Crystallization of FCC and BCC Liquid Metals Studied by Molecular Dynamics Simulation
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metals Article Crystallization of FCC and BCC Liquid Metals Studied by Molecular Dynamics Simulation Dmitri V. Louzguine-Luzgin 1,2,* and Andrey I. Bazlov 3,4 1 WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan 2 Mathematics for Advanced Materials-OIL, National Institute of Advanced Industrial Science and Technology (AIST), Sendai 980-8577, Japan 3 Department of Physical Metallurgy of Non-Ferrous Metals, National University of Science and Technology “MISiS”, 119049 Moscow, Russia; [email protected] 4 Laboratory for Mechanics of Advanced Bulk Nanomaterials for Innovative Engineering Applications, St. Petersburg State University, 7/9 Universitetskaya nab., 199034 St. Petersburg, Russia * Correspondence: [email protected]; Tel.: +81-(22)217-5957; Fax: +81-(22)217-5957 Received: 6 October 2020; Accepted: 13 November 2020; Published: 18 November 2020 Abstract: The atomic structure variations on cooling, vitrification and crystallization processes in liquid metals face centered cubic (FCC) Cu are simulated in the present work in comparison with body centered cubic (BCC) Fe. The process is done on continuous cooling and isothermal annealing using a classical molecular-dynamics computer simulation procedure with an embedded-atom method potential at constant pressure. The structural changes are monitored with direct structure observation in the simulation cells containing from about 100 k to 1 M atoms. The crystallization process is analyzed under isothermal conditions by monitoring density and energy variation as a function of time. A common-neighbor cluster analysis is performed. The results of thermodynamic calculations on estimating the energy barrier for crystal nucleation and a critical nucleus size are compared with those obtained from simulation. The differences in crystallization of an FCC and a BCC metal are discussed. Keywords: atomic structure; vitrification; crystallization; molecular-dynamics computer simulation 1. Introduction Crystallization of metals and alloys from the melt (liquid state) takes place by nucleation and growth [1]. This process has occupied the minds of scientists for quite some time owing to still unresolved issues, especially related to high nucleation and growth rates of pure substances. Pure metals are known to exhibit a high crystal nucleation rate at a low enough temperature [1] and high growth rates in a wide temperature range [2]. Crystallization of different substances [3,4] including liquid metals [5] and alloys [6] has been studied by molecular-dynamics (MD) simulation with various potentials. Furthermore, MD simulation of glass transition of pure metals, such as Fe [7,8], Ni [9,10], Cu [11], Al [12] and other metals [13] has been performed. In a recent work possible heterogeneous nucleation of Fe was studied at 0.67Tm and 0.58Tm (Tm is the melting point which in pure metals is equal to the liquidus temperature Tl)[14]. However, one should mention that Tm of 2400 K given by the potential used is significantly overestimated compared to the experimental value. Recent embedded atom potentials provide a better correspondence to the experimental values. The crystallization behavior of other metals was also studied via MD simulation [15] and compared with the experimental data [16]. The energy barriers for crystallization of pure metals were also compared with those obtained from computer simulation [17]. In the present work the atomic structure variation, vitrification and crystallization processes in liquid metals (FCC Cu and BCC Fe) are simulated on continuous cooling and isothermal Metals 2020, 10, 1532; doi:10.3390/met10111532 www.mdpi.com/journal/metals Metals 2020, 10, x FOR PEER REVIEW 2 of 11 atomic structure variation, vitrification and crystallization processes in liquid metals (FCC Cu and MetalsBCC2020 Fe), 10 are, 1532 simulated on continuous cooling and isothermal annealing using a classical2 ofMD 11 computer simulation procedure with an embedded-atom method potential at constant pressure. annealing2. Computational using a classicalProcedure MD computer simulation procedure with an embedded-atom method potential at constant pressure. Molecular dynamics (MD) computer simulation using a software package for classical 2.molecular Computational dynamics Procedure (LAMMPS) [18] was used to model the crystallization process of Fe and Cu metals at periodic boundary conditions. The simulation was performed at 1 fs time step using the embeddedMolecular atom dynamics potentials (MD) for computer Cu [19] and simulation Fe [20] usingat nearly a software constant package temperature for classical and pressure. molecular In dynamicsorder to let (LAMMPS) crystallization [18] was occur, used the to cubic model cell the size crystallization was typically process chosen of to Fe be and about Cu metals10 nm. at A periodictypical crystalline boundary conditions.cell of the atoms The simulation containing was108,000 performed for FCC at and 1 fs 128,000 time step atoms using for the BCC embedded structure atomwas potentialsheated to forof 2500 Cu [ 19K ]to and melt Fe [and20] atthen nearly cooled constant down temperature to a certain andtemperature. pressure. InIn ordersome tocases, let crystallizationlarger sized cells occur, were the used cubic as cell indicated. size was typicallyMelting is chosen confirmed to be aboutby the 10 radial nm. Adistribution typical crystalline function celland of stabilization the atoms containing of the 108,000density forvariation FCC and with 128,000 time. atoms Cooling for BCC was structure performed was heatedto different to of 2500temperatures K to melt andat about then 5 cooled × 1013 downK/s. Temperature to a certain temperature.upon simulation In some was cases,maintained larger at sized ±6 K cells (Figure were 1) usedwhile as pressure indicated. was Melting kept around is confirmed zero. by the radial distribution function and stabilization of the density variation with time. Cooling was performed to different temperatures at about 5 1013 K/s. × Temperature upon simulation was maintained at 6 K (Figure1) while pressure was kept around zero. ± 300 250 200 150 Frequency 100 50 0 744 745 746 747 748 749 750 751 752 753 754 755 756 Temperature (K) Figure 1. Frequency distribution of temperature for Cu held at 750 K fitted with the Gaussian function 2 withFigure R >1.0.99. Frequency The results distribution were similar of temperature for all other cases.for Cu held at 750 K fitted with the Gaussian function with R2 > 0.99. The results were similar for all other cases. Neither Fe nor Cu evaporated in the molten state as should have happened at zero pressure, likelyNeither because Fe there nor was Cu notevaporated enough timein the for molten a gaseous state phase as should to nucleate have happened from inside at the zero atomic pressure, cell (alikely gaseous because phase there has was to overcome not enough an time energy for barriera gaseou tos bephase formed to nucleate as well from as a crystallineinside the atomic one) and cell absence(a gaseous of the phase surfaces has to owing overcome to periodic an energy boundary barrier conditions. to be formed A thermostatas well as a was crystalline used to one) control and theabsence temperature of the surfaces [21,22] whileowing pressureto periodic was bounda maintainedry conditions. by a Barostat A thermostat [23]. A was software used to package control “OVITO”the temperature [24] was used[21,22] to visualizewhile pressure and analyze was mainta the simulationined by results.a Barostat Adaptive [23]. A Common software Neighbor package Analysis“OVITO” (CNA) [24] [was25] was used used to tovisualize analyze structuraland analyze changes the insimulation Fe and Cu. results. Adaptive Common 3.Neighbor Results andAnalysis Discussion (CNA) [25] was used to analyze structural changes in Fe and Cu. 3. ResultsThe density and Discussion changes on heating and cooling as a function of temperature are illustrated in Figure2a. Equilibrium liquid state was obtained at 2500 K in less than 1 ps. The holding time was also varied The density changes on heating and cooling as a function of temperature are illustrated in from 1 to 100 ps without visible changes in the liquid structure and density. Thus, the atomic cells have Figure 2a. Equilibrium liquid state was obtained at 2500 K in less than 1 ps. The holding time was been kept for at least 10 ps at 2500 K prior to cooling. also varied from 1 to 100 ps without visible changes in the liquid structure and density. Thus, the atomic cells have been kept for at least 10 ps at 2500 K prior to cooling. Metals 2020, 10, 1532 3 of 11 Metals 2020, 10, x FOR PEER REVIEW 3 of 11 9.0 8.5 Heating ) 3 Cooling 8.0 Heating Cu 7.5 Cooling Density (g/cm Density Fe 7.0 f Tg Cu Tl Fe Tl 6.5 300 600 900 1200 1500 1800 2100 2400 2700 Temperature (K) (a) 4 3 2 PDF(R) 300 K 1 2500 K 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 R (nm) (b) 0.3 1.2 Cu 0.2 0.8 max min /PDF min PDF PDF 0.1 0.4 Fe 0.0 0 400 800 1200 1600 2000 Temperature (K) (c) Figure 2. 2. DensityDensity changes changes on on heating heating and and cooling cooling of Cu of Cuand andFe as Fe a asfunction a function temperature temperature (a). Pair (a). distributionPair distribution functions functions (PDFs) (PDFs) of Fe ofin Feliquid in liquid (2500 (2500 K) and K) glassy and glassy (300 (300K) state K) state(b). The (b). values The values of pair of • distributionpair distribution function function first first minimum minimum PDF PDFmin ( ) (and) and ratios ratios of of PDF PDFmin/PDF/PDFmaxmax (()N ()(c) cfor) for Cu Cu (violet) (violet) min • min and Fe (blue). Vitrification of both Fe and Cu liquids was attained at the cooling rate of about 5 × 1013 K/s (Figure 2). At the cooling rate of 5 × 1012 K/s and lower the studied metals start to crystallize directly Metals 2020, 10, 1532 4 of 11 Vitrification of both Fe and Cu liquids was attained at the cooling rate of about 5 1013 K/s × (Figure2).