Simulation on the Factors Affecting the Crystallization Process of FeNi Alloy by Molecular Dynamics.

This paper investigates the crystallization process of FeNi alloys with different impurity concentrations of Ni(x) [x = 10% (Fe90Ni10), 20% (Fe80Ni20), 30% (Fe70Ni30), 40% (Fe60Ni40), and 50% (Fe50Ni50)] at temperature (T) = 300 K and Fe70Ni30 at heating rates of 4 × 1012, 4 × 1013, and 4 × 1014 K/s at different temperatures, T = 300, 400, 500, 600, 700, 900, 1100, and 1300 K. Molecular dynamics models with the Sutton-Chen embedded interaction potential and recirculating boundary conditions are used to calculate the molecular parameters of alloys, such as radial distribution function, total energy of the system (E tot), size (l), and crystallization temperature (through the relationship between E tot and T). The common neighborhood analysis method is used to confirm the theoretical results of crystallization for Fe-Fe, Fe-Ni, and Ni-Ni. The annealing process did not have an effect on the crystallization process of FeNi alloys. The effect of Ni content, heating rate, and annealing time on structural unit numbers, such as face-centered cubic, hexagonal close-packed, blocked cubic center, and amorphous, and the crystallization process of FeNi alloys is also investigated.

Introduction

Nowadays, FePt,[1] CoPt3,[2] CoPt,[3] CoRh,[4] and NiFe[5] alloys are being used in many application fields such as biology,[6,7] adsorption,[8,9] data storage,[10,11] high-density storage,[12−14] photocatalysts,[15,16] chemical sensors,[17−19] and biomedicine.[20−22] FeNi alloys have received great attention from scientists thanks to their interesting properties: magnetic,[23] photocatalytic,[24,25] antioxidant,[26,27] and biomedical.[28] This material is suitable for biomedical applications because they exhibit magnetic superparamagnetic properties and thus can be used for various applications dealing with drug delivery, hyperthermia, and magnetic resonance imaging.[29] Experimental, theoretical, and simulation methods are used to investigate the structure of FeNi alloys. With the experimental method, FeNi alloys were successfully fabricated by the evaporation method at temperature (T) = 1823 K[30] with Fe concentrations of 36%, and the size (D) varies from 20 nm to 100 nm;[31] the hydrogenation reaction gives spherical nanoparticles with size smaller than 35 nm;[32] and the plasma treatment in the mixture of H2 and Ar leads to nanoparticles with nanoscale size.[33] The latter depends on the temperature and air flow rate,[34] pyrolysis conditions,[35] and preparative methods.[36−38] Fe1–Ni alloys with size 10–25 nm[39,40] are being implemented very little by the experimental method, whereas the simulation method is considered the most interesting method because of its ability to study at the atomic level without the consumption of energy as in the experimental methods. They were built by molecular dynamics (MD) method, Monte-Carlo method, combined with interaction potentials, such as the average effective field theory,[41] atomic method, Finnis and Sinclair,[42,43] and embedded interaction Sutton–Chen (SC).[44,45] The obtained results are highly accurate. To study the structure of FeNi materials,[46] Daw and Nguyen have used the MD method with the embedded interaction SC,[5,47] in combination with the parameters of Meyer and Entel.[48] The experimental method and simulation method can be combined to obtain high-precision results.[49−54] Ni has a face-centered cubic (FCC) structure and Fe has a blocked cubic center (BCC) structure; however, hybridization leads to new structures. The change of alloy structure depends on various factors including solute concentration, atomic number, temperature, annealing time, and so forth. The solute concentration (x) of Fe in Ni1–Fe alloy can reach 100% at high temperatures, ranging from T = 1183 K to T = 1665 K,[55] whereas at low temperatures, the impurity concentration can reach a maximum of x = 66%.[55,56] In addition, scientists used the electron model[57−60] to study the defect buttons, defects, and surface properties of materials.[36,61] To study the structure and phase transition temperature of CuNi and CuAu, energy alignment method,[62] the ability method of Blaha et al.,[63] and the network constants of the material[64] are used. With the MD simulation method, Grujicic et al. have successfully studied the effect of impurity concentration[65,66] and have established the relationship between the FCC and BCC structural phases. Lavrentiev et al.[67] determined the effect of concentration of Ni impurities in Fe1–Ni from x = 5% to x = 75% on the phase transition temperature (Tm) = 800 K; in the FCC structure, the crystallization temperature, Tg = 600 K. Recently, we have successfully studied the effect of the impurity concentration of Fe in Ni1–Fe nanoparticles, with x = 10, 30, and 50%, on the radial distribution function (RDF) structural unit numbers, FCC, hexagonal close-packed (HCP), and amorphous (Amor).[5] In addition, with the concentration of Cu solids of 33% in AlCu, the transition temperature (Tm) is found to be 821 K,[76] whereas an increase in the number of CuNi atoms leads to an increase in the concentration of solute Ni,[77] and Ag increases in CuAg.[78] As previously mentioned that FeNi is a promising material, however, the molecular structure is not reported in the literature. Moreover, the effect of inlet conditions such as heating rate, impurity concentration, and annealing time at a molecular level is investigated by using the MD method with the embedded interaction potential SC and recirculation boundary conditions. Various molecular parameters are calculated for these alloys, which will be useful for a better understanding of the behavior of these alloys at a molecular level.

Results and Discussion

Effect of Impurity Concentration

The effect of Ni concentration in the alloys on the shape and RDF of samples Fe90Ni10, Fe80Ni20, Fe70Ni30, Fe50Ni50 (FeNi), and Fe60Ni40 is shown in Figure . Figure a shows that Fe90Ni10 at T = 300 K has a cube shape, created by two types of atoms, Fe and Ni, in which Fe atoms are in red color and Ni atoms are in blue color. The first peak position of RDF has a value, r = 2.45 Å, height g(r) of 5.03 (Figure b), size (l) = 7.46 nm, and the total energy of the system (Etot) = −2188.47 eV. An increase in the impurity concentrations (x) of Ni in FeNi alloys from Fe90Ni10 to Fe80Ni20, Fe70Ni30, Fe60Ni40, and FeNi leads to an increase in the r value from 2.45 Å to 2.45, 2.48, 2.60, and 2.60 Å; g(r) decreases from 5.03 to 4.73, 4.46, 4.28, and 4.71; l increases from 7.46 nm to 7.50, 7.54, 7.59, and 7.63 nm, and Etot decreases from −2188.47 eV to −3437.55, −4703.88, −5929.33, and −7175.27 eV (Table ).

Figure 1

Shape (a) and RDF (b) of sample Fe90Ni10 at a temperature of 300 K.

Table 1

Size, Total Energy of the System, Position, and Height of RDF FeNi Alloys with Different Ni Impurity Concentrations

FeNi alloys	Fe90Ni10	Fe80Ni20	Fe70Ni30	Fe60Ni40	FeNi	results
r (Å)	2.45	2.45	2.48	2.60	2.60	experiment 2.53 Å[21]
						simulation 2.49 Å[5]
g(r)	5.03	4.73	4.46	4.28	4.71
l (nm)	7.46	7.50	7.54	7.59	7.63
Etot (eV)	–2188.47	–3437.55	–4703.88	–5929.33	–7175.27

For Fe70Ni30, r = 2.48 Å, which is consistent with the experimental result (r = 2.53 Å)[21] and simulation results (r = 2.49 Å).[5] Besides, the effects of particle size (l) and Etot with the solute concentrations of Ni are shown in Figure .

Figure 2

Relationship between the size (l) and the solute concentration of Ni (a) and that between the total energy of the system (Etot) and the solute concentration of Ni (b).

The results show that the size (l) of FeNi alloys is always directly proportional to the solute concentration of Ni and satisfies the formula: l = 7.415 + 0.43x (Figure a); the energy of the system (Etot) is directly proportional with the solute concentration of Ni (−x) and satisfies the formula: Etot = −947.28 – 12 465.38x. Figure b shows that the solute concentration (x) has a significant influence on l and Etot of FeNi alloys. The obtained results show that l is directly proportional with x and Etot is directly proportional with −x. The results are in line with those recently reported by the simulation method[5] and the experiment method.[72] To confirm the accuracy of the obtained results, the visualization method and common neighborhood analysis (CNA) method have been used, and the results are shown in Figure , Table .

Figure 3

Structural unit number shapes of FeNi alloys: FCC structure (a), HCP structure (b), BCC structure (c), and Amor structure (d).

Table 2

Structural Unit Numbers of FeNi Alloys with Different Ni Impurity Concentrations

Ni doped concentration	FCC	HCP	BCC	Amor
Fe90Ni10	2168	1425	43	1688
Fe80Ni20i	3274	1130	109	811
Fe70Ni30	3547	1290	53	434
Fe60Ni40	1777	852	32	2663
Fe50Ni50	1722	1080	25	2497

Figure shows that FeNi alloys exhibits four types of structure: FCC structure (Figure a), HCP structure (Figure b), BCC structure (Figure c), and Amor structure (Figure d). An increase of Ni solute concentration from Fe90Ni10 to Fe80Ni20, Fe70Ni30, Fe60Ni40, and FeNi leads to an increase and then a decrease of the FCC, HCP, and BCC structure unit numbers, whereas the Amor structure unit number first decreases and then increases (Table ). This confirms that the increase of solute concentration of Ni in FeNi alloys leads to an increase of crystallization rate. This phenomena is not often observed. The largest crystallization process is observed when the solute concentration of Ni in FeNi alloy, x = 30%.

This result is consistent with those recently reported for Cu (33%) in AlCu,[76] the concentration of soluble Ni increases when the number of atoms CuNi[77] and Ag increases in CuAg.[78] To further investigate the effect of other factors on the molecular structure, FeNi alloy has been chosen as the reference, with a Ni-doped concentration of x = 30% (Fe70Ni30), to study in the next sections.

Effect of Heating Rate

Several molecular parameters of the sample Fe70Ni30 at T = 300 K as a function of heating rate (4 × 1012, 4 × 1013, and 4 × 1014 K/s) are shown in Table .

Table 3

Size, Energy, First Peak Position, and First Peak Position Height of RDF with Different Heating Rates

	FeNi alloys
heating rate (K/s)	4 × 1012	4 × 1013	4 × 1014	results (Å)
r (Å)	2.48	2.50	2.6	2.53[21]
				2.49[5]
g(r)	4.46	3.92	3.90
l (nm)	7.54	7.59	7.56
Etot (eV)	–4703.88	–4688.11	–4685.93

Table shows that Fe70Ni30 at T = 300 K with a heating rate of 4 × 1012 K/s has r = 2.48 Å, g(r) = 4.46, l = 7.54 nm, and Etot = −4703.88 eV. An increase in the heating rate from 4 × 1012 to 4 × 1013 and 4 × 1014 K/s leads to an increase of r from 2.48 Å to 2.60 Å and a decrease of g(r) from 4.46 to 3.90; l changes in the range from 7.54 to 7.59 nm; and Etot increases from −4703.88 eV to −4685.93 eV. These results show that the increase of the heating rate leads to the transfer of Fe70Ni30 from the crystalline state to amorphous state. To confirm the accuracy of the results, the visualization method and the CNA method are used, and the results are shown in Figure .

Figure 4

Structural shape (a1–c1) and the structural unit numbers of FeNi alloys (a2–c2) at different heating rates.

The results show that Fe70Ni30 with a heating rate of 4 × 1012 K/s has different structural shapes (Figure a1–c1) corresponding to the structural unit number: 3547 FCC, 1290 HCP, 53 BCC, and 434 Amor, respectively. When the heating rate is increased from 4 × 1012 to 4 × 1013 and 4 × 1014 K/s, the structural unit number of FCC decreased from 3547 FCC to 1912 FCC and 1055 FCC; HCP decreased from 1290 HCP to 1386 HCP and 736 HCP; BCC decreased from 53 BCC to 0.0 BCC and 37 BCC; and Amor increased from 434 Amor to 2026 Amor and 3496 Amor (Figure a2–c2). This confirms that the increase of the heating rate leads to a decrease in the crystallization process.

Influence of Temperature

The relationship between the energy of the system Etot and temperature T = 300, 400, 500, 600, 700, 900, 1100, and 1300 K is also investigated, and the results are shown in Figure .

Figure 5

Relationship between Etot and T.

Figure shows that Fe70Ni30 at T = 300 K has Etot = −4703.88 eV. When T is increased from 300 K to 400, 500, 600, 700, 900, 1100, and 1300 K, the l value increases from 75.41 nm to 75.47, 75.57, 75.64, 75.75, 75.93, 76.32, and 76.79 nm, and Etot increases from −4703.88 eV to −4699.06, −4691.34, −4685.80, −4677.88, −689.81, −4665.10, −4647.32, and −4631.61 eV (Figure ). The results show that an increase of T leads to an increase of l and Etot. When T increases from 300 K to 600 K and from 600 K to 1300 K, Etot increases linearly, and an interrupting point at T = 600 K, corresponding with Etot = −4685.80 eV, is observed. This value is assigned to the crystallization temperature (Tg) 600 K. This seems to be consistent with the experimental results (Tg = 593 K).[15,23,24] To confirm the accuracy of the obtained results, CNA and RDF methods are used, and the results are shown in Figure .

Figure 6

RDF (a) and structural unit numbers (b) of Fe70Ni30 at different temperatures.

Figure indicates that at T = 300 K, Fe70Ni30 has r = 2.48 Å and g(r) = 4.46. When T is increased from 300 K to 1300 K, r increases from 2.48 Å to 2.63 Å, and g(r) changes in the range from 4.46 to 4.06 (Figure a); however, the structural unit number of FCC remains unchanged when the temperature varies from 300 K to 600 K. When T > 600 K, FCC declines rapidly; HCP decreases slowly in the range from 300 K to 600 K. When T > 600 K, HCP decreases rapidly; BCC changes; and Amor lightly increases in the temperature range from 300 K to 600 K, and then Amor increases rapidly when T > 600 K (Figure b). This asserts that Fe70Ni30 has a thermal transition at T = 600 K.

Effect of Annealing Time

The results of Fe70Ni30 after the annealing process are shown in Figure .

Figure 7

Relationship between the total energy of the system Etot (a1), structural unit numbers (b1), RDF (c1), and structural shape (a2–d2) with different annealing times.

The results shows that Fe70Ni30 at an annealing time (t), t1 = 0.0 ps has Etot = −4685.80 eV. When annealing t increased from 0.0 ps to 450 ps, Etot remains almost unchanged (Figure a1). This confirms that after annealing time, there is no structural change; a negligible change in the structural unit numbers is also observed (Figure b1); RDF has a negligible change with the annealing time (Figure c1). Similar tendency has been observed for structural shapes (Figure a2–d2). When x = 30%, the crystallization process reaches the maximum value. When the annealing time is increased, the crystallization process remains stable. In other words, the crystallization of these alloys is relatively rapid and is completed after a very short time, and thus annealing is not necessary to improve the crystallization degree.

Conclusions

In this study, the crystallization process of FeNi alloys by the MD method is investigated. We have successfully described and calculated various molecular parameters for these alloys by using the SC interaction potential and recirculating boundary conditions. We show that the increase of the solute concentration (x) of Ni in FeNi alloys leads to an increase of the crystallization process and that a maximum value is obtained at x = 30%. Our findings show that the crystallization temperature (Tg) is found to be about 600 K and that the annealing time (t) does not affect the crystallization state. We have successfully established the relationship of x with l and Etot: l is proportional with x, whereas Etot is directly proportional with −x. These obtained results are supported by experimental and[72] simulation results.[5] Different types of structural unit numbers are found for these alloys including FCC, HCP, BCC, and Amor which are completely consistent with the experimental and theoretical results.[5,15,21,23,24]

Calculation Method

Initially, FeNi alloys with 5324 atoms at different solute concentrations of Ni, heating rate, temperature, and annealing time were randomly planted into a cube and then studied by MD method[68] with embedded interaction potential SC,[1,69−71] Verlet algorithm,[72] and recirculation boundary conditions.where r is the distance between two atoms i and j; a is the network constant; ρ is the atomic density i; Etot is the total energy of the system; Φ(r) is the energy between two atoms i and j; F(ρ) is the interaction force of atom i; rc = 3.15 Å is the interrupt radius; ε is the energy; and C, m, n, and N are the parameters of FeNi alloys. The parameters of FeNi alloys are presented in Table .

Table 4

Main Parameters of FeNi Alloys

material	εFeNi (×10–2 eV)a	aFeNi (Å)b	nFeNic	mFeNid	CFeNie
Fe	1.730	3.471	8.137	4.787	24.939
Ni	0.271	3.520	10	5	84.745

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After collecting the samples of FeNi alloys with different solute concentrations, x = 10% (Fe90Ni10), 20% (Fe80Ni20), 30% (Fe70Ni30), 40% (Fe60Ni40), and 50% (Fe50Ni50), Fe70Ni30, the heating rates are 4 × 1012, 4 × 1013, and 4 × 1014 K/s at T = 300 K; for the Fe70Ni30 sample, T = 300, 400, 500, 600, 700, 900, 1100, and 1300 K; t = 450 ps (corresponding to the moving step number of 1.8 × 105 steps; time of each step is of 2.5 fs) at T = 600 K. The temperatures of all samples were increased from 0 K to 2500 K to break the initial crystalline structure state and moved to a liquid state. When the temperature is conducted to 2500 K, the samples were cooled to different temperatures of 1300, 1100, 900, 700, 600, 500, 400, and 300 K, with the same heating rate, to switch from the liquid to crystalline state. The crystallization process of FeNi alloys is investigated through RDF, size (l), total energy of the system (Etot), structure (through shape, size, and relationship between the temperature (T) and Etot). CNA[73] is used to determine the structure unit number of FCC, HCP, BCC, and Amor structures, and the heating rate process of FeNi alloys is carried out by the Nosé–Hoover temperature regulator.[74,75]