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单晶Ce冲击相变的分子动力学模拟

第伍旻杰 胡晓棉

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单晶Ce冲击相变的分子动力学模拟

第伍旻杰, 胡晓棉

Molecular dynamics simulation of shock-induced isostructural phase transition in single crystal Ce

Diwu Min-Jie, Hu Xiao-Mian
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  • 金属Ce在室温条件下当压力达到约0.7 GPa时会发生一阶相变, 体积突变减小14%—17%, 相变前后两相分别为γ-Ce和α-Ce, 均为面心立方结构. 实验中发现冲击波在Ce中传播, 其波形存在明显的多波结构, 依次为 γ-Ce弹性前驱波、γ-Ce塑性波、γ-Ce → α-Ce相变波. 基于新发展的金属Ce的嵌入原子势, 对单晶Ce的冲击相变行为进行了分子动力学模拟. 模拟结果表明, 在一定强度下, 单晶Ce中的冲击波阵面分裂为多波结构, 波形结构与加载晶向明显相关: 在[001]和[011]晶向加载下表现为双波结构, 依次为前驱波和相变波; 在[111]晶向加载下波阵面分裂为弹性前驱波、γ-Ce塑性波、γ α相变波, 与已有的实验观察相一致. 冲击波速的Hugoniot关系在低强度加载下与实验符合得较好. 同时在此冲击相变过程中, 应力偏量对相变起促进作用, 相较于静水压加载, 冲击加载的相变压力条件更低一些.
    Cerium (Ce), a rare earth metal, undergoes a significant (14%−17%) and discontinuous volume shrinkage when subjected to ~0.7 GPa compression at ambient temperature: there happens a first-order isostructural phase transition from γ-Ce phase to α-Ce phase (these two phases are both face-centered-cubic (fcc) phase). Because of the αγ transition in Ce under shock compression, the shock front in cerium exhibits a 3-wave configuration: elastic precursor, plastic shock wave in γ-Ce, and phase transition wave corresponding to the γ α transition according to the experimental observation. In this paper, a recently developed embedded-atom-method (EAM) potential for fcc Ce is employed in the large-scale molecular dynamics simulations of shock loading onto single crystal Ce to study its dynamic behavior, especially the shock-induced αγ phase transition, and the orientation dependence with [001], [011] and [111] shock loading. The simulation results show single-wave or multi-wave configuration for shock wave profiles. Under the shock loading along the [001] or [011] crystallographic orientation, the shock wave possesses a 2-wave structure: an elastic precursor and a phase transition wave, while under shock loading along the [111] crystallographic orientation, the obtained shock wave shows a 3-wave profile as observed experimentally. Thus the shock wave structure is obviously dependent on loading orientation. The Hugoniot data obtained in MD simulation show good agreement with the experimental results. The shock loading MD simulation shows lower phase transition pressure than hydrostatic loading, indicating an accelerant role of the deviatoric stress played in the shock induced γ α phase transition in Ce. The local lattice structure before and after shocked are recognized with polyhedral template matching and confirmed with radial distribution functions. Under the [011] and [111] loading, the lattice structure maintains the fcc before and after the shocks, and experiences a collapse during the last shock (the second shock for the [011] loading and the third shock for the [111] loading). The lattice structure also maintains fcc before and after the first shock for the [001] loading, while after the second shock the structure type is considered to be body-centered-tetragonal (bct) which is a meta-stable structure resulting from the used EAM potential for Ce. The fcc lattice rotation after shock is observed in the [011] and [111] loading after the phase transition, while no re-orientation occurs in the [001] loading.
      通信作者: 胡晓棉, hu_xiaomian@iapcm.ac.cn
      Corresponding author: Hu Xiao-Mian, hu_xiaomian@iapcm.ac.cn
    [1]

    Koskenmaki D C, Gschneidner K A 1978 Handbook on the Physics and Chemistry of Rare Earths (Vol. 1) (Amsterdam: Elsevier North-Holland) pp337−377

    [2]

    潘昊, 胡晓棉, 吴子辉, 戴诚达, 吴强 2012 物理学报 61 206401Google Scholar

    Pan H, Hu X M, Wu Z H, Dai C D, Wu Q 2012 Acta Phys. Sin. 61 206401Google Scholar

    [3]

    Wang Y, Hector Jr L G, Zhang H, Shang S L, Chen L Q, Liu Z K 2008 Phys. Rev. B 78 104113Google Scholar

    [4]

    Decremps F, Belhadi L, Farber D L, Moore K T, Occelli F, Gauthier M, Polian A, Antonangeli D, Aracne-Ruddle C M, Amadon B 2011 Phys. Rev. Lett. 106 065701Google Scholar

    [5]

    Pavlovskii M N, Komissarov V V, Kutsar A R 1999 Combust. Expl. Shock Waves 35 88Google Scholar

    [6]

    Borisenok V A, Simakov V G, Volgin V A, Bel'skii V M, Zhernokletov M V 2007 Combust. Expl. Shock Wavea 43 476Google Scholar

    [7]

    Simakov V G, Borisenok V A, Bragunets V A, Volgin V A, Zhernokletov M V, Zocher M A, Cherne F J 2007 Shock Compression of Condensed Matter-2007, Pts 1 and 2 Kohala Coast, Hawaii, June 24−29, 2007 pp105−108

    [8]

    Yelkin V M, Kozlov E A, Kakshina E V, Moreva Y S 2006 Shock Compression of Condensed Matter-2005 Baltimore, Maryland July 31−August 5, 2005 pp77−80

    [9]

    El'kin V M, Kozlov E A, Kakshina E V, Moreva Y S 2006 Phys. Met. Metall. 101 232

    [10]

    El'kin V M, Mikhaylov V N, Petrovtsev A V, Cherne F J 2011 Phys. Rev. B 84 094120Google Scholar

    [11]

    Hu X, Pan H, Dai C, Wu Q 2012 Shock Compression of Condensed Matter - 2011, Pts 1 and 2 Chicago, Illinois, June 26-July 1, 2011 pp1567−1570

    [12]

    Kadau K, Germann T C, Lomdahl P S, Holian B L 2005 Phys. Rev. B 72 064120Google Scholar

    [13]

    Dupont V, Chen S P, Germann T C 2010 EPJ Web of Conferences Paris, France, May 24−28, 2010 p00009

    [14]

    第伍旻杰, 胡晓棉 2019 物理学报 68 203401Google Scholar

    Diwu M J, Hu X M 2019 Acta Phys. Sin. 68 203401Google Scholar

    [15]

    Plimpton S 1995 J. Comput. Phys. 117 1Google Scholar

    [16]

    Faken D, Jónsson H 1994 Comput. Mater. Sci. 2 279Google Scholar

    [17]

    Tsuzuki H, Branicio P S, Rino J P 2007 Comput. Phys. Commun. 177 518Google Scholar

    [18]

    Larsen P M, Schmidt S, Schiøtz J 2016 Modell. Simul. Mater. Sc. Eng. 24 055007Google Scholar

    [19]

    Stukowski A, Albe K 2010 Modell. Simul. Mater. Sc. Eng. 18 085001Google Scholar

    [20]

    Jensen B J, Cherne F J, Cooley J C, Zhernokletov M V, Kovalev A E 2010 Phys. Rev. B 81 214109Google Scholar

    [21]

    李俊, 吴强, 于继东, 谭叶, 姚松林, 薛桃, 金柯 2017 物理学报 66 146201Google Scholar

    Li J, Wu Q, Yu J D, Tan Y, Yao S L, Xue T, Jin K 2017 Acta Phys. Sin. 66 146201Google Scholar

    [22]

    郭扬波, 唐志平, 徐松林 2004 固体力学学报 25 417Google Scholar

    Guo Y B, Tang Z P, Xu S L 2004 Acta Mech. Solida Sin. 25 417Google Scholar

    [23]

    Blank V D, Estrin E I 2013 Phase Transitions in Solids under High Pressure (Boca Raton: CRC Press) pp193−198

    [24]

    Casadei M, Ren X, Rinke P, Rubio A, Scheffler M 2016 Phys. Rev. B 93 075153Google Scholar

    [25]

    Sheng H W, Kramer M J, Cadien A, Fujita T, Chen M W 2011 Phys. Rev. B 83 134118Google Scholar

    [26]

    Germann T C, Kadau K 2009 AIP Conf. Proc. 1195 1209

  • 图 1  不同加载晶向和强度(up)的密度剖面图(t = 80 ps)

    Fig. 1.  Density profiles of different loading orientation and strength (up) for t = 80 ps.

    图 2  [111]晶向冲击加载后晶体中的微结构 (a) 全部原子; (b) DXA分析显示位错并隐去了fcc结构原子. 绿色原子为局部fcc, 红色为hcp, 蓝色为bcc. (b) 中用管表示位错: 绿色为Shockley偏位错, 深蓝色为全位错, 浅蓝色为梯杆位错. up = 150 m·s–1, 时间t = 80 ps

    Fig. 2.  Microstructure of the sample shocked along [111]: (a) All atoms are shown; (b) only non-fcc atoms are shown. Color coding: Green for local fcc atoms; red for hcp; blue for bcc. Dislocations are illustrated with tubes in (b): Green for Shockley partials; deep blue for perfect fcc dislocations; light blue for stair-rod dislocations. up = 150 m·s–1, t = 80 ps.

    图 3  冲击加载后晶体中的微结构. 冲击晶向为 (a) [001]; (b), (c) [011]; (d), (e) [111]; (c), (e)中隐去了fcc结构原子. up = 200 m·s–1, 时间t = 80 ps

    Fig. 3.  Microstructure of the shocked samples. The shock orientation is along (a) [001], (b) and (c) [011], (d) and (e) [111], respectively. Atoms in fcc structure are hidden in (c) and (e). up = 200 m·s–1, t = 80 ps.

    图 4  单晶Ce的冲击Hugoniot关系 (a) Us-up关系; (b) P-u关系. 实验数据来自文献[20]. (b)中的“”表示统计标准差

    Fig. 4.  Shock Hugoniot for single crystal Ce: (a) Shock speed vs. piston velocity; (b) pressure vs. particle velocity. Experimental data is cited from Ref.[20]. The symbol in (b) represents the statistical standard error.

    图 5  不同晶向加载下的压力剖面图, up = 200 m·s–1, 时间t = 80 ps

    Fig. 5.  Pressure profile for each loading orientation at up = 200 m·s–1 and t = 80 ps.

    图 6  冲击相变的相变温度-压力状态与静水压相变条件

    Fig. 6.  Temperature-pressure condition of shock-induced and hydrostatic phase transition.

    图 7  冲击前后的径向分布函数

    Fig. 7.  Radial distribution function of the sample before and after the shocks.

    图 8  Ce冲击相变分界面, 隐去了原子体积较大的fcc. up = 200 m·s-1, 时间t = 80 ps (a) [001]; (b) [011]; (c) [111]

    Fig. 8.  Phase boundary of shock induced transition. Shock orientation: (a) [001]; (b) [011]; (c) [111]. The atoms of fcc structure with larger atomic volume are hidden. up = 200 m·s-1, t = 80 ps.

    图 9  [001]晶向不同加载强度下相变波后的微结构 (a) up[001] = 150 m·s–1; (b) up[001] = 200 m·s–1; (c) up[001] = 250 m·s–1; (d) up[001] = 300 m·s–1; (e) up[001] = 400 m·s–1; (f) up[001] = 500 m·s–1

    Fig. 9.  Microstructure of the sample after phase transition shock along [001] with listed piston velocity: (a) up[001] = 150 m·s–1; (b) up[001] = 200 m·s–1; (c) up[001] = 250 m·s–1; (d) up[001] = 300 m·s–1; (e) up[001] = 400 m·s–1; (f) up[001] = 500 m·s–1.

    图 10  沿四方变形路径(原子体积不变)以及单轴压缩(a不变仅改变c/a)路径变形的能量

    Fig. 10.  Comparison of the energy along tetragonal deforma-tion path (atomic volume preserved) and the path of constant a.

    表 1  单晶Ce计算模型详细参数

    Table 1.  Parameters of single crystal Ce sample for MD simulation.

    加载
    晶向
    x 轴晶向及
    尺寸/nm
    y 轴晶向及
    尺寸/nm
    z 轴晶向及
    尺寸/nm
    模型
    原子数
    [001][100][010][001]5.00×106
    25.825.8255.5
    [011][100]$ [0 1 \bar1] $[011]4.83×106
    25.825.5251.9
    [111]$ [\bar1 \bar1 2] $$ [1 \bar1 0] $[111]4.88×106
    25.925.6253.7
    下载: 导出CSV

    表 2  [001]晶向加载相变波后区域微结构组分(依据PTM分析)(%)

    Table 2.  Fraction for each type of microstructure (analyzed with PTM algorithm) in the part after phase transition shock along [001] (%).

    up[001] /m·s–1150200250300400500
    fcc66.144.124.611.82.10.4
    bcc30.151.671.484.996.197.4
    其他3.84.84.03.31.82.2
    下载: 导出CSV
  • [1]

    Koskenmaki D C, Gschneidner K A 1978 Handbook on the Physics and Chemistry of Rare Earths (Vol. 1) (Amsterdam: Elsevier North-Holland) pp337−377

    [2]

    潘昊, 胡晓棉, 吴子辉, 戴诚达, 吴强 2012 物理学报 61 206401Google Scholar

    Pan H, Hu X M, Wu Z H, Dai C D, Wu Q 2012 Acta Phys. Sin. 61 206401Google Scholar

    [3]

    Wang Y, Hector Jr L G, Zhang H, Shang S L, Chen L Q, Liu Z K 2008 Phys. Rev. B 78 104113Google Scholar

    [4]

    Decremps F, Belhadi L, Farber D L, Moore K T, Occelli F, Gauthier M, Polian A, Antonangeli D, Aracne-Ruddle C M, Amadon B 2011 Phys. Rev. Lett. 106 065701Google Scholar

    [5]

    Pavlovskii M N, Komissarov V V, Kutsar A R 1999 Combust. Expl. Shock Waves 35 88Google Scholar

    [6]

    Borisenok V A, Simakov V G, Volgin V A, Bel'skii V M, Zhernokletov M V 2007 Combust. Expl. Shock Wavea 43 476Google Scholar

    [7]

    Simakov V G, Borisenok V A, Bragunets V A, Volgin V A, Zhernokletov M V, Zocher M A, Cherne F J 2007 Shock Compression of Condensed Matter-2007, Pts 1 and 2 Kohala Coast, Hawaii, June 24−29, 2007 pp105−108

    [8]

    Yelkin V M, Kozlov E A, Kakshina E V, Moreva Y S 2006 Shock Compression of Condensed Matter-2005 Baltimore, Maryland July 31−August 5, 2005 pp77−80

    [9]

    El'kin V M, Kozlov E A, Kakshina E V, Moreva Y S 2006 Phys. Met. Metall. 101 232

    [10]

    El'kin V M, Mikhaylov V N, Petrovtsev A V, Cherne F J 2011 Phys. Rev. B 84 094120Google Scholar

    [11]

    Hu X, Pan H, Dai C, Wu Q 2012 Shock Compression of Condensed Matter - 2011, Pts 1 and 2 Chicago, Illinois, June 26-July 1, 2011 pp1567−1570

    [12]

    Kadau K, Germann T C, Lomdahl P S, Holian B L 2005 Phys. Rev. B 72 064120Google Scholar

    [13]

    Dupont V, Chen S P, Germann T C 2010 EPJ Web of Conferences Paris, France, May 24−28, 2010 p00009

    [14]

    第伍旻杰, 胡晓棉 2019 物理学报 68 203401Google Scholar

    Diwu M J, Hu X M 2019 Acta Phys. Sin. 68 203401Google Scholar

    [15]

    Plimpton S 1995 J. Comput. Phys. 117 1Google Scholar

    [16]

    Faken D, Jónsson H 1994 Comput. Mater. Sci. 2 279Google Scholar

    [17]

    Tsuzuki H, Branicio P S, Rino J P 2007 Comput. Phys. Commun. 177 518Google Scholar

    [18]

    Larsen P M, Schmidt S, Schiøtz J 2016 Modell. Simul. Mater. Sc. Eng. 24 055007Google Scholar

    [19]

    Stukowski A, Albe K 2010 Modell. Simul. Mater. Sc. Eng. 18 085001Google Scholar

    [20]

    Jensen B J, Cherne F J, Cooley J C, Zhernokletov M V, Kovalev A E 2010 Phys. Rev. B 81 214109Google Scholar

    [21]

    李俊, 吴强, 于继东, 谭叶, 姚松林, 薛桃, 金柯 2017 物理学报 66 146201Google Scholar

    Li J, Wu Q, Yu J D, Tan Y, Yao S L, Xue T, Jin K 2017 Acta Phys. Sin. 66 146201Google Scholar

    [22]

    郭扬波, 唐志平, 徐松林 2004 固体力学学报 25 417Google Scholar

    Guo Y B, Tang Z P, Xu S L 2004 Acta Mech. Solida Sin. 25 417Google Scholar

    [23]

    Blank V D, Estrin E I 2013 Phase Transitions in Solids under High Pressure (Boca Raton: CRC Press) pp193−198

    [24]

    Casadei M, Ren X, Rinke P, Rubio A, Scheffler M 2016 Phys. Rev. B 93 075153Google Scholar

    [25]

    Sheng H W, Kramer M J, Cadien A, Fujita T, Chen M W 2011 Phys. Rev. B 83 134118Google Scholar

    [26]

    Germann T C, Kadau K 2009 AIP Conf. Proc. 1195 1209

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  • 收稿日期:  2020-03-02
  • 修回日期:  2020-03-25
  • 刊出日期:  2020-06-05

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