104501. doi: 10.1063/1.3236365
[105]	BASSETT W A, SHEN A H, BUCKNUM M, et al. A new diamond anvil cell for hydrothermal studies to 2.5 GPa and from −190 to 1200 ℃ [J]. Review of Scientific Instruments, 1993, 64(8): 2340–2345. doi: 10.1063/1.1143931
[106]	ZHA C S, BASSETT W A. Internal resistive heating in diamond anvil cell for in situ X-ray diffraction and Raman scattering [J]. Review of Scientific Instruments, 2003, 74(3): 1255–1262. doi: 10.1063/1.1539895
[107]	WEIR S T, LIPP M J, FALABELLA S, et al. High pressure melting curve of tin measured using an internal resistive heating technique to 45 GPa [J]. Journal of Applied Physics, 2012, 111(12): 123529. doi: 10.1063/1.4730968
[108]	KOMABAYASHI T, FEI Y W, MENG Y, et al. In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell [J]. Earth and Planetary Science Letters, 2009, 282(1/2/3/4): 252–257. doi: 10.1016/J.EPSL.2009.03.025
[109]	KOMABAYASHI T, PESCE G, SINMYO R, et al. Phase relations in the system Fe-Ni-Si to 200 GPa and 3900 K and implications for Earth’s core [J]. Earth and Planetary Science Letters, 2019, 512: 83–88. doi: 10.1016/j.jpgl.2019.01.056
[110]	BOEHLER R, ROSS M, SÖDERLIND P, et al. High-pressure melting curves of argon, krypton, and xenon: deviation from corresponding states theory [J]. Physical Review Letters, 2001, 86(25): 5731–5734. doi: 10.1103/PhysRevLett.86.5731
[111]	BOEHLER R, ROSS M, BOERCKER D B. High-pressure melting curves of alkali halides [J]. Physical Review B, 1996, 53(2): 556–563. doi: 10.1103/PhysRevB.53.556
[112]	BOEHLER R, ROSS M, BOERCKER D B. Melting of LiF and NaCl to 1 Mbar: systematics of ionic solids at extreme conditions [J]. Physical Review Letters, 1997, 78(24): 4589–4592. doi: 10.1103/PhysRevLett.78.4589
[113]	SHEN G Y, LAZOR P. Measurement of melting temperatures of some minerals under lower mantle pressures [J]. Journal of Geophysical Research: Solid Earth, 1995, 100(B9): 17699–17713. doi: 10.1029/95JB01864
[114]	SANTAMARÍA-PÉREZ D, MUKHERJEE G D, SCHWAGER B, et al. High-pressure melting curve of helium and neon: deviations from corresponding states theory [J]. Physical Review B, 2010, 81(21): 214101. doi: 10.1103/PhysRevB.81.214101
[115]	KIMURA T, OHFUJI H, NISHI M, et al. Melting temperatures of MgO under high pressure by micro-texture analysis [J]. Nature Communications, 2017, 8(1): 15735. doi: 10.1038/ncomms15735
[116]	ANDRAULT D, MORARD G, GARBARINO G, et al. Melting behavior of SiO₂ up to 120 GPa [J]. Physics and Chemistry of Minerals, 2020, 47(2): 10. doi: 10.1007/s00269-019-01077-3
[117]	SEILER F, IGRA O. Hypervelocity launchers [M]. Cham: Springer, 2016.
[118]	CHEN G Q, AHRENS T J. High-pressure melting of iron: new experiments and calculations [J]. Philosophical Transactions of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 1996, 354(1711): 1251–1263. doi: 10.1098/rsta.1996.0047
[119]	YOO C S, HOLMES N C, ROSS M, et al. Shock temperatures and melting of iron at Earth core conditions [J]. Physical Review Letters, 1993, 70(25): 3931–3934. doi: 10.1103/PhysRevLett.70.3931
[120]	TURNEAURE S J, SHARMA S M, GUPTA Y M. Crystal structure and melting of Fe shock compressed to 273 GPa: in situ X-ray diffraction [J]. Physical Review Letters, 2020, 125(21): 215702. doi: 10.1103/PhysRevLett.125.215702
[121]	HERTZBERG A, BRUCKNER A P, BOGDANOFF D W. Ram accelerator: a new chemical method for accelerating projectiles to ultrahigh velocities [J]. AIAA Journal, 1988, 26(2): 195–203. doi: 10.2514/3.9872
[122]	CROZIER W D, HUME W. High-velocity, light-gas gun [J]. Journal of Applied Physics, 1957, 28(8): 892–894. doi: 10.1063/1.1722882
[123]	BOSLOUGH M B, AHRENS T J. A sensitive time-resolved radiation pyrometer for shock-temperature measurements above 1500 K [J]. Review of Scientific Instruments, 1989, 60(12): 3711–3716. doi: 10.1063/1.1140480
[124]	RAV A S, SAXENA A K, JOSHI K D, et al. Time resolved radiation pyrometer for transient temperature measurement [J]. AIP Conference Proceedings, 2011, 1349(1): 451–452. doi: 10.1063/1.3605928
[125]	BOSLOUGH M B. Shock-induced chemical reactions in nickel-aluminum powder mixtures: radiation pyrometer measurements [J]. Chemical Physics Letters, 1989, 160(5/6): 618–622. doi: 10.1016/0009-2614(89)80074-0
[126]	TAN H, DAI C D, ZHANG L Y, et al. Method to determine the melting temperatures of metals under megabar shock pressures [J]. Applied Physics Letters, 2005, 87(22): 221905. doi: 10.1063/1.2043248
[127]	TAN H, AHRENS T J. Shock temperature measurements for metals [J]. High Pressure Research, 1990, 2(3): 159–182. doi: 10.1080/08957959008201036
[128]	NELLIS W J, YOO C S. Issues concerning shock temperature measurements of iron and other metals [J]. Journal of Geophysical Research:Solid Earth, 1990, 95(B13): 21749–21752. doi: 10.1029/JB095iB13p21749
[129]	ALFÈ D, GILLAN M J, PRICE G D. The melting curve of iron at the pressures of the Earth’s core from ab initio calculations [J]. Nature, 1999, 401(6752): 462–464. doi: 10.1038/46758
[130]	ANDERSON O L, ISAAK D G. Calculated melting curves for phases of iron [J]. American Mineralogist, 2000, 85(2): 376–385. doi: 10.2138/am-2000-2-317
[131]	BELONOSHKO A B, AHUJA R, JOHANSSON B. Quasi-ab initio molecular dynamic study of Fe melting [J]. Physical Review Letters, 2000, 84(16): 3638–3641. doi: 10.1103/PhysRevLett.84.3638
[132]	LAIO A, BERNARD S, CHIAROTTI G L, et al. Physics of iron at Earth’s core conditions [J]. Science, 2000, 287(5455): 1027–1030. doi: 10.1126/science.287.5455.1027
[133]	ALFÈ D, PRICE G D, GILLAN M J. Iron under Earth’s core conditions: liquid-state thermodynamics and high-pressure melting curve from ab initio calculations [J]. Physical Review B, 2002, 65(16): 165118. doi: 10.1103/PhysRevB.65.165118
[134]	ANDERSON O L, ISAAK D G, NELSON V E. The high-pressure melting temperature of hexagonal close-packed iron determined from thermal physics [J]. Journal of Physics and Chemistry of Solids, 2003, 64(11): 2125–2131. doi: 10.1016/S0022-3697(03)00112-4
[135]	ALFÈ D. Temperature of the inner-core boundary of the Earth: melting of iron at high pressure from first-principles coexistence simulations [J]. Physical Review B, 2009, 79(6): 060101(R). doi: 10.1103/PhysRevB.79.060101
[136]	SOLA E, ALFÈ D. Melting of iron under Earth’s core conditions from diffusion Monte Carlo free energy calculations [J]. Physical Review Letters, 2009, 103(7): 078501. doi: 10.1103/PhysRevLett.103.078501
[137]	KOMABAYASHI T, FEI Y W. Internally consistent thermodynamic database for iron to the Earth’s core conditions [J]. Journal of Geophysical Research: Solid Earth, 2010, 115(B3): B03202. doi: 10.1029/2009JB006442
[138]	BOUCHET J, MAZEVET S, MORARD G, et al. Ab initio equation of state of iron up to 1500 GPa [J]. Physical Review B, 2013, 87(9): 094102. doi: 10.1103/PhysRevB.87.094102
[139]	ZHANG W J, LIU Z Y, LIU Z L, et al. Melting curves and entropy of melting of iron under Earth’s core conditions [J]. Physics of the Earth and Planetary Interiors, 2015, 244: 69–77. doi: 10.1016/j.pepi.2014.10.011
[140]	DOROGOKUPETS P I, DYMSHITS A M, LITASOV K D, et al. Thermodynamics and equations of state of iron to 350 GPa and 6000 K [J]. Scientific Reports, 2017, 7: 41863. doi: 10.1038/srep41863
[141]	SUN T, BRODHOLT J P, LI Y G, et al. Melting properties from ab initio free energy calculations: iron at the Earth’s inner-core boundary [J]. Physical Review B, 2018, 98(22): 224301. doi: 10.1103/PhysRevB.98.224301
[142]	CUONG T D, PHAN A D. Efficient analytical approach for high-pressure melting properties of iron [J]. Vacuum, 2021, 185: 110001. doi: 10.1016/j.vacuum.2020.110001
[143]	WILLIAMS Q, JEANLOZ R, BASS J, et al. The melting curve of iron to 250 gigapascals: a constraint on the temperature at Earth’s center [J]. Science, 1987, 236(4798): 181–182. doi: 10.1126/science.236.4798.181
[144]	BOEHLER R, VON BARGEN N, CHOPELAS A. Melting, thermal expansion, and phase transitions of iron at high pressures [J]. Journal of Geophysical Research: Solid Earth, 1990, 95(B13): 21731–21736. doi: 10.1029/JB095iB13p21731
[145]	BOEHLER R. Temperatures in the Earth’s core from melting-point measurements of iron at high static pressures [J]. Nature, 1993, 363(6429): 534–536. doi: 10.1038/363534a0
[146]	SAXENA S K, SHEN G, LAZOR P. Temperatures in Earth’s core based on melting and phase transformation experiments on iron [J]. Science, 1994, 264(5157): 405–407. doi: 10.1126/science.264.5157.405
[147]	SHEN G Y, MAO H K, HEMLEY R J, et al. Melting and crystal structure of iron at high pressures and temperatures [J]. Geophysical Research Letters, 1998, 25(3): 373–376. doi: 10.1029/97GL03776
[148]	SHEN G Y, PRAKAPENKA V B, RIVERS M L, et al. Structure of liquid iron at pressures up to 58 GPa [J]. Physical Review Letters, 2004, 92(18): 185701. doi: 10.1103/PhysRevLett.92.185701
[149]	MA Y Z, SOMAYAZULU M, SHEN G Y, et al. In situ X-ray diffraction studies of iron to Earth-core conditions [J]. Physics of the Earth and Planetary Interiors, 2004, 143/144: 455–467. doi: 10.1016/j.pepi.2003.06.005
[150]	BOEHLER R, SANTAMARÍA-PÉREZ D, ERRANDONEA D, et al. Melting, density, and anisotropy of iron at core conditions: new X-ray measurements to 150 GPa [J]. Journal of Physics: Conference Series, 2008, 121: 022018. doi: 10.1088/1742-6596/121/2/022018
[151]	JACKSON J M, STURHAHN W, LERCHE M, et al. Melting of compressed iron by monitoring atomic dynamics [J]. Earth and Planetary Science Letters, 2013, 362: 143–150. doi: 10.1016/j.jpgl.2012.11.048
[152]	AQUILANTI G, TRAPANANTI A, KARANDIKAR A, et al. Melting of iron determined by X-ray absorption spectroscopy to 100 GPa [J]. Proceedings of the National Academy of Sciences of the United States of America, 2015, 112(39): 12042–12045. doi: 10.1073/pnas.1502363112
[153]	ZHANG D Z, JACKSON J M, ZHAO J Y, et al. Temperature of Earth’s core constrained from melting of Fe and Fe_0.9Ni_0.1 at high pressures [J]. Earth and Planetary Science Letters, 2016, 447: 72–83. doi: 10.1016/j.jpgl.2016.04.026
[154]	MORARD G, BOCCATO S, ROSA A D, et al. Solving controversies on the iron phase diagram under high pressure [J]. Geophysical Research Letters, 2018, 45(20): 11074–11082. doi: 10.1029/2018GL079950
[155]	SINMYO R, HIROSE K, OHISHI Y. Melting curve of iron to 290 GPa determined in a resistance-heated diamond-anvil cell [J]. Earth and Planetary Science Letters, 2019, 510: 45–52. doi: 10.1016/j.jpgl.2019.01.006
[156]	BROWN J M, MCQUEEN R G. Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa [J]. Journal of Geophysical Research: Solid Earth, 1986, 91(B7): 7485–7494. doi: 10.1029/JB091iB07p07485
[157]	BASS J D, SVENDSEN B, AHRENS T J. The temperature of shock compressed iron [M]//MANGHNANI M H, SYONO Y. High-Pressure Research in Mineral Physics: A Volume in Honor of Syuniti Akimoto. Terra Scientific Publishing Company, 1987: 393–402.
[158]	李西军. 铁高压熔化线研究 [D]. 北京: 中国工程物理研究院, 2000. LI X J. Study on high pressure iron melting curve [D]. Beijing: China Academy of Engineering Physics, 2000.
[159]	李西军, 龚自正, 刘福生, 等. 铁高压熔化线的测量——熔化机理的影响 [J]. 高压物理学报, 2001, 15(3): 221–225. doi: 10.11858/gywlxb.2001.03.009 LI X J, GONG Z Z, LIU F S, et al. A problem in measurements of high pressure melting curve of iron: influence of melting mechanism on the melting temperature [J]. Chinese Journal of High Pressure Physics, 2001, 15(3): 221–225. doi: 10.11858/gywlxb.2001.03.009
[160]	AHRENS T J, HOLLAND K G, CHEN G Q. Phase diagram of iron, revised-core temperatures [J]. Geophysical Research Letters, 2002, 29(7): 1150. doi: 10.1029/2001GL014350
[161]	PING Y, COPPARI F, HICKS D G, et al. Solid iron compressed up to 560 GPa [J]. Physical Review Letters, 2013, 111(6): 065501. doi: 10.1103/PhysRevLett.111.065501
[162]	孙峪怀. 铁的高压物态方程与熔化线研究 [D]. 成都: 西南交通大学, 2009. SUN Y H. Study on the equation of state and melting curve of iron [D]. Chengdu: Southwest Jiaotong University, 2009.
[163]	HARMAND M, RAVASIO A, MAZEVET S, et al. X-ray absorption spectroscopy of iron at multimegabar pressures in laser shock experiments [J]. Physical Review B, 2015, 92(2): 024108. doi: 10.1103/PhysRevB.92.024108
[164]	TORCHIO R, OCCELLI F, MATHON O, et al. Probing local and electronic structure in warm dense matter: single pulse synchrotron X-ray absorption spectroscopy on shocked Fe [J]. Scientific Reports, 2016, 6(1): 26402. doi: 10.1038/srep26402
[165]	ERRANDONEA D, SCHWAGER B, DITZ R, et al. Systematics of transition-metal melting [J]. Physical Review B, 2001, 63(13): 132104. doi: 10.1103/PhysRevB.63.132104
[166]	JEANLOZ R, KAVNER A. Melting criteria and imaging spectroradiometry in laser-heated diamond-cell experiments [J]. Philosophical Transactions of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 1996, 354(1711): 1279–1305. doi: 10.1098/rsta.1996.0049
[167]	DEWAELE A, MEZOUAR M, GUIGNOT N, et al. High melting points of tantalum in a laser-heated diamond anvil cell [J]. Physical Review Letters, 2010, 104(25): 255701. doi: 10.1103/PhysRevLett.104.255701
[168]	ERRANDONEA D, MACLEOD S G, BURAKOVSKY L, et al. Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions [J]. Physical Review B, 2019, 100(9): 094111. doi: 10.1103/PhysRevB.100.094111
[169]	STUTZMANN V, DEWAELE A, BOUCHET J, et al. High-pressure melting curve of titanium [J]. Physical Review B, 2015, 92(22): 224110. doi: 10.1103/PhysRevB.92.224110
[170]	ANZELLINI S, MONTESEGURO V, BANDIELLO E, et al. In situ characterization of the high pressure-high temperature melting curve of platinum [J]. Scientific Reports, 2019, 9(1): 13034. doi: 10.1038/s41598-019-49676-y
[171]	WECK G, RECOULES V, QUEYROUX J A, et al. Determination of the melting curve of gold up to 110 GPa [J]. Physical Review B, 2020, 101(1): 014106. doi: 10.1103/PhysRevB.101.014106
[172]	LORD O T, WOOD I G, DOBSON D P, et al. The melting curve of Ni to 1 Mbar [J]. Earth and Planetary Science Letters, 2014, 408: 226–236. doi: 10.1016/j.jpgl.2014.09.046
[173]	ERRANDONEA D, BURAKOVSKY L, PRESTON D L, et al. Experimental and theoretical confirmation of an orthorhombic phase transition in niobium at high pressure and temperature [J]. Communications Materials, 2020, 1(1): 60. doi: 10.1038/s43246-020-00058-2
[174]	DEWAELE A, MEZOUAR M, GUIGNOT N, et al. Melting of lead under high pressure studied using second-scale time-resolved X-ray diffraction [J]. Physical Review B, 2007, 76(14): 144106. doi: 10.1103/PhysRevB.76.144106
[175]	ANDRAULT D, MORARD G, BOLFAN-CASANOVA N, et al. Study of partial melting at high-pressure using in situ X-ray diffraction [J]. High Pressure Research, 2006, 26(3): 267–276. doi: 10.1080/08957950600897013
[176]	BOCCATO S, TORCHIO R, KANTOR I, et al. The melting curve of nickel up to 100 GPa explored by XAS [J]. Journal of Geophysical Research: Solid Earth, 2017, 122(12): 9921–9930. doi: 10.1002/2017JB014807
[177]	LI F F, CUI Q L, HE Z, et al. Brillouin scattering spectroscopy for a laser heated diamond anvil cell [J]. Applied Physics Letters, 2006, 88(20): 203507. doi: 10.1063/1.2205164
[178]	ZHANG J S, BASS J D, ZHU G H. Single-crystal Brillouin spectroscopy with CO₂ laser heating and variable q [J]. Review of Scientific Instruments, 2015, 86(6): 063905. doi: 10.1063/1.4922634
[179]	DI CICCO A, TRAPANANTI A. Study of local icosahedral ordering in liquid and undercooled liquid copper [J]. Journal of Non-Crystalline Solids, 2007, 353(32): 3671–3678. doi: 10.1016/j.jnoncrysol.2007.05.150
[180]	PASCARELLI S, MATHON O, MAIRS T, et al. The time-resolved and extreme-conditions XAS (TEXAS) facility at the European Synchrotron Radiation Facility: the energy-dispersive X-ray absorption spectroscopy beamline ID24 [J]. Journal of Synchrotron Radiation, 2016, 23(1): 353–368. doi: 10.1107/S160057751501783X
[181]	LORD O T, WALTER M J, DASGUPTA R, et al. Melting in the Fe-C system to 70 GPa [J]. Earth and Planetary Science Letters, 2009, 284(1/2): 157–167. doi: 10.1016/J.EPSL.2009.04.017
[182]	HRUBIAK R, MENG Y, SHEN G Y. Microstructures define melting of molybdenum at high pressures [J]. Nature Communications, 2017, 8: 14562. doi: 10.1038/ncomms14562
[183]	KARANDIKAR A, BOEHLER R. Flash melting of tantalum in a diamond cell to 85 GPa [J]. Physical Review B, 2016, 93(5): 054107. doi: 10.1103/PhysRevB.93.054107
[184]	YANG L X, KARANDIKAR A, BOEHLER R. Flash heating in the diamond cell: melting curve of rhenium [J]. Review of Scientific Instruments, 2012, 83(6): 063905. doi: 10.1063/1.4730595
[185]	ERRANDONEA D. The melting curve of ten metals up to 12 GPa and 1600 K [J]. Journal of Applied Physics, 2010, 108(3): 033517. doi: 10.1063/1.3468149
[186]	BASU A, FIELD M R, MCCULLOCH D G, et al. New measurement of melting and thermal conductivity of iron close to outer core conditions [J]. Geoscience Frontiers, 2020, 11(2): 565–568. doi: 10.1016/j.gsf.2019.06.007
[187]	BOEHLER R. The phase diagram of iron to 430 kbar [J]. Geophysical Research Letters, 1986, 13(11): 1153–1156. doi: 10.1029/GL013i011p01153
[188]	KUPENKO I, DUBROVINSKY L, DUBROVINSKAIA N, et al. Portable double-sided laser-heating system for Mössbauer spectroscopy and X-ray diffraction experiments at synchrotron facilities with diamond anvil cells [J]. Review of Scientific Instruments, 2012, 83(12): 124501. doi: 10.1063/1.4772458
[189]	APRILIS G, STROHM C, KUPENKO I, et al. Portable double-sided pulsed laser heating system for time-resolved geoscience and materials science applications [J]. Review of Scientific Instruments, 2017, 88(8): 084501. doi: 10.1063/1.4998985
[190]	ZHANG D Z, JACKSON J M, ZHAO J Y, et al. Fast temperature spectrometer for samples under extreme conditions [J]. Review of Scientific Instruments, 2015, 86(1): 013105. doi: 10.1063/1.4905431
[191]	BELONOSHKO A B, AHUJA R, JOHANSSON B. Molecular dynamics study of melting and fcc-bcc transitions in Xe [J]. Physical Review Letters, 2001, 87(16): 165505. doi: 10.1103/PhysRevLett.87.165505
[192]	BELONOSHKO A B, AHUJA R, JOHANSSON B. Stability of the body-centred-cubic phase of iron in the Earth’s inner core [J]. Nature, 2003, 424(6952): 1032–1034. doi: 10.1038/nature01954
[193]	SALAMAT A, FISCHER R A, BRIGGS R, et al. In situ synchrotron X-ray diffraction in the laser-heated diamond anvil cell: melting phenomena and synthesis of new materials [J]. Coordination Chemistry Reviews, 2014, 277/278: 15–30. doi: 10.1016/j.ccr.2014.01.034
[194]	GLAZYRIN K, POUROVSKII L V, DUBROVINSKY L, et al. Importance of correlation effects in hcp iron revealed by a pressure-induced electronic topological transition [J]. Physical Review Letters, 2013, 110(11): 117206. doi: 10.1103/PhysRevLett.110.117206
[195]	WANG Y, WANG J J, HERMANN A, et al. Electronically driven 1D cooperative diffusion in a simple cubic crystal [J]. Physical Review X, 2021, 11(1): 011006. doi: 10.1103/PhysRevX.11.011006
[196]	HRUBIAK R, MENG Y, SHEN G Y. Experimental evidence of a body centered cubic iron at the Earth’s core condition [J/OL]. arXiv preprint arXiv: 1804.05109. (2018-04-13)[2021-08-02]. https://arxiv.org/abs/1804.05109.
[197]	LORD O T, WANN E T H, HUNT S A, et al. The NiSi melting curve to 70 GPa [J]. Physics of the Earth and Planetary Interiors, 2014, 233: 13–23. doi: 10.1016/j.pepi.2014.05.005
[198]	GEBALLE Z M, JEANLOZ R. Origin of temperature plateaus in laser-heated diamond anvil cell experiments [J]. Journal of Applied Physics, 2012, 111(12): 123518. doi: 10.1063/1.4729905
[199]	MENG Y, SHEN G, MAO H K. Double-sided laser heating system at HPCAT for in situ X-ray diffraction at high pressures and high temperatures [J]. Journal of Physics: Condensed Matter, 2006, 18(25): S1097–S1103. doi: 10.1088/0953-8984/18/25/S17
[200]	SHEN G Y, MAO H K, HEMLEY R J. Laser-heated diamond anvil cell technique: double-sided heating with multimode Nd: YAG laser [C]//Proceedings of the Advance Materials '96 New Trends in High Pressure Research, 3rd International Symposium Advanced Materials. Ibaraki: National Institute for Research in Inorganic Materials, 1996.
[201]	BOEHLER R. Laser heating in the diamond cell: techniques and applications [J]. Hyperfine Interactions, 2000, 128(1): 307–321. doi: 10.1023/A:1012648019016
[202]	ERRANDONEA D, SOMAYAZULU M, HÄUSERMANN D, et al. Melting of tantalum at high pressure determined by angle dispersive X-ray diffraction in a double-sided laser-heated diamond-anvil cell [J]. Journal of Physics: Condensed Matter, 2003, 15(45): 7635–7649. doi: 10.1088/0953-8984/15/45/003
[203]	NGUYEN J H, HOLMES N C. Iron sound velocities in shock wave experiments [J]. AIP Conference Proceedings, 2000, 505(1): 81–84. doi: 10.1063/1.1303426
[204]	WASSERMAN E, STIXRUDE L, COHEN R E. Thermal properties of iron at high pressures and temperatures [J]. Physical Review B, 1996, 53(13): 8296–8309. doi: 10.1103/PhysRevB.53.8296
[205]	HONG N T, HIEU H K. High-pressure melting curves of and phases of iron [J]. VNU Journal of Science: Mathematics-Physics, 2019, 35(4): 99–105. doi: 10.25073/2588-1124/VNUMAP.4382
[206]	BELASHCHENKO D K. Estimation of the thermodynamic characteristics of the Earth’s core using the embedded atom model [J]. Geochemistry International, 2014, 52(6): 456–466. doi: 10.1134/S0016702914060020
[207]	ZHUANG J Y, WANG H J, ZHANG Q, et al. Thermodynamic properties of ε-Fe with thermal electronic excitation effects on vibrational spectra [J]. Physical Review B, 2021, 103(14): 144102. doi: 10.1103/PhysRevB.103.144102
[208]	HIEU H K, HAI T T, HONG N T, et al. Pressure dependence of melting temperature and shear modulus of hcp-iron [J]. High Pressure Research, 2017, 37(3): 267–277. doi: 10.1080/08957959.2017.1318131
[209]	VAN HUNG V, HAI D T, BINH L T T. Melting curve of metals with defect: pressure dependence [J]. Computational Materials Science, 2013, 79: 789–794. doi: 10.1016/j.commatsci.2013.07.042
[210]	KRESSE G, JOUBERT D. From ultrasoft pseudopotentials to the projector augmented-wave method [J]. Physical Review B, 1999, 59(3): 1758–1775. doi: 10.1103/PhysRevB.59.1758
[211]	BLÖCHL P E. Projector augmented-wave method [J]. Physical Review B, 1994, 50(24): 17953–17979. doi: 10.1103/PhysRevB.50.17953
[212]	DAW M S, FOILES S M, BASKES M I. The embedded-atom method: a review of theory and applications [J]. Materials Science Reports, 1993, 9(7/8): 251–310. doi: 10.1016/0920-2307(93)90001-U
[213]	LINDEMANN F A. The calculation of molecular vibration frequencies [J]. Zeitschrift fur Physik, 1910, 11: 609–612.
[214]	WOLF G H, JEANLOZ R. Lindemann melting law: anharmonic correction and test of its validity for minerals [J]. Journal of Geophysical Research: Solid Earth, 1984, 89(B9): 7821–7835. doi: 10.1029/JB089iB09p07821
[215]	KUSHWAH S S, TOMAR Y S, UPADHYAY A K. On the volume-dependence of the Grüneisen parameter and the Lindemann law of melting [J]. Journal of Physics and Chemistry of Solids, 2013, 74(8): 1143–1145. doi: 10.1016/j.jpcs.2013.03.014
[216]	SIMON F, GLATZEL G. Bemerkungen zur Schmelzdruckkurve [J]. Zeitschrift für Anorganische und Allgemeine Chemie, 1929, 178(1): 309–316. doi: 10.1002/zaac.19291780123
[217]	KRAUT E A, KENNEDY G C. New melting law at high pressures [J]. Physical Review, 1966, 151(2): 668–675. doi: 10.1103/PhysRev.151.668
[218]	杜宜瑾. 凝聚态物理研究 [M]. 合肥: 安徽大学出版社, 1998. DU Y J. Research on condensed matter physics [M]. Hefei: Anhui University Press, 1998.
[219]	WANG Z W, LAZOR P, SAXENA S K. A simple model for assessing the high pressure melting of metals: nickel, aluminum and platinum [J]. Physica B: Condensed Matter, 2001, 293(3/4): 408–416. doi: 10.1016/S0921-4526(00)00542-1
[220]	LI J, FEI Y. Experimental constraints on core composition [J]. Treatise on Geochemistry, 2014, 3: 527–557. doi: 10.1016/B978-0-08-095975-7.00214-X
[221]	MCDONOUGH W F. Compositional model for the Earth’s core [J]. Treatise on Geochemistry, 2014, 3: 559–577. doi: 10.1016/B978-0-08-095975-7.00215-1
[222]	SAKAMAKI K, TAKAHASHI E, NAKAJIMA Y, et al. Melting phase relation of FeH_x up to 20 GPa: implication for the temperature of the Earth’s core [J]. Physics of the Earth and Planetary Interiors, 2009, 174(1/2/3/4): 192–201. doi: 10.1016/j.pepi.2008.05.017
[223]	ASANUMA H, OHTANI E, SAKAI T, et al. Static compression of Fe_0.83Ni_0.09Si_0.08 alloy to 374 GPa and Fe_0.93Si_0.07 alloy to 252 GPa: implications for the Earth’s inner core [J]. Earth and Planetary Science Letters, 2011, 310(1/2): 113–118. doi: 10.1016/j.jpgl.2011.06.034
[224]	ASANUMA H, OHTANI E, SAKAI T, et al. Melting of iron-silicon alloy up to the core-mantle boundary pressure: implications to the thermal structure of the Earth’s core [J]. Physics and Chemistry of Minerals, 2010, 37(6): 353–359. doi: 10.1007/s00269-009-0338-7
[225]	FISCHER R A, CAMPBELL A J, CARACAS R, et al. Equation of state and phase diagram of Fe-16Si alloy as a candidate component of Earth’s core [J]. Earth and Planetary Science Letters, 2012, 357/358: 268–276. doi: 10.1016/j.jpgl.2012.09.022
[226]	FISCHER R A, CAMPBELL A J, REAMAN D M, et al. Phase relations in the Fe-FeSi system at high pressures and temperatures [J]. Earth and Planetary Science Letters, 2013, 373: 54–64. doi: 10.1016/j.jpgl.2013.04.035
[227]	FISCHER R A, CAMPBELL A J, CARACAS R, et al. Equations of state in the Fe-FeSi system at high pressures and temperatures [J]. Journal of Geophysical Research: Solid Earth, 2014, 119(4): 2810–2827. doi: 10.1002/2013JB010898
[228]	SEAGLE C T, HEINZ D L, CAMPBELL A J, et al. Melting and thermal expansion in the Fe-FeO system at high pressure [J]. Earth and Planetary Science Letters, 2008, 265(3/4): 655–665. doi: 10.1016/j.jpgl.2007.11.004
[229]	KOMABAYASHI T. Thermodynamics of melting relations in the system Fe-FeO at high pressure: implications for oxygen in the Earth’s core [J]. Journal of Geophysical Research: Solid Earth, 2014, 119(5): 4164–4177. doi: 10.1002/2014JB010980
[230]	OZAWA H, TAKAHASHI F, HIROSE K, et al. Phase transition of FeO and stratification in Earth’s outer core [J]. Science, 2011, 334(6057): 792–794. doi: 10.1126/science.1208265
[231]	FEI Y W, BROSH E. Experimental study and thermodynamic calculations of phase relations in the Fe-C system at high pressure [J]. Earth and Planetary Science Letters, 2014, 408: 155–162. doi: 10.1016/j.jpgl.2014.09.044
[232]	CAMPBELL A J, SEAGLE C T, HEINZ D L, et al. Partial melting in the iron-sulfur system at high pressure: a synchrotron X-ray diffraction study [J]. Physics of the Earth and Planetary Interiors, 2007, 162(1/2): 119–128. doi: 10.1016/j.pepi.2007.04.001
[233]	KAMADA S, OHTANI E, TERASAKI H, et al. Melting relationships in the Fe-Fe₃S system up to the outer core conditions [J]. Earth and Planetary Science Letters, 2012, 359/360: 26–33. doi: 10.1016/j.jpgl.2012.09.038
[234]	KAMADA S, TERASAKI H, OHTANI E, et al. Phase relationships of the Fe-FeS system in conditions up to the Earth’s outer core [J]. Earth and Planetary Science Letters, 2010, 294(1/2): 94–100. doi: 10.1016/j.jpgl.2010.03.011
[235]	MORARD G, ANDRAULT D, GUIGNOT N, et al. In situ determination of Fe-Fe₃S phase diagram and liquid structural properties up to 65 GPa [J]. Earth and Planetary Science Letters, 2008, 272(3/4): 620–626. doi: 10.1016/j.jpgl.2008.05.028
[236]	CHUDINOVSKIKH L, BOEHLER R. Eutectic melting in the system Fe-S to 44 GPa [J]. Earth and Planetary Science Letters, 2007, 257(1/2): 97–103. doi: 10.1016/j.jpgl.2007.02.024
[237]	MORI Y, OZAWA H, HIROSE K, et al. Melting experiments on Fe-Fe₃S system to 254 GPa [J]. Earth and Planetary Science Letters, 2017, 464: 135–141. doi: 10.1016/j.jpgl.2017.02.021
[238]	TERASAKI H, KAMADA S, SAKAI T, et al. Liquidus and solidus temperatures of a Fe-O-S alloy up to the pressures of the outer core: implication for the thermal structure of the Earth’s core [J]. Earth and Planetary Science Letters, 2011, 304(3/4): 559–564. doi: 10.1016/j.jpgl.2011.02.041
[239]	HUANG H J, HU X J, JING F Q, et al. Melting behavior of Fe-O-S at high pressure: a discussion on the melting depression induced by O and S [J]. Journal of Geophysical Research: Solid Earth, 2010, 115(B5): B05207. doi: 10.1029/2009JB006514
[240]	ZHANG Y J, SEKINE T, HE H L, et al. Shock compression of Fe-Ni-Si system to 280 GPa: implications for the composition of the Earth’s outer core [J]. Geophysical Research Letters, 2014, 41(13): 4554–4559. doi: 10.1002/2014GL060670
[241]	ZHANG L, FEI Y W. Effect of Ni on Fe-FeS phase relations at high pressure and high temperature [J]. Earth and Planetary Science Letters, 2008, 268(1/2): 212–218. doi: 10.1016/j.jpgl.2008.01.028
[242]	HIROSE K, LABROSSE S, HERNLUND J. Composition and state of the core [J]. Annual Review of Earth and Planetary Sciences, 2013, 41(1): 657–691. doi: 10.1146/annurev-earth-050212-124007
[243]	ZHANG Y J, SEKINE T, HE H L, et al. Experimental constraints on light elements in the Earth’s outer core [J]. Scientific Reports, 2016, 6: 22473. doi: 10.1038/srep22473
[244]	DZIEWONSKI A M, ANDERSON D L. Preliminary reference Earth model [J]. Physics of the Earth and Planetary Interiors, 1981, 25(4): 297–356. doi: 10.1016/0031-9201(81)90046-7
[245]	ALFÈ D, GILLAN M J, PRICE G D. Composition and temperature of the Earth’s core constrained by combining ab initio calculations and seismic data [J]. Earth and Planetary Science Letters, 2002, 195(1/2): 91–98. doi: 10.1016/S0012-821X(01)00568-4
[246]	GUBBINS D, ALFÈ D, MASTERS G, et al. Can the Earth’s dynamo run on heat alone? [J]. Geophysical Journal International, 2003, 155(2): 609–622. doi: 10.1046/j.1365-246X.2003.02064.x
[247]	VOČADLO L, ALFÈ D, GILLAN M J, et al. The properties of iron under core conditions from first principles calculations [J]. Physics of the Earth and Planetary Interiors, 2003, 140(1/2/3): 101–125. doi: 10.1016/j.pepi.2003.08.001
[248]	NGUYEN J H, AKIN M C, CHAU R, et al. Molybdenum sound velocity and shear modulus softening under shock compression [J]. Physical Review B, 2014, 89(17): 174109. doi: 10.1103/PhysRevB.89.174109
[249]	WANG J, COPPARI F, SMITH R F, et al. X-ray diffraction of molybdenum under shock compression to 450 GPa [J]. Physical Review B, 2015, 92(17): 174114. doi: 10.1103/PhysRevB.92.174114
[250]	LUO S N, AHRENS T J. Shock-induced superheating and melting curves of geophysically important minerals [J]. Physics of the Earth and Planetary Interiors, 2004, 143/144: 369–386. doi: 10.1016/j.pepi.2003.04.001
[251]	DAI C D, JIN X G, ZHOU X M, et al. Sound velocity variations and melting of vanadium under shock compression [J]. Journal of Physics D: Applied Physics, 2001, 34(20): 3064–3070. doi: 10.1088/0022-3727/34/20/310
[252]	LANDA A, SÖDERLIND P, YANG L H. Ab initio phase stability at high temperatures and pressures in the V-Cr system [J]. Physical Review B, 2014, 89(2): 020101(R). doi: 10.1103/PhysRevB.89.020101
[253]	ZHANG T T, WANG S C, SONG H F, et al. Melting curve of vanadium up to 470 GPa simulated by ab initio molecular dynamics [J]. Journal of Applied Physics, 2019, 126(20): 205901. doi: 10.1063/1.5124520
[254]	KLUG D D. Melting points agree under pressure [J]. Physics, 2010, 3: 52. doi: 10.1103/Physics.3.52
[255]	SAMANTA A, TUCKERMAN M E, YU T Q, et al. Microscopic mechanisms of equilibrium melting of a solid [J]. Science, 2014, 346(6210): 729–732. doi: 10.1126/science.1253810