Chemical Physics Letters 502 (2011) 207–210

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Chemical Physics Letters

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Molecular dynamics investigation of structural evolution of fcc Fenanoparticles under heating process

Liang Wu a, Yang Zhang a, Yu-Hua Wen a,⇑, Zi-Zhong Zhu a, Shi-Gang Sun b,⇑a Department of Physics, and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Chinab State Key Laboratory of Physical Chemistry of Solid Surfaces, Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 25 October 2010In final form 16 December 2010Available online 21 December 2010

0009-2614/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.cplett.2010.12.051

⇑ Corresponding authors. Fax: +86 592 218 9426.E-mail addresses: yhwen@xmu.edu.cn (Y.-H. We

Sun).

The energetic and structural evolutions of fcc Fe nanoparticles under heating process have been investi-gated by molecular dynamics simulations, and the phase transition between fcc and bcc phases isaddressed. It is found that the solid–solid transition from fcc to bcc phase happens prior to the melting,accompanied with the particle shape from initial sphere into ellipsoid. The critical temperatures of phasetransition and melting are inversely proportional to the particle diameters. It is demonstrated that highpercentage of surface atoms may be beneficial to the phase transition of fcc Fe nanoparticles.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Over the past decade, materials based on nanometer-sizedstructures have attracted a great deal of interest because of theirpotential applications in electronic, optoelectronic, and electrome-chanical systems [1]. As one of the most important metallic nano-structures, Fe nanoparticles have exhibited a wide range ofapplications such as magnetic recording media [2,3], biomedicalapplications [4], and catalysts [5,6].

It is well known that bulk Fe belongs to the bcc structure underambient temperature and pressure, and transforms into the fccstructure at temperatures above 1185 K. Experimentally, bcc Fenanoparticles have been prepared successfully by means of ther-mal decomposition or electrochemical route [7,8]. Although fccbulk Fe is thermodynamically unstable at ambient conditions,there are many attempts made in the past to stabilize the fcc struc-ture of Fe specimens at room temperature. An effective approach isto decrease the size of Fe materials [9–11]. For example, Fe singlecrystals with nanometer size and fcc structure remained structur-ally stable and exhibited ferromagnetic at room temperature [9].Fcc Fe nanoparticles with novel twinned structures have also beensynthesised recently [10,11], and the size-dependent shapes of Fenanoparticles have been discovered [11,12].

Theoretically, Fe nanoparticles have been investigated exten-sively. Their melting and nucleation processes [13–15] have at-tracted considerable attention. Bcc Fe nanoparticle washomogeneous melted from the surface at a melting point duringheating, whereas a nucleus was generated near one side of a liquiddroplet and solidification spread toward another side during cool-

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n), sgsun@xmu.edu.cn (S.-G.

ing [13]. The melting and nucleation temperatures were decreasedwith reduced particle size and were lower than their bulk counter-part [13–15]. It is found that fcc Fe particles without defects do nottransform to bcc but retain their metastability [16]. However, themajority of available theoretical studies have addressed on bcc Fenanoparticles. Less is known about the thermal stability of fcc Fenanoparticles although they have been prepared experimentally.

In this Letter, we will employ molecular dynamics simulationsto investigate the energetic and structural evolution of Fe nanopar-ticles with fcc structure under heating, and address size-dependentthermal stability. A brief description of the simulation methods isgiven in the following section. The calculated results, discussion,and comparisons with other results are presented in the Section 3.The main conclusions are summarized in the Section 4.

2. Details of simulation methodology

At present, there are several available empirical potentials todescribe the interatomic actions in iron. Among these interatomicpotentials, the Finnis–Sinclair (F–S) potential [17], which are basedon the second-moment approximation of the tight-bonding formu-lation, can capture qualitatively the nature of the phase transitionfrom the fcc phase to the bcc phase mainly due to two reasons: (i)an energetic transition based on the F–S potential along the Bainpath is reasonable; and (ii) the cohesive energy per atom in thebcc phase is lower than that in the fcc phase, and independent ofthe temperature [18]. It has been confirmed to reproduce the basicstructural and dynamics properties of iron very well [19,20]. More-over, the F–S potential describes the thermal properties of bcc met-als very well by comparison with other EAM or MEAM potentials[20]. Based on the above consideration, the F–S potential has beenadopted to describe the interatomic actions of Fe nanoparticles inour simulations.

208 L. Wu et al. / Chemical Physics Letters 502 (2011) 207–210

A series of spherical Fe nanoparticles are constructed from largefcc single crystals of iron. The diameters of these nanoparticlesvary from 2.96 to 7.39 nm. To make our simulations more reliable,we employ constant temperature molecular dynamics (NVT-MD)to allow energy fluctuations of the systems. The equations of atom-ic motion are integrated by the Verlet-Velocity algorithm [21] witha time step of 2.5 fs. Each nanoparticle is heated from 300 to2200 K with the temperature increment of 50 K to ensure com-pletely melting, and equilibrated for 200 ps at each temperature.Subsequently, each nanoparticle is cooled from 2200 to 300 K byusing the same rate. The desired temperature is maintained by aNose–Hoover thermostat [22].

3. Results and discussion

Generally, the discrepancy of melting point lies between exper-imental and theoretical studies. For bcc bulk Fe, the melting pointof 2400 ± 10 K [14] calculated by the F–S potential, is about fourthirds of the experimental value of 1811 K. Considered that super-heating to temperature beyond the equilibrium melting point hasbeen confirmed in surface-free perfect crystals [23], the differencebetween experimental and theoretical results is not remarkable.Furthermore, this difference does not affect the investigation ofthe thermodynamics behavior of Fe nanoparticles.

Figure 1 illustrates the temperature dependence of the potentialenergy of fcc Fe nanoparticle under the heating process. It can beseen from potential energy that there is an obvious decrease from850 to 900 K and a sharp increase at temperature of 1800 K or so.Due to the fact that the temperature of solid to liquid phase tran-sition can be identified by the variation in the potential energy[24], the overall melting point of fcc Fe nanoparticle has been de-duced to be about 1900 K. In comparison with the calculated valueof bcc bulk Fe, the melting points of fcc Fe nanoparticles are signif-icantly reduced by about 500 K. Further analysis on the meltingmechanism of Fe nanoparticles show that the premelting is origi-nated from the surface and results in their overall melting at themelting point, which is consistent with Ni, Au, Ag, and Pt nanopar-ticles [25–29]. It should be noted that a significant difference existsbetween Fe and other metallic nanoparticles under heating. Forother metallic nanoparticles, the potential energy monotonicallyincreases with rising temperature, whereas for fcc Fe nanoparticle,the potential energy suddenly decreases when the temperaturerises to a critical point before melting, as shown in Figure 1. This

Figure 1. Temperature dependence of potential energies of fcc Fe nanoparticle with2491 atoms during heating and cooling processes. For comparison, the result of bccFe nanoparticle with 2565 atoms under heating is also presented.

indicates that fcc Fe nanoparticle exhibits a dynamics evolutiondifferent from other metallic nanoparticles under heating.

To explore further the dynamics evolution of fcc Fe nanoparti-cle, we employ the common neighbor analysis (CNA) [30] to char-acterize the local crystal structure. In this analysis, the bondsbetween an atom and its nearest neighbors are examined to deter-mine the crystal structure. The different types of pairs are associ-ated with different type of local order. All bonded pairs in the fcccrystal are of type 1421, whereas the hcp crystal has equal num-bers of type 1421 and 1422. Both type 1441 and 1661 are the mainbonded pairs in the bcc crystal. Considering that iron has three dif-ferent crystal structures, namely bcc, fcc, and hcp ones, here wehave classified atoms into four categories by the CNA method.Atoms in a local fcc order are considered to be fcc atoms; atomsin a local bcc order are considered to be bcc atoms; atoms in a localhcp order are classified as hcp atoms whose occurrence in fcc crys-tal is regarded as the structure of stacking faults; atoms in all otherlocal orders are considered to be unidentified atoms.

Figure 2 shows the snapshots of cross section of fcc Fe nanopar-ticle at different temperatures during heating. Temperature depen-dence of the percentages of four categories of atoms for thenanoparticle has also been illustrated in this figure. There are aconsiderable proportion of unidentified atoms (about 33% of allatoms) at low temperature (300 K) due to the presence of a largenumber of surface atoms. However, the interior of the nanoparticleretains original fcc structure (see Figure 2a), which is also identi-fied by the about 67% proportion of fcc atoms. With the increasedtemperature, part of fcc atoms transform into unidentified ones. Nobcc and hcp atoms are found in the nanoparticle below 850 K.

Remarkable changes of the structure and percentage of atomsoccur in the Fe nanoparticle under further heating. From 850 to900 K, the proportion of bcc atoms is increased sharply from 0%to 30.7% or so, and the proportion of fcc atoms is reduced from42.3% to nearly zero simultaneously. It is seen from Figure 2c thatfcc structures have disappeared completely and some bcc atomsoccur, indicating that the solid–solid phase transition happens inthe nanoparticle. Moreover, it is observed that there is an expan-sion in the Y- and Z-directions and a simultaneous contraction inthe X-direction. As a consequence, the shape of nanoparticlechanges accordingly from initial sphere into ellipsoid. Such

Figure 2. (a–e) Snapshots of cross section of fcc Fe nanoparticles consisting of 2491atoms at five different temperatures during heating. Coloring denotes localstructure: red, fcc; blue, bcc; and cyan, unidentified. (f) Percentages of fourcategories of atoms of fcc Fe nanoparticle are shown as a function of temperatureduring heating. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

L. Wu et al. / Chemical Physics Letters 502 (2011) 207–210 209

solid–solid phase transition was also observed in fcc bulk Fe onlywhen the system could change its volume in at least two directions[20]. The shape change of Fe nanoparticle can be interpreted qual-itatively by the Bain path [31]. However, high energy barrier lies inthe direct transformation from fcc to bcc phase by the Bain path. Infact, the martensitic transformation is realized by a series of jumpsand rearrangements by a group of atomic displacements [32].

The proportion of bcc atoms becomes smaller and smaller withincreased temperature due to the thermal vibration of atoms. Themelting occurs preferentially at the surface during the heating pro-cess because surface atoms have fewer nearest neighbors andweaker bonding compared with other atoms, which has been ver-ified by lots of experimental studies and theoretical calculations[25–29,33]. After phase transition, no significant change has beenfound in the potential energy and percentages of four categoriesof atoms. The nanoparticle has retained its ellipsoidal shape untilmelting (see Figure 2d and e).

Figure 3 illustrates the melting point and martensitic transfor-mation temperature of the fcc Fe nanoparticles as a function of par-ticle diameter. Clearly, the melting point is inversely proportionalto the particle diameter (see Figure 3a). The lowering of meltingpoint with decreasing particle size can be predicated by theGibbs–Thomson equation based on the frame of classical thermo-dynamics [34]. In our study, the fcc Fe nanoparticle has trans-formed completely into bcc Fe nanoparticles prior to melting.Therefore, the Gibbs–Thomson effects can also be used to elucidatesuch size-dependent melting of fcc Fe nanoparticles. The meltingpoint of the bulk, obtained by extrapolating the particle diameterto infinity, is 2326 K, close to the simulated bcc bulk iron of 2400 K.

Besides, the temperature of martensitic transformation is gen-erally inversely proportional to the particle diameter (see Fig-ure 3b), indicating that the smaller the diameter, the larger thesurface-to-volume ratio, and hence the easier the phase transitionoccurs. This result is analogous to that of bcc Fe nanowires in thesolid–solid phase transition [35]. For bulk iron, however, it is noteasy to trigger solid–solid phase transition by heating or coolingvia molecular dynamics simulations [20]. The inclusion of high de-fect densities is necessary for fcc–bcc phase transitions. Further-

Figure 3. The temperatures of (a) melting and (b) phase transition as a function ofthe inverse of particle diameter.

more, such solid–solid phase transition does not happen in largenanoparticles without defects [16]. However, at small sizes, largesurface-to-volume ratio and high surface free energy could play akey role in the determination of the phase transition of Fe nanopar-ticles. High percentage of surface atoms may be beneficial to theprocess of solid–solid phase transition although there are no de-fects and vacancies in the interior of Fe nanoparticles.

It is worth noticing that no solid–solid phase transition occursin bcc Fe nanoparticles. Figure 1 also illustrates the temperaturedependent potential energy of bcc Fe nanoparticle under the heat-ing process. It is seen that the potential energy of bcc Fe nanopar-ticle, different from that of fcc Fe one, increases monotonicallyfrom 300 to 1800 K, followed by a sharp rise beyond 1850 K, indi-cating the overall melting of bcc Fe nanoparticle. The melting pointof bcc nanoparticle is approximately equal to that of fcc one. Wehave repeated the dynamics simulations of seven bcc Fe nanopar-ticles with total atomic numbers from 1067 to 15 389, and solid–solid phase transition is not found. Furthermore, we have alsoinvestigated the dynamics evolution of melted fcc Fe nanoparticleduring cooling from 2200 to 300 K. The temperature dependence ofpotential energy has also been illustrated in Figure 1. It can be seenthat the crystallization takes place and a bcc nanoparticle forms fi-nally at 1350 K or so. The potential energy of the bcc nanoparticleis partly overlapped with that of the unmelted bcc one and is lowerthan that of the fcc one. The transition from bcc to fcc phase hasnot been observed during cooling process. The aforementioned re-sults should be attributed to the F–S potential applied in the pres-ent work because in this potential the bcc phase has the smallestfree energy for all temperatures up to the melting temperature[19]. Therefore, the F–S potential does not feature the bcc-to-fccequilibrium phase transition which real iron shows. Even so, theF–S potential can be still believable in the description of thedynamics process of the fcc to bcc phase transition of bulk fcc Febecause it can capture the nature of this phase transition qualita-tively [18,20]. Naturally, it should be expected that this potentialcould reproduce the fcc to bcc phase transition of fcc Fe nanopar-ticles correctly. The phase transition of iron under heating or cool-ing is a rather complicated dynamics process because this processis involved with multi-phase transformation and competition,which requires our further studies.

4. Conclusions

In this Letter, we have employed molecular dynamics ap-proaches with the Finnis–Sinclair many-body potential to investi-gate the structural evolution of fcc Fe nanoparticles undercontinuous heating. The common neighbor analysis methods areused to explore the phase transition between fcc and bcc phases.The results show that in these nanoparticles, the martensitic trans-formation from fcc to bcc phase occurs prior to melting, accompa-nied simultaneously by the shape change from initial sphere toellipsoid. The critical temperatures of melting and phase transitionof the fcc Fe nanoparticles are proportional to the inverse of parti-cle diameter. Our results verify that high percentage of surfaceatoms may be responsible for the phase transition of fcc Fe nano-particles. These results could be instructive for future experimentalor theoretical studies in Fe nanoparticles.

Acknowledgement

This work was supported by the grants from NSFC (Grant Nos.20833005, and 10702056), the MOST (Grant No. 2007DFA40890)and Fujian Provincial Department of Science and Technology(Grant No. 2008I0025), China.

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