Theoretical study of III–V yttrium compounds

Computational Materials Science 39 (2007) 563–568 www.elsevier.com/locate/commatsci

Theoretical study of III–V yttrium compounds B. Amrani

a,*

, F. El Haj Hassan

b

a

b

Laboratoire de Traitement de Surface et Sciences des Mate´riaux, De´partement de Physique, Faculte´ des Sciences, Universite´ des Sciences et de la Technologie d’Oran (U.S.T.O.), Oran 31000, Algeria Laboratoire de Physique Des Mate´riaux, De´partement de Physique, Faculte´ des Sciences, Hadath, Beyrouth, Lebanon Received 30 July 2006; received in revised form 15 August 2006; accepted 15 August 2006

Abstract We have performed ab initio self-consistent calculations based on the full potential linear augmented plane wave method with the generalized gradient approximation to investigate the structural and the electronic properties of the less known yttrium III–V compounds: YN, YP, YAs and YSb in the rock-salt and cesium chloride structures. Ground state properties such as lattice constant, bulk modulus, pressure derivative of the bulk modulus and cohesive energy are reported in both NaCl (B1) and CsCl (B2) structures as well as structural transition pressure. We also give the band structure at equilibrium lattice constant and at transition pressure. Our results are in good agreement with numerous experimental and theoretical data where available, and provide predictions where they are not. Ó 2006 Elsevier B.V. All rights reserved. PACS: 62.20.Dc; 71.15.Ap; 71.20.Ps Keywords: FP-LAPW; GGA; YX compounds; High-pressure; Electronic and structural properties

1. Introduction The group-III–V have attracted extensive experimental and theoretical interest because of their technological applications. The question arises, how to extend the studies on the group III–V in order to have a new class of materials with promising properties that remain too interesting in device application? One possible way is to explore new III–V compounds such as YN, YP, YAs and YSb. Only a few theoretical papers and little experimental work have been devoted to the study of structural and electronic properties of this series of yttrium compounds. The structural properties of YN have been determined by Takeuchi et al. [1,2], Stampfl et al. [3] and De La Cruz et al. [4] using the full potential linearized augmented plane wave (FP-LAPW) method. Using the pseudopotential method, the pressure transition has been calculated by Herna´ndez et al. [5] for YSb. Recent high-pressure experi*

Corresponding author. E-mail address: [email protected] (B. Amrani).

0927-0256/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2006.08.009

ments from Hayashi et al. [6] studied YSb up to 45 GPa at room temperature and a first-order phase transition was reported from the B1 to B2 structure in this compound. We will concentrate in the present work on the bulk structural properties of yttrium compounds (YN, YP, YAs and YSb). We calculate the ground state total energy in the B1 and B2 structures using the full potential linearized augmented plane wave (FP-LAPW) method, which would complete the existing experimental and theoretical works. The article is organized as follows: In the next section we give a description of the ab initio theoretical method that we use to study the high-pressure phase. In Results and discussion we present our results and the comparison with the available experimental and theoretical studies. Finally, we present our conclusions. 2. Method of calculation The calculations were performed in the framework of density functional theory. We have employed the full

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B. Amrani, F. El Haj Hassan / Computational Materials Science 39 (2007) 563–568

potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code [7]. In this code, the crystal structures were decided under the condition that the total energy is minimized from all atomic configurations. The exchange and correlation effects were treated using the generalized gradient approximation (GGA) [8], since the GGA is more efficient to predict the phase transition pressure than the local-density approximation (LDA) [9]. To confirm the convergence

of our calculations, we carefully investigate the dependences of the total energy on the cutoff energy and the k-point set mesh according to the Monkhorst-Pack grid. As an example, the results are plotted in Fig. 1, for the YN (B1). In consideration of computational cost, we choose the cutoff energy to be in 220 eV, and the Brillouin-zone sampling mesh parameters for the k-point set are 47 for the rock-salt B1 structure, and 56 for the cesium chloride B2 structure.

-11.4

-12.84

-11.6

YN(B1)

-11.8

-12.86

-12.0

E(eV/cell)

Energy (eV/cell)

YN(B1)

-12.85

-12.2 -12.4

-12.87 -12.88 -12.89

-12.6 -12.90

-12.8 -12.91

-13.0 0

60

80

100

120

140

160

180

200

220

240

10

20

30

260

40

50

60

k-point sampling

Cuttof Energy (eV)

Fig. 1. Test of convergency of the total energy of YN (B1) at different computational parameters. (a) RKmax (b) k-point sampling.

-7.0

-6.5

YN(B1) YN(B2)

-7.5 -8.0

YAs(B1) YAs(B2)

-7.0

-8.5

-7.5

Energy (eV)

Energy (eV)

-9.0 -9.5 -10.0 -10.5 -11.0

-8.0 -8.5 -9.0

-11.5 -9.5

-12.0 -12.5

-10.0

-13.0 -13.5 16

18

20

22

24

26

28

30

32

34

36

38

-10.5 25

30

35

40

Volume (Å3)

45

50

55

60

65

Volume (Å3)

-6.0

YP(B1) YP(B2)

-6.5

-5.5

-7.5

-6.0

-8.0

-6.5

-8.5

Energy (eV)

Energy (eV)

-7.0

-9.0 -9.5 -10.0 -10.5

YSb(B1) YSb(B2)

-7.0 -7.5 -8.0 -8.5

-11.0 -9.0

-11.5 -12.0

-9.5

25

30

35

40

45

Volume (Å33)

50

55

60

35

40

45

50

55

60

65

70

Volume (Å3)

Fig. 2. Energy versus volume curves of the B1 (NaCl) and B2 (CsCl) phases for YN, YP, YAs and YSb compounds.

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3. Results and discussion 3.1. Structural properties The total energy of the scandium compounds YN, YP, YAs and YSb was calculated as a function of the volume in the B1 (NaCl) and B2 (CsCl) phases using the FPLAPW method, the results calculated for all compounds are given in Fig. 2. The curves were obtained by fitting

Table 1 Calculated lattice constant a, bulk modulus B, its pressure derivative B 0 and cohesive energy Ecoh at equilibrium volume for NaCl (B1) and CsCl (B2) phases for YX compounds

154.377 3.060 12.993 3.002 149.083 4.135 11.018

˚) a (A B (GPa) B0 Ecoh (eV/cell) ˚) a (A B (GPa) B0 Ecoh (eV/cell)

5.683 86.285 3.805 11.021 3.473 86.920 3.986 9.916

YP B1

B2

YAs B1

B2

YSb B1

B2

˚) a (A B (GPa) B0 Ecoh (eV/cell) ˚) a (A B (GPa) B0 Ecoh (eV/cell)

5.835 76.198 3.821 10.274 3.582 75.427 3.807 9.295

˚) a (A B (GPa) B0 Ecoh (eV/cell) ˚) a (A B (GPa) B0 Ecoh (eV/cell)

6.205 63.390 3.308 9.082 3.804 67.319 3.001 8.394

4.877a

4.93b, 4.85c, 4.77d 157b, 163c, 204d 3.50b, 4.77d 13.10b 3.01b 136b 4.11b 11.18b

G ¼ Etot þ PV  TS Cohesive energy (eV)

B2

B (GPa) B0 Ecoh (eV/cell) ˚) a (A B (GPa) B0 Ecoh (eV/cell)

4.915

6.155e 58 ± 3e 6.2 ± 0.6e

6.14f 61f 3.55f

3.53e

3.76f 69.4f 3.64f

The results are compared with the experiment and other theoretical works. a Ref. [11], at room temperature. b Ref. [1], using FP-LAPW (GGA). c Ref. [3], using FP-LAPW (GGA). d Ref. [3], using FP-LAPW (LDA). e Ref. [6], at room temperature. f Ref. [5], using LDA:PWPP.

Bulk modulus (GPa)

˚) a (A

Other theoretical works

ð1Þ

14 13 12 11 10 9 8 160 140 120 100 80 60 7.0

3

YN B1

Experiment

the calculated values to the Murnaghan’s equation of state [10]. The cohesive energy, lattice constant, bulk modulus and pressure derivative of the bulk modulus are given in Table 1, together with some theoretical results and the available experimental data. To the best of our knowledge there are no experimental or theoretical papers in the literature of investigations of the structural properties of YP and YAs compounds. The calculated lattice parameters and bulk modulus are in reasonable agreement with the experimental and previous calculations. Our calculated lattice parameter for YN is closer to the FP-LAPW results reported by Mancera et al. [1]. The small differences between the two FP-LAPW calculations are due to the different k-points sampling. For YSb, our result agrees with the recent LDA first-principles pseudopotential calculations [5]. The good agreement with other recent work for YN and YSb suggests that our predictions for YP and YAs are probably also accurate. It is clearly seen from Fig. 3 that the bulk modulus and the absolute value of the cohesive energy decrease from YN to YSb for both phases, i.e. from the lower to the higher atomic number. This suggests that YSb is more compressible than the other three compounds. The B1 (NaCl) structure in these compound is most stable and at high-pressure they transform to body-centred B2 (CsCl) structures. The pressure value for the structural phase transition Pt to the CsCl phase was determined by calculating the Gibb’s (G) free energies for two phases B1 and B2:

Lattice constant(Å )

Present work

565

6.5 6.0 5.5 5.0 4.5 4.0

YN

YP

YAs

YSb

Fig. 3. (a) Lattice constants, (b) bulk moduli and (c) cohesive energies of the yttrium compounds in the B1 (NaCl) phase.

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B. Amrani, F. El Haj Hassan / Computational Materials Science 39 (2007) 563–568 11

9

20.5 20.0

YN(B1)

8 7

19.5 P = 136.39 GPa t

19.0 18.5 18.0

YN(B2)

17.5 128 130 132 134 136 138 140 142 144

Pressure (GPa)

8

7

6

Volume per formula unit (Å3)

Gibbs free energy (eV)

10

YN(B1) YN(B2)

Gibbs free energy (eV)

3

Volume per formula unit (Å )

9 21.0

Pt = 136.39 GPa

6 5 4

34.5 34.0 33.5 YP(B1) 33.0 32.5 32.0 31.5 31.0 YP(B2) 30.5 30.0 29.5 48 50 52

YP(B1) YP(B2) P = 55.94 GPa t

54

56

58

60

62

Pressure (GPa)

3 2

Pt = 55.94 GPa

1 0 -1

5

-2 4 120

125

130

135

140

145

-3 35

150

40

45

50

55

Pressure (GPa)

60

65

70

75

80

Pressure (GPa)

8 6

3

3

2 0

Pt = 50.45 GPa

-2

2 1 0

47 46

YSb(B1) YSb(B2)

YSb(B1)

45 44

P = 28.61 GPa t

43 42 YSb(B2) 41 40 25

26

27

28

29

30

31

32

Pressure (GPa)

-1 -2

Pt = 28.61 GPa

-3

-4

-4

-6

-5

-8

-6

-10 10

3

4

Pressure (GPa)

4

Volume per formula unit (Å )

10

YAs(B1) YAs(B2)

37.0 36.5 36.0 YAs(B1) 35.5 35.0 34.5 P = 50.45 GPa t 34.0 33.5 33.0 YAs(B2) 32.5 32.0 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Gibbs free energy (eV)

Gibbs free energy (eV)

12

Volume per formula unit (Å )

5

14

-7

15

20

25

30

35

40

45

50

55

60

65

70

75

5

80

10

15

20

25

30

35

40

Pressure (GPa)

Pressure (GPa)

Fig. 4. Gibbs free energies per formula unit at temperature T = 0 K for YX (X = N, P, As and Sb) compounds in both structures B1 and B2 and the inset of shows the pressure–volume curve for B1 and B2 phases for YX (X = N, P, As and Sb) compounds.

Since the theoretical calculations are performed at T = 0 K, the Gibb’s free energy becomes equal to the enthalpy H ¼ Etot þ PV

ð2Þ

At a given pressure a stable structure is one for which the enthalpy has its minimum value and the transition pressures are calculated at which the enthalpies for the two phases are equal. We can avoid this construction and obtain this information directly from Fig. 1 by determining the common tangent between the thermodynamically stable structures as pressure is increased (or volume is decreased). The slope of the common tangent, which is the derivative of the total energy with respect to the volume, corresponds to minus the coexistence pressure for lowand high-pressure, and the volume for each phase at the transition (the transition volume) corresponds to that at the tangent point. It is straightforward to verify that the enthalpies of the two phases are equal at these points. We display the results obtained for YN, YP, YAs and YSb in Fig. 4. The calculated values of Pt and the transition volume are listed in Table 2. As to the best of our knowledge the value of the transition pressure for YP and YAs have not yet been measured or calculated, hence our results can serve as a prediction for future investiga-

tions. Our calculated value of transition pressure for YN is around 136 GPa which is an perfect agreement with Table 2 Calculated values of the transition pressure Pt and transition volumes for YX compounds, compared to the experimental and other theoretical works This work YN Pt (GPa) ˚ 3) VB1(Pt) (A ˚ 3) VB2(Pt) (A

136.39 20.07 18.15

YP Pt (GPa) ˚ 3) VB1(Pt) (A ˚ 3) VB2(Pt) (A

55.94 33.09 30.42

YAs Pt (GPa) ˚ 3) VB1(Pt) (A ˚ 3) VB2(Pt) (A

50.45 35.64 33.07

YSb Pt (GPa) ˚ 3) VB1(Pt) (A ˚ 3) VB2(Pt) (A

28.61 45.31 41.82

a b c

Ref. [1], using GGA:FP-LAPW. Ref. [6], at room temperature. Ref. [5], using LDA:PWPP.

Experiments

Calculations 138a 20.0a 18.3a

>26b

22.5c

B. Amrani, F. El Haj Hassan / Computational Materials Science 39 (2007) 563–568

the theoretical value of 138 GPa obtained in [1]. For YSb the transition pressure is equal to 28.61 GPa, in good agreement with experimental results [6], where the B2

567

(NaCl) phase starts at 28 GPa. In our previous work [12], we found similar transition, from NaCl to CsCl structures, for other compound.

8

12

6

10 8

4

6

EF

Energy (eV)

0

4

Energy (eV)

2

-2

2 0

EF

-2

-4

-4

-6

-6

YN(B1)

YP(B1)

-8

-8

-10

-10

-12

W

-12 -14

W

Λ

L

Δ

Γ

X

Z

W

Λ

L

Δ

Γ

X

Z

W

K

10

K

8 6

10

4

Energy (eV)

8 6

Energy (eV)

4 2 0

2 0

EF

-2 -4

EF

-6

-2

-8

-4

-10

YP(B2)

-12

-6

Λ

R

YN(B2)

Γ

Δ

X

Z

Σ

M

Γ

-8

Fig. 7. Band structures of B1 and B2 phases of YAs. The energy zero is taken at Ef.

-10 -12 -14

Λ

R

Γ

Δ

X

Z

Σ

M

Γ 12

Fig. 5. Band structures of B1 and B2 phases of YN. The energy zero is taken at Ef.

10 8 6

Energy (eV)

12 10 8

Energy (eV)

6 4

4 2 0

EF

-2 -4

2 0 -2

-8

-4

-10

-6

YSb(B1)

-6

EF

YP(B1)

W

-8

L

Λ

Δ

Γ

X

Z

W

K

-10

12

-12

W

L

Λ

Δ

Γ

X

Z

W

K

10 8

10

6

8

Energy (eV)

4 2 0

EF

-2

Energy (eV)

4

6

2

EF

0 -2 -4

-4

-6

-6

YP(B2)

YSb(B2)

-8

-8

-10

-10

-12

-12

R

Λ

Γ

Δ

X

Z

M

Σ

Γ

Fig. 6. Band structures of B1 and B2 phases of YP. The energy zero is taken at Ef.

R

Λ

Γ

Δ

X

Z

M

Σ

Γ

Fig. 8. Band structures of B1 and B2 phases of YSb. The energy zero is taken at Ef.

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B. Amrani, F. El Haj Hassan / Computational Materials Science 39 (2007) 563–568

3.2. Electronic properties The self-consistent scalar relativistic band structure for these compounds is calculated in B1 and B2 phases along the various symmetry lines within the GGA scheme. The band structures at ambient conditions and at high-pressure are given in Figs. 5–8. It can be seen that all these materials are metallic, with the exception of YN in B1 phase, for which the band structure indicate that this material is an almost zero indirect band gap, and a small direct transition at the X-point. It is very similar to the results reported by Mancera et al. [1] and Stampfl et al. [3]. However, there has been a longstanding debate in the literature as to whether YN is a semimetal or a semiconductor. It is well known that GGA seriously underestimates band gap (typically by a few eV), due to its incomplete cancellation of the self-interaction. This suggests that actual YN band gap may be considerably larger than the values obtained by the above-mentioned calculations. Stampfl performed local density-functional calculations, complemented with estimated screened exchange (sX) LDA and found that YN was a semiconductor with an indirect gap of 1 eV [3]. 4. Conclusions In this paper, we have applied a FP-LAPW method to study the effect of pressure on the structural and electronic properties of the scandium compounds YN, YP, YAs and YSb. Accurate structural parameters, lattice constant, bulk

modulus, pressure derivative, and transition pressure for the B1 ! B2 phase transition were calculated. We also report the electronic band structure of scandium compounds in the B1 and B2 phases. Hopefully these results will encourage further experimental work on YX compounds. References [1] L. Mancera, J.A. Rodrı´guez, N. Takeuchi, J. Phys. Condens. Mat. 15 (2003) 2625. [2] N. Takeuchi, Phys. Rev. B 66 (2002) 153405. [3] C. Stampfl, W. Mannstadt, R. Asahi, A.J. Freeman, Phys. Rev. B 63 (2001) 155106. [4] W. De La Cruz, J.A. Dı´az, L. Mancera, N. Takeuchi, G. Soto, J. Phys. Chem. Solids 64 (2003) 2273. [5] P.R. Herna´ndez, A. Munˇoz, Int. J. Quant. Chem. 101 (2005) 770. [6] J. Hayashi, I. Shirotani, K. Hirano, N. Ishimatsu, O. Shimomura, T. Kikegawa, Solid State Commun. 125 (2003) 543. [7] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties, Vienna University of Technology, Vienna, Austria, 2001. [8] J.P. Perdew, S. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [9] B. Amrani, T. Benmessabih, M. Tahiri, I. Chiboub, S. Hiadsi, F. Hamdache, Physica B 381 (2006) 179. [10] F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30 (1944) 5390. [11] P. Villars, L.D. Calvert, Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, American Society for Metals, Metals Park, OH, 1985. [12] B. Amrani, I. Chiboub, S. Hiadsi, T. Benmessabih, N. Hamdadou, Solid State Commun. 137 (2006) 395.