Structural, electronic and magnetic properties of Fe20Cr6Mn6 austenitic alloys with interstitial carbon and nitrogen atoms from density functional theory

Structural, electronic and magnetic properties of Fe20Cr6Mn6 austenitic alloys with interstitial carbon and nitrogen atoms from density functional theory

Journal of Magnetism and Magnetic Materials 504 (2020) 166663 Contents lists available at ScienceDirect Journal of Magnetism and Magnetic Materials ...

4MB Sizes 0 Downloads 6 Views

Journal of Magnetism and Magnetic Materials 504 (2020) 166663

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm

Research articles

Structural, electronic and magnetic properties of Fe20Cr6Mn6 austenitic alloys with interstitial carbon and nitrogen atoms from density functional theory

T



Z. Lva,b, , T. Liua, Z. Wua, K. Guana, Y. Lic a

Key Laboratory of Advanced Forging & Stamping Technology and Science (Yanshan University), Ministry of Education of China, Qinhuangdao 066004, China State Key Laboratory of Metastable Material Science and Technology, Yanshan University, Qinhuangdao 066004, China c Special Steel Institute, Iron and Steel Research Institute, Beijing 100081, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Fe-Cr-Mn alloy Crystal structure Interstitial solid solution Electronic structure First principles

Based on a 32-atom supercell system, the structural, electronic and magnetic properties of Fe20Cr6Mn6 alloys are calculated and analyzed using first-principles calculations. The effects of interstitial atoms (N and C) on the properties of Fe20Cr6Mn6 alloys are also discussed. In this 32-atom supercell system with an octahedral interstice in the center, there are four different atomic sites occupied by metal atoms (Fe, Cr and Mn). According to the differences of metal atoms at the different atomic sites, the Fe20Cr6Mn6 alloys have been defined as two structural models. Interstitial atoms (N or C) change the phase stability of Fe20Cr6Mn6 alloys. The supercell volumes increase linearly with the content of N (C) in the supercells for each alloy system. The bond lengths of Mn-C/N or Cr-C/N in the octahedral interstice, not as the supercell volume, do not increase linearly with the content of N (C). The spin moments of the Fe20Cr6Mn6 alloys are very small and the magnetic moments of I-MnCx/Nx alloys and I-Cr-Cx/Nx alloys increase slightly. In Fe20Cr6Mn6 alloys, the electrons transfer from Cr atoms to Fe and Mn atoms, and the ability to gain and lose electrons of metal atoms is changed by the addition of C or N atoms. There is an atomic attraction between metal atoms and C or N atoms from bond population analyses.

1. Introduction Austenitic stainless steels, due to the excellent comprehensive performance, are used in a wide variety of fields [1–4]. Carbon and nitrogen can be used to accomplish the corrosion performance and improve the mechanical properties by interstitial dissolution. A relatively large content of carbon or nitrogen in austenitic stainless steels can be obtained by chemical heat treatment and physical metallurgy [3–8]. This kind of austenite with a supersaturated solid solution of carbon and/or nitrogen is known as expanded austenite. The influence of interstitial atoms (N or C) on the structure and mechanical properties of the expanded austenite is of scientific interest and industrial value [4–10]. Recently, the effects of interstitial atoms in the austenite phase (γ-Fe) have been widely investigated. The structural, electronic and magnetic properties of γ-Fe with the interstitial atoms (H/C/N/B/O) have been calculated and reported [11–15]. The interstitial atoms change the Fe–Fe and Fe–H/C/N interactions in γ-Fe [11]. The magnetic structures are more stable than the non-magnetic ones for fcc-FenX

(X = C or N; n = 4 or 8) alloys [12]. Density functional theory (DFT) calculations show that the structures of fcc-Fe4N and fcc-Fe4C are metastable [13]. The magnetic properties and phase stability of fcc-Fe4X (X = B/C/N) alloys were obtained using first-principles calculations [15]. These studies are all based on the fcc phase (γ-Fe) included only Fe as a single metallic element [11–15]. Generally, austenitic stainless steels are multicomponent alloys, rich in Cr, Ni, Mn and Mo. The lattice expansion of Fe-Cr-Ni-N/C austenitic alloys with the addition of N or C was studied [5–9], while the crystal structure of the expanded austenite was elusive. The fcc-Fe crystal models [11–15] are not suitable for multicomponent austenitic steels, rich in Cr, Ni and Mn. In order to analyze multicomponent austenitic alloys, such as Fe-Cr-Ni and Fe-CrMn alloys, supercell systems have been built [16–18]. In the previous work, a 32-atom supercell system was built, which was successfully used to study the Fe18Cr6Mn8 alloys. The properties of Fe18Cr6Mn8 and Fe18Cr6Mn8N alloys were calculated from DFT. The effects of solute nitrogen on the magnetic properties and phase stability of Fe18Cr6Mn8 alloys were obtained [18]. In this work, 32-atom

⁎ Corresponding author at: Key Laboratory of Advanced Forging & Stamping Technology and Science (Yanshan University), Ministry of Education of China, Qinhuangdao 066004, China. E-mail address: [email protected] (Z. Lv).

https://doi.org/10.1016/j.jmmm.2020.166663 Received 11 May 2019; Received in revised form 19 February 2020; Accepted 24 February 2020 Available online 26 February 2020 0304-8853/ © 2020 Elsevier B.V. All rights reserved.

Journal of Magnetism and Magnetic Materials 504 (2020) 166663

Z. Lv, et al.

Fig. 1. Crystal structure of the super cell with 32 metal atoms: 32-atom super cell and different atomic sites for metal atoms: site I, II, III and IV (a); 13 octahedral interstices in the super cell from site 1 (in the center) to site 13 (b).

account for the magnetic properties, owing to the significant effect of Fe/Cr/Mn on magnetic systems. The convergence criteria for structural optimization and energy calculations were set to fine quality with the tolerance for the stress concentration factor, energy, maximum force and maximum displacement set to 10-6 eV/atom, 10−5 eV/atom, 0.3 eV/nm and 10−4 nm, respectively.

supercell systems are applied to study the Fe20Cr6Mn6 alloys and the structural models with interstitial N or C are constructed. One aim of this work is to investigate the effect of the content of interstitial N or C in the Fe-Cr-Mn alloy on the structural properties and the phase stability of Fe20Cr6Mn6 alloys. The electronic and magnetic properties of Fe20Cr6Mn6 alloys with different contents of C or N in the supercells are further examined.

3. Results and discussion 2. Crystal structure and calculation details

3.1. Phase stability

Fe, Cr and Mn, due to their similar atomic radii, can form Fe-Cr-Mn solid solutions with multiple components. With the suitable proportion of Mn, Fe-Cr-Mn alloys become austenitic stainless steels and the crystal structure can be approximatively modeled using a supercell with a 32atom system [17,18]. The γ-Fe crystal structure is the cubic space group Fm-3 m (S.G. No. 225) with four Fe atoms per unit cell [13–15]. A 32atom supercell system (space group Pm-3 m) with an octahedral interstice in the center [18] was built, as shown in Fig. 1. In this supercell, there are four different atomic sites for metal atoms, as shown in Fig. 1(a). The structural models of Fe20Cr6Mn6 alloys are obtained when Fe atoms in III and IV sites, and I and II sites are occupied by Cr and Mn. The Fe20Cr6Mn6 alloys have been defined as two structural models with the same atomic content: when Cr atoms occupy I sites, this alloy system is defined as I-Cr; when Mn atoms occupy I sites, the alloy system is defined as I-Mn. The octahedral interstice in the center of the supercell is defined as Interstice 1. The octahedral interstices near Interstice 1 are defined as Interstices 2 to 13 in turn, as shown in Fig. 1(b). When these octahedral interstices are occupied by different numbers of C atoms, the supercells are defined as ICr-Cx or I-Mn-Cx (x = 0–13). In parallel, when these octahedral interstices occupied by different numbers of N atoms, the supercells are defined as I-Cr-Nx or I-Mn-Nx (x = 0–13). In this work, x indicates the number of C or N atoms in the supercell. For example, the I-Mn-N3 alloy has three nitrogen atoms occupying Interstices 1 to 3 in the I-Mn alloy. In this work, 30 different Fe20Cr6Mn6Nx and Fe20Cr6Mn6Cx alloys were built and investigated. All calculations were carried out using the pseudopotential planewave method within DFT using the CASTEP code [19,20]. The exchange-correlation potential was evaluated using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional [21,22]. Ultra-soft pseudopotentials were used to describe the interactions between the core and valence electrons [23], and the Kohn-Sham one-electron states were expanded in a plane wave basis to 500 eV. The energy calculations in the first irreducible Brillouin zone were made using a 3 × 3 × 3 k-point Monkhorst-Pack grid method [24]. Spin polarization was included in the calculations to correctly

The formation enthalpy (ΔH) of Fe20Cr6Mn6Nx and Fe20Cr6Mn6Cx alloys from the elements (fcc-Fe, fcc-Cr, fcc-Mn, graphite and molecular N2) can be given as:

ΔEf = (Fe20 Cr6Mn6Nx) = E (Fe20 Cr6Mn6 Nx) − 20E (Fe) − 6E (Cr) − 6E (Mn) − xE (N) (1)

ΔEf = (Fe20 Cr6Mn 6Cx) = E (Fe20 Cr6Mn6 Cx) − 20E (Fe) − 6E (Cr) − 6E (Mn) − xE (C)

(2)

At T = 0 K and p = 0 Pa, the formation enthalpy equals the calculated formation energy (ΔE), i.e., ΔHf = ΔEf , when the zero-vibration contribution is ignored [25,26]. The formation energy can be used to represent the thermodynamic stability of Fe20Cr6Mn6Nx and Fe20Cr6Mn6Cx, as shown in Fig. 2. The formation energies of the I-Mn-C9/C11/C13 and I-Cr-N13 alloys are positive, which shows that they are of poor thermodynamic stability. The formation energies of Fe20Cr6Mn6(Cx/Nx), except I-Mn-C9/C11/C13 and I-Cr-N13, are negative, which shows that these alloys are of high thermodynamic stability. The formation energies of the I-Mn-Nx and I-Cr-Nx alloys approximatively decrease with increasing N content. The formation energy of I-Mn-N11 is reduced by −4.93 eV compared to the I-Mn alloy. The formation energy of I-CrN13 is reduced by −9.28 eV compared to the I-Cr alloy. The formation energies of I-Mn-C and I-Mn-C3 are slightly lower than the I-Mn alloy and the formation energy of I-Mn-N13 is 5.54 eV higher than the I-Mn alloy. The formation energies of I-Cr-C and I-Cr-C3 are lower than the ICr alloy and the formation energy of I-Cr-C13 is 2.77 eV higher than the I-Cr alloy. Overall, the I-Cr-Nx alloys are more stable than the I-Cr-Cx alloys, and the I-Mn-Nx alloys are more stable than the I-Mn-Cx alloys. The I-Cr-Nx alloys are more stable than the I-Mn-Nx alloys, and the I-CrCx alloys are more stable than the I-Mn-Cx alloys. This result is agreement with the stability of Cr and Mn nitrides and carbides. Chromium nitrides (carbides) with similar structures are more stable than manganese nitrides (carbides) [27–30]. 2

Journal of Magnetism and Magnetic Materials 504 (2020) 166663

Z. Lv, et al.

Fig. 3. Supercell volume vs. number of atom C/N in the supeercell.

Fig. 2. Change of formation energy with the content of N/C in the supercell.

Table 1 Calculated lattice constants a, b, c (0.1 nm) and α,β,γ (degree) of the supercells with Mn in I site. Alloy (Mn in I site)

a

b

c

α

β

γ

I-Mn I-Mn-C I-Mn-C3 I-Mn-C5 I-Mn-C7 I-Mn-C9 I-Mn-C11 I-Mn-C13 I-Mn-N I-Mn-N3 I-Mn-N5 I-Mn-N7 I-Mn-N9 I-Mn-N11 I-Mn-N13

6.9781 7.0227 7.1679 7.4081 7.4771 7.3462 7.4499 7.5575 7.0228 7.1711 7.4089 7.4398 7.3356 7.4583 7.5487

– – – – 7.4129 – – – – – – 7.3863 – – –

– – 6.9951 6.8724 7.0279 7.5470 7.5550 – – 6.9797 6.8492 9.0596 7.5019 7.4879 –

90 90 90 90 90 90 90 90 90 90 90 90 90 90 90

90 90 90 90 89.4 90 90 90 90 90 90 89.8 90 90 90

90 90 90.1 90 90 90 88.6 90 90 89.9 90 90 90 88.3 90

Table 2 Calculated lattice constants a, b, c (0.1 nm) and α,β,γ (degree) of the supercells with Cr in I site. Alloy (Cr in I site)

a

b

c

α

β

γ

I-Cr I-Cr-C I-Cr-C3 I-Cr-C5 I-Cr-C7 I-Cr-C9 I-Cr-C11 I-Cr-C13 I-Cr-N I-Cr-N3 I-Cr-N5 I-Cr-N7 I-Cr-N9 I-Cr-N11 I-Cr-N13

6.9780 7.0150 7.1658 7.3993 7.4673 7.3248 7.4464 7.5655 7.0095 7.1501 7.3607 7.3911 7.3234 7.4327 7.5285

– – – – 7.3821 – – – – – – 7.3431 – – –

– – 6.9729 6.8614 7.0388 7.5538 7.5329 – – 6.9727 6.8859 7.0935 7.4661 7.4624 –

90 90 90 90 90 90 90 90 90 90 90 90 90 90 90

90 90 90 90 89.4 90 90 90 90 90 90 89.8 90 90 90

90 90 90.3 90 90 90 89.4 90 90 90.0 90 90 90 89.2 90

3.2. Structural properties

Fig. 4. Equivalent lattice constant vs. content of C/N, number of atom (a) and mass percent of C/N (b), in the supeercell.

The ground-state properties of the supercells with solute atoms (Nx or Cx) in the octahedral interstice are analyzed through the total energy, which is calculated as a function of volume. The equilibrium atomic positions, bond lengths and lattice constants can be calculated using the Birch-Murnaghan equation of state [31]. The lattice constants

of the Fe20Cr6Mn6Nx and Fe20Cr6Mn6Cx alloys are listed in Tables 1 and 2. The lattice constants of the I-Mn alloy and the I-Cr alloy without solute atoms (N/C) are basically the same in the supercell (with the same structure); however, as solute atoms (N or C) dissolved in the I-Mn and I-Cr alloys, the differences in the lattice constants between the I3

Journal of Magnetism and Magnetic Materials 504 (2020) 166663

Z. Lv, et al.

Table 3 Lattice expansion by C/N dissolution and molar volume of C/N in austenite for stressed and unstressed retained austenite (Fe-C) and expanded austenite. The lattice expansion coefficient is given in nm/mass%. System

Lattice expansion coefficient

Composition range of validity yJ (J = N,C),

Stressed

I-Mn-Cx* I-Cr-Cx* I-Mn-Nx* I-Cr-Nx* Fe-Cr-Ni-C [8] Fe-Cr-Ni-C [32] Fe-C [33] Fe-Cr-Ni-C [32] Fe-C [33] Fe-Cr-Ni-C [34]

0.0036 0.0037 0.0031 0.0030 0.0028 0.0028

0–0.406 0–0.406 0–0.406 0–0.406 0–0.156 0–0.12

No No No No No No

0.0033 0.0041

0–0.09 0–0.12

No Yes

0.0046 0.0054

0–0.09 0–0.10

Yes Yes

* Present work.

Fig. 5. Bond length of Mn-C/N or Cr-C/N in the octahedral interstice of the supercell center.

Mn-Cx/Nx and I-Cr-Cx/Nx alloys with the same content solute atom become obvious. As solute atoms (N or C) dissolved in the alloys, the crystal lattice of the supercell is distorted and the cell volume increases with increasing the content of N or C (x value) for the I-Mn-Cx/Nx and I-Cr-Cx/Nx alloys. The effect of the N solid solution on the crystal lattice of the supercell is slightly less than that of C. The curves of the supercell volume vs. the number of N or C in the supercells are given in Fig. 3. It can be concluded that the supercell volumes increase linearly with the content of N (C) for each alloy system. The increasing rates of the supercell volumes are different for the I-Mn-Cx/Nx and I-Cr-Cx/Nx alloys. The slopes of the fitted curves are about 7.22, 7.27, 7.01 and 6.77 for I-Mn-Cx, I-Cr-Cx, I-Mn-Nx and ICr-Nx, respectively. The increasing rate of I-Mn-Cx (I-Cr-Cx) is larger than that of I-Mn-Nx (I-Cr-Nx). The linear relation between the dependence of the lattice parameter (a0) and the carbon (or nitrogen) content was also found in Fe-Cr-Ni-C/N systems [5,8]. In this work, in order to calculate the lattice expansion coefficient (in nm/mass%), the equivalent lattice content of the primitive cell (a0) was calculated from the supercell volume. Fig. 4 shows the equivalent lattice constant vs. the content of N(C) in the alloy systems. From Fig. 4, the equivalent lattice constant increase linearly with the content of N (C) for each alloy system. Table 3 lists the lattice expansion coefficients of the Fe-Cr-Ni-C/ N alloys and Fe-C system from literature reports [5,8,32–34]. In Table 3, the lattice expansion coefficients are listed in nm/mass%. The linear expansion coefficients range from 0.0030 to 0.0037 (in nm/mass

Fig. 6. Calculated spin total density of states of I-Mn-Cx alloys (a), I-Cr-Cx alloys (b), I-Mn-Nx alloys (c), and I-Cr-Nx alloys (d).

4

Journal of Magnetism and Magnetic Materials 504 (2020) 166663

Z. Lv, et al.

octahedron. Fig. 5 shows the bond length of Mn-C/N or Cr-C/N in the center octahedral interstice of each alloy. The bond length of Mn-C ranges from 0.19281 nm to 0.19781 nm in the I-Mn-Cx alloy, with the longest one being 2.6% longer than the shortest one. The Mn-C bond of I-Mn-C is the shortest and the Mn-C bond of I-Mn-C13 is the longest for the I-Mn-Cx alloys. The bond length of Cr-C ranges from 0.19495 nm to 0.19890 nm in the I-Cr-Cx alloys and the longest one is 2.0% longer than the shortest one. The Cr-C of I-Cr-C is the shortest and the Cr-C of ICr-C9 is the longest for the I-Cr-Cx alloys. The bond length of Mn-N ranges from 0.19190 nm to 0.20508 nm in the I-Mn-Nx alloys, with the longest one being 6.9% longer than the shortest one. The Mn-N bond of I-Mn-N is the shortest and the Mn-N bond of the I-Mn-N9 is the longest for the I-Mn-Nx alloy. The bond length of Cr-N ranges from 0.19336 nm to 0.20288 nm in the I-Cr-Nx alloy and the longest one is 4.9% longer than the shortest one. The Cr-N bond of I-Cr-N is the shortest and the Cr-N bond of I-Cr-N11 is the longest for the I-Cr-Cx alloys. From Fig. 5, the bond length, not as the supercell volumes, does not increase linearly with the content of N or C, especially in the I-Mn-Nx and I-Cr-Nx alloys. The bonds of M−N in the I-Cr-N13 (or I-Mn-N13) alloy are not the longest and the center octahedral interstice could be compressed in the Fe20Cr6Mn6Nx alloys.

Fig. 7. Calculated magnetic moments of the supercells.

%) for these austenite alloy systems. The lattice expansion coefficients (in nm/mass%) of I-Cr-Nx, I-Mn-Nx, I-Cr-Cx and I-Mn-Cx are 0.0030, 0.0031, 0.0037 and 0.0036, respectively. It can be seen that the lattice expansion coefficient of the Fe-Cr-Mn-C system is larger than that of the Fe-Cr-Mn-N system. The lattice expansion coefficients of this work are in the range (0.0028–0.0054 nm/mass%) from the literatures. According to the literature [5,8], yN (yC) was defined as the number of N (or C) atoms per metal atom in the austenitic alloys, e.g. in the work yN/ C = x/32. The bond length of M−C or M−N in the center octahedral interstice of each alloy can be used to indicate the size of the central

3.3. Electronic and magnetic properties The electronic structures of the Fe20Cr6Mn6Cx/Nx alloys are characterized and compared, and the effects of the solid solution atoms (N/ C) on the Fe20Cr6Mn6 system are discussed further. The density of states (DOSs), Mulliken population analysis and electron density distribution maps are used to characterize the electronic structures and chemical bonding of the Fe20Cr6Mn6Cx/Nx system. Fig. 6 show the calculated spin DOSs of the I-Mn-Cx, I-Cr-Cx, I-Mn-Nx and I-Cr-Nx alloys,

Fig. 8. Electron density difference map of the (0 0 1) plane across the center atom plotted from −0.5 e/Å3 (red) to 0.1 e/Å3 (blue) and the bond population of Mn/FeC/N labeled, I-Mn-C (a), I-Mn-C3 (b), I-Mn-C5 (c), I-Mn-N (d) , I-Mn-N3 (e) and I-Mn-N5 (f) . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 5

Journal of Magnetism and Magnetic Materials 504 (2020) 166663

Z. Lv, et al.

Fig. 9. Electron density difference map of the (0 0 1) plane across the center atom plotted from −0.6 e/Å3 (red) to 0.2 e/Å3 (blue) and the bond population of Cr/FeC/N labeled, I-Cr-C (a), I-Cr-C3 (b), I-Cr-C5 (c), I-Cr-N (d), I-Cr-N3 (e) and I-Cr-N5 (f). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 4 Calculated average charge (e) of atom in the supercells with Mn in I site.

Table 5 Calculated average charge (e) of atom in the supercells with Cr in I site.

Alloy

Fe

Mn

Cr

C

N

Alloy

Fe

Mn

Cr

C

N

I-Mn I-Mn-C I-Mn-C3 I-Mn-C5 I-Mn-C7 I-Mn-C9 I-Mn-C11 I-Mn-C13 I-Mn-N I-Mn-N3 I-Mn-N5 I-Mn-N7 I-Mn-N9 I-Mn-N11 I-Mn-N13

−0.1 −0.1 −0.05 −0.01 0.07 0.13 0.19 0.24 −0.1 −0.05 −0.01 0.06 0.11 0.17 0.22

−0.01 0.05 0.12 0.22 0.26 0.35 0.41 0.49 0.03 0.11 0.20 0.26 0.32 0.41 0.51

0.34 0.39 0.36 0.36 0.29 0.21 0.13 0.07 0.39 0.36 0.25 0.28 0.0.25 0.17 0.11

– −0.64 −0.65 −0.67 −0.65 −0.65 −0.64 −0.64 – – – – – – –

– – – – – – – – −0.57 −0.60 −0.63 −0.62 −0.63 −0.63 −0.63

I-Cr I-Cr-C I-Cr-C3 I-Cr-C5 I-Cr-C7 I-Cr-C9 I-Cr-C11 I-Cr-C13 I-Cr-N I-Cr-N3 I-Cr-N5 I-Cr-N7 I-Cr-N9 I-Cr-N11 I-Cr-N13

−0.1 −0.08 −0.03 0.04 0.10 0.16 0.20 0.25 −0.08 −0.03 0.02 0.08 0.13 0.17 0.22

−0.01 0.01 0.03 0.10 0.09 0.12 0.11 0.11 0.01 0.02 0.06 0.08 0.11 0.14 0.16

0.34 0.36 0.38 0.31 0.32 0.31 0.38 0.42 0.35 0.38 0.40 0.37 0.40 0.44 0.48

– −0.57 −0.63 −0.65 −0.63 −0.64 −0.63 −0.62 – – – – – – –

– – – – – – – – −0.56 −0.60 −0.63 −0.62 −0.63 −0.62 −0.63

Fig. 7. The magnetic moments of the Fe20Cr6Mn6 alloys (I-Mn and I-Cr alloys) without interstitial atoms (C/N) are close to zero (0.04 μB/cell). There are obvious differences in magnetic characteristics between Fe20Cr6Mn6 and Fe18Cr6Mn8 alloys [18]. The magnetic moments of the Fe18Cr6Mn8 alloys are much larger than that of the Fe20Cr6Mn6 alloys. The sensibility of the spin moments, especially for Fe atoms, to the local short-range order in the crystal [35], is mainly the primary cause of magnetic difference between the Fe20Cr6Mn6 and Fe18Cr6Mn8 alloys. After the C/N solid solution, the magnetic moments of I-Mn-Cx/Nx and I-Cr-Cx/Nx alloys increase slightly, which indicates the effects of C/N addition on the magnetic properties of the Fe20Cr6Mn6 alloys are not obvious. The values of the magnetic moments of these alloys range

respectively. The DOS of these alloy systems are similar to each other, and no energy gaps near the Fermi level indicate their metallic nature. After the carbon solid solution, the carbon’s 2 s bands range from −12.5 eV to −11.4 eV and the hybridization of C 2p (with metal atom 3d) takes place from about −8.2 eV to −5.9 eV in the I-Mn-Cx and I-CrCx alloys. After the nitrogen solid solution, the nitrogen’s 2 s bands range from −17.2 eV to −15.9 eV in the I-Mn-Nx and I-Cr-Nx alloys and the hybridization of N 2p (with metal atom 3d) takes place from about −8.7 eV to −6.5 eV. Comparing the up with down densities, the up and down states of these alloys are close to symmetric, which indicates that the spin moments of the alloys are very small. The magnetic moments of all alloys are calculated, as shown in 6

Journal of Magnetism and Magnetic Materials 504 (2020) 166663

Z. Lv, et al.

0.87 μB/cell. In the Fe20Cr6Mn6 alloys, the electrons transfer from Cr atoms to Fe and Mn atoms. With the addition of C or N atoms, the ability of Fe to gain electrons decreases with increasing nitrogen and carbon, and the electrons mainly transfer from metal atoms to N/C atoms in the Fe20Cr6Mn6Cx/Nx alloys. The bond populations of Fe-C, Mn-C, Cr-C, Fe-N, Mn-N and Cr-N are positive, which shows that there is an atomic attraction between metal atoms and C or N atoms. Nitrogen and carbon atoms, in the Fe20Cr6Mn6Cx/Nx alloys, display obviously electronegativity.

from 0.42 μB/cell to 0.87 μB/cell. The transfer of electrons in space can be reflected from the electron density difference maps. Electron density difference maps of the (0 0 1) plane across the center atom of I-Mn-Cx/Nx (x = 1, 3 or 5) and I-Cr-Cx/ Nx (x = 1, 3 or 5) alloys are plotted, as shown in Fig. 8 and Fig. 9. The electron density difference can be determined from the equation:

Δρ = {ρcrystal −

∑ ρat },

where ρcrystal and ρat are the electron densities of these crystals (i.e. IMn-C, I-Mn-N, I-Cr-C and I-Cr-N) and the corresponding free atoms, respectively. The electronic density of Fe/Mn/Cr decreases and that of N/C increases in these alloys, so the transfer of electrons takes place between Fe/Mn/Cr and N/C atoms. There are metallic bonds between metal atoms, such as Fe-Fe, Mn-Mn, Cr-Cr, Fe-Mn, Fe-Cr and Mn-Cr. In addition, covalent and ionic bonds exist between metal and interstitial atoms, such as Fe-C, Mn-C, Cr-C, Fe-N, Mn-N and Cr-N. The charge of each atom and the population analysis of Fe/Mn/Cr-C/N were obtained from the Mulliken method. In Figs. 8 and 9, the charges of atoms and bond populations of Fe/Mn/Cr-C/N in the (0 0 1) plane (across the center atom) of the I-Mn-Cx/Nx (x = 1, 3 or 5) and I-Cr-Cx/ Nx (x = 1, 3 or 5) alloys are also shown. The calculated charges of Fe/ Mn/Cr and C/N atoms are various in the I-Mn-Cx/Nx and I-Cr-Cx/Nx alloys. C and N atoms are with negative charges and metal atoms (Fe/ Mn/Cr) have positive charges, which further illustrates the electron transfer from Fe/Mn/Cr to C/N atoms in these alloys. The bond populations of Fe-C, Mn-C, Cr-C, Fe-N, Mn-N and Cr-N are positive, which shows that there is an atomic attraction between metal atoms and C or N atoms. The charges of the atoms were calculated with the Mulliken method, as shown in Tables 4 and 5. In the Fe20Cr6Mn6 alloys, the electrons transfer from Cr atoms to Fe/Mn atoms, while the electrons transfer from Cr/Mn atoms to Fe atoms in the Fe18Cr6Mn8 alloys [18]. In the Fe20Cr6Mn6 alloys, the ability of losing electrons decreases from Cr, Mn to Fe in turn. The number of electrons transferred in the Fe18Cr6Mn8 alloys [18] is more than that in the Fe20Cr6Mn6 alloys. With the addition of C or N atoms, the ability of Fe to gain electrons decreases with increasing nitrogen and carbon, and the electrons mainly transfer from metal atoms to N/C atoms in the Fe20Cr6Mn6Cx/Nx alloys. Nitrogen and carbon, in the Fe20Cr6Mn6Cx/Nx alloys, display obviously electronegativity. In I-Mn-Cx/Nx alloys, the charges of Cr decrease with the increase of C or N. In I-Cr-Cx/Nx alloys, the charges of Fe/Mn atoms increase with the increase of C or N.

CRediT authorship contribution statement Z. Lv: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Project administration, Resources, Software, Supervision, Validation, Writing - review & editing. T. Liu: Data curation, Formal analysis, Investigation, Writing - original draft. Z. Wu: Investigation, Methodology. K. Guan: Investigation, Methodology, Writing - original draft. Y. Li: Investigation, Supervision, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The project is supported by the Natural Science Foundation of Hebei Province for Distinguished Young Scholar (E2017203036). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jmmm.2020.166663. References [1] C. Garcia-Cabezon, Y. Blanco, M.L. Rodriguez-Mendez, F. Martin-Pedrosa, Characterization of porous nickel-free austenitic stainless steel prepared by mechanical alloying, J. Alloys Compd. 716 (2017) 46–55, https://doi.org/10.1016/j. jallcom.2017.05.045. [2] H. Berns, S. Riedner, V. Gavriljuk, Y. Petrov, A. Weihrauch, Microstructural changes in high interstitial stainless austenitic steels due to ballistic impact, Mater. Sci. Eng. A. 528 (2011) 4669–4675, https://doi.org/10.1016/j.msea.2011.02.062. [3] Z.H. Wang, W.T. Fu, S.H. Sun, H. Li, Z.Q. Lv, D.L. Zhao, Mechanical behavior and microstructural change of a high nitrogen CrMn austenitic stainless steel during hot deformation, Metall. Mater. Trans. A. 41 (2010) 1025–1032, https://doi.org/10. 1007/s11661-009-0153-2. [4] V.G. Gavriljuk, B.D. Shanina, H. Berns, Ab initio development of a high-strength corrosion-resistant austenitic steel, Acta Mater. 56 (2008) 5071–5082, https://doi. org/10.1016/j.actamat.2008.06.021. [5] T. Christiansen, M.A.J. Somers, Controlled dissolution of colossal quantities of nitrogen in stainless steel, Metall. Mater. Trans. A. 37 (2006) 675–682, https://doi. org/10.1007/s11661-006-0039-5. [6] J. Oddershede, T.L. Christiansen, K. Stahlc, M.A.J. Somers, Extended X-ray absorption fine structure investigation of nitrogen stabilized expanded austenite, Scripta Mater. 62 (2010) 290–293, https://doi.org/10.1016/j.scriptamat.2009.11. 021. [7] Y. Qiao, J. Chen, H. Zhou, Y. Wang, Q. Song, H. Li, Z. Zheng, Effect of solution treatment on cavitation erosion behavior of high-nitrogen austenitic stainless steel, Wear. 424–425 (2019) 70–77, https://doi.org/10.1016/j.wear.2019.01.098. [8] T.S. Hummelshøj, T.L. Christiansen, M.A.J. Somers, Lattice expansion of carbonstabilized expanded austenite, Scripta Mater. 63 (2010) 761–763, https://doi.org/ 10.1016/j.scriptamat.2010.05.031. [9] B.K. Brink, K. Ståhl, T.L. Christiansen, J. Oddershede, G. Winther, M.A.J. Somers, On the elusive crystal structure of expanded austenite, Scripta Mater. 131 (2017) 59–62, https://doi.org/10.1016/j.scriptamat.2017.01.006. [10] B.K. Brink, K. Ståhl, T.L. Christiansen, C. Frandsen, M.F. Hansen, M.A.J. Somers, Composition-dependent variation of magnetic properties and interstitial ordering in homogeneous expanded austenite, Acta Mater. 106 (2016) 32–39, https://doi.org/ 10.1016/j.actamat.2015.12.043. [11] Y. Kong, R.J. Zhou, F.S. Li, Spin-polarized linear muffin-tin orbitals calculation of the interstitial-atom effect in γ-Fe4Z (Z=H, C, N), Phys. Rev. B. 54 (1996) 5460,

4. Conclusions A 32-atom supercell of the Fe20Cr6Mn6 system with an octahedral interstice in the center has been built. The Fe20Cr6Mn6 alloys are defined as two structural models: one where six Cr atoms form the central octahedron (I-Cr alloy) and the other where six Mn atoms form the central octahedron (I-Mn alloy). N or C atoms in interstitial sites change the phase stability of the Fe20Cr6Mn6 alloys. The I-Cr-Nx alloys are more stable than the I-Cr-Cx and I-Mn-Nx alloys, and the I-Cr-Cx and IMn-Nx alloys are more stable than the I-Mn-Cx alloys (with the same value of x). The supercell volumes increase linearly with the content of C/N in the supercells. The linear lattice expansion coefficients (in nm/ mass%) of I-Cr-Nx, I-Mn-Nx, I-Cr-Cx and I-Mn-Cx are 0.0030, 0.0031, 0.0037 and 0.0036, respectively. The lattice expansion coefficient of the Fe-Cr-Mn-C system is slightly larger than that of the Fe-Cr-Mn-N system. The bond length of Mn-C/N or Cr-C/N in the octahedral interstice, not as the supercell volumes, does not increase linearly with the content of N/C, especially in I-Mn-N and I-Cr-N alloys. The magnetic moments of the Fe20Cr6Mn6 alloys without interstitial atoms (C/ N) are close to zero. After the C/N solid solution, the magnetic moments of the I-Mn-Cx/Nx and I-Cr-Cx/Nx alloys increase slightly and the values of the magnetic moments of these alloys range from 0.42 μB/cell to 7

Journal of Magnetism and Magnetic Materials 504 (2020) 166663

Z. Lv, et al.

[24] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B. 13 (1976) 5188–5192, https://doi.org/10.1103/physrevb.13.5188. [25] Z. Lv, S. Xiao, Z. Xiao, L. Qian, W. Wang, Y. Zhou, W. Fu, Structural properties and bonding characteristic of interfaces between VN and VC from density functional calculations, J. Alloy Compd. 718 (2017) 139–149, https://doi.org/10.1016/j. jallcom.2017.04.325. [26] D. Zhao, Y. Zhou, J. Fan, T. Liu, Y. Nie, W. Fu, Z. Lv, Structural properties and phase stability of primary Y phase (Ti2SC) in Ti-stabilized stainless steel from experiments and first principles, Materials. 12 (2019) 1118, https://doi.org/10.3390/ ma12071118. [27] B. Wang, Q. Zhang, Z.F. Zhang, Z.Q. Lv, W.T. Fu, Effect of Cr on electronic and magnetic properties of χ-carbide (Fe, Cr)5C2, J. Magn. Magn. Mater. 392 (2015) 1–5, https://doi.org/10.1016/j.jmmm.2015.05.023. [28] M.W. Guo, Z.Q. Lv, M.G. Qv, Z.P. Shi, W.T. Fu, Structural, electronic and magnetic properties of χ-carbides Fe5-xMnxC2 (x=1–5) from density-functional theory calculations, Solid State Sci. 26 (2013) 110–114, https://doi.org/10.1016/j. solidstatesciences.2013.09.001. [29] M. Aoki, H. Yamane, M. Shimada, T. Kajiwara, Single crystal growth of Mn2N using an In-Na flux, Mater. Res. Bull. 39 (2004) 827–832, https://doi.org/10.1016/j. materresbull.2004.02.014. [30] Z. Lv, Z. Shi, Y. Gao, Z.H. Wang, S. Shu, W. Fu, Electronic and elastic properties of εphases Cr2-xVxN (x = 0, 1, 2) from density-functional calculations, J. Alloys Compd. 583 (2014) 79–84, https://doi.org/10.1016/j.jallcom.2013.08.116. [31] F.D. Murnaghan, The compressibility of media under extreme pressures, Proc. Natl. Acad. Sci. USA 30 (1944) 244–247, https://doi.org/10.2307/87468. [32] H. Kahn, G. Michal, F. Ernst, A.H. Heuer, Poisson effects on X-ray diffraction patterns in low-temperature-carburized austenitic stainless steel, Metall. Mater. Trans. A. 40 (2009) 1799–1804, https://doi.org/10.1007/s11661-009-9814-4. [33] L. Cheng, A. Bottger, T.H. de Keijser, E.J. Mittemeijer, Lattice parameters of ironcarbon and iron-nitrogen martensites and austenites, Scripta Mater. 24 (1990) 509–514, https://doi.org/10.1016/0956-716X(90)90192-J. [34] Y. Sun, X. Li, T. Bell, Structural characteristics of low temperature plasma carburised austenitic stainless steel, Mater. Sci. Technol. 15 (1999) 1171–1178, https://doi.org/10.1179/026708399101505077. [35] Z.Q. Lv, F.C. Zhang, S.H. Sun, Z.H. Wang, P. Jiang, W.H. Zhang, W.T. Fu, Firstprinciples study on the mechanical, electronic and magnetic properties of Fe3C, Comput. Mater. Sci. 44 (2008) 690–694, https://doi.org/10.1016/j.commatsci. 2008.05.006.

https://doi.org/10.1103/PhysRevB.54.5460. [12] E.L. Peltzer, Y. Bianca, J. Desimoni, N.E. Christensen, Electronic structure of FCCFenX (X=C, N; n=4, 8) alloys, Physica B: Condensed Matter. 354 (2004) 341–344, https://doi.org/10.1016/j.physb.2004.09.075. [13] A. Leineweber, T. Hickel, B. Azimi-Manavi, S.B. Maisel, Crystal structures of Fe4C vs. Fe4N analysed by DFT calculations: Fcc-based interstitial superstructures explored, Acta Mater. 140 (2017) 433–442, https://doi.org/10.1016/j.actamat.2017. 08.059. [14] A.V. dos Santos, C.A. Samudio Perez, Ab initio investigation of the substitution effects of 2p elements on the electronic structure of γ-Fe4X (X = B, C, N, and O) in the ground state, J. Mater. Res. 31 (2016) 202–212, https://doi.org/10.1557/jmr. 2015.394. [15] Z.Q. Lv, Y. Gao, S.H. Sun, M.G. Qv, Z.H. Wang, Z.P. Shi, W.T. Fu, Electronic, magnetic and elastic properties of γ-Fe4X (X = B/C/N) from density functional theory calculations, J. Magn. Magn. Mater. 333 (2013) 39–45, https://doi.org/10. 1016/j.jmmm.2012.02.114. [16] J. Liu, P. Han, M. Dong, G. Fan, G. Qiao, J. Yang, Influence of Ni and N on generalized stacking-fault energies in Fe–Cr–Ni alloy: a first principle study, Physica B: Condensed Matter. 407 (2012) 891–895, https://doi.org/10.1016/j.physb.2011.12. 111. [17] F. Dong, First-Principles Study of Cr-Mn Steels Austenitic Point Defects, Yanshan University, D. China, 2014. [18] Y. Zhou, Y. Li, W. Wang, L. Qian, S. Xiao, Z. Lv, Effect of interstitial nitrogen in Fe18Cr6Mn8 austenitic alloys from density functional theory, J. Magn. Magn. Mater. 463 (2018) 57–63, https://doi.org/10.1016/j.jmmm.2018.05.034. [19] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965) A1133–A1138, https://doi.org/10.1103/PhysRev. 140.A1133. [20] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Phys. Rev. B. 136 (1964) 864–871, https://doi.org/10.1103/physrev.136.b864. [21] J.A. White, D.M. Bird, Implementation of gradient-corrected exchange-correlation potentials in Car-Parrinello total-energy calculations, Phys. Rev. B. 50 (1994) 4954–4957, https://doi.org/10.1103/PhysRevB.50.4954. [22] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868, https://doi.org/10.1103/ physrevlett.77.3865. [23] D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B. 41 (1990) 7892–7895, https://doi.org/10.1103/ PhysRevB.41.7892.

8