Metallization of Hydrogen under Static High Pressure and  the Inelastic X-ray Scattering Technique

LI Bing; DING Yang; WANG Lin; WENG Zuqian; YANG Wenge; JI Cheng; YANG Ke; MAO Ho-kwang

doi:10.11858/gywlxb.20210864

Volume 35 Issue 5

Sep 2021

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Abstract

References

Chinese Journal of High Pressure Physics > 2021 > 35(5): 050101.

JIANG Yi-Xuan, WANG Xing-Zhe, HE Hong-Liang. Channel Induced Electro-Mechanical Breakdown Model for Porous PZT95/5 Ceramics in Quasi-Static Electric Fields[J]. Chinese Journal of High Pressure Physics, 2014, 28(6): 680-685. doi: 10.11858/gywlxb.2014.06.006

Citation:

LI Bing, DING Yang, WANG Lin, WENG Zuqian, YANG Wenge, JI Cheng, YANG Ke, MAO Ho-kwang. Metallization of Hydrogen under Static High Pressure and the Inelastic X-ray Scattering Technique[J]. Chinese Journal of High Pressure Physics, 2021, 35(5): 050101. doi: 10.11858/gywlxb.20210864

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Metallization of Hydrogen under Static High Pressure and the Inelastic X-ray Scattering Technique

doi: 10.11858/gywlxb.20210864

LI Bing^1
,,
DING Yang¹,
WANG Lin^{1, 2},
WENG Zuqian^{1, 3},
YANG Wenge¹,
JI Cheng¹,
YANG Ke⁴,
MAO Ho-kwang^{1,*
,
,}

1.
Center for High Pressure Science and Technology Advanced Research, Beijing 100094, China
2.
Center for High Pressure Science, State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, Hebei, China
3.
School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China.
4.
Shanghai Synchrotron Radiation Facility (SSRF), Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201204, China

Received Date: 11 Aug 2021
Rev Recd Date: 06 Sep 2021

Abstract

Abstract

The research on hydrogen under high pressure has always been a hot topic both in experimental and theoretical physics, the enthusiasm is rooted from the pursuit of its pressure-induced metallic state – metallic hydrogen. The pressure induced metallization of hydrogen is an electric phase transition from a wide gap insulator to a small gap semiconductor, and finally to a closed gap metal. However, due to the limitation of high pressure experiment conditions, the bandgap and electronic structure of the wide-gap hydrogen has never been directly observed. In this paper we will discuss the technical challenge and the development of experiment research on hydrogen metallization, meanwhile we will present our experiment results and the technical advance on the direct measurement of the wide-gap hydrogen by using inelastic X-ray scattering technique, and finally the outlook.
- hydrogen,
- ultra-high pressure,
- inelastic X-ray scattering

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1. 引言

铁电陶瓷(Pb(Zr, Ti)O₃)PZT95/5是指Zr和Ti的物质的量之比约95/5、铁电相(Ferroelectric Phase, FE)和反铁电相(Anti-Ferroelectric Phase, AFE)共存的一类铁电功能性材料。经过电极化的PZT95/5铁电陶瓷在外部高压机械加载的作用下, 能够发生从铁电相到反铁电相的转变, 释放束缚电荷并形成高功率的瞬态电源, 因此PZT95/5铁电陶瓷广泛用于脉冲能源装置中^[1-3]。近些年, 人们为了提高PZT95/5铁电陶瓷用作爆炸铁电体电源时的放电效率, 在材料制备过程中加入造孔剂, 从而制备出低密度的多孔PZT95/5陶瓷材料, 具有较优的电学和力学性能^[4-9]。

与致密材料相比, 多孔PZT95/5铁电陶瓷材料的抗冲击能力增强, 铁电-反铁电冲击相变压力降低, 从而其放电效率得到提高^[10-11]; 然而, 由于放电过程中所处的强电场, 及自身内部的孔隙、缺陷等因素影响, 多孔PZT95/5铁电陶瓷比致密材料更易产生电击穿失效现象, 从而影响其放电效率, 甚至导致电源失效。多孔PZT95/5铁电陶瓷在强电场作用下的电击穿现象是一个非常复杂的瞬态过程, 贯穿于材料内部, 往往难以观察。同时, 影响铁电陶瓷材料电击穿失效的临界电场强度的因素很多, 如制备工艺、微观结构、点缺陷、气孔、密度等^[12-14]。目前, 关于多孔铁电陶瓷的研究主要集中在采用不同制备工艺提高材料的抗击穿能力上。Shin等人^[14]在研究BaTiO₃陶瓷的电击穿强度时发现, 随着烧结温度的提高, 孔洞的尺寸增大, 材料的电击穿强度降低; 杨洪^[15]利用传统固相法、非均相沉淀法、热压和陶瓷复合技术等方法, 制备出不同微观结构和性能的PZT95/5型铁电陶瓷, 其中利用热压烧结方式制备的PZT95/5陶瓷抗击穿强度最高。也有部分工作对多孔铁电陶瓷材料的击穿特性进行了描述。Geis等人^[16]发现, PZT53/47铁电陶瓷的抗击穿能力随材料孔隙率的增加而线性降低; 曾涛^[17]通过实验测试不同造孔剂、不同孔隙率铁电陶瓷材料的击穿电场强度, 给出了击穿场强随孔隙率变化的规律, 并采用Gerson等人提出的串联孔洞模型^[18]解释孔隙率对多孔PZT95/5铁电陶瓷的抗电击穿强度的影响, 指出微裂纹和不规则的本征孔洞是容易发生电击穿的弱点处。近年来, 基于实验观测的固体介电质材料的电击穿通道等微观图像, 一些学者从电击穿机制(如热击穿、电-机械击穿、弱点击穿、本征击穿等)入手, 研究电击穿失效的机理^[19-20], 给出了定性解释^[21]。但由于材料内部缺陷的随机性及多样性, 相关理论和模型对临界电场的预测往往与实验结果不符, 甚至相差几个数量级, 定量预测模型的研究也少有开展。

基于固体电介质的通道电-机械击穿机理, 及铁电陶瓷孔洞局部放电理论, 本研究拟建立一种多孔铁电陶瓷导电通道诱导的电击穿模型, 通过分析铁电陶瓷材料的通道裂纹扩展所需克服的总电-机械能量, 预测静电场中多孔铁电陶瓷材料的临界击穿电场强度, 并与材料孔隙率、介电常数、微观机制通道特征半径等建立关联。

2. 静电场中多孔铁电陶瓷的电击穿失效模型

考虑一静电场作用下的多孔铁电陶瓷材料, 假设击穿通道从材料内部的孔洞或裂纹、缺陷处开始, 端部呈半径为r的半球形。记通道扩展方向的长度为dl, 体积为dV, 则导电通道内部的静电能W_es可表示为

$W_{\mathrm{es}}=\frac{1}{2} \boldsymbol{D} \boldsymbol{E} \mathrm{d} V=\frac{1}{2} \boldsymbol{D} \boldsymbol{E} \pi r^{2} \mathrm{d} l$

(1)

式中:E为导电通道端部孔洞处的电场强度; D为电位移矢量, 且有D=ε₀ε_rE, ε₀和ε_r分别是真空介电常数和铁电陶瓷材料的相对介电常数。

一般而言, 由于材料内部存在裂纹, 使电场非均匀分布, 因此通道裂纹内部的电场与外加电场的分布不同。在外加电场的作用下, 通道内的气体被电离为导体, 导致孔洞表面产生感应电荷, 同时孔洞内也存在空间自由电荷。这两部分电荷使孔洞周围的电场发生变化, 从而引起孔洞局部放电^[22-23]。为了分析方便, 不妨假设通道内的电场E均匀分布, 且与外电场E₀存在如下关系

$\boldsymbol{E}=h \boldsymbol{E}_{0}$

(2)

式中:h为电场局部分布因子。它与铁电陶瓷材料的介电常数及通道形状有关, 可以表示为^[24]

$h=\frac{k \varepsilon_{\mathrm{r}}}{1+(k-1) \varepsilon_{\mathrm{r}}}$

(3)

式中:k为无量纲常数, 与通道尺寸和取向有关。考虑一般情形, 可将通道看作椭球形状(a, b分别为长、短半轴), 当a/b≪1时, 表示一沿电场方向的微裂纹通道, 即

$k = \left\{ \begin{array}{l} \frac{\left[\left(\frac{b}{a}\right)^{2}-1\right]^{\frac{3}{2}}}{\left(\frac{b}{a}\right)^{2}\left\{\sqrt{\left(\frac{b}{a}\right)^{2}-1}-\arctan \left[\sqrt{\left(\frac{b}{a}\right)^{2}}-1\right]\right\}} & a / b<1\\ 3 &a / b = 1 \end{array} \right.$

(4)

进一步, 通道裂纹的电-机械能可表示为

$W_{\mathrm{em}}=\frac{1}{2} \boldsymbol{\sigma \gamma} \mathrm{d} V=\frac{1}{2} \boldsymbol{\sigma \gamma} \pi r^{2} \mathrm{d} l$

(5)

式中:σ=ε₀ε_rE²/2, 为静电场引起的Maxwell应力; γ=σ/Y为应变, Y为杨氏模量。结合(1)式~(5)式, 通道处的总能量可表示为静电能与电-机械能之和, 即

$W_{\mathrm{es}}+W_{\mathrm{em}}=\frac{1}{2} \boldsymbol{D} \boldsymbol{E} \pi r^{2} \mathrm{d} l+\frac{1}{2} \boldsymbol{\sigma \gamma} \pi r^{2} \mathrm{d} l=\left(\frac{1}{2} \varepsilon_{0} \varepsilon_{\mathrm{r}} h^{2} \boldsymbol{E}_{0}^{2}+\frac{\varepsilon_{0}^{2} \varepsilon_{\mathrm{r}}^{2} h^{4}}{8 Y} \boldsymbol{E}_{0}^{4}\right) \pi r^{2} \mathrm{d} l$

(6)

固体介质的通道电-机械击穿模型认为, 材料内部存在通道裂纹, 在外电场作用下, 导电通道裂纹的能量为静电能和电-机械能(弹性能)之和。随着外加电场的增强, 通道裂纹开裂、蔓延扩展, 此时需要克服通道的表面能W_fs。当外部静电能和电-机械能高于通道裂纹的表面能时, 电介质被击穿破坏^[25-26], 相应的表面能表示如下

$W_{\mathrm{fs}}=2 G \pi r \mathrm{~d} l$

(7)

式中:G为铁电陶瓷材料的机械能释放率。铁电陶瓷的临界机械能释放率G_c一般为10~20 J/m^[27]。

导电通道扩展以致铁电陶瓷材料击穿破坏的临界准则为

$W_{\mathrm{es}}+W_{\mathrm{em}} \geqslant W_{\mathrm{fs}}$

(8)

结合(6)式、(7)式, 并求解(8)式, 不难得到电击穿的临界电场强度E_c为

$E_{\mathrm{c}}=\left(1-\frac{1}{k}\right)\left[\frac{2}{r \varepsilon_{0} \varepsilon_{\mathrm{r}}}\left(\sqrt{r^{2} Y^{2}+4 G_{\mathrm{c}} r Y}-r Y\right)\right]^{\frac{1}{2}}$

(9)

为了表征多孔材料的相关电性参数和力学参数, 以致密PZT95/5铁电陶瓷的相关参数为基准, 采用多孔材料性能表征方法^[28-29], 获得多孔PZT95/5陶瓷的相对介电常数及等效杨氏模量

$\begin{aligned} \varepsilon_{\mathrm{r}} & =\varepsilon_{\mathrm{r}}^{0}\left[1-\left(\frac{p}{k_{\mathrm{s}}}\right)^{\frac{2}{3}}\right] \end{aligned}$

(10)

$\begin{aligned} Y & =Y^{0}(1-\alpha p)^{n} \end{aligned}$

(11)

式中: 分别对应于致密PZT95/5铁电陶瓷的相对介电常数和杨氏模量; p为多孔材料的孔隙率; k_s为孔的形状因子, 对球形孔一般取k_s=1, 不规则形状孔取k_s=0.5;α, n为材料常数。对于一些多孔PZT95/5铁电陶瓷, 已有实验表明, 等效杨氏模量与孔隙率近似呈线性关系, 即n=1^[8]。

将(10)式代入临界电场强度表达式(9)式, 可得不同孔隙率下PZT95/5的击穿临界电场强度

$E_{\mathrm{c}}=\left(1-\frac{1}{k}\right)\left\{\frac{2 k_{\mathrm{s}}^{2 / 3}}{r \varepsilon_{0} \varepsilon_{\mathrm{r}}^{0}\left(k_{\mathrm{s}}^{2 / 3}-p^{2 / 3}\right)}\left[\sqrt{r^{2}\left(Y^{0}\right)^{2}(1-\alpha p)^{2}+4 G_{\mathrm{c}} r Y^{0}(1-\alpha p)}-r Y^{0}(1-\alpha p)\right]\right\}^{\frac{1}{2}}$

(12)

对于致密材料(即p=0), (12)式可以进一步简化为

$E_{\mathrm{c}}=\left(1-\frac{1}{k}\right)\left\{\frac{2}{r \varepsilon_{0} \varepsilon_{\mathrm{r}}^{0}}\left[\sqrt{r^{2}\left(Y^{0}\right)^{2}+4 G_{\mathrm{c}} r Y^{0}}-r Y^{0}\right]\right\}^{\frac{1}{2}}$

(13)

3. 结果分析与讨论

基于第2节建立的多孔PZT95/5铁电陶瓷材料在静电场作用下的电击穿模型, 预测不同孔隙率的铁电陶瓷材料的击穿临界电场强度, 并与实验测量值进行对比分析。

在外加电场作用下, 材料内部的裂纹尖端处往往由于电势分布梯度大而出现局部电场增强现象, 故最易发生电击穿, 其次是不规则气孔。取铁电陶瓷内部的椭球形气孔, 其长、短轴比a/b=0.1, 可近似视为一裂纹。此外, 已有的多孔铁电陶瓷材料内部微观特征及击穿通道的扫描电子显微镜图像表明:通道特征尺寸一般为微米级, 而且随着材料孔隙率的增加而增大^[17]。我们据此来选取计算预测中的通道特征半径。

表 1给出了不同孔隙率条件下, 静电场中铁电陶瓷的电击穿实验结果以及模型预测结果。可以看出:电击穿临界电场强度的预测值和实验值处于同一数量级, 且有部分结果在数值上吻合良好; 随着材料孔隙率的增加, 电击穿临界电场强度降低; 采用热烧结方式制备的致密陶瓷孔隙率近似为零, 电击穿临界场强值最大, 甚至比正常烧结的致密(实际上仍有一定的孔隙率)PZT95/5陶瓷高1个数量级; 此外, 加入球形聚甲基丙烯酸甲酯(Polymethylmethacrylate, PMMA)造孔剂的多孔PZT95/5陶瓷比加入不规则形状糊精(Dextrin)的多孔PZT95/5陶瓷具有更高的抗电击穿强度。

表 1 不同孔隙率及不同造孔剂的PZT95/5铁电陶瓷材料的击穿临界电场强度

Table 1. Dielectric breakdown strength of PZT95/5 ceramics with different porosities and pore formers

Material^[17]	Porosity/ (%)	Relative dielectric constant	Young's modulus/(GPa)	Path size/(μm)	Predicted breakdown strength/(kV/m)	Experimental breakdown strength/(kV/m)
Dense material by hot-press method	0.4	314	148	1.00	16 500	15 000
Dense	4.1	309	148	5.00	7 460	6 800
PMMA (Spherical shape)	7.2	281	136	6.00	7 140	-
	11.2	252	121	7.00	6 980	-
	13.5	241	112	8.00	6 680	6 600
Dextrin (Irregular pores)	8.9	249	121	7.50	6 790	6 650
Dextrin (Irregular pores)	10.7	236	112	8.00	6 750	6 550

下载: 导出CSV

| 显示表格

一般而言, 固体材料的内部微结构特征及电学、力学性能均能影响到其电击穿特性。多孔铁电材料的电击穿临界场强表达式((12)式或(13)式)也清晰地表明, 材料的孔隙率、介电常数、杨氏模量及导电通道特征尺寸等均能影响其电击穿临界场强。

图 1和图 2分别给出了电击穿临界场强随材料孔隙率及导电通道特征尺寸变化的曲线。计算时, 取造孔剂为球形, 即k_s=1。从图 1可以看出, 对于同一通道半径, 随着孔隙率的增加, 电击穿临界场强变化不大; 而图 2则表明对于某一孔隙率, 随着导电通道特征尺寸的增大, 电击穿强度显著降低。铁电陶瓷临界电击穿场强随电击穿通道特征尺寸变化明显, 材料孔隙率越大, 内部电击穿通道特征尺寸越大, 由此导致铁电陶瓷材料的电击穿场强显著降低。该结果与已有的一些实验结果定性上一致。

图 1 PZT95/5陶瓷电击穿场强随孔隙率的变化曲线

Figure 1. Dielectric breakdown strength of PZT95/5 ceramics as a function of porosity

下载: 全尺寸图片幻灯片

图 2 PZT95/5陶瓷电击穿场强随通道特征尺寸的变化曲线

Figure 2. Dielectric breakdown strength of PZT95/5 ceramics as a function of path feature size

下载: 全尺寸图片幻灯片

4. 结论

(1) 成功建立了材料内部存在导电通道时多孔铁电陶瓷的电击穿模型, 并基于此模型, 给出了不同孔隙率下铁电陶瓷的电击穿临界场强, 其预测结果与实验测试结果吻合良好, 证实了本模型的可靠性;

(2) 铁电陶瓷的临界电击穿场强随电击穿通道特征尺寸变化明显, 材料孔隙率越大, 内部电击穿通道特征尺寸越大, 电击穿场强显著降低;

(3) 本模型可进一步推广到冲击波作用下铁电陶瓷材料的去极化和电失效分析中。

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