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两相界面的原子尺度结构对相界面迁移行为具有重要影响. 高分辨透射电子显微分析表明钢中马氏体相界面具有高度为若干原子层间距的台阶结构, 然而目前Fe合金马氏体相变的模拟研究工作中绝大多数使用非台阶型相界面结构作为模拟初始模型. 本文基于拓扑模型和相变位错理论构建了Fe合金FCC/BCC台阶型相界面初始模型, 采用分子动力学模拟方法研究了Fe合金马氏体相界面的迁移行为. 研究结果表明, 当两相界面具有约束共格匹配关系及台阶结构时, 体系发生FCC → BCC马氏体相变并呈现典型的非扩散切变特征; 相变过程中FCC/BCC宏观尺度相界面沿其法线方向以(4.4 ± 0.3) × 102 m/s的速度迁移, 且相界面在迁移过程中始终保持稳定的台阶结构和相对平直的宏观界面形貌特征; 相变位错的滑移速度高达(2.8 ± 0.2) × 103 m/s, 相变位错阵列沿台阶面的协同侧向滑移不仅是马氏体台阶结构宏观相界面迁移的微观机制, 也是马氏体相变宏观形状应变的主要来源; 采用分子动力学模拟方法获得的Fe合金马氏体相变晶体学特征参量与拓扑模型的解析解数值非常接近, 相变产生的整体宏观形状应变由平行于相界面的剪切应变和垂直于相界面的法向应变两部分组成.The martensitic transformation between the high-temperature face-centered cubic (FCC) phase and the low-temperature body-centered cubic (BCC) phase in iron-based alloys has been studied for years, which plays a critical role in controlling microstructures and hence properties of the alloys. Generally, the BCC structure martensitic phase forms from the FCC parent phase, involving a collective motions of atoms over a distance less than the interatomic distance in the vicinity of the interphase boundary. Thus the structure of interphase boundary separating the FCC and BCC phases is the key characteristics to quantitatively understanding the mechanism and kinetics of martensitic transformation. Due to the difficulty in observing the atomic motions taking place at a velocity as high as the speed of sound, the experimental investigation on the migration of FCC/BCC interphase boundary during the transformation is as yet limited. Noteworthily, molecular dynamics (MD) simulation has been applied to studying the martensitic transformation, in particular for investigating the mobility of the FCC/BCC interphase boundary in iron. However, in most of the MD studies the atomistically planar interfaces of {111}FCC // {110}BCC are considered as the initial configuration of the interphase boundary between FCC and BCC phases, which is in contradiction to the high-resolution TEM observations. In fact, the FCC/BCC interphase boundary, which is known as the macroscopic habit plane, is a semi-coherent interface consisting of several steps and terrace planes on an atomic scale. In the present work, the atomic configuration of a terrace-step FCC/BCC interphase boundary of iron is built in terms of the topological model. The MD simulation is conducted to clarify the mechanism of interphase boundary migration in the FCC-to-BCC transformation. The results show that the FCC/BCC boundary migrates along its normal at the expense of FCC phase as a result of the lateral motions of the transformation dislocations. Meanwhile, the interphase boundary maintains the stable terrace-step structure during the transformation. Further examinations reveal that the transformation dislocations move steadily at a velocity as high as (2.8 ± 0.2) × 103 m/s, affecting the migration of the interphase boundary with a constant velocity of about (4.4 ± 0.3) × 102 m/s. The effective migration velocity of FCC/BCC interface exhibits dynamic properties consistent with the characteristic features commonly observed in a displacive martensitic transformation. Additionally, the motion of transformation dislocations gives rise to the macroscopic shape strain composed of a shear component
$ {\varGamma _{{\rm{yz}}}} = 0.349$ parallel to the boundary and a dilatation$ {\varGamma _{{\rm{zz}}}} = 0.053$ normal to the boundary in the MD simulation, which is close to the crystallographic calculations by the topological model.-
Keywords:
- transformation dislocation /
- interphase boundary migration /
- molecular dynamics simulation /
- topological model of martensitic transformation
[1] Porter D A, Easterling K E 1992 Phase Transformations in Metals and Alloys (2nd Ed.) (London: Chapman and Hall) p1
[2] 徐祖耀 1999 马氏体相变与马氏体(北京: 科学出版社) 第1页
Xu Z Y 1999 Martensitic Transformation and Martensite (Beijing: Science Press) p1 (in Chinese)
[3] Christian J W 2002 The Theory of Transformation in Metal and Alloys (Amsterdam: Elsevier) p1
[4] Honeycombe R W K, Bhadeshia H K D H 2006 Steels: Microstructure and Properties (3rd Ed.) (Amsterdam: Elsevier) p1
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图 2 自然状态(a)和约束共格状态(b)下FCC和BCC相晶格点阵在x轴方向上的匹配状态图
Fig. 2. The atomic configuration of interphase boundary between FCC and BCC crystals in (a) natural state and (b) constraint coherent state (in which the atoms are colored by their centrosymmetry parameters).
图 3 相变位错Burgers矢量bD形成过程示意图
Fig. 3. Depiction of the formation of a transformation dislocation bD by eliminating the “gap” between parent and martensite crystals.
图 4 具有台阶结构特征的FCC/BCC相界面复相体系初始模型
Fig. 4. Atomic configuration of the FCC-BCC biphasic system in Fe alloy evaluated by coordination number method where FCC crystal, BCC crystal and interphase boundary are represented by green, red and yellow dots respectively.
图 5 非共格FCC-BCC复相体系在0−10 ns内的径向分布函数图 (a)及各相原子比例分数随相变时间变化关系曲线(b); 约束共格FCC-BCC复相体系在0−25 ps内的径向分布函数图(c) 及各相原子比例分数随相变时间变化关系曲线(d)
Fig. 5. RDF of the FCC-BCC system with (a) incoherent and (c) constraint coherent boundary; and evolution of the phase fractions with (b) incoherent and (d) constraint coherent boundary.
图 6 FCC→BCC相变中约束共格台阶型相界面位置随时间变化关系曲线及晶体结构转变过程模拟结果
Fig. 6. Curves of the constraint coherent FCC/BCC boundary location versus time within 20 ps and snapshots of the crystal structure evolution process by MD simulation.
图 7 FCC和BCC晶体非台阶型
${(111)_{{\rm{FCC}}}}$ //${(110)_{{\rm{BCC}}}}$ 相界面初始结构Fig. 7. View on the FCC/BCC boundary of
${(111)_{{\rm{FCC}}}}$ //${(110)_{{\rm{BCC}}}}$ interface (in which the atoms are colored in terms of their potential energy).
图 8
${(111)_{{\rm{FCC}}}}$ //${(110)_{{\rm{BCC}}}}$ 非台阶型相界面迁移及两相晶体结构演变过程模拟结果 (a) 0 ps; (b) 15 ps; (c) 30 psFig. 8. Snapshots of the evolution of the local structure and propagation of the
${(111)_{{\rm{FCC}}}}$ //${(110)_{{\rm{BCC}}}}$ boundary at different times: (a) 0 ps; (b) 15 ps; (c) 30 ps (in which the atoms are colored by their coordinate number where green: FCC, red: BCC and yellow: phase boundary).
图 9 台阶面上原子在10.0和10.2 ps 时的位移前后状态图
Fig. 9. Atomic displacements on the terrace plane of (111)FCC//(110)BCC (in which the transformed configuration at 10.2 ps is superposed over the configuration at 10.0 ps).
图 10 约束共格FCC/BCC相界面在 (a) 10.0 ps和 (b) 10.2 ps时的微观结构以及相界面近邻原子位移状态图(c)
Fig. 10. Configuration of the step-like constraint coherent interface between FCC and BCC crystals at (a) 10.0 ps and (b) 10.2 ps evaluated by common neighbor analysis method; and (c) the atomic displacements near the transforming boundary.
图 11 FCC和BCC相在1.0 ps时约束共格台阶面上的应变分布图
Fig. 11. Distribution of the strain field along the constraint coherent terrace plane calculated by relative displacements of atoms’ neighbors within a given cutoff radius of 3.2 Å.
图 12 拓扑模型中台阶型FCC/BCC相界面上的相变位错结构示意图
Fig. 12. Schematic illustration of the transformation dislocation configuration at the stepped FCC/BCC boundary in the topological model.
表 1 FCC → BCC相变晶体学特征参量的分子动力学模拟结果与拓扑模型计算值的比较
Table 1. Comparison of the FCC → BCC transformation crystallographic characteristics obtained by MD simulation and topological model.
MD simulation TM calculation Macroscopic habit plane index (575)FCC (0.501, 0.706, 0.501)FCC Line direction of transformation dislocation $[1 0 \bar1]_{\rm P}$ $ \rm [1 0 \bar1]_{P} $ Spacing of transformation dislocation/nm 1.294 1.244 Shear direction $[7 \overline{10} 7]_{\rm P}$ $ [7 \overline{10} 7]_{\rm P} $ Shear magnitude 0.349 0.344 Dilation 0.053 0.058 Phase boundary migration velocity/ m·s–1 (4.4 ± 0.3) × 102 – 
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[1] Porter D A, Easterling K E 1992 Phase Transformations in Metals and Alloys (2nd Ed.) (London: Chapman and Hall) p1
[2] 徐祖耀 1999 马氏体相变与马氏体(北京: 科学出版社) 第1页
Xu Z Y 1999 Martensitic Transformation and Martensite (Beijing: Science Press) p1 (in Chinese)
[3] Christian J W 2002 The Theory of Transformation in Metal and Alloys (Amsterdam: Elsevier) p1
[4] Honeycombe R W K, Bhadeshia H K D H 2006 Steels: Microstructure and Properties (3rd Ed.) (Amsterdam: Elsevier) p1
[5] Shibata A, Murakami T, Morito S, Furuhara T, Maki T 2008 Mater. Trans. 49 1242
Google Scholar
[6] Maki T 2012 Phase Transformation in Steels (Cambridge: Woodhead Publishing) p34
[7] Wayman C M 1964 Introduction to the Crystallography of Martensitic Transformations (New York: MacMillan) p1
[8] Moritani T, Miyajima N, Furuhara T, Maki T 2002 Scr. Mater. 47 193
Google Scholar
[9] Ogawa K, Kajiwara S 2004 Philos. Mag. 84 2919
Google Scholar
[10] Hirth J P 1994 J. Phys. Chem. Solids 55 985
Google Scholar
[11] Hirth J P, Pond R C 1996 Acta Mater. 44 4749
Google Scholar
[12] Pond R C, Celotto S, Hirth J P 2003 Acta Mater. 51 5385
Google Scholar
[13] Pond R C, Ma X, Chai Y W, Hirth J P 2007 Dislocation in Solids (Amsterdam: Elsevier) p225
[14] Ma X, Pond R C 2008 Mater. Sci. Eng. A481-482 404
[15] Wei Z Z, Ma X, Zhang X P 2014 Philos. Mag. Lett. 94 288
Google Scholar
[16] Ma X, Wei Z Z, Zhang X P 2014 J. Mater. Sci. 49 4648
Google Scholar
[17] 韦昭召, 马骁, 张新平 2018 金属学报 54 1461
Google Scholar
Wei Z Z, Ma X, Zhang X P 2018 Acta Metall. Sin. 54 1461
Google Scholar
[18] Mohammed A, Sehitoglu H 2020 Acta Mater. 183 93
Google Scholar
[19] Bos C, Sietsma J, Thijsse B 2006 Phys. Rev. B 73 104117
Google Scholar
[20] Suiker A S J, Thijsse B J 2013 J. Mech. Phys. Solids 61 2273
Google Scholar
[21] Wang B J, Urbassek H M 2013 Phys. Rev. B 87 104108
Google Scholar
[22] Wang B J, Urbassek H M 2014 Comput. Mater. Sci. 81 170
Google Scholar
[23] Tateyama S, Shibuta Y, Suzuki T 2008 Scr. Mater. 59 971
Google Scholar
[24] Tateyama S, Shibuta Y, Kumagai T, Suzuki T 2011 ISIJ Int. 51 1710
Google Scholar
[25] Ou X, Sietsma J, Santofimia M J 2016 Modell. Simul. Mater. Sci. Eng. 24 055019
Google Scholar
[26] Song H, Hoyt J J 2012 Acta Mater. 60 4328
Google Scholar
[27] Maresca F, Curtin W A 2017 Acta Mater. 134 302
Google Scholar
[28] Engin C, Sandoval L, Urbassek H M 2008 Modell. Simul. Mater. Sci. Eng. 16 035005
Google Scholar
[29] Finnis M W, Sinclair J E 1984 Philos. Mag. A 50 45
Google Scholar
[30] Plimpton S 1995 J. Comput. Phys. 117 1
Google Scholar
[31] Stukowski A 2009 Modell. Simul. Mater. Sci. Eng. 18 015012
[32] Faken D, Jonsson H 1994 Comput. Mater. Sci. 2 279
Google Scholar
[33] Shimizu F, Ogata S, Li J 2007 Mater. Trans. 48 2923
Google Scholar
[34] Chiao Y H, Chen I W 1990 Acta Metall. Mater. 38 1163
Google Scholar
[35] Hirth J P, Lothe J 1982 Theory of Dislocations (New York: McGraw-Hill) p1
[36] Hirth J P, Mitchell J N, Schwartz D S, Mitchell T E 2006 Acta Mater. 54 1917
Google Scholar
[37] Chai Y W, Kim H Y, Hosoda H, Miyazaki S 2008 Acta Mater. 56 3088
Google Scholar
[38] Yu Z Z, Clapp P C 1989 Metall. Trans. A 20 1617
Google Scholar
[39] Meyer R, Entel P 1998 Phys. Rev. B 57 5140
Google Scholar
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