Progress on Atomic Simulations of Phase Transition of Iron under Dynamic Loading

WANG Kun; XIAO Shifang; ZHU Wenjun; CHEN Jun; HU Wangyu

doi:10.11858/gywlxb.20210729

Volume 35 Issue 4

Aug 2021

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Abstract

References

Chinese Journal of High Pressure Physics > 2021 > 35(4): 040110.

YUAN Qin, LI Shuaiqi, ZHOU Li, HE Duanwei. Reciprocating Phase Transitions Behavior of Germanium under High Pressure[J]. Chinese Journal of High Pressure Physics, 2022, 36(5): 051104. doi: 10.11858/gywlxb.20220578

Citation:

WANG Kun, XIAO Shifang, ZHU Wenjun, CHEN Jun, HU Wangyu. Progress on Atomic Simulations of Phase Transition of Iron under Dynamic Loading[J]. Chinese Journal of High Pressure Physics, 2021, 35(4): 040110. doi: 10.11858/gywlxb.20210729

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Progress on Atomic Simulations of Phase Transition of Iron under Dynamic Loading

doi: 10.11858/gywlxb.20210729

WANG Kun^1
,,
XIAO Shifang^{2,*
,
,},
ZHU Wenjun³,
CHEN Jun⁴,
HU Wangyu^{1,*
,
,}

1.
College of Materials Science and Engineering, Hunan University, Changsha 410082, Hunan, China
2.
School of Physics and Electronics, Hunan University, Changsha 410082, Hunan, China
3.
National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, CAEP, Mianyang 621999, Sichuan, China
4.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received Date: 03 Mar 2021
Rev Recd Date: 16 Apr 2021

Abstract

Abstract

$\alpha$ ↔ $\varepsilon$ transformation of iron is a prototype of high-pressure phase transition in metals. With the progress of detecting technology, mechanism and dynamics of the phase transition have being investigated in depth. Laser-driven in situ X-ray observation combined with non-equilibrium molecular dynamics simulation is one of the most effective approach to the issue. In present paper, the progress of atomic investigations on plasticity and phase transformation of iron under dynamic loading is reviewed. The effects of high-pressure interatomic potential of iron, crystal anisotropy, impact strength, strain rate, strain gradient and various initial crystal defects on phase transformation mechanism, phase transformation and spalling of iron are analyzed. Meanwhile, the latest progress of our researches on nonplanar-loading responses of iron is reported. Finally, the conclusion and prospect are given.
- high-pressure structural transition,
- plasticity,
- spall,
- molecular dynamics,
- interatomic potential,
- iron

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对物质施加一定范围的压力时，处于高压环境的物质致密度增加，在发生相变之前，虽然晶格被压缩，但是原子与原子之间的相对位置不发生改变，仍然以原来的晶体结构存在。当施加的压力更高时，晶格失稳，原子与原子之间不再保持原有的位置关系，原子发生重组，形成新的晶体结构，即发生压致相变^[1-3]。从旧相失稳坍塌到新相形核生长，整个过程中物质所处的高压环境会阻碍原子的长程扩散，从而抑制新相晶粒长大，相对于常压或低压环境下的相变，压致相变过程通常会让物质的晶粒得到细化^[4-6]。

物质发生压致相变时，在新相成核阶段，高压能够降低成核的激活能，促进成核；在新相生长阶段，高压可以提升原子的生长激活能，减缓相变过程中新相的生长速率，从而抑制新相晶粒的长大^[4-10]。既然高压能够在物质相变过程中抑制新相晶粒的长大，让物质的晶粒得到细化，能否使这种晶粒细化效果得到累积？若要实现晶粒细化效果累积，需要使物质经历多次相变；若要使一种材料经历多次相变，一般需要让该材料在高压作用下发生可逆相变。

本研究将实现物质在升卸压过程中多次相变的实验方法称为往复压致相变法^[11]。前期本课题组选用 Bi、Fe、Si 3种物质进行了往复压致相变实验^[11]，结果表明，往复压致相变法对Si有很好的晶粒细化效果。分析发现，Si可以在0～20 GPa的升卸压过程中发生可逆相变，在卸压过程中从高压相到常（低）压相的相变为扩散型相变。Fe同样能在0～20 GPa的升卸压过程中发生可逆相变，但整个过程中涉及到的相变均为位移型相变。据此推测，在往复压致相变过程中，如果存在扩散型相变，往复压致相变对物质的晶粒细化效果更明显。

根据现有的实验结论，推测能够发生可逆相变且在相变过程中涉及扩散型相变的物质能够在往复压致相变过程中实现明显的晶粒细化效果。为了验证该猜想，本研究选用与Si性质相似、同属第四主族的半导体材料Ge进行往复压致相变实验。如图1所示，Ge在常温常压下以立方相金刚石结构（DC Ge）存在，在8～12 GPa相变为金属相β-Sn结构（β-Sn Ge），卸压到8 GPa以下后会相变为亚稳相四方相ST12（ST12 Ge），ST12 Ge与β-Sn Ge之间的相变为可逆相变^[12-16]。本研究将对Ge在高压下的往复压致相变过程中的晶粒细化规律以及相的演化行为进行研究。

图 1 锗的晶胞结构及相变路径

Figure 1. Unit cell structure and phase transition path of germanium

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1. 实　验

1.1 块体样品制备

选用直径为4 mm、高度为1 mm、晶向为<111>的金刚石结构锗（DC Ge）单晶圆片（纯度高于99.99%）作为初始样品，其晶体结构、X射线衍射（X-ray diffraction，XRD）谱及光学照片如图2所示。

图 2 立方金刚石结构锗的晶胞图(a)以及初始样品的XRD谱(b)和光学照片(c)

Figure 2. (a) Unit cell diagram of cubic diamond-structured germanium, (b) XRD pattern of the initial sample, (c) optical microscope photograph of the initial sample

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采用四川大学研制的含有二级增压装置的6×8 MN六面顶压机进行实验^[17-19]。如图3(a)和图3(b)所示，选用棱长为14 mm的掺钴氧化镁八面体作为传压介质，8个截角为8 mm的碳化钨硬质合金立方块作为二级增压装置产生高压，将初始样品放置在八面体的中心位置。腔体压力由Bi、ZnTe、ZnS等标定^[20]。实验过程中，保持升、卸压速率一致，均为5 GPa/h，保压时间为10 min，最高压力为15 GPa，中间压力为7 GPa，详细的压力-时间（p-t）曲线如图3(c)所示。

图 3 (a) 实验组装示意图（用MgO八面体对样品进行包裹）；(b) 含有二级增压装置的6×8 MN六面顶压机示意图（组装好的样品和MgO八面体放置在由8个碳化钨硬质合金截角立方块合围成的八面体压腔的中心位置，通过二级增压装置对样品施加高压）；(c) 实验中的压力-时间曲线（5次往复加压-卸压实验曲线）

Figure 3. (a) Schematic diagram of the assembly used in the experiment, the sample was wrapped within a magnesia octahedron; (b) schematic diagram of a 6×8 MN cubic press with a secondary booster device, the assembled sample was placed in the center of the carbide blocks, and subjected to high pressure through a secondary booster device; (c) pressure-time curve used during the experiment (the above figure is the curve of the five-cycle reciprocating experiment)

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1.2 高压原位XRD实验

在北京同步辐射装置4W2高压线站完成了Ge的高压原位轴向XRD实验，对Ge在往复相变过程中的相变行为和晶粒尺寸变化规律进行了研究。选用台面尺寸为500 μm的金刚石压砧（diamond anvil cell，DAC）进行实验，选择Re封垫，封垫的预压厚度约为20 μm，样品孔的直径为150 μm，无传压介质。实验过程中的腔体压力由Au和红宝石标定。X射线光斑尺寸为20 μm×30 μm。实验后，用Fit 2D对衍射图进行分析^[21]，用Peakfit对峰宽进行拟合。

2. 实验结果与分析讨论

2.1 形貌表征

利用6×8 MN六面顶压机，使块体单晶Ge样品在0～15 GPa经历多次往复压致相变，图4显示了经历3次和5次往复压致相变后所得样品和初始样品的扫描电子显微镜（scanning electron microscope，SEM）图像。从图4中可以看出：经历3次往复压致相变之后，初始单晶块体Ge的晶粒细化到几百纳米；经历5次往复压致相变之后，块体Ge的最细晶粒达到几十纳米，并且晶粒与晶粒之间结合紧密。这说明往复压致相变成功将块体Ge样品的晶粒细化。

图 4 (a) 经历3次往复压致相变样品的 SEM 图像（晶粒细化到几百纳米）；(b) 经历5次往复压致相变样品的SEM图像（最小晶粒细化到几十纳米）；(c) 初始样品的 SEM 图像

Figure 4. (a) SEM image of the sample undergoing three cycles of reciprocating pressure-induced phase transitions, and the grains have been refined to several hundreds of nanometers; (b) SEM image of the sample undergoing five cycles of reciprocating pressured-induced phase transitions, and the smallest grains have been refined to several tens of nanometers; (c) SEM image of the initial sample

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经历5次往复压致相变后样品的XRD谱如图5所示。除ST12 Ge的衍射峰外，还观测到明显的GeO₂的衍射峰，精修结果显示GeO₂占1.4%。这应该是由于晶粒细化后，样品的比表面积增大，增加了其与空气中氧气的接触面积，致使样品表面发生氧化，从而间接验证了往复压致相变对晶粒的细化效应。

图 5 往复5次所得样品的XRD谱和Rietveld拟合曲线

Figure 5. XRD pattern and Rietveld fitting curve of the sample undergoing five cycles of reciprocating pressing

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对往复5次升卸压过程的样品进行了透射电子显微镜（transmission electron microscope，TEM）测试，结果如图6所示。在往复5次升卸压的样品中观测到了非晶区域，对该区域进行选区电子衍射（selected area electron diffraction，SAED），得到了明显的非晶环（见图6(b)）；并且，在高分辨透射电子显微镜（high resolution transmission electron microscope，HRTEM）图像（图6(c)）中没有观测到有序的晶格排列，对HRTEM图像进行反傅里叶变换（inverse Fourier transform，iFFT），如图6(d)所示，可以明显地观测到该区域内原子以长程无序状态排列，进一步验证了其非晶结构。

图 6 (a) 往复5次所得样品的TEM图像（可见大片非晶区域）；(b) 图6(a)中红圈区域的SAED图像（出现明显的非晶环）；(c) 图6(b)对应的HRTEM图像（原子呈长程无序状态）；(d) HRTEM图像的iFFT图像；(e)～(f) 低倍数下的非晶区域

Figure 6. (a) TEM topographic image of the sample undergoing five cycles of reciprocating pressing, and a large amorphous region was found; (b) SAED image of the red circle region shown in (a), an obvious amorphous ring appears; (c) HRTEM image of the region in (b), where atoms were observed to exhibit long-range disorder; (d) iFFT image of the HRTEM image region; (e)–(f) amorphous regions of random distributions observed at low magnifications

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2.2 原位电阻测量

对样品在3～6次往复压致相变的电阻变化进行了原位测量。实验所用组装如图7(a)所示。采用四电极法对样品进行原位电阻测量，对样品施加恒定的电流，通过记录样品两端的电压变化来反映样品电阻的变化。对Ge施加压力至相变压力时，Ge将从半导体相转变为金属相，对应的电阻（电压）下降至接近零。

图 7 (a)原位电阻测量实验所用组装示意图；(b) 3～6次往复压致相变实验测得的原位压力-电压（电阻）曲线

Figure 7. (a) Schematic diagram of the assembly used in electric resistance measurement experiments; (b) in situ pressure-voltage (resistance) curves corresponding to three to six cycles of reciprocating pressure-induced phase transitions experiments

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图7(b)显示了3～6次往复压致相变实验对应的原位电阻测量曲线，其中：C代表升压过程，D代表卸压过程，数字代表往复压致相变的次数。从图7(b)可以看出，随着往复压致相变次数的增加，样品相变为金属相所需的压力更高，从侧面印证了样品晶粒随着往复压致相变次数的增加而不断细化。轩园园^[22] 的研究表明，随着样品粒径的减小，样品的比表面积急剧增大，从常（低）压相转变到高压相的势垒增大，导致相变压力随着粒径的减小而增大。该结论与本研究结果一致。

2.3 往复压致相变过程中的动力学研究

在原位电阻测量中，可以通过电阻的相对变化量反映相变的完成情况，即

$x(t)=\Delta R(t)/ \Delta R_{\rm {tot}}$

(1)

式中： $x(t)$ 为相变百分比随时间的变化， $\Delta R(t)$ 为某段时间内电阻的改变量，ΔR_tot为相变过程中电阻的总变化量。在相变动力学的JMAK方程中， $x(t)$ 可以表示为

$x(t)=1-{\rm{exp}}({-kt^{n}})$

(2)

式中：k为与激活能有关的常数， $n$ 为Avrami指数。对式(2)两端求对数，可得

$n={\rm{ln}}[-{\rm{ln}}(1-x)]/{\rm{ln}}\,t$

(3)

Avrami指数n是动力学研究中的一个重要参数，能够反映相变过程中的成核情况^[23-25]，不同相变类型的Avrami指数对应的成核情况不同。

3～6次往复压致相变过程对应的Avrami指数变化情况如图8所示，其中：短横线后面的C和D代表往复压致相变中的升压和卸压过程，如3CD-D表示第3次往复压致相变中的卸压过程。统计相同的压力区间内升卸压过程中Avrami指数的变化情况，结果表明：在升压过程中，Avrami指数由大变小；在卸压过程中，Avrami指数由小变大。同时还统计了升卸压过程中Avrami指数最大值对应的压力区间，如图9和表1所示，其中：n_max、n_med、n_min分别为Avrami指数的最大值、中值、最小值。可以看出：在升压过程中，新相集中在11～12 GPa成核；在卸压过程中，新相集中在8～9 GPa成核。这是因为在卸压过程中腔体压力由高到低，可能出现腔体实际压力相对于系统加载油压滞后的现象，导致升卸压过程中集中成核的压力区间不同。另外，随着往复压致相变次数的增加，样品的Avrami指数整体呈现增大的趋势，说明随着往复压致相变次数的增加，形核位点不断增加，从而从侧面反映了样品晶粒得到细化，数量更多、粒径更小的晶粒为新相的形成提供更多的成核位点。

图 8 3~6次往复压致相变过程中Avrami指数的变化规律

Figure 8. Variation of the Avrami index during the experimental process of three to six cycles of reciprocating pressure-induced phase transitions

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表 1 Avrami 指数与时间和压力的对应关系

Table 1. Avrami index corresponding to time and pressure

Process	n	ln t	p/GPa	Process	n	ln t	p/GPa
3CD-D	13.92^a	8.06–8.20	9.07–8.43	5CD-D	18.55^a	8.46–8.58	9.22–8.32
	4.50^b	7.69–8.06	10.52–9.07		7.13^b	8.14–8.46	11.23–9.22
	2.14^c	7.08–7.69	12.02–10.52		4.90^c	7.70–8.14	12.73–11.23
4CD-C	27.30^a	7.75–7.81	11.81–12.06	6CD-C	22.09^a	7.46–7.60	11.08–11.31
	8.22^b	7.81–8.00	12.06–12.62		5.43^b	7.60–7.94	11.31–12.58
	3.86^c	8.00–8.48	12.62–14.82		3.16^c	7.94–8.52	12.58–14.97
4CD-D	21.90^a	8.45–8.57	8.99–8.25	6CD-D	45.00^a	8.48–8.52	8.79–8.40
	6.87^b	8.16–8.45	11.10–8.99		21.15^b	8.03–8.48	9.81–8.79
	3.12^c	7.48–8.16	13.37–11.10		5.40^c	7.71–8.33	12.60–9.81
5CD-C	17.73^a	31.87–33.14	11.31–11.81
	5.26^b	33.14–37.00	11.81–13.17
	3.39^c	37.00–44.87	13.17–15.13
Note: Superscript lowercase letters a, b and c represent the maximum, the median and the minimum values of the Avrami index during the compression and decompression process, respectively.

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| 显示表格

图 9 高Avrami指数对应的升卸压过程的压力区间

Figure 9. Maximum Avrami index corresponding to the pressure range

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2.4 Ge的往复压致相变过程机理

图10给出了DC Ge 、β-Sn Ge、ST12 Ge晶格的(001)面示意图。在升压过程中，DC Ge到β-Sn Ge的相变可以看作DC Ge中的晶格原子沿 (100)面和(010)面的拉伸以及沿(001)面的压缩，虽然体积压缩率达到18.4%，但是在相变过程中只涉及键长的变化，未涉及键角的扭曲，是典型的位移型相变^[26]。而在卸压过程中，β-Sn Ge到ST12 Ge的相变不仅涉及键长变化和较高的体积变化率，同时还涉及大键角扭曲，相变后原子与原子之间的相对位置发生了明显的改变，属于扩散型相变^[27-29]。在高压的作用下，Ge原有相的晶体结构遭到破坏，原子位置发生变化，形成新的晶体结构。在新相生长阶段，高压作用会抑制原子的长程扩散，从而抑制新相晶粒的长大，达到细化晶粒的效果。特别是扩散型相变，高压对其晶粒生长的抑制作用更明显。此外，β-Sn Ge与ST12 Ge之间能够相互转化，属于可逆相变。因此，通过对样品进行往复升卸压，使其经历多次相变，高压对晶粒的细化效果得以累积，最终制备出具有超细纳米结构的块体材料。

图 10 DC Ge (a)、β-Sn Ge (b)、ST12 Ge (c)晶格的(001)面示意图

Figure 10. Schematic diagrams of the (001) planes: (a) DC Ge, (b) β-Sn Ge, and (c) ST12 Ge

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当高压对样品的细化效果叠加到一定程度时，最细晶粒达到纳米级别，而纳米级β-Sn Ge晶粒在卸压过程中不一定会再相变为ST12 Ge纳米晶，而更倾向于转化为非晶，这是因为当晶粒细化到纳米尺寸后，随着样品的比表（界）面积和表（界）面能的急剧增大，无法提供足够高的使ST12 Ge新相形核的驱动力，此时 β-Sn Ge跨越更低的势垒形成非晶状态^{[22, 30]}。此外，也可以把非晶结构的形成看作高压对抑制原子长程扩散的极致情形，此时原子只能进行短程扩散移动，达到相变压力点时，母相晶格失稳坍塌，驱动力又不足以使原子通过长程扩散形成规则排列的新相晶体结构。

2.5 Ge的原位XRD实验

TEM、SEM以及XRD谱均显示了高压往复相变对Ge的晶粒细化效果，但是在XRD谱中并没有观测到纳米材料应有的峰的宽化现象和非晶峰。为了进一步验证实验结果，在北京同步辐射光源进行了高压往复相变的原位XRD测试，结果如图11所示。其中：图11(a)为第5次升卸压过程的原位XRD谱，在0～15 GPa压力范围内经历了ST12 Ge—β-Sn Ge—ST12 Ge两次相变。对2～5次往复压致相变后卸到常压的样品的XRD谱（见图11(b)）和特征峰的峰宽进行了分析（见图11(c)），并未观测到明显的非晶峰和峰的宽化现象。

图 11 (a)第5次往复相变升卸压过程采集的原位XRD谱（在 0～15 GPa压力区间完成了 ST12 Ge—β-Sn Ge—ST12 Ge两次相变）；(b) 往复2～5次后卸压到 0 GPa 时样品的XRD谱；(c) 图11(b)中 XRD谱中特征峰的峰宽变化

Figure 11. (a) In-situ XRD patterns collected during the fifth reciprocating phase transition compressing (0–15 GPa) and decompressing (15–0 GPa) process, two phase transitions of ST12 Ge–β-Sn Ge–ST12 Ge were completed; (b) XRD patterns collected after two to five cycles of experimental pressure uploading and decompressing to 0 GPa; (c) the full width at half maxima (FWHM) of characteristic peaks of XRD patterns in (b)

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在往复5次样品的SEM图像中观测到有些区域的晶粒仍为微米级。如图12所示，这些微米级晶粒与纳米晶区及非晶区共同存在，由于微米晶粒区域的XRD峰强远大于纳米区域和非晶区域的峰强，掩盖了纳米晶和非晶衍射峰的峰宽变化，因此未观测到XRD谱发生明显的宽化和非晶峰。

图 12 XRD区域示意图

Figure 12. Schematic of XRD regions

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对样品的晶态区进行SAED，如图13所示，得到了明显的多晶衍射环，证明了其晶体结构特征，但是在HRTEM图像中仍然发现了部分非晶区域。根据文献[31-32]报道，ST12 Ge会在加热后转变为DC Ge，对ST12 Ge纯相样品进行差热分析（differential scanning calorimetry，DSC）测试，得到其相变温度为529.56 K。在此温度区间未观测到其他峰，样品未熔化。这意味着ST12 Ge在熔化前会先转变为DC Ge，因而无法测得常压下ST12 Ge的熔点，也就无法推断ST12 Ge的再结晶温度。根据往复5次实验样品中出现的大晶粒区域，推断加压过程中ST12 Ge发生了再结晶现象，导致部分区域的晶粒长大。样品最终呈现的纳米晶、非晶区域和微米晶区域交错产生的现象是高压抑制晶粒生长和再结晶导致晶粒长大两种驱动力相互博弈的结果。

图 13 (a) 往复5次后样品另一区域的SEM图像（在该区域观测到了微米级晶粒）；(b) 往复5次后样品晶态区的SAED图像（观测到明显的多晶环）；(c) 多晶区域的HRTEM图像（在多晶区域仍然存在部分非晶区，A和B分别为非晶区和多晶区的iFFT图像）；(d) ST12 Ge样品加热的DSC曲线（发现1个吸热峰，对应ST12 Ge到DC Ge的相变温度）；(e) 在相变温度加热1 h后的XRD谱（表明样品已经全部转化为DC Ge）

Figure 13. (a) SEM image of another area in the sample with five cycles of reciprocation, in which grains in the size of micrometers were observed; (b) SAED pattern of the crystal region in the sample undergoing five cycles of reciprocation, showing the obvious polycrystalline ring; (c) HRTEM image of the polycrystalline region, in which some amorphous regions still exist, A and B are the iFFT images of the amorphous and polycrystalline regions, respectively; (d) DSC curve of the ST12 Ge sample heated, an endothermic peak was found, corresponding to the phase transition temperature from ST12 Ge to DC Ge; (e) XRD pattern after heating for 1 h at the phase transition temperature, the sample has been completely transformed into DC Ge

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3. 结　论

基于6×8 MN六面顶压机的二级增压装置和DAC装置，结合高压原位XRD技术，对Ge在高压往复压致相变过程中的相变行为和晶粒尺寸变化规律进行了研究。结果表明：在经历5次往复相变后，晶粒细化到纳米级，且有部分区域转化为非晶，证实了高压往复相变对晶粒细化的效果，从而提供了一种制备纳米晶块体和非晶材料的新思路。同时，在部分区域仍然存在微米大小的晶粒，推测在加压过程中ST12 Ge发生再结晶进而导致晶粒长大。样品最终呈现出纳米晶、非晶区域和微米晶粒区域交错分布的现象，这应该是高压抑制晶粒生长以及再结晶导致晶粒长大两种动力学机制相互博弈的结果。

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