Development of Reactive Force Field for Fe-C

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Physical Chemistry Chemical Physics View Article Online

DOI: 10.1039/C7CP05958B

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Carburization of Iron Kuan Lu,1,2,3Chun-Fang Huo,*,2 Wen-Ping Guo,2 Xing-Wu Liu,1,2,3 Yuwei Zhou,1,2,3 Qing Peng,*,4 Yong Yang,1,2 Yong-Wang Li,1,2 and Xiao-Dong Wen*,1,2

1

State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of

Sciences, Taiyuan, Shanxi 030001, PR China;

2

National Energy Center for Coal to Clean Fuels, Synfuels China Co., Ltd., Huairou District,

Beijing 101400, P. R. China

3

University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, P. R.

China

4

Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI

48109 (USA)

Physical Chemistry Chemical Physics Accepted Manuscript

Development of Reactive Force Field for Fe-C interaction to Visit

Physical Chemistry Chemical Physics

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DOI: 10.1039/C7CP05958B


promising way to investigate the carburization of iron which is pivotal in preparation of desired iron-based materials and catalysts. However, it is challenge to develop a reliable ReaxFF to describe the Fe-C interaction, especially for involving bond rearrangement. In the work, we develop an exclusive set of Reactive Force Field (ReaxFF) parameters, denoted as RPOIC-2017, to describe the diffusion behavior of carbon atoms in the α-Fe system. It inherited some partial parameters in 2012 (ReaxFF-2012) which is suitable to the hydrogen adsorption and dissociation. This set of parameters is trained against data from first-principles calculations, including the equations of state of α-Fe, the crystal constant of Fe3C and Fe4C, variety of periodic surface structures with varying carbon coverages, as well as the barriers of carbon diffusion in the α-Fe bulk and on diverse surfaces. The success in predicting the carbon diffusion coefficient and the diffusion barrier using the developed RPOIC-2017 potential, demonstrates the superior than traditional MEAM potential. The new ReaxFF for Fe-C interaction developed in the work is not only essential for the design of novel iron based materials, but also could understand atomic arrangement and interfacial structure of iron carbides.


ABSTRACT: The approach of molecular dynamics with Reactive Force Field (ReaxFF) is

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Iron Carbides are not only important materials in our life, but also to be the intrinsic activity phases for many reactions, such as Fischer-Tropsch synthesis (FTS), iron and steel industry and carbon nanotube synthesis, etc. Among the applications on catalysts, iron carbides are commonly believed to be the active phases for FTS1-5 which offers a very promising pathway, to transform shale gas, coal and biomass into fuels, and thus to meet the challenge of global environment changes and energy demands. Another critical case6, 7 is about the iron and steel industry, in which the Fe-C interaction is of great importance for metal dusting8, 9. In addition, Fe-C interaction plays an important role in the growth of carbon nanotubes with iron as the catalyst10-12. For Fischer-Tropsch synthesis, it is commonly believed that the actual active phases are the iron carbides, i.e., χ-Fe5C2 and θ-Fe3C. Several experimental studies have already reported about the formation of carbides. Ding et al5 found that the phase transformation of iron phases involves a α-Fe2O3→Fe3O4→FeO→α-Fe process in the H2 atmosphere and the reduced iron species could be converted to different iron carbides under CO or syngas atmosphere13. Ziyu Yang et al14 implemented the modulation of phase transform by interfering with the penetration of C atoms with Cl ions. Nevertheless, to date, there are few studies regarding the intricacies of carburization of iron at the atomic level, the critical stage for iron-based catalysts. For iron and steel industry, the carburization of iron ore in the CO-CO2 atmosphere has been studied by S. Geng and co-workers15 through the gas based direct reduction method. Their results showed that before carbon diffusing into the iron bulk driven by the chemical potential gradient, the CO molecules were firstly adsorbed on to the


1. Introduction



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this carbon source, the CO2 molecules finally desorb from the iron surface. The deposited carbon can penetrate into the iron forming many carbides6, 7. As for nanomaterials, iron carbides as an ancient advanced material may also catalyze the growth of carbon nanofibers16. All these reports are from the offline experiments, in which no phase-change between observed phases and in situ phases has been assumed, and may have a large deviation from the online results. There are attempts2,

11, 17, 18

from the atomic-scale methods to explore the above

processes. Among them, the first-principles calculations are restricted to small molecules and time scales around picoseconds. Therefore, empirical force-field are in general used to evaluate the forces and other dynamic behavior, such as mechanical behavior and atoms diffusion, to close the gap between quantum mechanical calculations and experiments. The key is the interatomic potential should be able to regenerate correctly the fundamental physical and chemical properties. A embedded-atom method (MEAM) created by Baskes19 is a very important interatomic potential for the atomic simulation, it is only successful and reliable for alloy system20-22to reproduce the physical properties, including elastic properties, structural properties, surface properties, thermal properties, etc. However, this force field could not deal with the chemical reaction well. The ReaxFF (reactive force field) method raised by Adri C. T. van Duin and co-workers23 in 2001 is one approach to describe reaction and can well reproduce the physical properties24-26, because this method allows the bonds breaking and forming according to the


iron surface, followed by the occurrence of some reactions, producing the carbon atoms. With

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they developed the ReaxFF parameters for hydrocarbons. In 2010, Masoud Aryanpour et al27 trained the ReaxFF parameters for thermodynamics of iron oxide by an abundant training set consisting of the lattice parameter of some iron minerals and some iron redox actions. Following that, Chenyu Zou and Adri C. T. van Duin28 jointly developed the Fe/C/H system’s parameters for Fischer-Tropsch synthesis to describe the hydrogen adsorption and dissociation behavior on the surfaces of iron and iron carbides. In the same year, they29 published another paper about CO methanization that CO provides the carbon source in the F-T process. But the one point must be stressed here is that though Chenyu Zou and although Adri C. T. van Duin had considered the equations of state (EOS) of Fe3C and the surface energy of Fe5C2, they were not enough to describe the diffusion of carbon, because their study focused on the behavior of hydrogen atoms. Recently, Md Mahbubul Islam et al30 developed a set of parameters used to explore hydrogen embrittlement whose parent-parameters came from the parameters for FTS28 merged with the parameters for carbon condensed phase31. In this work, we firstly fit the parameters named the RPOIC-2017 for Fe-C interaction to substantial data from first-principles calculations on the diffusion of carbon in the carburization and deposition process of iron, then briefly describe the force field validation. Finally, we give a simulation about the carbon diffusion in the α-Fe related to carburization in various conditions by ReaxFF with a comparison with MEAM.

2. Computational methods 2.1 First-principles calculations


distance between atoms and is suitable for large systems (>> 10000 atoms). Concurrently,



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implemented in the Vienna Ab initio simulation package (VASP)32, 33. We employed the projector-augmented-wave (PAW) method proposed by Kresse and Joubert34 which is an all-electron DFT technique to present the electron-ionic interaction. The electron exchange correlation was treated by the well-known generalized gradient approximation in Perdew-Burke-Ernzerhof form (GGA-PBE)35 which can give a more accurate description of iron properties than ultrasoft pseudopotentials36. For the sake of exact description of the magnetic properties of iron, the calculation of Spin-polarization was carried out, which is also essential to the adsorption energy calculation. In order to ensure the energy errors are within the reasonable extent, an energy cutoff of 400 eV and the second order Methfessel-Paxton37 electron smearing with σ=0.1 eV were used. The equations of state of iron carbides were fitted to Murnaghan’s equations of state38. The nudged elastic band (NEB)39 was exploited to assess the energy profiles along the selected diffusion pathway.

2.2 ReaxFF method ReaxFF is an empirical force filed based on the concept of bond order23. ReaxFF is the function of bond length and bond energy and it allows bond breaking and forming in a dynamic simulation. The general form40 of ReaxFF energy is presented below:

E systerm = E bond + E lp + E over + E under + E val + E tors + E C2 + E triple + E conj + E H -bond + E vdw + E Coulomb

(1)

One of the most important features of ReaxFF is the use of electronegativity equilibration method (EEM)41 with shielding to calculate the charge distribution updating every iteration during the ReaxFF molecular dynamics (RMD) simulation that determines the


All first-principles data included in the trainset were done using the DFT method

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orders calculation also updates every iteration which firmly establishes the bonded interaction and the non-bonded interactions. The parameters (RPOIC-2017) were fitted to data from first-principles calculation using our own code related to genetic algorithm coupling the least squares method. The full set of ReaxFF potential functions are supplied in Supporting Information. RMD simulation was performed by the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)42 adopting a time step of 0.25 fs. The Berendsen thermostat43 was used to control the temperature with a damping constant 100 ps. Energy minimized via a conjugate gradient was conducted prior to each RMD simulation. The trajectories were dumped every 0.1 ps. The maximum simulation time is 500 ps.

2.3 Modified embedded atom method In 1992, the Modified Embedded Atom Method (MEAM) potential was firstly proposed by Baskes19to describe the interaction between atoms. MEAM is a pairwise interactions. The total energy of a system is given in the following form:

  E=∑  Fi (ρi )+ 12 ∑ φij (R ij )  i  j(≠i) 

(2)

Different from Embedded Atom Model (EAM), MEAM has angular terms, which make it suitable for modeling metal and alloys as well as covalently bonded materials. The detail of MEAM potential functions are supplied in Supporting Information. For MEAM molecule dynamics, we employed the potential developed by Laalitha22 in


geometry of material and further affects the total potential energy of materials. The bond



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RMD simulation except that the time step and the simulation time were changed to be 1 fs and 2 ns, respectively.

3. Parameterization of ReaxFF Extensive VASP calculations were performed to build a comprehensive trainset, including the crystal constant of α-Fe (body-centered cubic, BCC crystal with space group Im-3m with space group number of 229) unit cell and iron carbides (Fe3C and Fe4C), the surface energy of different iron surfaces, the energy barrier of carbon diffusion in bulk and on different surfaces and the adsorption energy of a varying carbon atoms on different iron surfaces. Then, the trainset was used to optimize the parameter for Fe-C interaction. The reparameterized parameters including general, two-body, off-diagonal and three-body parameters are summarized in Tables 1-3 along with ReaxFF-2012 for comparison.

Table 1. General parameters for Fe/C/H Parameters RPOIC-2017 36.0409 11.7404 22.3085

P(boc1) P(boc2) P(lp3)

ReaxFF-2012* 50.0000 9.5469 60.4850

*For ReaxFF-2012 and the definition of parameters, see references 28 and 23.

Table 2. Two body and off-diagonal parameters for Fe/C/H

Fe-C(two-body)

De(sigma)

Parameters RPOIC-2017 ReaxFF-2012* 78.6009 113.1509


2014 to conduct the MD by LAMMPS42. The other simulation parameters are same as the

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Fe-Fe(two-body)

Fe-C(off-diagonal)

P(be1) P(be2) P(bo1) P(bo2) De(sigma) P(be1) P(be2) P(bo1) P(bo2) Dij Rvdw alfa ro(sigma)

0.8712 1.1811 -0.1666 2.6110 42.6354 0.2124 0.5024 -0.0532 6.8414 0.5077 0.3058 6.2910 1.2466

0.6400 1.0000 -0.1450 4.1504 41.4611 0.2931 0.6294 -0.0512 6.8013 0.3999 1.4558 11.0036 1.3918

*For ReaxFF-2012 and the definition of parameters, see references 28 and 23.

Table 3. Three body parameters for Fe/C/H

C-C-Fe

C-Fe-C

C-Fe-Fe

Fe-C-Fe

Thetao P(val1) P(val2) P(val7) P(val4) Thetao P(val1) P(val2) P(val7) P(val4) Thetao P(val1) P(val2) P(val7) P(val4) Thetao P(val1) P(val2) P(val7)

parameters RPOIC-2017 ReaxFF-2012* 7.0310 29.2291 17..9932 39.0677 0.4327 1.2584 0.1623 0.0100 0.8694 1.6263 2.3514 7.0546 1.5811 39.3227 0.4500 1.0694 0.3458 0.7210 2.7984 3.1133 55.5054 47.3783 0.5990 1.0170 3.6398 7.8341 0.9539 2.8546 0.7441 1.0000 17.0269 33.2812 28.9696 34.6443 2.9302 3.0111 0,0856 0.1701


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P(val4)

1.1201

1.0510

3.1 Surface energy of different iron surfaces The surface energy depends on the crystallographic orientation and determines the stability of the crystal planes. In order to consider the atomic geometry effect, we fitted the EOS based on the VASP data from first-principles calculations to obtain the α-Fe crystal constant and used it to calculate the surface energy. From the E-V relation of α-Fe in Figure 1, we can learn that the ReaxFF can perfectly reproduce the equilibrium lattice constant of α-Fe in VASP data, a=2.85Å, which is in good agreement with the literature value 2.83Å44 and the experimental value 2.86Å45. Surface energies have been calculated using ReaxFF and compared with the literature for α-Fe including three low and four high index surfaces, namely (100), (110), (111) and (210), (211), (310), (321), respectively (Figure 2). The surface energy came from Esur = (Eslab – N*Ebulk )/2A0,where Eslab and Ebulk are the energy of the slab and the unit cell, respectively, N is the number of unit cell in slab and A0 is the surface area of slab. As can be seen from Figure1 that all different surface energies predicted by ReaxFF are consistent with the literature3. That is, The ReaxFF can accurately reproduce the VASP data of surface energies and the relative stability of typical surfaces.



*For ReaxFF-2012 and the definition of parameters, see reference 28 and 23.

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Figure 1. Equations of state (left) and surface energy (right) of different surfaces of α-Fe calculated by VASP and ReaxFF.



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sites. Character scheme: T (top), B (bridge), 4F (four-fold), S1A (subsurface first type O-site), S1B (subsurface second type O-site), SB (short bridge), LB (long bridge), 3F (three fold), sur (surface), sub (subsurface), S1 (the first subsurface), S2 (the second subsurface), DH (deep hollow), qff (quasi four fold) and SH (shallow hollow).

3.2 Crystal constant of Fe3C and Fe4C Owing to the Fe3C and Fe4C transformation from the α-Fe and face-centered cubic (FCC) γ-iron, respectively, we performed a series of structural optimization of Fe3C, Fe4C/Tet and Fe4C/Oct to fit the equilibrium lattice constant out of consideration for different crystal irons interaction with the carbon. The crystal constant calculated from ReaxFF and VASP is presented in the Table 4. For our current force field parameters, we obtained the crystal parameters of Fe3C, Fe4C/Tet, Fe4C/Oct is a=4.97 Å, a=3.64 Å and a=3.61 Å, respectively, which are comparable with 5.06 Å46, 3.84 Å47, 3.76 Å47-49 from VASP value and 5.09 Å50, 3.88 Å51, 3.77 Å48 from experimental value52.

Table 4. Crystal constant for Fe3C and Fe4C. Crystal Constant (Å) Carbides

VASP(Exp.)

RPOIC-2017

ReaxFF-2012

Fe3C

5.06(5.09)

4.97

5.02

Fe4C/Tet

3.84(3.88)

3.64

3.71

Fe4C/Oct

3.76(3.77)

3.61

3.79

3.3 Carbon diffusion in bulk


Figure 2. Top view and side view of different surfaces of α-Fe and corresponding surface

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and tetrahedral site (T-site). It is well known that the most likely hopping mechanism for interstitial diffusion of carbon is from one O-site to another O-site via T-site in the bulk α-Fe44. We calculated the formation energy of one carbon occupying the O-site and the T-site, respectively, and the diffusion barrier was obtained as the energy difference. As shown in Figure 3, the value calculated by RPOIC-2017 is 19.93 Kcal/mol, which is in excellent agreement with the literature value 19.83 Kcal/mol44 and is also agree well with the experimental value 20.06 Kcal/mol53. However, The ReaxFF-2012 gives a terrible result. This indicates that our new parameters set RPOIC-2017 is better in simulating the carbon diffusion in the α-Fe.

Figure 3. Diffusion energy of carbon in iron bulk. Iron atom (blue) and Carbon atom (black).

3.4 Carbon diffusion on surface To study the behavior of carbon atoms on iron surfaces and into subsurfaces, we calculated the energy barriers of one carbon atom diffusing from one stable surface site to another or to a subsurface site, as well as the energy of carbon diffusion between the different subsurface sites (O-site and T-site). All results for carbon diffusion are shown in Figure 4.


The bulk α-Fe has two types of typical interstitial sites, i.e., octahedral site (O-site)



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3.4.1 Carbon diffusion on Fe (100) For the Fe (100) surface, the C atoms are prior to occupy the 4-fold site17, 54. Here, three possible pathways for carbon diffusion are examined, i.e., from one 4-fold site (4F) to the nearest 4-fold site and from the 4-fold site to the O-site of first subsurface (S1A and S1B). From the energy profile in Figure 4, we can see that the RPOIC-2017 predicted the barriers for three C diffusion pathways are 39.87 Kcal/mol (4F → 4F), 31.23 Kcal/mol (4F → S1A) and 26.48 Kcal/mol (4F → S1B), respectively, which are in the same sequence as the data (46.30 Kcal/mol54 > 42.70 Kcal/mol54 > 31.22 Kcal/mol54) given by VASP.

3.4.2 Carbon diffusion on Fe (110) For the most stable surface Fe (110), three carbon diffusion pathways, from one long-bridge (LB) site to the nearest long-bridge, from LB to subsurface site (S1A) and diffusion between two S1A sites are considered. All results calculated by ReaxFF and VASP are displayed in Figure 4. The results show that the diffusion from LB to S1A (19.02 Kcal/mol) is relatively easier than from LB to LB (23.49 Kcal/mol) calculated by ReaxFF. Though compared with the VASP data, their energy order is reverse (25.36 Kcal/mol54 > 22.35 Kcal/mol54) for LB → S1A and LB → LB, respectively, their corresponding value are pretty close. And their energy remains smaller than the barrier of Fe (100), that is, the ReaxFF reproduced correctly the different surface diffusion barrier order (4F → S1A > LB →S1A; 4F → 4F > LB → LB) of carbon. The barrier of carbon diffusion between subsurface sites is



The corresponding adsorption sites are illustrated in Figure 2.

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error range28, 55-57.

3.4.3 Carbon diffusion on Fe (111) Besides the barrier from one quasi fourfold (qff) site to the nearest quasi fourfold site for the Fe (111) surface, we also considered the reaction barrier for a dimer with two single carbon occupying the nearest qff sites and the barrier for one carbon diffusing from one site in the first subsurface further into a deeper site in the second subsurface. The corresponding illustrations have been presented in Figure 4. The RPOIC-2017 well reproduces the reaction barrier, 28.61 Kcal/mol, of two single carbon forming a dimer on the Fe (111)surface in good agreement with the VASP value 30.03 Kcal/mol58. The diffusion barriers of qff → qff and S1 → S2 are 25.17 Kcal/mol and 20.40 Kcal/mol, respectively, which are a bit higher compared with the VASP data 22.09 Kcal/mol58 and 15.36 Kcal/mol58. In a word, the RPOIC-2017 can reproduce the reasonable diffusion barrier of carbon related to α-Fe. However, diffusion barriers calculated by ReaxFF-2012 can only correctly describe the pathways of 4F → 4F and qff → qff.


19.00 Kcal/mol, a little higher than the VASP value 16.86 Kcal/mol54 but still in accepted



Figure 4. Diffusion barrier of carbon on different surfaces, into subsurface and between subsurfaces. The 1st row presents the diffusion process of carbon on Fe (100) surface, the 2nd row and the last line present the cases of Fe (110) surface and the Fe (111) surface, respectively.

3.5 Adsorption energy Figure 5 shows the complete list of carbon binding energy with different sites at surface and subsurface for the Fe (100), the Fe (110) and the Fe (111) surfaces. The energies of some predicted structures calculated by VASP, RPOIC-2017 and ReaxFF-2012 are shown in Figure 5 (d). We adopted the average adsorption energy per atom defined as Eads(C) = Eads/n, Eads=Eslab+nC- Eslab - nEC, where Eads is the adsorption energy for all adsorbed carbons, n



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carbon based on the graphite and Eslab+nC is the total energy of several carbons adsorbing on the iron slab. The results show that while theRPOIC-2017 underestimates the value of carbon adsorbing on the top site (T-1C) and the bridge site (B-site) of Fe (100) surface it can appropriately describe the thermodynamic behavior of carbon to avoid adsorbing stably on such sites. The difference between the adsorption energies of the most stable site of four-fold site (4F-1C) calculated by RPOIC-2017 and VASP falls within an accepted error range28, 55-57. The other energies of several carbon atoms including two, three and four atoms adsorbing on the surface and the subsurface of Fe (100) surface, such as two carbon atoms on the subsurface in the form of c (2 × 2), are also in good agreement with the VASP data54, 58, suggesting the new parameters can describe the thermodynamics behavior involving the multiple carbon atoms and the Fe (100) surface. However, the results calculated by ReaxFF-2012 either have an opposite energy trend or have a large deviation when the trend is correct.


is the number of corresponding atom, Eslab is the energy of iron slab, EC is the energy of single



Figure 5. Adsorption energy of carbon on different sites for the Fe (100) surface (a), the Fe (110) surface (b), the Fe (111) surface (c) and predicted structures (d). 4F4F-c (2 × 2)-2C means that there are two carbon atoms adsorbing on two separate 4Fsites and presents the structure of c (2 × 2), others can be inferred by analogy. The top view of all structures are supplied in Supporting Information.

The adsorption energies of the short bridge (SB) and the long bridge (LB) site are overestimated and that of the top site is underestimated for the Fe (110) surface. There also exists a different degree of overestimation or underestimation in the other sites of the Fe (110) surface, but all these values are still closer to the VASP value54, 58 and more accurate than the values calculated by ReaxFF-2012. The adsorption energy of the top site of the Fe (111)



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such sites, they will diffuse quickly to a more stable site, such as the qff site or the deep hollow (DH) site. On the Fe (111) surface, we have considered more carbon atoms from two carbon atoms to six atoms, and from dimers to trimers and to chains, and so on. The results show that the new parameters can also nicely present the thermodynamic behavior of carbons on the high energy surface of iron. We thus conclude that the RPOIC-2017 is appropriate to describe the Fe-C interaction. Additionally, we predicted the energies of some structures, which were not included in the trainset, about carbon adsorbed on different surfaces involving several carbons calculated by RPOIC-2017 and ReaxFF-2012, and compared them with the VASP data54, 58. The results also show that our parameters give a reasonable value comparable to the VASP values. This implies that RPOIC-2017 has good portability to in modeling Fe-C systems.

4. Application of new parameters in RMD simulations: carbon atoms diffusion in α-Fe To investigate the carbon diffusion coefficient or rather self-diffusion coefficient in bulk under as close to real conditions as possible, we performed a series of RMD simulations in NVT ensemble with a range of carbon concentrations from 10-4 to 10-2 (carbon concentration here is the quantity rate of carbon atoms to iron atoms). We used two systems: 8 × 8 × 8 and 20 × 20 × 20 three-dimensional periodic bulk iron systems. We studied the diffusion in temperature ranged from 700 K and 1300 K with a 100 K interval. This range is carefully selected so that there is no significant deviation from real temperature of F-T conditions. The reason why we adopted the maximum temperature exceeding the phase transformation


surface is higher than the VASP data54, 58 indicating that when the carbon atoms adsorb on



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the critical conditions. Additionally, iron-iron interaction in the γ phase has been considered by Chenyu Zou and Adri C. T. van Duin28. Diffusion coefficient of carbon was obtained by calculating the means square displacement (MSD) when the system reached an equilibrium. We used the Einstein’s relation to calculate the MSD and corresponding diffusion coefficient. The diffusion coefficients have reached a stable value when simulation time reaches to 300 ps. The apparent barrier of diffusion was calculated using the Arrhenius equation59. We used the coefficients of 500 ps at all temperatures and calculated their corresponding natural logarithm. After obtaining the lnD, we used a linear-fitting method to analyse the relationship between D and 1000/T. Figure 6 shows the variation of diffusion coefficient or rather self-diffusion coefficient for carbon concentrations of 2.0 × 10-2 and a linear relation can be observed between the natural logarithm of diffusion coefficient and the reciprocal of temperature. The mean diffusion coefficient at 1136 K is 5.3× 10-10 m2/s agreeing well with the experimental data60 of 5.6 × 10-10 m2/s at 863 ℃. The diffusion barrier is 0.70 eV, which is a bit underestimation to the experimental data 0.81-0.87 eV53, 60 and the literature value 0.86 eV17. The underestimation can be attributed to a perfect crystal used in simulations. We presented the expression of diffusion coefficient as a function of temperature: D(T) =4.6 ×10-7exp(-8088.75/T) m2/s, then we extrapolated the diffusion coefficient at 500 K and 600 K, which helps to understand the carburization of iron in the low and high F-T temperature range. The diffusion coefficients are calculated to be 4.3 × 10-14 m2/s and 6.4 × 10-13 m2/s for temperature 500 K and 600 K, respectively. It is worth noting that when temperature is


temperature from the α-Fe to the γ-Fe is to investigate the carbon diffusion coefficient under

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of simulation of carburization. We also present the result of the MEAM potential, its corresponding barrier is only 0.33eV which implies that it is not suitable to employ the diffusion behavior of carbon in the α-Fe. The details of MSD and Arrhenius equations are supplied in Supporting Information.

Figure 6. Diffusion coefficient vs. time (left) and corresponding InD vs. reciprocal of temperature from 700 K to 1300 K with the linear fitted straight line (right).

5. Concluding remarks We fitted a parameter sets (RPOIC-2017) to describe the interaction of Fe-C relating to the carburization of iron in this paper which is obtained from fitting the VASP data or experimental data, including the equations of state, the surface energies, the thermal adsorption energies and the dynamic diffusion barriers. The present results show a remarkable agreement with both the VASP data and the experimental data indicating that our parameters have tremendously improvement over the ReaxFF-2012 and have a good transportability. In addition, we applied the new parameters to explore the thermal and dynamic behavior of carbon diffusion on different iron surfaces. We demonstrated that the RPOIC-2017 can well


relatively lower, like 500 K and 600 K, the time scale of 500 ps can not meet the requirement



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self-diffusion of carbon in iron bulk under various conditions as close to real conditions as possible. The results of self-diffusion show that the carbon diffusion barriers are very close to both the experimental and the VASP values, and the self-diffusion coefficient is in good agreement with the experimental value at 863 ℃. The success in exploring carbon diffusion demonstrates the well transportability of RPOIC-2017. We demonstrated that our potential is superior to traditional MEAM potential in modeling diffusion. Further studies and applications besides formation, adsorption, equation of state, structure properties, and diffusion are expectable. The new ReaxFF developed in the work can be benefit for the design of novel iron based materials, but also could understand atomic arrangement and interfacial structure of Fe-C systems.


reproduce the VASP data. Furthermore, we performed the RMD simulation of the

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ASSOCIATED CONTENT

Supporting Information. Description of the ReaxFF and MEAM potential functions with the calculation of MSD and barrier are provided in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * Xiao-Dong Wen ([email protected]); Chunfang Huo ([email protected]); Qing Peng ([email protected]) Conflicts of interest There are no conflicts to declare.

ACKNOWLEDGMENT The authors are grateful for the financial support from the National Natural Science Foundation of China (No. 21473229 and No. 91545121), and Synfuels China, Co. Ltd. We also acknowledge National Thousand Young Talents Program of China, Hundred-Talent Program of Chinese Academy of Sciences and Shanxi Hundred-Talent Program. We are



DOI: 10.1039/C7CP05958B



DOI: 10.1039/C7CP05958B


Finally, the authors would like to dedicate the work to Professor Roald Hoffmann on the occasion of his 80th birthday.

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Development of Reactive Force Field for Fe-C

Development of Reactive Force Field for Fe-C

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