School of Materials and Chemical Engineering, Xi'an Technological University, Xi'an 710021, China
Cite this article:
Dandan FAN, Junfeng XU, Yanan ZHONG, Zengyun JIAN. Effect of Superheated Temperature and Cooling Rate on the Solidification of Undercooled Ti Melt. Acta Metall Sin, 2018, 54(6): 844-850.
Undercooling is an important parameter to characterize the process of solidification and the physical properties of the melt. However, the traditional experimental conditions do not provide mature technical conditions and experimental platforms for the study of this subject. Molecular dynamics simulation method can not only study the experimental process and the organization structure, but also break through the limited conditions of the laboratory, and provide advanced prediction for scientific research. In order to study the influences of superheated temperature and cooling rate on the undercooling of the homogeneous nucleation and the solidified structure, the solidification of undercooled Ti melt was studied by molecular dynamics simulation in this work; and the solidified structure was then analyzed by the radial analysis, the H-A key type analysis and the largest groups of cluster analysis. The results show that, the nucleation undercooling of Ti melt increases with the rise of superheated temperature. In the undercooling vs temperature curve there are two inflection points at 2100 K (T1) and 2490 K (T2), which correspond to the breaking-start temperature and breaking-end temperature for bond pair of nucleation cluster. In this temperature range, the number of nucleation clusters decreases with rise of temperature. When the superheated temperature is higher than T2, the nucleation undercooling approaches a constant. On the other hand, the nucleation undercooling of Ti melt increases with the accelerate of cooling rate until an anomalous structure is formed, and in the numbers of the bonds of the structure vs different cooling rate curves, the number of 1541, 1551 and 1431 bond types gradually adds with cooling rate going up. In addition, when the cooling rate is less than 1.0×1011 K/s, the hcp and bcc inlaid crystalline structures are obtained after the solidification of Ti melt. When the cooling rate is greater than or equal to 1.0×1013 K/s, two kinds of crystalline structure are reduced, and the microstructures are mainly amorphous. When the cooling rate ranges between 1.0×1011 K/s and 1.0×1013 K/s, its structure is a mixture of crystalline and amorphous. From the results of radial distribution, H-A bond type and atomic cluster analysis, it was found that the critical cooling rate for amorphous structure is determined as 1.0×1013 K/s.
Fig.1 Melting point simulated by embedded atom method (EAM) potential function
Ts
Tc
ΔT
2006
917
1023
2036
910
1030
2100
904
1036
2250
899
1041
2320
896
1044
2350
894
1046
2400
888
1052
2450
879
1061
2490
874
1066
2540
874
1066
2600
874
1066
Table 1 Crystallization temperature Tc and undercooling ΔT of melt Ti from cooling under different Ts (K)
Fig.2 Potential energies of Ti system vs temperature under different superheated temperatures Ts
Fig.3 ΔT as a function of Ts for Ti melt
Fig.4 The potential energy vs temperature of the melt Ti under different cooling rates Rc
Fig.5 ΔT-lgRc curve of Ti melt
Fig.6 Radial distribution function curve of Ti solidified under different Rc
Fig.7 Numbers of the bonds in the structure of metal Ti solidified under different Rc
Rc / (Ks-1)
Tc / K
ΔT / K
1.0×109.8
913.37
1026.63
1.0×1010
907.26
1032.74
1.0×1010.5
882.83
1057.17
1.0×1011
876.79
1063.21
1.0×1011.5
857.17
1082.83
1.0×1012
799.76
1140.24
Table 2 Tc and ΔT of the melt Ti under different Rc
Rc / (Ks-1)
Nc
Nbcc
Nfcc
Nhcp
1.0×109.8
22300
1852
0
20448
1.0×1010
17276
8349
0
8927
1.0×1010.5
17283
11770
0
5513
1.0×1011
13697
8298
0
5399
1.0×1011.5
21586
6781
0
14805
1.0×1012
18743
5384
0
12909
1.0×1012.5
6315
3150
0
3165
1.0×1013
579
162
0
417
1.0×1013.5
216
58
0
158
1.0×1014
96
17
0
79
1.0×1014.5
43
6
0
37
1.0×1015
35
4
0
31
1.0×1015.5
4
1
0
3
1.0×1016
2
1
0
1
Table 3 Total number of atoms in the final configuration and crystalline clusters after solidification under different Rc
Fig.8 Microstructures of Ti melt after solidification under Rc=1.0×109.8 K/s (a), Rc=1.0×1010 K/s (b), Rc=1.0×1010.5 K/s (c), Rc=1.0×1011 K/s (d), Rc=1.0×1011.5 K/s (e), Rc=1.0×1012 K/s (f), Rc=1.0×1012.5 K/s (g), Rc=1.0×1013 K/s (h), Rc=1.0×1013.5 K/s (i), Rc=1.0×1014 K/s (j), Rc=1.0×1014.5 K/s (k) and Rc=1.0×1015 K/s (l) (Yellow for bcc structure, purple for hcp structure, the blank for amorphous. Insets show the enlarged views)
[1]
Jian Z Y, Chang F E, Ma W H, et al.Metal nucleation and undercooling[J]. Sci. China, 2000, 30E: 9(坚增运, 常芳娥, 马卫红等. 金属熔体的形核和过冷度[J]. 中国科学, 2000, 30E: 9)
[2]
Mortensen A, Flemings M C.Solidification of binary hypoeutectic alloy matrix composite castings[J]. Metall. Mater. Trans., 1996, 27A: 595
[3]
Jian Z Y, Kuribayashi K, Jie W Q.Critical undercoolings for the transition from the lateral to continuous growth in undercooled silicon and germanium[J]. Acta Mater., 2004, 52: 3323
[4]
Xu J F, Xiang M, Dang B, et al.Relation of cooling rate, undercooling and structure for rapid solidification of iron melt[J]. Comput. Mater. Sci., 2017, 128: 98
[5]
Feng Y.Study on non-equilibrium solidification mechanism of Al-Si alloys [D]. Chongqing: Chongqing University, 2008(冯毅. Al-Si合金的非平衡凝固机理研究 [D]. 重庆: 重庆大学, 2008)
[6]
Si N C, Zhao L G, Sun K Q.Influence of melt thermal history on structure of melt Al-Cu alloy[J]. Nonferrous Met., 2008, 60(4): 22(司乃潮, 赵罗根, 孙克庆. 熔体热历史对Al-Cu合金熔体结构的影响[J]. 有色金属, 2008, 60(4): 22)
[7]
Li J Y, Liu R S, Zhou Z, et al.A simulation study for the effects of initial conditions of liquid metals on solidification microstructures[J]. Chin. J. At. Mol. Phys., 1998, 15(2): 193(李基永, 刘让苏, 周征等. 液态金属的初始状态对凝固微结构影响的模拟研究[J]. 原子与分子物理学报, 1998, 15(2): 193)
[8]
Hou Z Y, Dong K J, Tian Z A, et al.Cooling rate dependence of solidification for liquid aluminium: A large-scale molecular dynamics simulation study[J]. Phys. Chem. Chem. Phys., 2016, 18: 17461
[9]
Hou Z Y, Tian Z A, Liu R S, et al.Formation mechanism of bulk nanocrystalline aluminium with multiply twinned grains by liquid quenching: A molecular dynamics simulation study[J]. Comput. Mater. Sci., 2015, 99: 256
[10]
Zhang H T, Liu R S, Hou Z Y, et al.A simulation study for the effects of cooling rate on evolution of microstructures during solidification of liquid metal Ga[J]. Acta Phys. Sin., 2006, 55: 2409(张海涛, 刘让苏, 侯兆阳等. 冷速对液态金属Ga凝固过程中微观结构演变影响的模拟研究[J]. 物理学报, 2006, 55: 2409)
[11]
Zhang T, Zhang X R, Guan L.Molecular dynamics simulations of the solidification of liquid Au[J]. J. Shandong Univ. Technol., 2002, 32: 57(张弢, 张晓茹, 管立. 贵金属Au冷却过程的分子动力学研究[J]. 山东工业大学学报, 2002, 32: 57)
[12]
Lin Y, Liu R S, Tian Z A, et al.Effect of cooling rates on microstructures during solidification process of liquid metal Zn[J]. Acta Phys.-Chim. Sin., 2008, 24: 250(林艳, 刘让苏, 田泽安等. 冷却速率对液态金属Zn快速凝固过程中微观结构的影响[J]. 物理化学学报, 2008, 24: 250)
[13]
Allen M P.Introduction of molecular dynamics simulation [A]. Computational Soft Matter: From Synthetic Polymers to Proteins, Lecture Notes[C]. Julich: John von Neumann Institute for Computing, 2004: 43
[14]
Bhat M H, Molinero V, Soignard E, et al.Vitrification of a monatomic metallic liquid[J]. Nature, 2007, 448: 787
[15]
Pan S P, Qin J Y, Wang W M, et al.Origin of splitting of the second peak in the pair-distribution function for metallic glasses[J]. Phys. Rev., 2011, 84B: 092201
[16]
Alkhateb H, Al-Ostaz A, Cheng A H D. Molecular dynamics simulations of graphite-vinylester nanocomposites and their constituents[J]. Carbon Lett., 2010, 11: 316
[17]
Cao A J, Yuan Y T.Atomistic study on the strength of symmetric tilt grain boundaries in graphene[J]. Appl. Phys. Lett., 2012, 100: 211912
[18]
Ebrahimi S, Montazeri A, Rafii-Tabar H.Molecular dynamics study of the interfacial mechanical properties of the graphene-collagen biological nanocomposite[J]. Comput. Mater. Sci., 2013, 69: 29
[19]
Mortazavi B, Ahzi S.Thermal conductivity and tensile response of defective graphene: A molecular dynamics study[J]. Carbon, 2013, 63: 460
[20]
Xia L, Chen S, Lu J S, et al.The development and application of the interatomic potentials of precious metals for molecular dynamics simulation[J]. Preci. Met., 2013, 34(4): 82(夏璐, 陈松, 陆建生等. 分子动力学模拟用贵金属势函数的应用与发展[J]. 贵金属, 2013, 34(4): 82)
[21]
Okita S, Verestek W, Sakane S, et al.Molecular dynamics simulations investigating consecutive nucleation, solidification and grain growth in a twelve-million-atom Fe-system[J]. J. Cryst. Growth, 2017, 474: 140
[22]
Plimpton S.Fast parallel algorithms for short-range molecular dynamics[J]. J. Comput. Phys., 1995, 117: 1
[23]
Nosé S.A molecular dynamics method for simulations in the canonical ensemble[J]. Mol. Phys., 1984, 52: 255
Daw M S, Baskes M I.Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals[J]. Phys. Rev., 1984, 29B: 6443
[26]
Daw M S.Model of metallic cohesion: The embedded-atom method[J]. Phys. Rev., 1989, 39B: 7441
[27]
Gao A H.Effect of melt thermal history on the solidification behaviors of metals [D]. Xi'an: Xi'an Technological University, 2013(高阿红. 熔体热历史对金属凝固特性影响的研究 [D]. 西安: 西安工业大学, 2013)
[28]
Zhong Y N.Study on the structure of metal melt and solidification behavior by molecular dynamic simulation method [D]. Xi'an: Xi'an Technological University, 2016(钟亚男. 金属熔体结构及凝固特性的分子动力学模拟 [D]. 西安: 西安工业大学, 2016)
[29]
Xu J F, Dang B, Fan D D, et al.Effect of melt superheating treatment on the latent heat release of Sn[J]. Metall. Mater. Trans., 2017, 48A: 1133
[30]
Sapozhnikov F A, Ionov G V, Dremov V V.An adaptive template method for analyzing crystal structures and defects in molecular dynamics simulations of high-rate deformations[J]. Russ. J. Phys. Chem., 2008, 2B: 238
[31]
Jian Z Y, Chen J, Chang F E, et al.Simulation of molecular dynamics of silver subcritical nuclei and crystal clusters during solidification[J]. Sci. China Technol. Sci., 2010, 53: 3203
[32]
Jian Z Y, Gao A H, Chang F E, et al.Molecular dynamics simulation of the critical and subcritical nuclei during solidification of nickel melt[J]. Acta Phys. Sin., 2013, 62: 056102(坚增运, 高阿红, 常芳娥等. Ni熔体凝固过程中临界晶核和亚临界晶核的分子动力学模拟[J]. 物理学报, 2013, 62: 056102)
[33]
Nie Y Z, Xie Y Q, Peng H J, et al.First-principles study of thermal properties of metal Ti[J]. J. Cent. South Univ.(Sci. Technol.), 2007, 38: 1072(聂耀庄, 谢佑卿, 彭红建等. 金属Ti热学性质第一原理研究[J]. 中南大学学报(自然科学版), 2007, 38: 1072)
[34]
Wang L, Bian X F, Li H.Liquid-solid transition and crystal growth of metal Cu by molecular dynamics simulation[J]. J. Phys. Chem. Sin., 2000, 16: 825(王丽, 边秀房, 李辉. 金属Cu液固转变及晶体生长的分子动力学模拟[J]. 物理化学学报, 2000, 16: 825)
[35]
Schroers J.Condensed-matter physics: Glasses made from pure metals[J]. Nature, 2014, 512: 142
[36]
Zhong L, Wang J W, Sheng H W, et al.Formation of monatomic metallic glasses through ultrafast liquid quenching[J]. Nature, 2014, 512: 177
