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Titanium (Ti) has many advantages including high specific strength, low density, and biocompatibility, and is an excellent option for biomedical implant applications. Traditionally manufacturing processes have great difficulties in processing the hexagonal α-Ti with complex geometries, which would be transformed into the BCC β-Ti at high temperatures. Additive manufacturing (AM) or metal three-dimensional(3D) printing has made it possible to accurately fabricate Ti products with complex morphology. As nanoparticles have been used in the AM processing, an interesting issue arises naturally to understand packing changes of Ti particles with nanometer size during heating and cooling. The information provides the possibility in understanding the processing-structure-property-performance relations in the AM processes with the intent of producing the desirable microstructural features, and thus achieving the mechanical properties comparable or even superior to the conventionally manufactured parts. Because of lacking appropriate experimental techniques, computational approach becomes a good option to obtain various static and dynamic properties of metals reliably, in bulk or surface configurations. On a nanoscale, as the number of atoms in one particle increases, the computational cost increases exponentially and the data complexity increases correspondingly. Molecular dynamics (MD) simulation is a well-established technique to characterize microscopic details in these systems involving combined behaviors of atom movements and locally structural rearrangements. In this paper we conduct the simulations within the framework of embedded atom method provided by Pasianot et al. to study packing transformations of Ti nanoparticles upon heating and cooling on an atomic scale. Based on the calculation of the potential energy per atom, pair distribution function, pair analysis, and the specific heat capacity, the results show that the particle size and temperature changes play key roles in the packing transformations. Small size particles preferentially form icosahedral geometries. As the particle size increases, particles can hold their HCP packing at room temperature. Upon heating, the structural transformation from HCP to BCC occurs in these large size particles, and there coexist the HCP structure and the BCC structure. At a high temperature, these particles present the melting behavior similar to that of the bulk phase. When the molten particles are cooled, the atoms in the particles undergo melting-BCC-HCP structural transition, and the freezing temperature lags behind the melting temperature. The simulations provide an estimate of the critical size, and are applicable to classical theory for melting the Ti particles.
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Keywords:
- metal /
- nanoparticles /
- computer simulation /
- phase transition
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图 1 300 K下势能随时间步的变化
Figure 1. The potential energy varying with timesteps.
图 2 原子间键对示意图
Figure 2. Schematic diagram of atomic pairs.
图 3 原子平均能量随温度的变化
Figure 3. The average energy per atom for Ti nanoparticles with different sizes.
图 4 Ti13对分布函数和原子堆积二维投影图
Figure 4. The pair distribution functions and atomic packing of the Ti13.
图 5 Ti57粒子在升温-降温过程中不同温度下的对分布函数 (a)升温; (b)降温
Figure 5. The pair distribution functions of Ti57 nanoparticles under heating and cooling processes: (a) Heating process; (b) cooling process.
图 6 Ti401粒子在升温-降温过程中不同温度下的对分布函数 (a)升温; (b)降温
Figure 6. The pair distribution functions of Ti401 nanoparticles under heating and cooling processes: (a) Heating process; (b) cooling process.
图 7 Ti1111纳米粒子的键对比例分数随温度变化曲线 (a)升温; (b)降温
Figure 7. Variations of pair fraction in Ti1111 nanoparticles: (a) Heating process; (b) cooling process.
图 8 Ti纳米粒子势能-温度斜率随粒径的变化
Figure 8. Slope of potential-temperature varying with the diameters of Ti nanoparticles.
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[1] Sharpless N E, DePinho R A 2007 Nat. Rev. Mol. Cell Biol. 8 703
Google Scholar
[2] Griffith L G, Naughton G 2002 Science 295 1009
Google Scholar
[3] Stoltz J 2012 Regener. Med. Cell. Ther. 77 111
[4] Amini A R, Laurencin C P, Nukavarapu S P 2012 Crit. Rev. Biomed. Eng. 40 363
Google Scholar
[5] Wysocki B, Idaszek J, Szlązak K, Strzelczyk K, Brynk T, Kurzydlowski K J, Święszkoski W 2016 Materials 9 197215
[6] Elias C N, Lima J H C, Valiev R, Meyers M A 2008 JOM 60 46
[7] Attar H, Calin M, Zhang L C, Scudino S, Eckert J 2014 Mater. Sci. Eng. A 593 170
Google Scholar
[8] Zhang L C, Attar H 2016 Adv. Eng. Mater. 18 463
Google Scholar
[9] Froes F H 2012 Adv. Mater. Processes 170 16
[10] Urlea V, Brailovski V 2017 J. Mater. Process. Technol. 242 1
Google Scholar
[11] Herzog D, Sevda V, Wycik E, Emmelmann C 2016 Acta Mater. 117 371
Google Scholar
[12] Bourell D, Kruth J P, Leu M, Levy G, Rosen D, Beese A M, Clare A 2017 CIRP Annals Manuf. Technol. 66 659
Google Scholar
[13] Liu Y J, Li S J, Wang H L, Hou W T, Hao Y L, Yang R, Sercombe T B, Zhang L C 2016 Acta Mater. 113 56
Google Scholar
[14] Prashanth K G, Shahabi H S, Attar H, Srivastava V C, Ellendt N, Uhlenwinkel V, Eckert J, Scudino S 2015 Add. Manuf. 6 1
[15] Zhang L C, Klemm D, Eckert J, Hao Y L, Sercombe T B 2011 Scrip. Mater. 65 21
[16] Gu D D, Meiners W, Wissenbach K, Poprawe R 2012 Int. Mater. Rev. 57 133
Google Scholar
[17] Sames W J, List F A, Pannala S, Dehoff R R, Babu S S 2016 Int. Mat. Rev. 61 315
Google Scholar
[18] Piseri P, Mazza T, Bongiorno G, Lenardi C, Ravagnan L, Foglia F D, DiFonzo F, Coreno M, DeSimone M, Prince K C, Milani P 2006 New J. Phys. 8 136
Google Scholar
[19] Qu X 2017 Mater. Sci. Technol. 33 822
Google Scholar
[20] Buesser B, Pratsinis S E 2015 J. Phys. Chem. C 119 10116
Google Scholar
[21] Mazzone A M 2000 Philos. Mag. B 80 95
Google Scholar
[22] Chepkasov I V, Gafner Y Y, Gafner S L 2016 J. Aerosol Sci. 91 33
Google Scholar
[23] Gould A L, Logsdail A J, Catlow C R A 2015 J. Phys. Chem. C 119 623
Google Scholar
[24] Mottet C, Rossi G, Baletto F, Ferrando R 2005 Phys. Rev. Lett. 95 035501
Google Scholar
[25] Zhang L 2016 J. Phys. Soc. Jpn. 85 054602
[26] Levchenko E V, Evteev A V, Lorscheider T, Belova I V, Murch G E 2013 Comput. Mater. Sci. 79 316
Google Scholar
[27] Zhang L 2019 Adv. Eng. Mater. 21 1800531
Google Scholar
[28] Zhang L 2019 Prog. Nat. Sci.: Mater. Inter. 29 237
Google Scholar
[29] Mendelev M I, Underwood T L, Ackland G J 2016 J. Chem. Phys. 145 154
[30] Farkas D 1994 Modell. Simul. Mater. Sci. Eng. 2 975
Google Scholar
[31] Pasianot R, Savino E 1992 Phys. Rev. B 45 12704
Google Scholar
[32] Rose J H, Smith J R, Guinea F, Ferrante J 1984 Phys. Rev. B 29 2963
[33] 钱泽宇, 张林 2015 64 243103
Google Scholar
Qian Z Y, Zhang L 2015 Acta Phys. Sin. 64 243103
Google Scholar
[34] 张林, 李蔚, 刘永利, 孙本哲, 王佳庆 2011 金属学报 47 1080
Zhang L, Li W, Liu Y L, Sun B Z, Wang J Q 2011 Acta Metall. Sin. 47 1080
[35] 宋成粉, 樊沁娜, 李蔚, 刘永利, 张林 2011 60 063104
Google Scholar
Song C F, Fan Q N, Li W, Liu Y L, Zhang L 2011 Acta Phys. Sin. 60 063104
Google Scholar
[36] Tayson W R, Miller W A 1977 Surf. Sci. 62 267
Google Scholar
[37] Aghemenloh E, Idiodi J O A, Azi S O 2009 Comput. Mater. Sci. 10 1016
[38] 姬德朋, 王绍青 2015 金属学报 51 597
Google Scholar
Ji D P, Wang S Q 2015 Acta Metall. Sin. 51 597
Google Scholar
[39] 汤剑锋 2016 博士学位论文(长沙: 湖南大学)
Tang J F 2016 Ph. D. Dissertation (Changsha: Hunan University) (in Chinese)
[40] Lewis L J, Jensen P, Barrat J L 1997 Phys. Rev. B 56 2248
Google Scholar
[41] Kofman R, Cheyssac P, Aouaj A, Lereah Y, Deutschera G, Ben-Davida T, Penissonc J M, Bourret A 1994 Surf. Sci. 303 231
Google Scholar
[42] 冯黛丽, 冯妍卉, 张欣欣 2013 62 083602
Google Scholar
Feng D L, Feng Y H, Zhang X X 2013 Acta Phys. Sin. 62 083602
Google Scholar
[43] 汪志刚, 吴亮, 张杨, 文玉华 2011 60 096105
Wang Z G, Wu L, Zhang Y, Wen Y H 2011 Acta Phys. Sin. 60 096105
[44] Zhang L, Sun H X 2010 Phys. Status. Solidi. A 207 1178
Google Scholar
[45] Xu S N, Zhang L, Qi Y, Zhang C B 2010 Phys. B 405 632
Google Scholar
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