Abnormal breakdown of Stokes-Einstein relation in liquid aluminium

doi:10.1088/1674-1056/26/1/016102

Abstract We present the results of systematic molecular dynamics simulations of pure aluminium melt with a well-accepted embedded atom potential. The structure and dynamics were calculated over a wide temperature range, and the calculated results (including the pair correlation function, self-diffusion coefficient, and viscosity) agree well with the available experimental observations. The calculated data were used to examine the Stokes-Einstein relation (SER). The results indicate that the SER begins to break down at a temperature T_x (~1090 K) which is well above the equilibrium melting point (912.5 K). This high-temperature breakdown is confirmed by the evolution of dynamics heterogeneity, which is characterised by the non-Gaussian parameter α₂(t). The maximum value of α₂(t), α_2,max, increases at an accelerating rate as the temperature falls below T_x. The development of α_2,max was found to be related to the liquid structure change evidenced by local five-fold symmetry. Accordingly, we suggest that this high-temperature breakdown of SER has a structural origin. The results of this study are expected to make researchers reconsider the applicability of SER and promote greater understanding of the relationship between dynamics and structure.

Keywords: diffusion viscosity dynamics heterogeneity local five-fold symmetry

Received: 24 February 2016
Revised: 07 October 2016
Accepted manuscript online:

PACS:	66.20.Cy	(Theory and modeling of viscosity and rheological properties, including computer simulation)
	66.10.cg	(Mass diffusion, including self-diffusion, mutual diffusion, tracer diffusion, etc.)
	02.70.Ns	(Molecular dynamics and particle methods)
	61.20.Ja	(Computer simulation of liquid structure)

Fund: Project supported by the National Basic Research Program of China (Grant No. 2011CB012900), the National Natural Science Foundation of China (Grant No. 51171115), the Natural Science Foundation of Shanghai City, China (Grant No. 10ZR1415700), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100073120008), and the Program for New Century Excellent Talents in Universities of China. This work is partially supported by Alexander von Humboldt Foundation.

Corresponding Authors: Xiu-Jun Han
E-mail: xjhan@sjtu.edu.cn

Cite this article:

Chen-Hui Li (李晨辉), Xiu-Jun Han(韩秀君), Ying-Wei Luan(栾英伟), Jian-Guo Li(李建国) Abnormal breakdown of Stokes-Einstein relation in liquid aluminium 2017 Chin. Phys. B 26 016102

[1]	Glicksman M E 2011 Principles of Solidification (New York:Springer)
[2]	Ngai K L 2011 Relaxation and Diffusion in Complex Systems (New York:Springer)
[3]	Tyrrell H J V and Harris K R 1984 Diffusion in Liquids (London:Butterworths)
[4]	Balucani U and Zoppi M 1994 Dynamics of the Liquid State (Oxford:Clarendon)
[5]	Einstein A 1956 Investigations on the Theory of Brownian Movement (New York:Dover)
[6]	Sutherland W 1905 Philos. Mag. 9 781
[7]	Chang I and Sillescu H 1997 J. Phys. Chem. B 101 8794
[8]	Bordat P, Affouard F, Descamps M and Müller-Plathe F 2003 J. Phys. -Condens. Matter 15 5397
[9]	Kumar S K, Szamel G and Douglas J F 2006 J. Chem. Phys. 124 214501
[10]	Chathoth S M and Samwer K 2010 Appl. Phys. Lett. 97 221910
[11]	Cicerone M T and Ediger M D 1996 J. Chem. Phys. 104 7210
[12]	Gotze W and Sjogren L 1992 Rep. Prog. Phys. 55 241
[13]	Das S P 2004 Rev. Mod. Phys. 76 785
[14]	Han X J and Schober H R 2011 Phys. Rev. B 83 224201
[15]	Jaiswal A, Egami T and Zhang Y 2015 Phys. Rev. B 91 134204
[16]	Li F, Liu X J, Hou H Y, Chen G and Chen G L 2011 J. Appl. Phys. 110 013519
[17]	Shen B, Liu C Y, Jia Y, Yue G Q, Ke F S, Zhao H B, Chen L Y, Wang S Y, Wang C Z and Ho K M 2014 J. Non-Cryst. Solids 383 13
[18]	Jakse N and Pasturel A 2013 Sci. Rep. 3 3135
[19]	Recoules V and Crocombette J P 2005 Phys. Rev. B 72 104202
[20]	Li H, Wang G H, Zhao J and Bian X F 2002 J. Chem. Phys. 116 24
[21]	Smith P M, Elmer J W and Gallegos G F 1999 Scripta Mater. 40 937
[22]	Cherne III F J and Deymier P A 2001 Scripta Mater. 45 985
[23]	Demmel F, Szubrin D, Pilgrim W C and Morkel C 2011 Phys. Rev. B 84 014307
[24]	Kargl F, Weis H, Unruh T and Meyer A 2012 J. Phys.-Conf. Ser. 340 012077
[25]	Wang D and Overfelt R A 2002 Int. J. Thermophys. 23 1063
[26]	Yamasaki T, Kanatani S, Ogino Y and Inoue A 1993 J. Non-Cryst. Solids 156-158 441
[27]	Plimpton S 1995 J. Comput. Phys. 117 1
[28]	Mendelev M I, Kramer M J, Becker C A and Asta M 2008 Philos. Mag. 88 1723
[29]	Li C H, Han X J, Luan Y W and Li J G 2015 Chin. Phys. B 24 116101
[30]	Parrinello M and Rahman A 1980 Phys. Rev. Lett. 45 1196
[31]	Nosé S 1984 J. Chem. Phys. 81 511
[32]	Hoover W G 1985 Phys. Rev. A 31 1695
[33]	Swope W C, Andersen H C, Berens P H and Wilson K 1982 J. Chem. Phys. 76 637
[34]	Waseda Y 1980 The Structure of Non-Crystalline Materials (New York:McGraw-Hill)
[35]	Morris J R, Dahlborg U and Calvo-Dahlborg M 2007 J. Non-Cryst. Solids 353 3444
[36]	Schenk T, Holland-Moritz D, Simonet V, Bellissent R and Herlach D M 2002 Phys. Rev. Lett. 89 075507
[37]	Chen K Y, Liu H B, Li X P, Han Q Y and Hu Z Q 1995 J. Phys. -Condens. Matter 7 2379
[38]	Rapaport D C 2004 The Art of Molecular Dynamics Simulation, 2004 edition (Cambridge:Cambridge University Press)
[39]	Allen M P and Tildesley D J 1987 Computer Simulation of Liquids (Oxford:Clarendon)
[40]	Vogel H 1921 Phys. Z. 22 645
[41]	Fulcher G S 1925 J. Am. Ceram. Soc. 8 339
[42]	Tammann G and Hesse G 1926 Z. Anorg. Allg. Chem. 156 245
[43]	Egelstaff P 1967 An Introduction to the Liquid State (London:Academic Press)
[44]	Hansen J P and McDonald I R 2006 Theory of Simple Liquids, 3rd edn. (London:Academic Press)
[45]	Rahman A 1964 Phys. Rev. A 136 405
[46]	Caprion D, Matsui J and Schober H R 2000 Phys. Rev. Lett. 85 4293
[47]	Lee G W, Gangopadhyay A K, Kelton K F, Hyers R W, Rathz T J, Rogers J R and Robinson D S 2004 Phys. Rev. Lett. 93 037802
[48]	Kelton K F, Lee G W, Gangopadhyay A K, Hyers R W, Rathz T J, Rogers J R, Robinson M B and Robinson D S 2003 Phys. Rev. Lett. 90 195504
[49]	Liu H R, Liu R S, Zhang A L, Hou Z Y, Wang X and Tian Z A 2007 Chin. Phys. 16 3747
[50]	Zhang J X, Li H, Zhang J, Song X G and Bian X F 2009 Chin. Phys. B 18 4949
[51]	Hou Z Y, Liu R S, Tian Z A and Wang J G 2011 Chin. Phys. B 20 066102
[52]	Wang L, Zhang Y N, Mao X M and Peng C X 2007 Chin. Phys. Lett. 24 2319
[53]	Frank F C 1952 Proc. R. Soc. A 215 43
[54]	Kim T H and Kelton K F 2007 J. Chem. Phys. 126 054513
[55]	Ganesh P and Widom M 2006 Phys. Rev. B 74 134205
[56]	Leocmach M and Tanaka H 2012 Nat. Commun. 3 974
[57]	Shen Y T, Kim T H, Gangopadhyay A K and Kelton K F 2009 Phys. Rev. Lett. 102 057801
[58]	Di Cicco A, Trapananti A and Faggioni S 2003 Phys. Rev. Lett. 91 135505
[59]	Han X J, Li J G and Schober H R 2016 J. Chem. Phys. 144 124505
[60]	Cheng Y Q and Ma E 2011 Prog. Mater. Sci. 56 379
[61]	Pasturel A, Tasci E S, Sluiter M H F and Jaske N 2010 Phys. Rev. B 81 140202
[62]	Jakse N, Nguyen T L T and Pasturel A 2013 J. Appl. Phys. 14 063514
[63]	Cheng Y Q, Sheng H W and Ma E 2008 Phys. Rev. B 78 014207
[64]	Finney J L 1970 Proc. R. Soc. A 319 495
[65]	Finney J L 1977 Nature 266 309
[66]	Delogu F 2009 Phys. Rev. B 79 064205
[67]	Itoh K, Hashi K, Aoki K, Mori K, Sugiyama M and Fukunaga T 2007 J. Alloys Compd. 434-435 180
[68]	Hao S G, Wang C Z, Kramer M J and Ho K M 2010 J. Appl. Phys. 107 053511
[69]	Peng H L, Li M Z and Wang W H 2013 Appl. Phys. Lett. 102 131908
[70]	Cheng Y Q, Ma E and Sheng H W 2008 Appl. Phys. Lett. 93 111913
[71]	Peng H L, Li M Z and Wang W H 2011 Phys. Rev. Lett. 106 135503
[72]	Wakeda M, Shibutani Y, Ogata S and Park J 2007 Intermetallics 15 139
[73]	Cheng Y Q, Cao A J, Sheng H W and Ma E 2008 Acta Mater. 56 5263

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Abnormal breakdown of Stokes-Einstein relation in liquid aluminium

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