Phase transitions of palladium under dynamic shock compression

Liu Ze-Tao; Chen Bo; Ling Wei-Dong; Bao Nan-Yun; Kang Dong-Dong; Dai Jia-Yu

doi:10.7498/aps.71.20211511

Abstract

For palladium (Pd) as a typical high-pressure standard material, studying its structural changes and thermodynamic properties under extreme conditions is widely demanded and challenging. Particularly, the solid-solid phase transition process of Pd under shock loading is understood still scarcely. In this paper, using the classical molecular dynamics simulations with embedded atom method (EAM) based on the interatomic potential, we investigate the phase transition of single crystal Pd from atomic scale under shock loading. A series of structural features is observed in a pressure range of 0–375 GPa, revealing that the structure feature transforms from the initial face-centered cubic (FCC) structure to the stacking faults body-centered cubic (BCC) structure with hexagonal close-packed (HCP) structure, and finally complete melting. Under shock loading of $ \left\langle {100} \right\rangle $ oriented bulk Pd, we find the transformation to BCC structure can take place almost at 70.0 GPa, which is much lower than the previous static calculation result. In addition, we find that the phase transition depends on the direction initially impacting crystal. Under impacting along the $ \left\langle {110} \right\rangle $ direction and the $ \left\langle {111} \right\rangle $ direction, the FCC-BCC phase transition pressures increase to 135.8 GPa and 165.4 GPa, respectively. Also, the introduction of defects will increase the phase transition pressure of FCC-BCC by 20–30 GPa in comparison with perfect crystals, which is verified by the distribution of the potential energy. An interesting phenomenon that FCC-BCC transition pressure of Pd decreases under shock loading is found in this work, which provides a new theoretical insight into the application of high pressure experiments in the future.

Keywords:

Authors and contacts

Department of Physics, National University of Defense Technology, Changsha 410073, China

Corresponding author: Chen Bo, chenbochain@nudt.edu.cn ; Dai Jia-Yu, jydai@nudt.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11774429, 12104507), the NSAF Joint Fund, China (Grant No. U1830206), the National Key R&D Program of China (Grant No. 2017YFA0403200), and the China Postdoctoral Science Foundation (Grant No. 2019M664024).

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References

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[35]	Stukowski A 2009 Modell. Simul. Mater. Sci. Eng. 18 015012
[36]	韦昭召, 马骁, 柯常波, 张新平 2020 物理学报 69 136102 Google Scholar Wei Z Z, Ma X, Ke C B, Zhang X P 2020 Acta Phys. Sin. 69 136102 Google Scholar
[37]	Kien P H 2014 Int. Scholarly Res. Not. 2014 253627
[38]	Sun H Y, Kang D D, Hou Y, Dai J Y 2017 Matter Radiat. at Extremes 2 287 Google Scholar
[39]	Neogi A, Mitra N 2017 Sci. Rep. 7 1 Google Scholar
[40]	Honeycutt J D, Andersen H C 1987 J. Phys. Chem. 91 4950 Google Scholar
[41]	Schiøtz J, Tolla F D D, Jacobsen K W 1998 Nature 391 561 Google Scholar
[42]	Stukowski A 2012 Model. Simul. Mater. Sci. Eng. 20 045021 Google Scholar
[43]	Faken D, Jónsson H 1994 Comput. Mater. Sci. 2 279 Google Scholar
[44]	Tsuzuki H, Branicio P, Rino J 2007 Comput. Phys. Commun. 177 518 Google Scholar
[45]	Zeng Q Y, Dai J Y 2020 Sci. China Phys. Mech. Astron. 63 263011 Google Scholar
[46]	Walsh J M, Rice M H, Mcqueen R G, Yarger F L 1957 Phys. Rev. 108 196 Google Scholar
[47]	Marsh S P 1979 Los Alamos Shock Hugoniot Data (Berkeley: University of California Press)
[48]	Thiel M V 1997 Compendium of Shock Wave Data (Livermore: Lawrence Livermore National Laboratory) Report UCRL 50108
[49]	Mcqueen R G, Marsh, S P, Taylor J W, Fritz J N, Carter W J 1970 The Equation of State of Solids from Shock Wave Studies (New York: Academic) pp348–350

Cited By

图 1 理论计算得到的雨贡纽P-V曲线与冲击实验数据的比较

Figure 1. Hugoniot P-V curves compared with the shock experimental data and theoretical results.

DownLoad: Full-Size Img PowerPoint

图 2 (a)沿$\left\langle {100} \right\rangle $晶向冲击后不同结构特征的钯的原子分数与纵向应力的关系; (b)不同结构特征随纵向应力变化的可视化表示; (c)温度与纵向应力的关系, 其中红色点线图为刘中利等^[24]冲击熔化的分子动力学模拟数据

Figure 2. (a) Fraction of atoms with different structural features versus longitudinal stress along the crystallographic direction $\left\langle {100} \right\rangle $; (b) visual representation of the variation of different structural features with longitudinal stress; (c) temperature versus longitudinal stress, the red dotted line plot shows the MD simulation data of Liu et al.^[24] shock melting.

DownLoad: Full-Size Img PowerPoint

图 3 沿不同晶向冲击后的结果　(a) $\left\langle {100} \right\rangle $晶向; (b) $\left\langle {110} \right\rangle $晶向; (c) $\left\langle {100} \right\rangle $晶向. 其中实线表示冲击速度在5.0—7.8 km/s范围内结构的RDF图像, 点划线表示与之对应的配位数曲线, 黑色虚线位置指向初始状态下的第一峰的位置

Figure 3. Results along different crystallographic directions: (a) $\left\langle {100} \right\rangle $; (b) $\left\langle {110} \right\rangle $; (c) $\left\langle {111} \right\rangle $. The solid lines indicate radial distribution functions of deformed micro-structure shocked at a range of shock velocity of 5.0–7.8 km/s. The dotted lines indicate the coordination number curves that correspond to the RDF, and the dashed lines points to the position of the first peak in the initial state.

DownLoad: Full-Size Img PowerPoint

图 4 利用a-CNA方法得到的沿不同晶向冲击的不同结构比例随压强的变化　(a) $\left\langle {110} \right\rangle $晶向; (b) $\left\langle {111} \right\rangle $晶向

Figure 4. Fraction of atoms with different structural versus compressing stress along different crystallographic directions obtained by a-CNA: (a) $\left\langle {110} \right\rangle $; (b) $\left\langle {111} \right\rangle $.

DownLoad: Full-Size Img PowerPoint

图 5 (a)不同缺陷率的晶体结构在冲击压缩后温度与压力的关系; (b), (c), (d)分别表示冲击压缩下含不同缺陷率体系的原子类别占比随冲击压强的变化

Figure 5. (a) Comparison of Hugoniot P-T curve among crystal structures with different porosities defects; (b), (c), (d) comparison of phase transition processes of atoms of system with variation porosities defects under shock compression.

DownLoad: Full-Size Img PowerPoint

图 6 (a)完美晶体与含缺陷晶体在冲击前后的势能差值分布图; (b)不同体系中势能差值的概率分布曲线

Figure 6. (a) Distribution diagram of potential energy difference between perfect crystal and defective crystal before and after compression; (b) probability distribution curves of potential energy differences in perfect crystal and defective crystal.

DownLoad: Full-Size Img PowerPoint

[1]	Graziani F, Desjarlais M P, Redmer R, Trickey S B 2014 Frontiers and Challenges in Warm Dense Matter (Vol. 1) (Switzerland: Springer) pp1–3
[2]	Moses E I, Boyd R N, Remington B A, Keane C J, Al-Ayat R 2009 Phys. Plasmas 16 041006 Google Scholar
[3]	Mitchell A C, Nellis W J, Moriarty J A, Heinle R A, Holmes N C, Tipton R E, Repp G W 1991 J. Appl. Phys. 69 2981 Google Scholar
[4]	Nagao H, Nakamura K J, Kondo K, Ozaki N, Takamatsu K, Ono T, Shiota T, Ichinose D, Tanaka K A, Wakabayashi K 2006 Phys. Plasmas 13 052705 Google Scholar
[5]	Yokoo M, Kawai N, Nakamura K G, Kondo K I 2008 Appl. Phys. Lett. 92 051901 Google Scholar
[6]	Nellis W J, Weir S T, Mitchell A C 1996 Science 273 936 Google Scholar
[7]	Weir S T, Mitchell A C, Nellis W J 1996 Phys. Rev. Lett. 76 1860 Google Scholar
[8]	Hartley N J, Brown S, Cowan T E, Cunningham E, Döppner T, Falcone R W, Fletcher L B, Frydrych S, Galtier E, Gamboa E J 2019 Sci. Rep. 9 1
[9]	Briggs R, Coppari F, Gorman M G, Smith R F, Tracy S J, Coleman A L, Fernandez-Panella A, Millot M, Eggert J H, Fratanduono D E 2019 Phys. Rev. Lett. 123 045701 Google Scholar
[10]	Sharma S M, Turneaure S J, Winey J M, Li Y, Rigg P, Schuman A, Sinclair N, Toyoda Y, Wang X, Weir N, Zhang J, Gupta Y M 2019 Phys. Rev. Lett. 123 045702 Google Scholar
[11]	Li Q J, Liu B B 2016 Chin. Phys. B 25 076107 Google Scholar
[12]	Guo Y L, Wei J H, Liu X, Ke X Z, Jiao Z Y 2021 Chin. Phys. B 30 016101 Google Scholar
[13]	Lu M Y, Huang Y P, Tian F B, Li D, Duan D F, Zhou Q, Cui T 2020 Chin. Phys. B 29 053104 Google Scholar
[14]	Hesse R W 2007 Jewelry-Making Through History: an Encyclopedia (Westport: Greenwood Publishing Group) p146
[15]	Colon P, Pradelle-Plasse N, Galland J 2003 Dent. Mater. 19 232 Google Scholar
[16]	Harper C A 1997 Passive Electronic Component Handbook. McGraw-Hill Professional (New York: McGraw-Hill) pp580
[17]	Fleischmann M, Pons S, Hawkins M 1989 J. Electroanal. Chem. 261 301 Google Scholar
[18]	Mutschele T, Kirchheim R 1987 Scr. Mater. 21 1351101
[19]	Pundt A, Sachs C, Winter M, Reetz M T, Fritsch D, Kirchheim R 1999 J. Alloys Compd. 293-295 480
[20]	Bonivardi A L, Baltanas M A 1994 React. Kinet. Catal. Lett. 52 95
[21]	Eastman J A, Thompson L J, Kestel B J 1993 Phys. Rev. 48 84 Google Scholar
[22]	Foiles S M, Adams J B 1989 Phys. Rev. B 40 9
[23]	Foiles S M, Baskes M I, Daw M S 1986 Phys. Rev. B 33 7983 Google Scholar
[24]	Liu Z L, Yang J H, Cai L C, Jing F Q, Alfѐ D 2011 Phys. Rev. B 83 144113 Google Scholar
[25]	Errandonea D 2013 Phys. Rev. B 87 054108 Google Scholar
[26]	Jeong J W, Chang K 1999 J. Phys. Condens. Matter 11 3799 Google Scholar
[27]	Liu Z L, Zhang X L, Cai L C 2015 J. Chem. Phys. 11 637
[28]	Zheng Z Y, Zhao J J 2016 Chin. Phys. B 25 076202 Google Scholar
[29]	孙小伟, 褚衍东, 刘子江, 刘玉孝, 王成伟, 刘维民 2005 物理学报 54 5830 Google Scholar Sun X W, Zhe Y D, Liu Z J, Liu Y X, Wang C W, Liu W M 2005 Acta Phys. Sin. 54 5830 Google Scholar
[30]	段芳莉, 王家序, 雒建斌, 温诗铸 2007 物理学报 56 6552 Google Scholar Duan F L, Wang J X, Luo J B, Weng S Z 2007 Acta Phys. Sin. 56 6552 Google Scholar
[31]	邵建立, 王裴, 秦承森, 周洪强 2007 物理学报 56 5389 Google Scholar Shao J L, Wang F, Qing C S, Zhou H Q 2007 Acta Phys. Sin. 56 5389 Google Scholar
[32]	周化光, 林鑫, 王猛, 黄卫东 2013 物理学报 62 056803 Google Scholar Zhou H G, Lin X, Wang M, Huang W D 2013 Acta Phys. Sin. 62 056803 Google Scholar
[33]	Plimpton S J 1995 J. Comput. Phys. 117 1 Google Scholar
[34]	Reed E J, Fried L E, Joannopoulos J D 2003 Phys. Rev. Lett. 90 235503 Google Scholar
[35]	Stukowski A 2009 Modell. Simul. Mater. Sci. Eng. 18 015012
[36]	韦昭召, 马骁, 柯常波, 张新平 2020 物理学报 69 136102 Google Scholar Wei Z Z, Ma X, Ke C B, Zhang X P 2020 Acta Phys. Sin. 69 136102 Google Scholar
[37]	Kien P H 2014 Int. Scholarly Res. Not. 2014 253627
[38]	Sun H Y, Kang D D, Hou Y, Dai J Y 2017 Matter Radiat. at Extremes 2 287 Google Scholar
[39]	Neogi A, Mitra N 2017 Sci. Rep. 7 1 Google Scholar
[40]	Honeycutt J D, Andersen H C 1987 J. Phys. Chem. 91 4950 Google Scholar
[41]	Schiøtz J, Tolla F D D, Jacobsen K W 1998 Nature 391 561 Google Scholar
[42]	Stukowski A 2012 Model. Simul. Mater. Sci. Eng. 20 045021 Google Scholar
[43]	Faken D, Jónsson H 1994 Comput. Mater. Sci. 2 279 Google Scholar
[44]	Tsuzuki H, Branicio P, Rino J 2007 Comput. Phys. Commun. 177 518 Google Scholar
[45]	Zeng Q Y, Dai J Y 2020 Sci. China Phys. Mech. Astron. 63 263011 Google Scholar
[46]	Walsh J M, Rice M H, Mcqueen R G, Yarger F L 1957 Phys. Rev. 108 196 Google Scholar
[47]	Marsh S P 1979 Los Alamos Shock Hugoniot Data (Berkeley: University of California Press)
[48]	Thiel M V 1997 Compendium of Shock Wave Data (Livermore: Lawrence Livermore National Laboratory) Report UCRL 50108
[49]	Mcqueen R G, Marsh, S P, Taylor J W, Fritz J N, Carter W J 1970 The Equation of State of Solids from Shock Wave Studies (New York: Academic) pp348–350

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