Progress on Atomic Simulations of Phase Transition of Iron under Dynamic Loading
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摘要: 铁的
$\alpha $ ↔$\varepsilon$ 相变是金属高压相变研究领域的经典范例，随着测试技术的进步，其相变机制与动力学研究不断深入，基于激光加载的原位X射线观察结合非平衡分子动力学模拟研究是解决该问题最有效的手段之一。为此，综述了铁在动态载荷下塑性与相变的原子模拟研究进展，综合分析了铁的高压势函数，平面应变加载下晶体的各向异性、冲击强度、应变率、应变梯度、各种初始晶体缺陷等对铁相变机制的影响，以及铁的相变与层裂，同时报道了铁在非平面加载下响应规律研究的最新进展，最后进行了归纳总结和展望。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.-
Key words:
- high-pressure structural transition /
- plasticity /
- spall /
- molecular dynamics /
- interatomic potential /
- iron
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图 3 (a) MAEAM势预测的物态方程与实验及第一原理计算结果的对比，(b) 采用MAEAM势与改进的Ackland势的计算结果对比[49, 52-54]
Figure 3. (a) Comparison of equations of states predicted by MAEAM potential with experiments and the first-principle calculations, (b) Comparison of the results between MAEAM potential and modified Ackland potential[49, 52-54]
图 6 实现高应变率加卸载的3种方法：(a)活塞加载，(b)对称撞击，(c)均匀单轴压缩（“M”表示材料，箭头表示活塞或材料的运动方向，灰色梯度表示材料受到碰撞时形成的冲击波）
Figure 6. Three simulation approaches of de-/compression under high strain rates: (a) piston loadings, (b) symmetric impingements and (c) uniform uniaxial compressions, where “M” represents materials and the arrows show the motion directions of the piston and materials, and shock waves initiated around the impinging moment are illustrated by the grayscale
图 8 (a)不同冲击晶向与冲击强度下单晶铁的相变（红色、黄色、浅蓝色和深蓝色分别表示hcp原子、fcc原子、bcc原子和缺陷原子），(b)冲击晶向与惯习面的关系[34]
Figure 8. (a) Phase transition of single crystalline iron under different shock directions and shock strength (The meaning of the colors is: red (hcp atoms), yellow (fcc atoms), light blue (bcc atoms) and dark blue (defects).); (b) relationship between the shock direction and habit plane[34]
图 12 （a）斜波加载下临界失稳应变与应变梯度的依赖关系；（b）
$ \widetilde {{{B}}} $ 的最小本征值（Cmin）随单轴应变的变化；（c）～（d）分别以$ {\widetilde {T}}_{\rm{min}}^{1} $ 和$ {\widetilde {T}}_{\rm{min}}^{3} $ 表示的应变-应变梯度空间中的等高图（$ {\widetilde {T}}_{\rm{min}}^{1} $ 和$ {\widetilde {T}}_{\rm{min}}^{3} $ 分别为$ \widetilde {{T}} $ 沿x和z方向分量的最小本征值，图中所有的A对应于相同的应变）[62]Figure 12. (a) Critical instability strain versus strain gradient under ramp compressions; (b) minimumeigenvalue of
$ \widetilde {{{B}}} $ versus uniaxial strain; (c) and (d) are the contour plot$ {\widetilde {T}}_{\rm{min}}^{1} $ and$ {\widetilde {T}}_{\rm{min}}^{3} $ in the strain vs. strain gradient space, where$ {\widetilde {T}}_{\rm{min}}^{1} $ and$ {\widetilde {T}}_{\rm{min}}^{3} $ are the minimum eigenvalue of the x- and z-component of$ \widetilde {{T}} $ (In the figures, “A” corresponds to the same strain.)[62]
图 16 含有孪晶的双晶铁样品在最大粒子速度为0.4 km/s的斜波压缩下31 ps时的局部构型（红色表示hcp原子，蓝色表示bcc原子，右图hcp晶胞中黄色的原子面对应于左图中黄色方框标记的原子面）[74]
Figure 16. Local configuration of bicrystal iron sample containing a twin at 31 ps under ramp compressions with a maximum particle velocity of 0.4 km/s (Red denotes hcp atom and blue denotes bcc atom. The right figure shows a unit cell of hcp phase, where the yellow atomic face corresponds to the atomic face marked with yellow square in the left figure.)[74]
图 17 在0.5 km/s的粒子速度下
$\varSigma3$ 扭转晶界(a)与$\varSigma3$ 倾斜晶界(b)的冲击塑性与相变（冲击波沿z方向传播，在两种样品中分别对应于<110>和<111>晶向）[75]Figure 17. Shock-induced plasticity and phase transition of
$\varSigma3$ twist grain boundary (a) and$\varSigma3$ tilt grain boundary (b) under the shock with a particle velocity of 0.5 km/s, where shock wave propagates along z direction, corresponding to <110> and <111> crystallographic direction, respectively[75]
图 20 激光冲击实验回收的铁样品：(a)样品初始温度293 K，层裂面处的最高加载状态处于
$\alpha$ →$\varepsilon $ 相变边界上；(b) 样品初始温度673 K，层裂面处的最高加载状态处于两相共存区[81]Figure 20. Iron samples recovered after laser shocks (a) at 293 K, where the maximum loading state of the spall plane is on the
$\alpha $ →$\varepsilon $ phase transition boundary, and (b) at 673 K, where the maximum loading state of the spall plane locates at the two-phase-coexistence region[81]
图 21 柱面内爆(a)和外爆(b)冲击加载示意图（蓝色表示试样，紫色圆环表示柱形势能面，红色箭头表示加载方向）
Figure 21. Schematic diagram of the shock loading by cylindrical (a) implosion and (b) explosion (The blue part represents the sample, the purple ring represents the energy surface of the column, and the red arrow represents the loading direction.)
图 22 （a）柱面轴沿单晶Fe [001]晶向在内爆冲击下垂直于柱面轴的横截面内的原子速率分布，（b）10 ps时垂直柱面轴横截面内的局域温度分布
Figure 22. (a) Atom velocity distribution in the cross section perpendicular to the cylindrical axis under implosion impact along [001] direction of Fe single crystal, and (b) the local temperature distribution in the cross section perpendicular to the cylindrical axis at 10 ps
图 23 柱面轴沿单晶Fe [001]晶向在内爆冲击下（vp = 0.6 km/s）局域微结构随时间的演变（红色表示hcp结构原子，绿色表示以层错形式出现的fcc结构原子，灰色表示位错线周围的其他结构类型的原子，为清晰起见，未相变的bcc结构原子已被删除）
Figure 23. Evolutions of local microstructures with time under the implosive impacting with the cylindrical axis along [001] direction of Fe single crystal (vp = 0.6 km/s) (Red indicates hcp atoms, green indicates fcc atoms in the forms of stacking faults, and gray indicates other atoms distributed around dislocation lines. For clarity, bcc atoms without phase transition have been removed.)
图 24 柱面外爆冲击后试样内局域微结构、速度波剖面、应力波剖面和温度分布
Figure 24. Local microstructure, velocity profile, stress profile and temperature distribution in the sample after cylindrical explosions
图 25 柱面外爆冲击后试样内部的局域微结构(a)以及hcp相变变体c轴取向极图(b)
Figure 25. Local microstructure inside the sample (a) and polar figure of the c-axis showing different hcp variants (b)
a1 a2 a3 a4 a5 a6 A1 A2 −31.807065 36.158663 12.237970 −72.863506 156.864024 200.148093 72.868383 −100.944857 r1 r2 r3 r4 r5 r6 R1 R2 1.450000 1.430000 1.080000 0.990000 0.930000 0.866025 1.300000 1.200000 
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m n F0 g0 $\alpha $ $\;\beta $ $\gamma $ 55.847 0.289 2.1952807 1 9.17×10−3 4.15 5.01 $\;\rho $e Pe k0 k1 k2 k3 kc 10.875221 10.443309 −3.6918979 −0.3369724 −0.4937837 −0.3210981 0.3
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表 3 改进的Ackland势与MAEAM势预测的铁主要物理性质与有关第一原理计算及实验结果的对比
Table 3. Comparisons of key properties of iron predicted using modified Ackland potential and MAEAM potential with the first-principle-base calculations or experimental results
Method Basic properties a0/Å $E{\rm{_c}} $/eV $E{ \rm{^{f,1}_{1v} }}$/eV $E{ \rm{^{f,2}_{1v} }} $/eV ${\gamma }{_{\rm{unf} }^{110}}$/(J·m−2) ${\gamma }{_{\rm{unf} }^{112}}$/(J·m−2) Modified-Ackland 2.866 4.316 1.89 1.83 0.669 0.769 MAEAM 2.8606 4.28 2.09 1.86 0.652 0.710 Ref. 2.8606[41]
2.88[42]
2.86[43]4.28[44] 2.07[42]
1.95[43]2.0[37] 0.47 (GGA)[45]
0.59 (LDA)[45]Method Basic properties Elastic Vibrational $\Delta $Efcc-bcc/eV $\Delta $Ehcp-bcc/eV C11/GPa C12/GPa C44/GPa ${\nu }{_{N}^{ {\rm{T} }1}}$ /THz Modified-Ackland 0.135 0.191 243.7 145.3 116.3 10.83 MAEAM 0.034 0.016 243 138 127 9.39 Ref. 243.1[46]
243.0[47]138.1[46]
138.0[47]121.9[46]
127.0[47]9.26[48] Method Vibrational Others ${\nu }{_{N}^{ {\rm{T} }2} }$/THz ${\nu }{_{N}^{\rm{L} }}$/THz ${\nu }{_{H}}$/THz ${\nu }{_{P}}$/THz $p{_T}$/GPa $T{\rm{_m}}$/K Modified-Ackland 5.99 3.85 9.77 8.61 13.75 MAEAM 5.93 2.86 9.18 7.16 11 1807 Ref. 6.46[48] 4.47[48] 8.49[48] 7.19[48] 10[49]
10.5[50]1813[51]
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