A systematic, first-principles study of the structural preference and magnetic properties of mononitrides of the d-block metals

A systematic, first-principles study of the structural preference and magnetic properties of mononitrides of the d-block metals

Journal of Alloys and Compounds 603 (2014) 172–179 Contents lists available at ScienceDirect Journal of Alloys and Compounds journal homepage: www.e...

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Journal of Alloys and Compounds 603 (2014) 172–179

Contents lists available at ScienceDirect

Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom

A systematic, first-principles study of the structural preference and magnetic properties of mononitrides of the d-block metals Valty´r Freyr Hlynsson a, Egill Skúlason a,b, Anna L. Garden a,⇑ a b

Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland

a r t i c l e

i n f o

Article history: Received 16 December 2013 Received in revised form 20 February 2014 Accepted 24 February 2014 Available online 5 March 2014 Keywords: Transition metal nitrides Rocksalt Zincblende Lattice constants Magnetic moments

a b s t r a c t First principles calculations are used to investigate the structural properties of mononitrides of the 3d, 4d and 5d transition metals (Groups III-XI), in the rocksalt (NaCl) and zincblende (ZnS) crystal structures. Trends in lattice constants and stability are established. Magnetic properties of 3d transition metal mononitrides are investigated, both at equilibrium and under conditions of compression and strain. The present study represents a consistent reference set of the properties of transition metal mononitrides, calculated within the same theoretical framework. Such a consistent data set is of great use in comparing and contrasting properties of the various transition metal nitrides. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Transition metal (TM) mononitrides have been gathering increasing interest by researchers in recent times. Such nitrides often exhibit interesting structural properties, for example high hardness, brightness and melting point [1,2]. TM mononitrides can take on various crystal structures. For most nitrides, the natural structure has been reported as the cubic rocksalt (NaCl, RS) structure or zincblende (ZnS, ZB) structure, however, other structures such as the hexagonal wurtzite structure are possible [3]. It is commonly believed that, in general, the early transition metal mononitrides adopt the RS structure and the later nitrides adopt the ZB structure. However, there exist many reports that contradict this assumption. For example, RuN, a Group VIII metal nitride, was reportedly synthesized in the RS phase using laser ablation [4]. Furthermore, different structures have been obtained depending on synthesis method; films of ZB CoN have been grown under Ar/N2 [5], whereas RS CoN has been reported by decomposition of Co(NH2)3 [6]. It is thus evident that these assumed trends do not hold in all cases and a more detailed investigation into the structural preference is desirable. There have been a number of first-principles studies undertaken to elucidate the likely crystal structure and resulting properties of the TM mononitrides. Widely varying results of the ⇑ Corresponding author. Tel.: +354 7719551. E-mail address: [email protected] (A.L. Garden). http://dx.doi.org/10.1016/j.jallcom.2014.02.153 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.

structural properties also exist; for example, the RS phase of TiN has been calculated to have a lattice constant of between 4.18 and 4.32 Å[7,8] and the ZB phase of FeN between 4.23 and 4.36 Å[9,10]. Clearly, the structural properties of TM mononitrides are highly dependent on the theoretical model used. To date, there is no study that calculates the properties of all TM nitrides with the same theoretical method, thus comparison of the various TM nitrides and establishing trends is difficult. Nitrides of the 3d transition metals have been shown to exhibit interesting magnetic properties [11]. It has been suggested that ferromagnetic nitrides have the potential to act as a source of spin injection in non-magnetic semiconductors for use in spintronics [12,13]. Mononitrides seem particularly promising in this regard as previous studies on FexNy noted increasing magnetization with decreasing nitrogen content [14]. There have been few experimental studies of the magnetic properties of the transition metal nitrides. Both RS and ZB phases of FeN have been investigated experimentally and found to be non-magnetic and antiferromagnetic, respectively [15]. ZB CoN has been found to be paramagnetic in character [5]. To the authors’ knowledge, the only strongly magnetic transition metal nitrides that have been studied experimentally are MnN and CrN, both in the RS phase [16,17]. Both were found to be antiferromagnetic, with magnetic moments of 3.3 and 2.4 lB for MnN and CrN, respectively. Several theoretical calculations have been performed on a selection of the 3d TM mononitrides. The calculated magnetic moment of RS MnN was found to be in good agreement with experiment

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[18]. CoN has been studied in both RS and ZB phases and found to be non-magnetic up until a critical volume, after which the magnetism increases quickly [9,19]. Similar behavior was found for ZB FeN [19]. While it is clear from the above examples that a number of studies exist on various structural and magnetic properties of TM nitrides, these are conducted under different experimental conditions or with different computational approaches and the results are not necessarily consistent. In the design of a material for a desired application it is useful to have an overview of trends in predicted properties so that the most appropriate material can be selected. The motivation of the present work is to present a comprehensive and systematic study of the structural and magnetic properties of the 3d, 4d, and 5d transition metal mononitrides, all calculated within the same theoretical framework, which is currently lacking in the literature. Reasonably comprehensive theoretical studies of the 4d and 5d TM mononitrides have been undertaken by Chen and Jian, but with different DFT functionals (LDA, PBE) as used here [20]. A similar study was undertaken by Brik and Ma of some of the 3d TM mononitrides, but only the weakly magnetic nitrides and only the rock salt phases were considered [21]. Herein we will pay particular attention to these works and compare with the current functional (RPBE). The chosen RPBE functional is often used in the calculation of surface reactions as it has been shown to yield more accurate adsorption energies than the conventional PBE [22]. Thus the outcomes of this work are twofold. Firstly, we will obtain a full and consistent set of the structural and magnetic properties of TM mononitrides and establish trends across the periodic table. Secondly, by comparing our RPBE results to previous PBE and LDA results we will obtain insight into the magnitude of effects caused by the choice of functional, which can aid in interpretation of other theoretical works.

2. Methodology Calculations were carried out using density function theory (DFT) using the Vienna ab initio Simulation Package (VASP) [23] and the revised Perdew–Burke– Ernzerhof (RPBE) functional approximation [22]. The valence electrons were represented with a plane-wave basis with an energy cutoff of 350 eV and 6  6  4 Monkhorst-Pack k-point sampling. The different numberp offfiffiffi k-points pffiffiffi used in each direction reflects the dimensions of the simulation cell (a= 2; a= 2, a). For calculations of magnetic moments the energy cutoff and k-points were increased to 400 eV and 8  8  8, respectively. The SCF convergence threshold was set to 1  107 eV. The interaction between ions and electrons is described by the projector-augmented wave (PAW) method [24,25].

3. Results and discussion 3.1. 4d and 5d transition metal mononitrides 3.1.1. Lattice constants Results for the 4d and 5d TM mononitrides will be presented first, as these are known to be non-magnetic and thus simpler. The calculated lattice constants are presented in Tables 1 and 2. TcN was excluded from this study due to the nonexistance of Tc in nature. Experimental measurements of the lattice constants for 4d and 5d nitrides are rather scarce and comparison is only possible for YN, ZrN, NbN, HfN, TaN [26] and RuN [4], all in the RS phase. For all except RuN, RPBE overestimates the lattice constant by 0.07–0.11 Å. The lattice constant of RuN is underestimated by 0.07 Åusing RPBE. In comparison with the PBE functional as calculated by Chen et al. and Stampfl et al., the lattice constant calculated using RPBE is larger [20,7]. As PBE can be seen to underestimate the experimental lattice constant, the use of both RPBE and PBE could represent an upper and lower bound to the experimental lattice constant. Both RS and ZB lattice constants of the 4d and 5d nitrides as a function of number of d-electrons are shown pictorially in Fig. 1. The first point of note is that, for a given TM mononitride, the lattice constant of the ZB phase is consistently larger than that of the RS phase, by 0.3 Å. This is consistent with the coordination of the atoms in each structure. In the RS structure the atoms occupy octahedral sites and are thus 6-coordinate, whereas the atoms in the ZB structure occupy tetrahedral sites and are 4-coordinate. Thus the atoms in the ZB crystal are less strongly-bonded and the crystal is somewhat larger. The lattice constant for both crystal structures decreases across the period up until RuN (Group VIII in Period 4) and WN (Group VI in Period 5) after which it increases again. This can be rationalized by considering the occupation of the bonding and antibonding states. At the minimum lattice constant all binding states are full and all antibonding states are empty. As the number of d-electrons increases, antibonding states become occupied and the binding in the crystal becomes weaker, resulting in a larger lattice constant [20]. A curious result is noted for the RS phase of the 5d nitrides; WN, ReN and OsN are calculated with RPBE to all have the same lattice constant, in contrast to an obvious variation exhibited in the data set of Chen et al. when calculated using PBE and CASTEP (see Table 2). However, when the previous study was refined using PBE and VASP Chen et al. also noted the similarity of the lattice constants for RS WN, ReN and OsN, showing that this is not an artifact of the RPBE functional.

Table 1 Calculated lattice constants (a, in Å) of 4d transition metal mononitrides.

Rocksalt This work Prev. calc.

Functional

YN

ZrN

NbN

MoN



RuN

RhN

PdN

AgN

RPBE LDAa PBEa PW91c

4.95

4.85 4.88

4.65 4.57 4.52 4.57 4.54

4.48 4.41 4.36 4.42 4.39

4.40 4.33 4.27 –

– – – –

4.38 4.29 4.22, 4.32b – 4.45b

4.38 4.35 4.30 –

4.47 4.40 4.33 –

4.70 4.59 4.50 –

5.35 – – 5.19

5.03 4.95 4.89 4.90

4.81 4.75 4.70 4.70

4.68 4.64 4.58 4.58

– – – –

4.60 4.56 4.50 4.47

4.65 4.53 4.47 4.51

4.79 4.63 4.58 4.62

4.99 4.71 4.64 4.79

Expt.d Zincblende This work Prev. calc.

a b c d e

From From From From From

Ref. Ref. Ref. Ref. Ref.

RPBE LDAa PBEa LDSAe [20] unless otherwise stated. [4]. [7]. [26] unless otherwise stated. [32].

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Table 2 Calculated lattice constants (a, in Å) of 5d transition metal mononitrides.

Rocksalt This work Prev. Calc.

Zincblende This work Prev. Calc. a b c

Functional



HfN

TaN

WN

ReN

OsN

IrN

PtN

AuN

RPBE LDAa PBEa PW91b Expt.c

– – – –

4.57 4.56 4.49 4.54 4.52

4.44 4.40 4.39 4.42 4.39

4.37 4.46 4.43 –

4.37 4.31 4.26 –

4.37 4.33 4.28 –

4.40 4.41 4.36 –

4.54 4.50 4.44 –

4.74 4.68 4.60 –

RPBE LDAa PBEa

– – -

4.95 5.02 4.97

4.79 4.74 4.73

4.70 4.73 4.71

4.64 4.57 4.54

4.62 4.57 4.52

4.68 4.64 4.60

4.82 4.79 4.73

5.03 4.99 4.91

From Ref. [20]. From Ref. [7]. From Ref. [26].

5.4

ZB

5 4.8 4.6 4.4 4.2 YN

ZrN

RS ZB

5.2

Lattice constant / Å

5.2

Lattice constant / Å

5.4

RS

5 4.8 4.6 4.4 4.2 HfN

NbN MoN RuN RhN PdN AgN

TaN

WN

ReN OsN

IrN

PtN

AuN

Fig. 1. Calculated lattice constants of 4d (left) and 5d (right) transition metal mononitrides in the rocksalt (RS) and zincblende (ZB) phases.

3.1.2. Phase preference The relative stability of the RS and ZB phases can be evaluated from the transition pressure of phase transformations. In this work the ZB to RS transition pressure is estimated using the common tangent method whereby the variation in energy with volume is plotted for each phase and the negative of the slope of the tangent line common to both curves represents the transition pressure. Two examples (NbN and PdN) are shown in Fig. 2 and the remaining plots are given in the Supplementary information. ZB to RS transition pressures for all 4d and 5d mononitrides are given in Table 3 and pictorially in Fig. 3. A negative transition pressure indicates that the RS phase is more stable that the ZB phase. From Fig. 3 it is apparent that the early transition metal mononitrides are indeed more stable in RS form, with YN, ZrN, NbN, HfN and TaN

−9.5

all exhibiting negative ZB to RS transition pressures. As the number of d-electrons increases the transition pressure becomes positive and thus the ZB structure is favored. The magnitude of the transition pressure indicates the degree of stability; for the 4d mononitrides the highest transition pressure occurs for RuN, suggesting that it has the highest preference for ZB structure. For the 5d nitrides this occurs for OsN. After these points the transition pressure decreases again and for AgN it is negative, indicating that the RS form is again more favorable. It is interesting to note that the 5d nitrides in general have larger transition pressures. This implies a much stronger preference for ZB for the 5d nitrides. Previous calculations of the transition pressures by Chen et al. are also presented in Table 3 [20]. In general, the RPBE calculated transition pressures of this work are lower than the previous

−5.2

RS

RS

ZB

ZB

−5.3

Energy per atom / eV

Energy per atom / eV

−9.6 −9.7 −9.8 −9.9 −10

−5.4 −5.5 −5.6 −5.7 −5.8

−10.1 18

20

22

24

26

28 3

Volume per atom / Å

30

32

18

20

22

24

26

28

30

32

3

Volume per atom / Å

Fig. 2. Energy (per atom, in eV) as a function of volume (per atom, in Å3) of rocksalt and zincblende phases of NbN (left) and PdN (right). The negative of the slope of the common tangent line yields the zincblende (ZB) to rocksalt (RS) transition pressure (5 GPa and 5 GPa for NbN and PdN, respectively).

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V.F. Hlynsson et al. / Journal of Alloys and Compounds 603 (2014) 172–179 Table 3 Zincblende to rocksalt transition pressures (in GPa) of 4d and 5d transition metal mononitrides.

This work (RPBE) Prev. Calc.a (PBE)

This work (RPBE) Prev. Calc.a (PBE) a

YN

ZrN

NbN

MoN



RuN

RhN

PdN

AgN

4

6

5

4



34

19

5

2



16

12

6



62

51

5

7



HfN

TaN

WN

ReN

OsN

IrN

PtN

AuN



5

3

5

27

49

38

11

2



5

14

2

39

89

72

11

2

study the stability is estimated by considering the energy required to form the nitride from the bulk transition metal in its most stable form and gaseous N2 according to Eq. (1).

1 DEf ¼ EðTMNÞ  ½EðTMbulk Þ þ EðN2 Þ 2

From Ref. [20].

results, calculated using PBE. However, they exhibit the same trend of the early transition metal nitrides being most stable in the RS phase and reaching a maximum at RuN and OsN. The exceptions are AuN and HfN, the relative stability of which differs between the two studies. However for AuN the absolute value is very close to zero and for HfN the previous result seems to be somewhat spurious. 3.1.3. Thermodynamic stability In Section 3.1.2 the relative stabilities of RS and ZB phases of the transition metal mononitrides were considered. However, this gives no indication of the stability of the nitride with respect to decomposition into its constituent elements. Elastic constants can be used to estimate the stability of a given nitride [20]. In this

A positive formation energy indicates that it is thermodynamically favorable for the nitride to decompose spontaneously into its constituent elements. The formation energies for the 4d and 5d mononitrides are presented in Fig. 4. Of the 4d mononitrides, YN, ZrN, NbN and MoN exhibit negative formation energies and hence should be thermodynamically stable. Fewer of the 5d nitrides are likely to be stable, with only HfN and TaN having appreciably negative formation energies. For all of these nitrides, both RS and ZB phases are stable. This result is in contrast to the stability predicted by Chen and Jiang using the elastic constants [20]. In their study, many additional nitrides were found to be stable. In addition, there have been experimental observations of some of these nitrides predicted to be unstable by the present calculations. However, it is pertinent to note that the formation energies calculated in the present study include neither free energy corrections nor kinetic barriers. The free energy corrections are likely to be similar for the TM and TMN species, so the contribution will be only from 1 N , on the order of 0.3 eV [27]. In a concurrent study, the kinetic 2 2 barriers for TM nitride decomposition have been estimated [28]. For most nitrides, the kinetic barriers to decomposition are 1 eV. Thus it is likely that the ZB phases of RuN, RhN, ReN, OsN and IrN are stable. Overall, the same trends of phase preference are observed from transition pressure and formation energy comparisons.

50

30

Transition Pressure / GPa

Transition Pressure / GPa

35

25 20 15 10 5 0 −5 −10 YN

ð1Þ

ZrN

NbN MoN RuN RhN

PdN

40 30 20 10 0 −10 HfN

AgN

TaN

WN

ReN OsN

IrN

PtN

AuN

6

6 RS

4

Formation Energy per atom / eV

Formation Energy per atom / eV

Fig. 3. Zincblende to rocksalt transition pressures of 4d (left) and 5d (right) transition metal mononitrides.

ZB

2 0 −2 −4 −6 −8 YN

ZrN

NbN

MoN RuN

RhN

PdN

AgN

RS

4

ZB

2 0 −2 −4 −6 −8 HfN

TaN

WN

ReN

OsN

IrN

PtN

AuN

Fig. 4. Formation energy (per atom) of 4d (left) and 5d (right) transition metal monotrides from the constituent elements in their most stable form (bulk metal and gaseous N2). Both rocksalt (RS) and zincblende (ZB) phases are shown. The crystal structures of the bulk metals were taken to be either bcc (Nb, Mo, Ta, W), hcp (Y, Zr, Ru, Hf, Re, Os) or fcc (Rh, Pd, Ag, Ir, Pt, Au). The lattice constants for the bulk metals are taken from Ref. [35].

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Table 4 Equilibrium lattice constants (a, in Å) of non-spin-polarized 3d transition metal mononitrides.

c

Rocksalt

Zincblende

This work.

Expt.

Prev. calc.

This work

ScN TiN CuN

4.56 4.29 4.23

4.44a 4.235a –

4.51–4.52b, 4.44c, 4.25b, 4.18c, –

4.95 4.64 4.47

ZB SP ZB NSP RS SP RS NSP

4.8

Lattice constant / Å

a b

Nitride

5

Ref. [29]. PBE, from Refs. [30,31,21]. LDA, from Ref. [21].

4.6

4.4

4.2

3.2. 3d transition metal mononitrides 3.2.1. Equilibrium properties Calculations for the 3d TM mononitrides are not as straightforward as for the 4d and 5d nitrides as the possibility of magnetic ordering must be considered. In this study, VN, CrN, MnN, FeN, CoN and NiN are treated as spin-polarized whereas ScN, TiN and CuN are not, on the basis of previous spin-polarized calculations [21]. Three magnetic orderings are considered, namely ferromagnetic (FM), antiferromagnetic (AFM) and non-magnetic (NM). Various directions of antiferromagnetic ordering are possible, depending on the crystal axis along which the spins alternate. An investigation of the energy difference between the AFM-[111], AFM-[100] and AFM-[010] solutions in MnN was conducted. It was found that the energy difference between each of these solutions, both at equilibrium and at compressed and extended cell volumes, was on the order of 0.01 eV. This difference is obviously very small and, more importantly, much smaller than the difference between these different AFM orderings and the FM and NM solutions. Thus only the computationally simpler AFM-[111] configuration is considered herein. The calculated equilibrium lattice constants are presented in Tables 4 and 5 for the non-spin-polarized and spin-polarized 3d mononitrides, respectively. Considering first the nonspin-polarized nitrides, there exists no information in the literature on the ZB phase. To the authors’ knowledge, the only

4 ScN

TiN

VN

CrN

MnN

FeN

CoN

NiN

CuN

Fig. 5. Calculated lattice constants of spin-polarized (SP) and non-spin-polarized (NSP) 3d transition metal mononitrides in both rocksalt (RS) and zincblende (ZB) phases. The spin-polarized solution corresponds to the lowest energy magnetic ordering.

experimentally-determined lattice constants are for ScN and TiN in the RS structure [29]. The calculated results of this study are in good agreement with these available experimental results, especially for TiN, where the difference is only 0.05 Å [29]. The calculated lattice constants of this work agree well with previous calculations [30,21,31]. Of the spin-polarized nitrides in Table 5, both the RS and ZB phases of NiN as well as the ZB phase of FeN and CoN were found to be non-magnetic at equilibrium, in agreement with the available previous calculations [9,19]. In both RS (AFM) and ZB (FM) phases, VN exhibits a rather low magnetic moment; accordingly the energy differences between the magnetic and non-magnetic solutions are minimal. A similar situation is observed for RS CoN, which has a magnetic moment of 0.370 lB in the lowest energy FM phase, although the lattice constants and energies are almost identical to the non-magnetic solution. The equilibrium lattice constant of RS VN has been measured experimentally and is in good agreement

Table 5 Lattice constants (a), relative energy (DE) and magnetic moment (lB ) of antiferromagnetic (AFM), ferromagnetic (FM) and non-magnetic (NM) structures of spin-polarized 3d transition metal mononitrides. a/Å

a b c d e f g h

lB

DE/eV

AFM

FM

NM

Rocksalt VN CrN MnN FeN CoN NiN

4.17 4.19 4.21 4.13 – –

– 4.20 4.20 4.17 4.04 –

4.16 4.09 4.04 4.06 4.04 4.11

Zincblende VN CrN MnN FeN CoN NiN

– 4.43 4.38 – – –

4.50 4.43 4.33 – – –

4.47 4.36 4.30 4.27 4.29 4.35

Expt.

4.15a, 4.13b

4.27d

4.31g 4.28h, 4.30

f

AFM

FM

NM

Calc.

0.00 0.00 0.00 0.00 – –

– 0.31 0.22 0.04 0.00 –

0.02 0.69 1.58 0.67 0.01 0.00

0.654 2.450 3.302 2.528 0.370e 0.000

– 0.16 0.00 – – –

0.00 0.00 0.15 – – –

0.05 0.64 0.17 0.00 0.00 0.00

0.984 2.003 2.143 0.000 0.000 0.000

From Ref. [33]. From Ref. [16]. From Ref. [17]. From Ref. [6]. Magnetic moment of FM CoN in RS phase. However, a nonmagnetic solution (lB ¼ 0:000) is equally possible. From Ref. [5]. From Ref. [15]. From Ref. [34].

Expt.

2.400b 3.300c 0.000f

0.000

c

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4

3 2.5

Magnetic moment / µB

Magnetic moment / µ B

4

VN CrN MnN FeN CoN NiN

3.5

2 1.5 1 0.5

VN CrN MnN FeN CoN NiN

3.5 3 2.5 2 1.5 1 0.5

0

0 4

4.2

4.4

4.6

4.8

4

5

4.2

4.4

Lattice constant / Å

4.6

4.8

5

5.2

5.4

5.6

Lattice constant / Å

Fig. 6. Magnitude of the magnetic moment as a function of lattice constant for spin-polarized 3d transition metal mononitrides. Both rocksalt (left) and zincblende (right) phases are shown. The equilibrium lattice constant is indicated by a black marker.

ScN

TiN −9.2

−7.5 −8 −8.5 −9 −9.5

−9.3 −9.4 −9.5 −9.6 −9.7 −9.8

20

25

30

35

40

18

20

3

22

26

28

30

16

18

20

22

24

26

Energy per atom / eV

−8.3 −8.4 −8.5 −8.6 −8.7 −8.8 −8.9

28

14

16

18

20

22

24

−7 −7.2 −7.4 −7.6 −7.8 −8 18

−8 −8.5

12

14

20

22

24 3

Volume per atom / Å

26

−5.6 −5.8 −6 −6.2 −6.4 −6.6 14

16

18

18

20

22

3

−4.3

RS ZB

12

16

Volume per atom / Å

−6.8 16

−7.5

−9 10

26

Energy per atom / eV

−6.8

28

CuN

−5.4

Energy per atom / eV

−6.6

26

−7

NiN

−6.4

24

RS − AFM RS − FM RS − NM ZB − NM

Volume per atom / Å

RS − AFM RS − FM RS − NM ZB − AFM ZB − NM

22

−6.5

3

CoN −6.2

20

FeN

−8.2

Volume per atom / Å

14

18

3

RS − AFM RS − FM RS − NM ZB − AFM ZB − FM ZB − NM

−8.1

3

12

16

Volume per atom / Å

−9 14

14

MnN RS − AFM RS − FM RS − NM ZB − AFM ZB − FM ZB − NM

−8.5 −8.6 −8.7 −8.8 −8.9 −9 −9.1 −9.2 −9.3 −9.4 −9.5 12

RS − AFM RS − FM RS − NM ZB − AFM ZB − FM ZB − NM

Volume per atom / Å

CrN

Energy per atom / eV

24

−8.7 −8.8 −8.9 −9 −9.1 −9.2 −9.3 −9.4 −9.5 −9.6 −9.7 12

3

Volume per atom / Å

Energy per atom / eV

15

Energy per atom / eV

VN

RS ZB

Energy per atom / eV

RS ZB

Energy per atom / eV

Energy per atom / eV

−7

20

22

24 3

Volume per atom / Å

26

RS ZB

−4.4 −4.5 −4.6 −4.7 −4.8 −4.9 −5 −5.1 14

16

18

20

22

24

26

28

3

Volume per atom / Å

Fig. 7. Energy (per atom in eV) as a function of volume (per atom in Å3) of rocksalt (RS) and zincblende (ZB) phases of 3d transition metal mononitrides. The negative of the slope of the common tangent line yields the zincblende to rocksalt transition pressure.

(within 0.04 Å) with the present value [29]. The lowest energy magnetic configurations of CrN, MnN and FeN in the RS phase were all found to be AFM. The magnetic moment is large (>2.4 lB ) in all cases. There is a correspondingly large difference in energy compared with the non-magnetic solution. For RS FeN, the energy difference between the AFM and FM ordering is small (<0.05 eV) and

thus it is concluded that both magnetic configurations are possible at equilibrium. For the ZB phase, both CrN and MnN exhibit strong magnetism, with preferred ordering of FM and AFM, respectively. The variation of lattice constant with the number of d-electrons is shown in Fig. 5. For the spin-polarized nitrides both magnetic and non-magnetic lattice constants are presented. Similar to the

V.F. Hlynsson et al. / Journal of Alloys and Compounds 603 (2014) 172–179

3.2.2. Magnetic properties under compression and strain In Section 3.2.1, only the magnetism at equilibrium was considered. However, it is well-known that compression and strain can alter the magnetic properties of a crystal. The variation of the magnitude of magnetic moment with lattice constant is shown in Fig. 6. The magnetic ordering (AFM/FM/NM) is assumed to be the same as at equilibrium and transitions between the various magnetic orderings are not considered explicitly here. For both RS and ZB phases, the magnetic moment shows a general increase with increasing lattice constant. The exception is CrN, which in both the RS and ZB phases exhibits a decrease again at large strain. The increase in magnetic moment is not linear, in that a given nitride is non-magnetic at small lattice constants and sharply increases at some critical cell volume. This is particularly obvious for CoN in both phases and FeN in the ZB phase; at the equilibrium lattice constant the nitride is non-magnetic while only a small amount of strain induces rapidly increasing magnetism. This can have large impacts in materials design, where a particular material can be synthesized to be non-magnetic or magnetic as desired, with only a small perturbation to the crystal. 3.2.3. Phase preference The relative stability of the RS and ZB phases of the 3d nitrides are estimated from the ZB to RS transition pressure, calculated using the aforementioned common tangent method. Variations of energy with volume used to calculate the transition pressures are shown in Fig. 7, where the three magnetic orderings are treated explicitly. The resultant transition pressures are collected in Table 6 and presented pictorially in Fig. 8. The transition pressures for the 3d TM mononitrides show a similar trend as that of the 4d and 5d nitrides; the transition pressure is negative for the early TM mononitrides, indicating a preference for RS rather than ZB. The transition pressure increases with the number of d electrons, again reaching a maximum near the middle of the period, in this case FeN. Previous calculations of transition pressures are scarce, with only FeN and CoN being reported [19,9]. As with the case of the 4d and 5d nitrides, the use of RPBE in this work underestimates the transition pressure somewhat. However, the two previously reported transition pressure for FeN and CoN vary by 11 and 14 GPa, respectively, so clearly this quantity is difficult to estimate accurately. The common tangent method used in this study relies on a very accurate description of the energy at either compressed or expanded volumes. Very small changes in the shape of the inner

30 25

Transition Pressure / GPa

4d and 5d mononitrides, there is an obvious decrease in the lattice constant of the non-magnetic nitrides with increasing number of d-electrons until around the middle of the period, after which it increases. The lattice constant of magnetic nitrides is increased with respect to the non-magnetic solution, the magnitude of which increases with increasing magnetic moment. This can be seen from Fig. 5 by comparing the RS phase of VN, which has a very small magnetic moment and that of the strongly antiferromagnetic MnN. The larger lattice constant for magnetic nitrides can be rationalized by the metal atoms being more ‘‘atom-like’’ in character when spin-polarization is included [19].

20 15 10 5 0 −5 −10 ScN

TiN

VN

CrN

MnN

FeN

CoN

NiN

CuN

Fig. 8. Zincblende to rocksalt transition pressures of 3d transition metal mononitrides.

4 RS ZB

2

Formation Energy per atom / eV

178

0 −2 −4 −6 −8 −10 −12

ScN

TiN

VN

CrN

MnN

FeN

CoN

NiN

CuN

Fig. 9. Formation energy (per atom) of 3d transition metal monotrides from the constituent elements in their most stable form (bulk metal and gaseous N2). Both rocksalt (RS) and zincblende (ZB) phases are shown. The crystal structures of the bulk metals were taken to be either bcc (V, Cr, Mn, Fe), hcp (Sc, Ti, Co) or fcc (Ni, Cu). The lattice constants for the bulk metals are taken from Ref. [35]. Only the magnetic ordering at equilibrium is considered.

or outer walls of the energy curves can alter the transition pressure significantly. Closer inspection of the energy as a function of cell volume plots in Fig. 7 reveals an interesting point. FeN was found to be AFM at equilibrium, whereas at compressed cell volumes, the FM state is favoured. The energy difference is not large however, which further reiterates the possibility of FeN existing as both AFM and FM crystals, over a variety of cell volumes. 3.2.4. Thermodynamic stability The stability of each nitride is predicted by considering the formation energy, according to Eq. (1). The formation energies for

Table 6 Zincblende to rocksalt transition pressures (in GPa) of 3d transition metal mononitrides.

This work Prev. calc. a b

PBE, from Ref. [19]. PBE, from Ref. [9].

ScN

TiN

VN

CrN

MnN

FeN

CoN

NiN

CuN

5.7 –

6.9 –

2.9 –

2.9 –

2.2 –

26.5 47a, 58b

24.0 30a, 44b

10.6 –

3.4 –

V.F. Hlynsson et al. / Journal of Alloys and Compounds 603 (2014) 172–179

the 3d mononitrides are presented in Fig. 9. In contrast to the 4d and 5d mononitrides, most of the 3d mononitrides are predicted to be stable in both the RS and ZB forms. Only AgN, NiN and ZB CoN exhibit positive formation energies. Furthermore, the inclusion of kinetic effects is likely to add an additional barrier to decomposition of 1 eV (vide supra), thus NiN and ZB CoN are also likely stable. This is possibly the reason for the majority of the experimental studies being conducted on the 3d nitrides and indeed the reports of both RS and ZB phases being observed experimentally. 4. Conclusions First principles calculations were used to investigate the structural properties of mononitrides of the 3d, 4d and 5d transition metals (Groups III–XI), for rocksalt and zincblende crystal structures. The present results are in good agreement with the available experimental and theoretical data. Magnetic properties of 3d transition metal mononitrides have been investigated, both at equilibrium and under conditions of compression and strain. The present study represents a comprehensive reference set of the properties of transition metal mononitrides calculated within the same theoretical framework. Such information can be of great use in material design where specific structural or magnetic properties are desired. Acknowledgements This work was funded in part by the Icelandic Research Fund and the Icelandic Innovation Fund. The calculations were carried out on the Nordic High Performance Computer (Gardar) located in Iceland. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jallcom. 2014.02.153.

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