Please wait a minute...
Acta Metall Sin  2018, Vol. 54 Issue (6): 844-850    DOI: 10.11900/0412.1961.2017.00402
Orginal Article Current Issue | Archive | Adv Search |
Effect of Superheated Temperature and Cooling Rate on the Solidification of Undercooled Ti Melt
Dandan FAN, Junfeng XU, Yanan ZHONG, Zengyun JIAN()
School of Materials and Chemical Engineering, Xi'an Technological University, Xi'an 710021, China
Download:  HTML  PDF(4930KB) 
Export:  BibTeX | EndNote (RIS)      

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.

Key words:  undercooling      solidification      homogeneous nucleation      molecular dynamics     
Received:  25 September 2017     
ZTFLH:  TG113.12  
Fund: Supported by National Natural Science Foundation of China (No.51671151) and Science and Technology Program of Shaanxi Province (No.2016KJXX-87)

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.

URL:     OR

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
[24] Hoover W G.Canonical dynamics: Equilibrium phase-space distributions[J]. Phys. Rev., 1985, 31A: 1695
[25] 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
[1] LI Yuancai, JIANG Wugui, ZHOU Yu. Effect of Temperature on Mechanical Propertiesof Carbon Nanotubes-Reinforced Nickel Nano-Honeycombs[J]. 金属学报, 2020, 56(5): 785-794.
[2] LI Meilin, LI Saiyi. Motion Characteristics of <c+a> Edge Dislocation on the Second-Order Pyramidal Plane in Magnesium Simulated by Molecular Dynamics[J]. 金属学报, 2020, 56(5): 795-800.
[3] LI Gen, LAN Peng, ZHANG Jiaquan. Solidification Structure Refinement in TWIP Steel by Ce Inoculation[J]. 金属学报, 2020, 56(5): 704-714.
[4] LI Yuancai, JIANG Wugui, ZHOU Yu. Effect of Nanopores on Tensile Properties of Single Crystal/Polycrystalline Nickel Composites[J]. 金属学报, 2020, 56(5): 776-784.
[5] REN Zhongming,LEI Zuosheng,LI Chuanjun,XUAN Weidong,ZHONG Yunbo,LI Xi. New Study and Development on Electromagnetic Field Technology in Metallurgical Processes[J]. 金属学报, 2020, 56(4): 583-600.
[6] WANG Guiqin,WANG Qin,CHE Honglong,LI Yajun,LEI Mingkai. Effects of Silicon on the Microstructure and Propertiesof Cast Duplex Stainless Steel with Ultra-HighChromium and High Carbon[J]. 金属学报, 2020, 56(3): 278-290.
[7] DENG Congkun,JIANG Hongxiang,ZHAO Jiuzhou,HE Jie,ZHAO Lei. Study on the Solidification of Ag-Ni Monotectic Alloy[J]. 金属学报, 2020, 56(2): 212-220.
[8] ZHOU Xia,LIU Xiaoxia. Mechanical Properties and Strengthening Mechanism of Graphene Nanoplatelets Reinforced Magnesium Matrix Composites[J]. 金属学报, 2020, 56(2): 240-248.
[9] MA Xiaoqiang,YANG Kunjie,XU Yuqiong,DU Xiaochao,ZHOU Jianjun,XIAO Renzheng. Molecular Dynamics Simulation of DisplacementCascades in Nb[J]. 金属学报, 2020, 56(2): 249-256.
[10] ZHANG Jun,JIE Ziqi,HUANG Taiwen,YANG Wenchao,LIU Lin,FU Hengzhi. Research and Development of Equiaxed Grain Solidification and Forming Technology for Nickel-Based Cast Superalloys[J]. 金属学报, 2019, 55(9): 1145-1159.
[11] ZHANG Jian,WANG Li,WANG Dong,XIE Guang,LU Yuzhang,SHEN Jian,LOU Langhong. Recent Progress in Research and Development of Nickel-Based Single Crystal Superalloys[J]. 金属学报, 2019, 55(9): 1077-1094.
[12] XU Qingyan,YANG Cong,YAN Xuewei,LIU Baicheng. Development of Numerical Simulation in Nickel-Based Superalloy Turbine Blade Directional Solidification[J]. 金属学报, 2019, 55(9): 1175-1184.
[13] Junqin SHI,Kun SUN,Liang FANG,Shaofeng XU. Stress Relaxation and Elastic Recovery of Monocrystalline Cu Under Water Environment[J]. 金属学报, 2019, 55(8): 1034-1040.
[14] Wang LI,Qian SUN,Hongxiang JIANG,Jiuzhou ZHAO. Solidification of Al-Bi Alloy and Influence of Microalloying Element Sn[J]. 金属学报, 2019, 55(7): 831-839.
[15] Qingdong ZHANG,Shuo LI,Boyang ZHANG,Lu XIE,Rui LI. Molecular Dynamics Modeling and Studying of Micro-Deformation Behavior in Metal Roll-Bonding Process[J]. 金属学报, 2019, 55(7): 919-927.
No Suggested Reading articles found!