Molecular Dynamics Study on the Crystallization Process of Cubic Cu–Au Alloy
Abstract
:1. Introduction
2. Method of Calculation
3. Results and Discussion
3.1. Structural Characteristic Quantities
3.2. Factors Affecting the Structure and Crystallization Process of Cu–Au Alloy
3.2.1. Time of Each Move Steps
3.2.2. Temperature
3.2.3. Heat Annealing Time
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Satoh, A. Introduction to Practice of Molecular Simulation; Elsevier Inc.: Burlington, MA, USA, 2011. [Google Scholar]
- Mostowski, J.; Trippenbach, M.; Van, C.L. Phase Space Approach to Two-electron Atom Ionisation. In Proceedings of the Fourth International Conference on Multiphoton Processes, Boulder, CO, USA, 13–17 July 1987. [Google Scholar]
- Perla, B.; Jorge, M.S. Molecular Dynamics: From Classical to Quantum Methods; Elsevier: Amsterdam, The Netherlands, 1999. [Google Scholar]
- Van, C.L.; Goldstein, P. Concise Course in Nonlinear Partial Diferential Equations; Publishing House of the University of Zielona Góra: Zielona Góra, Poland, 2008. [Google Scholar]
- Basile, A.; Parmaliana, A.; Tosti, S.; Iulianelli, A.; Gallucci, F.; Espro, C.; Spooren, J. Hydrogen production by methanol steam reforming carried out in membrane reactor on Cu/Zn/Mg-based catalyst. Catal. Today 2008, 137, 17–22. [Google Scholar] [CrossRef]
- Yoo, W.; Li, C. Copper-catalyzed oxidative esterification of alcohols with aldehydes activated by Lewis acids. Tetrahedron Lett. 2007, 48, 1033–1035. [Google Scholar] [CrossRef]
- Fujitani, T.; Saito, M.; Kanai, Y.; Kakumoto, T.; Watanabe, T.; Nakamura, J.; Uchijima, T. The role of metal oxides in promoting a copper catalyst for methanol synthesis. Catal. Lett. 1994, 25, 271–276. [Google Scholar] [CrossRef]
- Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E.; et al. Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 2009, 324, 1312–1314. [Google Scholar] [CrossRef] [Green Version]
- Hutchings, G.J.; Brust, M.; Schmidbaur, H. Gold-an introductory perspective. Chem. Soc. Rev. 2008, 37, 1759–1765. [Google Scholar] [CrossRef]
- Ye, S.; Brown, A.P.; Stammers, A.C.; Thomson, N.H.; Wen, J.; Roach, L.; Bushby, R.J.; Coletta, P.L.; Critchley, K.; Connell, S.D. Sub-nanometer thick gold nanosheets as highly efficient catalysts. Adv. Sci. 2019, 1900911. [Google Scholar] [CrossRef] [Green Version]
- Valden, M.; Lai, X.; Goodman, D.W. Onset of catalytic activity of gold clusters on titania with the appearance of nonmetallic properties. Science 1998, 281, 1647–1650. [Google Scholar] [CrossRef] [Green Version]
- Haruta, M. Size- and support-dependency in the catalysis of gold Catal. Today 1997, 36, 153–166. [Google Scholar] [CrossRef]
- Ferrando, R.; Jellinek, J.; Johnson, R.L. Application of Copper–Gold Alloys in Catalysis: Current Status and Future Perspectives. Chem. Rev. 2008, 108, 846–890. [Google Scholar]
- Iwai, H.; Umeki, T.; Yokomatsu, M.; Egawa, C. Methanol partial oxidation on Cu–Zn thin films grown on Ni(1 0 0) surface. Surf. Sci. 2008, 602, 2541–2546. [Google Scholar] [CrossRef]
- Pérez-Hernandeza, R.; Mondragon Galiciaa, G.; Mendoza Anayaa, D.; Palaciosa, J.; Angeles-Chavezb, C.; Arenas-Alatorrec, J. Synthesis and characterization of bimetallic Cu-Ni/ZrO2 nanocatalysts: H2 production by oxidative steam reforming of methanol. Int. J. Hydrog. Energy 2008, 33, 4569–4576. [Google Scholar] [CrossRef]
- Bond, G.C.; Louis, C.; Thompson, D.T. Catalysis by Gold; World Scientific: Singapore, 2006. [Google Scholar]
- Corma, A.; Garcia, H. Supported gold nanoparticles as catalysts for organic reactions. Chem. Soc. Rev. 2008, 37, 2096–2126. [Google Scholar] [CrossRef] [PubMed]
- Nemoshkalenko, V.V.; Chuistov, K.V.; Aleshin, V.G.; Senkevich, A.I. Changes in energy structure of Cu3Au and CuAu3 alloys studied by the method of X-ray photoelectron spectroscopy. J. Electron Spectrosc. Relat. Phenom. 1976, 9, 169–173. [Google Scholar] [CrossRef]
- Daw, M.S.; Baskes, M.I. Model of metallic cohesion: The embedded-atom method. Phys. Rev. B 1989, 39, 7441. [Google Scholar] [CrossRef] [PubMed]
- Finnis, M.W.; Sinclair, J.E. A simple empirical N-body potential for transition metals. Phil. Mag. A 1984, 50, 45–55. [Google Scholar] [CrossRef]
- Murray, S.-D.; Stephen, M.-F.; Michael, I.-B. The embedded-atom method: A review of theory and applications. Mater. Sci. Rep. 1993, 9, 251–310. [Google Scholar]
- Ercolessi, F.; Parrinello, M.; Tosatti, E. Melting and equilibrium shape of icosahedral gold nanoparticles. Phil. Mag. A 1988, 58, 213. [Google Scholar] [CrossRef]
- Alavi, S. Molecular Simulations: Fundamentals and Practice; Wiley-VCH Verlag GmbH: Weinheim, Germany, 2020. [Google Scholar]
- Rapaport, D.C. The Art of Molecular Dynamics Simulation; Cambridge University Press: Cambridge, UK, 1995. [Google Scholar]
- Frenkel, D.; Smit, B. Understanding Molecular Simulation; Academic: San Diego, CA, USA, 1996. [Google Scholar]
- Dung, N.-T.; Cuong, N.-C.; Hung, T.-V. Molecular dynamics study of microscopic structures, phase transitions and dynamic crystallization in Ni nanoparticles. RSC Adv. 2017, 7, 25406–25413. [Google Scholar]
- Li, Q.; Peng, X.; Peng, T.; Tang, Q.; Zhang, X.; Huang, C. Molecular dynamics simulation of Cu/Au thin films under temperature gradient. Appl. Surf. Sci. 2015, 357, 1823–1829. [Google Scholar] [CrossRef]
- Potter, A.A.; Hoyt, J.J. A molecular dynamics simulation study of the crystal–melt interfacial free energy and its anisotropy in the Cu–Ag–Au ternary system. J. Cryst. Growth 2011, 327, 227–232. [Google Scholar] [CrossRef]
- Chepkasov, I.V.; Gafner, Y.Y.; Vysotin, M.A.; Redel, L.V. A study of melting of various types of Pt–Pd nanoparticles. Phys. Solid State 2017, 59, 2076–2081. [Google Scholar] [CrossRef]
- Baidyshev, V.S.; Gafner, Y.Y.; Gafner, S.L.; Redel, L.V. Thermal stability of Pt nanoclusters interacting to carbon sublattice. Phys. Solid State 2017, 59, 2512–2518. [Google Scholar] [CrossRef]
- Artrith, N.; Kolpak, A.M. Grand canonical molecular dynamics simulations of Cu–Au nanoalloys in thermal equilibrium using reactive ANN potentials. Comput. Mater. Sci. 2015, 110, 20–28. [Google Scholar] [CrossRef]
- The Materials Project. Materials Data on CuAu by Materials Project; U.S. Department of Energy Office of Scientific and Technical Information: Berkeley, CA, USA, 2020. [CrossRef]
- Georg, Z.; Michele, R.; Clemens, M.; Daniel, S.; Cesare, F.; Jani, K. CuAu, a hexagonal two-dimensional metal, 2D. Mater 2020, 7, 045017. [Google Scholar]
- Çagın, T.; Dereli, G.; Uludogan, M.; Tomak, M. Thermal and mechanical properties of some fcc transition metals. Phys. Rev. B 1999, 59, 3468–3473. [Google Scholar] [CrossRef] [Green Version]
- Jacek, D. Quantum classical calculations of the nanomechanical properties of metals. Task Q. 2009, 13, 207–310. [Google Scholar]
- Ozdemir Kart, S.; Tomak, M.; Uludogan, M.; Cagın, T.J. Liquid properties of Pd–Ni alloys. Non-Cryst. Solids 2004, 337, 101–108. [Google Scholar] [CrossRef]
- Kart, S.O.; Tomak, M.; Cagın, T. Phonon dispersions and elastic constants of disordered Pd–Ni alloys. Phys. B 2005, 355382–355391. [Google Scholar] [CrossRef]
- Kart, H.H.; Uludogan, M.; Cagın, T.; Tomak, M.J. Simulation of crystallization and glass formation of binary Pd–Ag metal alloys. Non-Cryst. Solids 2004, 342, 6–11. [Google Scholar] [CrossRef]
- Kart, H.-H.; Tomak, M.; Çağin, T. Molecular Dynamics Study of Thermal Properties of Intermetallic Alloys. Turk. J. Phys. 2006, 30, 311–317. [Google Scholar]
- Kart, H.H.; Tomak, M.; Uludogan, M.; Cagın, T. Thermodynamical and mechanical properties of Pd–Ag alloys. Comput. Mater. Sci. 2004, 32, 107–117. [Google Scholar] [CrossRef]
- Hashmi, A.S.K.; Hutchings, G.J. Gold-Katalyse. Angew. Chem. 2006, 118, 8064–8105. [Google Scholar] [CrossRef]
- Liu, X.; Wang, A.; Li, L.; Zhang, T.; Mou, C.Y.; Lee, J.F. Structural changes of Au–Cu bimetallic catalysts in CO oxidation: In situ XRD, EPR, XANES, and FT-IR characterizations. J. Catal. 2011, 278, 288–296. [Google Scholar] [CrossRef]
- Bazulev, A.N.; Samsonov, A.N.; Sdobnyakov, N.Y. Thermodynamic perturbation theory calculations of interphase tension in small objects. Russ. J. Phys. Chem. A 2002, 76, 1872–1876. [Google Scholar]
- Chen, S.; Jenkins, S.V.; Tao, J.; Zhu, Y.; Chen, J. Anisotropic Seeded Growth of Cu–M (M = Au, Pt, or Pd) Bimetallic Nanorods with Tunable Optical and Catalytic Properties. J. Phys. Chem. C 2013, 117, 8924–8932. [Google Scholar] [CrossRef]
- Williams, P.L.; Mishin, Y.; Hamilton, J.C. An embedded-atom potential for the Cu–Ag system. Model. Simul. Mater. Sci. Eng. 2006, 14, 817–833. [Google Scholar] [CrossRef]
- Whang, S.-H.; Pope, D.-P.; Liu, C.-T. High Temperature Aluminides and Intermetallics. In Proceedings of the Second International ASM Conference, San Diego, CA, USA, 16–19 September 1991; Volume 7. [Google Scholar]
- Arunachalam, V.S.; Cahn, R.W. Order-hardening in CuAu. J. Matter. Sci. 1967, 2, 160–170. [Google Scholar] [CrossRef]
- Volkov, A.Y. Structure and Mechanical Properties of CuAu and CuAuPd Ordered Alloys. Gold Bull. 2004, 37, 208–215. [Google Scholar] [CrossRef] [Green Version]
- Hidalgo-Alvarez, R. Structure and Functional Properties of Colloidal Systems; CRC Press: Boca Raton, FL, USA, 2009; pp. 180–184. [Google Scholar]
- Riccardo, F. Structure and Properties of Nanoalloys; Elsevier: Amsterdam, The Netherlands, 2016. [Google Scholar]
- Mikhail, S.; Alexander, Y.; Nikita, S. Structural transformation in nanowires CuAu I with superstructure of L10 of tetragonal symmetry at uni-axial tension deformation. Eng. Mater. 2014, 592–593, 51–54. [Google Scholar]
- Tsaregorodtsev, A.I.; Gorlov, N.V.; Dem’yanov, B.F.; Starostenkov, M.D. Atomic structure of antiphase boundaries and its impact on the lattice near the dislocations in ordered alloys with superstructure L12. Phys. Met. Metallogr. 1984, 58, 336–343. [Google Scholar]
- Dmitriev, S.V.; Kozlov, E.V.; Lomskih, N.V.; Starostenkov, M.D. The kinetics of disorder in the two-dimensional model of the alloy. Russ. Phys. J. 1997, 40, 285–286. [Google Scholar] [CrossRef]
- Papageorgiou, D.G.; Lagaris, I.E.; Papanicolaou, N.I.; Petsos, G.; Polatoglou, H.M. Merlin a versatile optimization environment applied to the design of metallic alloys and intermetallic compounds. Comput. Mater. Sci. 2003, 28, 125–133. [Google Scholar] [CrossRef]
- Wang, L.; Zhang, Y.; Yang, H.; Chen, Y. Structural simulation of super-cooled liquid Au–Cu, Au–Ag alloys. Phys. Lett. A 2003, 317, 489–494. [Google Scholar] [CrossRef]
- Han, X.J.; Chen, M.; Guo, Z.Y.J. Thermophysical properties of undercooled liquid Au–Cu alloys from molecular dynamics simulations. Phys. Condens. Matter. 2004, 16, 705–713. [Google Scholar] [CrossRef] [Green Version]
- Barrera, G.D.; de Tendler, R.H.; Isoardi, E.P. Structure and energetics of Cu-Au alloys. Model. Simul. Mater. Sci. Eng. 2000, 8, 1–37. [Google Scholar] [CrossRef]
- Metadjer, N.; Laref, A.; Khelifa, B.; Mathieu, C.; Bresson, S.; Aourag, H. Tight-binding calculation of structural properties of bulk Cu3Au and its corresponding clusters. Superlatt. Microstruct. 2001, 30, 21–28. [Google Scholar] [CrossRef]
- Pfeiler; Sprusil, B. Atomic ordering in alloys: Stable states and kinetics. Mater. Sci. Eng. A 2002, 324, 34–42. [Google Scholar] [CrossRef]
- Johansson, H.; Linde, J.O. Röntgenographische und elektrische Untersuchungen des CuAu-Systems. Ann. Phys. 1936, 25, 1–48. [Google Scholar] [CrossRef]
- Kuczynsk, C.; Hochman, R.F.; Doyama, M.J. Study of the Kinetics of Ordering in the Alloy AuCu. Appl. Phys. 1955, 26, 871–878. [Google Scholar] [CrossRef]
- He, R.; Wang, Y.C.C.; Wang, X.X.; Wang, Z.; Liu, G.; Zhou, W.; Wen, L.; Li, Q.; Wang, X.; Chen, X.; et al. Facile synthesis of pentacle gold–copper alloy nanocrystals and their plasmonic and catalytic properties. Nat. Commun. 2014, 5, 4327. [Google Scholar] [CrossRef] [Green Version]
- Bracey, C.L.; Ellis, P.R.; Hutchings, G.J. Application of copper-gold alloys in catalysis: Current status and future perspectives. Chem. Soc. Rev. 2009, 38, 2231–2243. [Google Scholar] [CrossRef] [PubMed]
- De Abajo, F.J.G.; Manjavacas, A. Plasmonics in atomically thin materials. Faraday Discuss 2015, 178, 87–107. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Tuan, T.Q.; Dung, N.T. Molecular dynamics factors affecting on the structure, phase transition of Al bulk. Phys. B Condens. Matter 2019, 570, 116–121. [Google Scholar]
- Dung, N.T.; Van, C.L. Effects of Number of Atoms, Shell Thickness, and Temperature on the Structure of Fe Nanoparticles Amorphous by Molecular Dynamics Method. Adv. Civ. Eng. 2021, 2021, 9976633. [Google Scholar]
- Dung, N.T.; Phuong, N.T. Factors affecting the structure, phase transition and crystallization process of AlNi nanoparticles. J. Alloy. Compd. 2020, 812, 152133. [Google Scholar]
- Tuan, T.Q.; Dung, N.T. Effect of heating rate, impurity concentration of Cu, atomic number, temperatures, time annealing temperature on the structure, crystallization temperature and crystallization process of Ni1-xCux bulk; x = 0.1, 0.3, 0.5, 0.7. Int. J. Mod. Phys. B 2018, 32, 1830009. [Google Scholar] [CrossRef]
- Dung, N.T. Influence of impurity concentration, atomic number, temperature and tempering time on microstructure and phase transformation of Ni1−xFex (x = 0.1, 0.3, 0.5) nanoparticles. Mod. Phys. Lett. B 2018, 32, 1850204. [Google Scholar] [CrossRef]
- Long, V.C.; Van, D.Q.; Dung, N.T. Ab Initio Calculations on the Structural and Electronic Properties of AgAu Alloys. ACS Omega 2020, 5, 31391–31397. [Google Scholar] [CrossRef]
- Dung, N.T.; Phuong, N.T. Molecular dynamic study on factors influencing the structure, phase transition and crystallization process of NiCu6912 nanoparticle. Mater. Chem. Phys. 2020, 250, 123075. [Google Scholar]
- Dung, N.T.; Cuong, N.C.; Van, D.Q. Study on the Effect of Doping on Lattice Constant and Electronic Structure of Bulk AuCu by the Density Functional Theory. J. Multiscale Model. 2020, 11, 2030001. [Google Scholar]
- Dung, N.T.; Van, C.L.; Țălu, Ș. The Structure and Crystallizing Process of NiAu Alloy: A Molecular Dynamics Simulation Method. J. Compos. Sci. 2021, 5, 18. [Google Scholar]
- Trung, V.Q.; Duong, T.T.; Tran; Chinh, N.T.; Vuong, N.T.; Hien, N.; Vinh, P.V.; Dung, N.T.; Duc, N.D.; Phuong, N.T. DFT Prediction of Factors Affecting the Structural Characteristics, the Transition Temperature and the Electronic Density of Some New Conjugated Polymers. Polymers 2020, 12, 1207. [Google Scholar]
- Chiang, I.C.; Chen, D.H. Synthesis of monodisperse FeAu nanoparticles with tunable magnetic and optical properties. Adv. Funct. Mater. 2007, 17, 1311–1316. [Google Scholar] [CrossRef]
- dos Santos, V.; Kuhnen, C.A. Electronic structure and magnetic properties of Ni/Au and Ni/Cu bilayers. Thin Solid Film. 1999, 350, 258–263. [Google Scholar] [CrossRef]
- Togasaki, N.; Okinaka, Y.; Homma, T.; Osaka, T. Preparation and characterization of electroplated amorphous gold–nickel alloy film for electrical contact applications. Electrochim. Acta 2005, 51, 882–887. [Google Scholar] [CrossRef]
- Molenbroek, A.M.; Nørskov, J.K.; Clausen, B.S. Structure and reactivity of Ni−Au nanoparticle catalysts, J. Phys. Chem. B 2001, 105, 5450–5458. [Google Scholar] [CrossRef]
- Antoniak, C.; Gruner, M.E.; Spasova, M.; Trunova, A.V.; Roemer, F.M.; Warland, A.; Krumme, B.; Fauth, K.; Sun, S.; Entel, P.; et al. A guideline for atomistic design and understanding of ultrahard nanomagnets. Nat. Commun 2011, 2, 528. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Sun, S.H.; Murray, C.B.; Weller, D.; Folks, L.; Moser, A. Monodisperse FePt nanoparticles and ferromagnetic FePt nanocrystal superlattices. Science 2000, 287, 1989–1992. [Google Scholar] [CrossRef]
- Gao, Y.; Shao, N.; Pei, Y.; Zeng, X.C. Icosahedral crown gold nanocluster Au43Cu12 with high catalytic activity. Nano Lett. 2010, 10, 1055–1062. [Google Scholar] [CrossRef]
- Sun, Q.; Ren, Z.; Wang, R.; Wang, N.; Cao, X. Platinum catalyzed growth of NiPt hollow spheres with an ultrathin shell. J. Mater. Chem. 2011, 21, 1925–1930. [Google Scholar] [CrossRef]
- Wang, R.M.; Zhang, H.Z.; Farle, M.; Kisielowski, C. Structural stability of icosahedral FePt nanoparticles. Nanoscale 2009, 1, 276–279. [Google Scholar] [CrossRef]
- Wang, R.M.; Dmitrieva, O.; Farle, M.; Dumpich, G.; Acet, M.; Mejia-Rosales, S.; Perez-Tijerina, E.; Yacaman, M.J.; Kisielowski, C. FePt icosahedra with magnetic cores and catalytic shells, J. Phys. Chem. C 2009, 113, 4395–4400. [Google Scholar] [CrossRef]
- Green, I.X.; Tang, W.J.; Neurock, M.; Yates, J.T. Spectroscopic observation of dual catalytic sites during oxidation of CO on a Au/TiO2 catalyst. Science 2011, 333, 736–739. [Google Scholar] [CrossRef]
- Rafii-Tabar, H.; Sutton, A.P. Long-range Finnis-Sinclair potentials for f.c.c. metallic alloys. Philos. Mag. Lett. 1991, 63, 217–224. [Google Scholar] [CrossRef]
- Kimura, Y.; Qi, Y.; Cagın, T.; Goddard, W.A., III. The quantum Sutton-Chen many-body potential for properties of fcc metals. In CalTech ASCI Technical Report 003; California Institute of Technology: Pasadena, CA, USA, 1998. [Google Scholar]
- Doye, J.P.K.; Wales, D.J. Global minima for transition metal clusters described by Sutton-Chen potentials. New J. Chem. 1998, 22, 733–744. [Google Scholar] [CrossRef] [Green Version]
- Qi, Y.; Cagin, T.; Kimura, Y.; Goddard, W.A. Molecular-dynamics simulations of glass formation and crystallization in binary liquid metals: Cu-Ag and Cu-Ni. Phys. Rev. B 1999, 59, 3527. [Google Scholar] [CrossRef] [Green Version]
- Sutton, A.P. Long-range finnis-sinclair potentials. Philos Mag. Lett. 1990, 61, 139–146. [Google Scholar] [CrossRef]
- Januszko, A. Phonon spectra and temperature variation of bulk properties of Cu, Ag, Au and Pt using Sutton-Chen and modified Sutton-Chen potentials. J. Phys. Chem. Solids 2015, 82, 67–75. [Google Scholar] [CrossRef]
- Yue, Q.; Tahir, Ç.; Yoshitaka, K.; Goddard, W.A., III. Viscosities of Liquid Metal Alloys from Nonequilibrium Molecular Dynamics. J. Comput.-Aided Mater. Des. 2001, 8, 233–243. [Google Scholar]
- Kart, H.H.; Tomak, M.; Cagın, T. Thermal and mechanical properties of Cu–Au intermetallic alloys. Model. Simul. Mater. Sci. Eng. 2005, 13, 657–669. [Google Scholar] [CrossRef]
- Todd, B.D.; Lynden-Bell, R.M. Surface and bulk properties of metals modelled with Sutton-Chen potentials. Surf. Sci. 1993, 281, 191–206. [Google Scholar] [CrossRef]
- Verlet, L. Computer “experiments“ on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. B 1967, 159, 98–103. [Google Scholar] [CrossRef]
- Sankaranarayanan, S.K.R.S.; Bhethanabotla, V.R.; Joseph, B. Molecular dynamics simulation study of the melting of Pd-Pt nanoclusters. Phys. Rev. B 2005, 71, 195415. [Google Scholar] [CrossRef] [Green Version]
- Tsuzuki, H.; Branicio, P.S.; Rino, J.P. Structural characterization of deformed crystals by analysis of common atomic neighborhood. Comput. Phys. Commun. 2007, 177, 518–523. [Google Scholar] [CrossRef]
- Honeycutt, J.D.; Andersen, H.C. Molecular dynamics study of melting and freezing of small lennard-jones clusters. J. Phys. Chem. 1987, 91, 4950–4963. [Google Scholar] [CrossRef]
- Ali, R.; Kamran, B. Identification of crystal structures in atomistic simulation by predominant common neighborhood analysis. Comput. Mater. Sci. 2017, 126, 182–190. [Google Scholar]
- Ackland, G.-J.; Jones, A.-P. Applications of local crystal structure measures in experiment and simulation. Phys. Rev. B 2006, 73, 054104. [Google Scholar] [CrossRef]
- Hoover, W.G. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 1985, 31, 1695–1697. [Google Scholar] [CrossRef] [Green Version]
- Xu, Y.H.; Wang, J.P. Direct Gas-phase synthesis of heterostructured nanoparticles through phase separation and surface segregation. Adv. Mater. 2008, 20, 994–999. [Google Scholar] [CrossRef]
- Nose, S.A. Unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984, 81, 511–519. [Google Scholar] [CrossRef] [Green Version]
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Quoc, T.T.; Long, V.C.; Ţălu, Ş.; Nguyen Trong, D. Molecular Dynamics Study on the Crystallization Process of Cubic Cu–Au Alloy. Appl. Sci. 2022, 12, 946. https://doi.org/10.3390/app12030946
Quoc TT, Long VC, Ţălu Ş, Nguyen Trong D. Molecular Dynamics Study on the Crystallization Process of Cubic Cu–Au Alloy. Applied Sciences. 2022; 12(3):946. https://doi.org/10.3390/app12030946
Chicago/Turabian StyleQuoc, Tuan Tran, Van Cao Long, Ştefan Ţălu, and Dung Nguyen Trong. 2022. "Molecular Dynamics Study on the Crystallization Process of Cubic Cu–Au Alloy" Applied Sciences 12, no. 3: 946. https://doi.org/10.3390/app12030946
APA StyleQuoc, T. T., Long, V. C., Ţălu, Ş., & Nguyen Trong, D. (2022). Molecular Dynamics Study on the Crystallization Process of Cubic Cu–Au Alloy. Applied Sciences, 12(3), 946. https://doi.org/10.3390/app12030946