First-principles investigation on the elastic, magnetic and electronic properties of MFe3N (M = Fe, Ru, Os)

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Chemical Physics Letters 449 (2007) 96–100 www.elsevier.com/locate/cplett

First-principles investigation on the elastic, magnetic and electronic properties of MFe3N (M = Fe, Ru, Os) Erjun Zhao a

a,b

, Hongping Xiang

a,b

, Jian Meng a, Zhijian Wu

a,*

Key Laboratory of Rare Earth Chemistry and Physics, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, PR China b Graduate School, Chinese Academy of Sciences, Beijing 100049, PR China Received 4 July 2007; in final form 10 October 2007 Available online 13 October 2007

Abstract The elastic, magnetic and electronic properties of MFe3N (M = Fe, Ru, Os) are investigated via first-principles calculations. The calculated results are in agreement with the experimental and other theoretical data. The high ratios of bulk modulus to shear modulus 2.7, 2.0, and 1.8 for c 0 -Fe4N, RuFe3N, and OsFe3N, respectively, indicate that they have good ductility. c 0 -Fe4N possesses the largest B/C44 (3.41) ratio, which suggests that it is much prone to shearing. The net magnetic moment per formula unit decreases from 9.90 for c 0 Fe4N, 7.66 for RuFe3N, to 6.80 lB for OsFe3N.  2007 Elsevier B.V. All rights reserved.

1. Introduction Transition-metal nitrides are of great importance due to its potential technological applications as high density magnetic recording materials [1–4]. In addition, some nitrides exhibit significantly high electrical resistivity and wear resistance [5]. Thus, this class of compounds has been the subject of experimental and theoretical studies from the point of chemical, thermal, mechanical, electrical and magnetic properties as well as microstructure [4–11]. Among these nitrides, c 0 -Fe4N has been investigated intensively by both theories [8–10,12–15] and experiments [3– 5,11,16–19]. The structure of c 0 -Fe4N is of the perovskitetype (space group Pm 3m). In the structure, one Fe is located at the corners with Wyckoff site 1a (denoted as Fe1a), the other three Fe atoms occupy the face centers with Wyckoff site 3c (denoted as Fe3c), while the nitrogen atoms occupy the body center with Wyckoff site 1b. In order to improve the magnetic properties of c 0 -Fe4N, its derivatives MFe3N

*

Corresponding author. Fax: +86 431 569 8041. E-mail address: [email protected] (Z. Wu).

0009-2614/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.10.036

(M = Ni, Pd, Pt, Co, Rh, Ir, Ru, Os) have been studied recently [8]. These compounds are isostructural to c 0 Fe4N, in which Fe–N layers are interleaved with Fe–M layers, while M atoms can substitute either Fe1a or Fe3c atoms. Further studies indicated that the atoms with larger atomic radius than that of Fe, such as Ru, Rh, Pd, Os, Ir, Pt, will occupy the 1a site [8–10]. Among these compounds, RhFe3N was predicted to be thermodynamically stable [8]. Later on, RhFe3N was synthesized experimentally [7], which confirmed the theoretical prediction [8]. For RhFe3N, the net or saturation magnetic moment was 8.3 lB per formula unit, and Curie temperature was about 505 K [7]. For IrFe3N, it was theoretically predicted to be unstable, but it is accessible for pressures higher than 37 GPa [8]. The physical properties of MFe3N (M = Co, Rh, Ir, Ni, Pd, Pt) have been investigated theoretically [20,21]. It was found that these compounds possess large ratios of bulk modulus to C44, indicating that they possess good ductibility. Therefore, they have the potential technological applications such as solid lubricants and microelectromechanical systems devices [20,21]. Although there are many studies available for c 0 -Fe4N, the studies on RuFe3N and OsFe3N are far and few between [8–10],

E. Zhao et al. / Chemical Physics Letters 449 (2007) 96–100

in particular for the mechanical properties. Since MFe3N (M = Fe, Ru, Os) phases possess fascinating physical properties, it is our motivation to study the electronic, magnetic and mechanical properties of the three compounds systematically. 2. Computational method All the calculations conducted in this Letter were in the presence of spin-polarization and performed within the CASTEP code [22], based on the density functional theory. Relativistic corrections are not included. The code is suitable for calculations using periodic boundary conditions to infinite lattice system. The Vanderbilt ultrasoft pseudopotential [23], which describes the interaction of valence electrons with ions, was used with the same cutoff energy of 500 eV. The Brillouin zone was employed by a 10 · 10 · 10 Monkhorst-Pack scheme of k-points mesh [24]. The exchange and correlation functional were treated by the generalized gradient approximation (GGA-PBE) [25]. Formation enthalpy was calculated from DH = E(MFe3N)E(solid M)2E(solid Fe)E(solid FeN). For the self-consistent field iterations, the convergence tolerance for geometry optimization were selected as the difference in total energy, the maximum ionic Hellmann– Feynman force, the stress tensor, and the maximum dis˚, placement being within 5.0 · 106 eV/atom, 0.01 eV/A ˚ , respectively. The calculated 0.02 GPa, and 5.0 · 104 A bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio were from the Voigt–Reuss–Hill approximations [26–28]. For the studied compounds, the crystal structure is assumed to be cubic Pm 3m (No. 221) for RuFe3N and OsFe3N (Fig. 1).

Fig. 1. Crystal structure of MFe3N (M = Fe, Ru, Os) in space Pm3m. Nitrogen atom occupies the body center with Wyckoff site 1b, iron atoms occupy the face centers with Wyckoff site 3c, while M occupies the corners with Wyckoff site 1a.

97

3. Results and discussion From Table 1, the calculated lattice parameters for c 0 Fe4N deviate by 0.7–0.8% to the experimental values [3,11], and by 1.4% to the previous theoretical values [8]. For RuFe3N and OsFe3N, our calculated lattice constants deviate by 4.1% to the previous theoretical values [8]. The calculated formation enthalpies are 0.0228, 0.6770, and 1.0612 eV for c 0 -Fe4N, RuFe3N, and OsFe3N, respectively. This is consistent with the corresponding theoretical data from the GGA calculation 0.0207 eV (2 kJ/mol), 0.6633 eV (64 kJ/mol), and 1.1193 eV (108 kJ/mol) [8]. From these data, it is evident that c 0 -Fe4N phase is thermodynamically stable due to its negative formation enthalpy. This is in agreement with the fact that c 0 -Fe4N phase was synthesized experimentally [3,11]. For RuFe3N and OsFe3N, the positive formation enthalpy indicates that they are thermodynamically unstable under ambient conditions. Similar to IrFe3N with positive formation enthalpy [8], high pressure and/or high temperature might be necessary to synthesize the two compounds. The key criteria for mechanical stability of a crystal are that the strain energy must be positive, which for a cubic crystal means that the elastic stiffness constants should satisfy the following criteria [29]: C11 > 0;

C44 > 0;

C11  C12 > 0; and C11 þ 2C12 > 0

From Table 1, it is seen that the elastic stiffness constants of the MFe3N phases satisfy the above conditions, implying that they are mechanically stable. The calculated bulk modulus of c 0 -Fe4N is 199.4 GPa, which is reasonable compared with the experimental values (155 [16], 196.1 [18], and 175.7 GPa [17]) and the previous theoretical values (172 [7], 162 GPa [21]). For RuFe3N and OsFe3N, the calculated bulk moduli are 198.6 and 239.7 GPa, respectively. Shear modulus and Young’s modulus increase from c 0 -Fe4N to OsFe3N. For OsFe3N, the calculated bulk modulus 239.7 GPa, shear modulus 132.9 GPa, and Young’s modulus 336.5 GPa are larger than those of c 0 Fe4N and MFe3N (M = Ru, Co [20], Rh [20], Ir [20], Ni [21], Pd [21], Pt [21]), while the Possion’s ratio is smaller. These indicate that OsFe3N is very promising to be used in the microelectromechanical devices. The calculated ratios of bulk modulus B to shear modulus G (or B/C44) are 2.71 (3.41), 1.98 (2.27), and 1.80 (1.89) for c 0 -Fe4N, RuFe3N, and OsFe3N, respectively. Pugh [30] proposed that the ratio of B/G represents a measure for machinable behavior. A high B/G value is associated with ductibility and the low value indicates brittleness. The critical value which separates ductile and brittle is at about 1.75. Based on Pugh’s notion [30], these compounds are ductile, which may have technological applications. The large B/G ratio was a result of the strong coupling within the Fe–N layer and the weak coupling between the Fe–N and Fe–M layers [21]. c 0 -Fe4N possesses the largest ratio of B/C44 (3.41) among MFe3N (M = Ru,

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E. Zhao et al. / Chemical Physics Letters 449 (2007) 96–100

Table 1 ˚ ), cell volume per formula unit V (A ˚ 3), elastic stiffness constants Cij (GPa), Calculated formation enthalpy per formula unit DH (eV), lattice parameters a (A bulk modulus B (GPa), shear modulus G (GPa), Young’s modulus E (GPa), Poisson’s ratio t, the local magnetic moment (lB) mM for M (M = Fe1a, Ru, Os), mFe for Fe (Fe3c site for c 0 -Fe4N), mN for N, and mTot (lB) for total magnetic moment per formula unit of MFe3N from the GGA-PBE calculation DH

a

V

C11

0.0228

3.765 3.797a 3.790c

53.37

337

C44

C12

B

G

131

199.4 175.7b 196d 155e 172g 162h

E

t

mM

mFe

mN

mTot

197

0.336

2.96 2.98a

2.30 2.01a

3.01f 2.84i,j 2.98k 3.10l 3.07m 2.98n

2.44f 2.25i,j 2.23k 1.94l 2.03m 1.79n

0.01m 0.02n

10.3f 9.63i,j 9.68k 8.92l 9.15m 8.39n

0

c -Fe4N GGA Exp.

Calc.

RuFe3N GGA Calc. OsFe3N GGA Calc. a b c d e f g h i j k l m n

Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref.

0.0207f

58.5

54.44c

3.817f

0.6770 0.6633f

3.792 3.85f

54.52

363

1.0612 1.1193f

3.778 3.82f

53.93

430

87.4

127

73.6

0.04

i,j

0.04 0.01k

9.90 9.01a

117

198.6

100.3

258

0.284

0.74 0.68j

2.30 1.89j

0.02 0.03j

7.66 6.39j

145

239.7

132.9

337

0.266

0.52 0.17i

2.08 1.60i

0.04 0.13i

6.80 5.1i

[11]. [17]. [3]. [18]. [16]. [8], from GGA calculation. [7], from GGA calculation. [21], from GGA calculation. [9], from GGA calculation. [10], from GGA calculation. [13], from local-spin-density approximation (LSDA) formulated by von Barth and Hedin, and parameterized by Janak (vBHJ). [14], from LSDA calculation. [12], from LSDA calculation formulated by vBHJ. [15], from LSDA calculation formulated by vBHJ.

Os, Co [20], Rh [20], Ir [20], Ni [21], Pd [21], Pt [21]), while OsFe3N has the smallest B/C44 value (1.89). This indicates that c 0 -Fe4N is much easier to shearing. The local magnetic moments for the MFe3N (M = Fe, Ru, Os) phases were given in Table 1. For c 0 -Fe4N, the calculated magnetic moment 2.96 lB at Fe1a site is 0.66 lB larger than 2.30 lB at Fe3c site. This is because Fe3c forms stronger covalent bonding with N atom than Fe1a, as explained in later section. The average magnetic moment per Fe atom in c 0 -Fe4N is 2.21 lB from the experiment [5], in agreement with our calculated value 2.48 lB. For RuFe3N, the total magnetic moment is 7.66 lB, with local magnetic moment of 0.74 lB for Ru, 2.30 lB for Fe and 0.02 lB for N. For OsFe3N, the local magnetic moments are 0.52, 2.08, and 0.04 lB for Os, Fe, and N, respectively. Although N and Fe (3c site for c 0 -Fe4N) have nearly the same magnetic moment for the three compounds, dramatic decrease of the magnetic moment of M at 1a site is observed, i.e., from 2.96 lB for Fe1a in c 0 Fe4N, 0.74 lB for Ru in RuFe3N to 0.52 lB for Os in OsFe3N. Thus, with the substitution of Ru and Os, the reduction of the total magnetic moment is from 9.90 lB per formula unit for c 0 -Fe4N, 7.66 lB for RuFe3N to 6.80 lB for OsFe3N.

The calculated partial and total density of states (DOS) of MFe3N (M = Fe, Ru, Os) were shown in Fig. 2. For c 0 Fe4N, the number of electrons at the Fermi level comes mainly from the spin down channel of the Fe 3d electrons (Fig. 2a). In the energy region from 1.0 to 0.0 eV of the spin up channel, there exists strong interaction between Fe3c 3d and N 2p orbitals, indicating the strong covalent bonding between Fe3c and N, while Fe1a 3d orbital does not hybridize with N 2p orbital in the same energy region. This is the reason that the magnetic moment of Fe1a (2.96 lB) is 0.66 lB larger than that of Fe3c (2.30 lB). For RuFe3N and OsFe3N (Fig. 2b and c), at the energy region from 1.0 to 0.0 eV of the spin up channel, besides the hybridization between Fe 3d and N 2p orbitals, M d orbitals are also hybridized strongly with N 2p orbital. This suggests that the covalent bonding between M (M = Ru, Os) and N is much stronger compared with Fe1a (in c 0 Fe4N) and N, which explains the reduction of magnetic moment for Ru and Os compared with Fe1a. In addition, the total density of states (TDOS) show that from 5.0 to 0.0 eV, there exists strong interaction between M d orbitals and Fe 3d orbitals. The TDOS show no energy gap at the Fermi energy level, indicating the metallic nature of the three compounds.

E. Zhao et al. / Chemical Physics Letters 449 (2007) 96–100

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Fig. 3. Enthalpy-pressure relationship between MFe3N (M = Ru, Os) and their initial reactants from the GGA-PBE calculation. (a) RuFe3N; (b) OsFe3N.

modynamically stable above 73 and 93 GPa, respectively. This is much higher than the 37 GPa of IrFe3N [8]. 4. Conclusions

Fig. 2. Partial and total density of states of (a) Fe4N; (b) RuFe3N; (c) OsFe3N from the GGA-PBE calculation. Vertical dotted lines at zero indicate the Fermi energy level.

Finally, since the formation enthalpy for RuFe3N (0.6770 eV) and OsFe3N (1.0612 eV) are positive, we studied the formation enthalpy as a function of pressure (Fig. 3). It is seen that RuFe3N and OsFe3N become ther-

The physical properties of MFe3N (M = Fe, Ru, Os) were studied by using the density functional theory. Our calculations indicate that the calculated quantities are in agreement with the available experimental and theoretical values. The high B/G values suggest that they are ductile. In particular, c 0 -Fe4N possesses the largest ratio of B/C44 (3.41), indicating that it is much prone to shearing. OsFe3N has the highest bulk and shear modulus among the studied compounds. The three compounds are ferromagnetic with the calculated magnetic moments per formula unit decreasing from 9.90, 7.66 to 6.80 lB for c 0 -Fe4N, RuFe3N and OsFe3N, respectively. The RuFe3N and OsFe3N phases may be accessible at pressures above 73 and 93 GPa, respectively. The obtained results might be interesting from the viewpoint of technological applications, because in addition to the traditional use of the magnetic phase, the damage tolerant properties have potential applications in

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microelectromechanical devices. We hope that our study could provide useful information for further experimental studies.

[10] [11] [12] [13]

Acknowledgement

[14]

The authors thank the National Natural Science Foundation of China for financial support (Grant Nos. 20773117, 20331030 and 20571073).

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