High pressure-induced phase transitions in AgI semiconducting compound up to 1 Mbar

Journal Pre-proof High pressure-induced phase transitions in AgI semiconducting compound up to 1 Mbar R. Yagoub, H. Rekab-Djabri, S. Daoud, S. Louhibi-Fasla, Manal M. Abdus Salam, S. Bahlouli, M. Ghezali PII:

S2352-2143(19)30298-9

DOI:

https://doi.org/10.1016/j.cocom.2019.e00452

Reference:

COCOM 452

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Computational Condensed Matter

Received Date: 15 November 2019 Revised Date:

22 December 2019

Accepted Date: 23 December 2019

Please cite this article as: R. Yagoub, H. Rekab-Djabri, S. Daoud, S. Louhibi-Fasla, M.M. S. Bahlouli, M. Ghezali, High pressure-induced phase transitions in AgI semiconducting compound up to 1 Mbar, Computational Condensed Matter, https://doi.org/10.1016/j.cocom.2019.e00452. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier B.V. All rights reserved.

High pressure-induced phase transitions in AgI semiconducting compound up to 1 Mbar R. Yagoub a, H. Rekab-Djabri b,c,, S. Daoud d, S. Louhibi-Fasla b, Manal M. Abdus Salame , S. Bahlouli a, and M. Ghezali b,f a

Laboratory of Plasma Physics Materials Conductor and their Applications LPPMCA Oran, USTO El M’Naouer, b

Laboratory of Micro and Nanophysics (LaMiN), National Polytechnic School Oran, ENPO-MA, BP 1523, El M’Naouer, 31000, Oran, Algeria

c d

Faculty of Nature and Life Sciences and Earth Sciences, Akli Mohand-Oulhadj University, 10000, Bouira, Algeria

Laboratory of Materials and Electronic Systems, Mohamed El Bachir El Ibrahimi University of Bordj Bou Arreridj, Bordj BouArreridj, 34000, Algeria e f

Department of Applied Physics, Tafila Technical University, Tafila 66110, Jordan

Faculty of Exact Sciences, Tahri Mohamed Bechar University, BP 417 Kanadissa Street, 08000 Bechar, Algeria

Keywords: AgI; structural properties; phase transition; DFT; FPLMTO. *Author to whom correspondence should be addressed; E-Mail: [email protected] , and [email protected]

Abstract: In this work, we have resorted to a recent version of the full potential linear muffin-tin orbitals (FP-LMTO) method based on the density functional theory (DFT), within both the local density approximation (LDA) and the generalized gradient approximation (GGA) for the calculation of the equilibrium structural parameters, and phase transition under high pressure of AgI semiconducting compound. Results are given for lattice parameters, bulk modulus and its first pressure derivative in different structures. In general, the use of the GGA approach in this work appears more appropriate than the LDA, and it is most correctly predicts the majority of the ground state properties for AgI material. The energy differences of NiAs (B81)/NaCl (B1) phases are around 1.76 and 1.15 meV, using the LDA and the GGA, respectively. Importantly, the phase transitions for this material from sixfolds coordinated NaCl-type structure (B1) to the eightfold coordinated CsCl-type structure (B2), and then to the hexagonal close packed HCP-type structure (A3) are possible under high pressure. Our calculations show that AgI semiconducting compound transforms firstly from B1 to B2 at pressure of around 55.58 GPa, and then from B2 to A3 at pressure of around 95.03 GPa, 1

respectively. 1. Introduction The silver halides, such as silver chloride (AgCl), silver bromide (AgBr) and silver iodide (AgI), which are members of the IB-VIIA compounds; were given a great attention during the last few decades. Many theoretical and experimental studies were reported on their different properties, due to their wide range of technological applications. Tiny crystals of these compounds are usually used in photographic processes, namely in making photographic films [1,2], due to their sensitivity to light. Silver halides, in particular silver iodide AgI binary compound, have also several other applications especially in photo and electrochemistry [3], catalysis [4,5], as liquid semiconductors [6] and holography [7]. The electronic structure of silver halides, in the valence band region, is more complicated than alkali halides [8]. This is a consequence of the presence of the cation (Ag+) 4d level in the top of the valence band region in degeneracy with the p-valence orbitals of the halogens which leads to very strong p–d hybridization. Recently, several ab-initio calculations were performed to investigate different physical properties of the binary silver halides semiconducting compounds under high pressure [9-12]. Unfortunately, these studies have been scarcely used in the investigation of AgI, as compared to other binary semiconductors [13-16]. At the end of last decade, Hull and Keen [17] performed X-ray diffraction (XRD) experiments on AgBr, AgCl and AgI in the NaCl structure, where they found that these compounds exhibit transitions to CsCl structure and/or to other structures under the influence of external high pressure. Using the density functional theory (DFT), within the local density approximation (LDA), calculations have been realized [18] in three main structures (B2, B1 and B3) for AgCl, in four structures (B1, B2, B3 and B81) for AgBr, and in five structures (B1, B2, B3, B81 and B4) for AgI. More recently, Rekab-Djabri et al. [19] studied AgBr1-xIx ternary alloys in both rock-salt (B1) and zinc-blende (B3) structures, using the LDA approximation. Their results

2

predicted on the optical, electronic, structural and elastic properties were found in general in good agreement with experiments and other theoretical data. Amrani et al. [20] found, using all-electron full-potential linearized augmented plane wave plus local orbitals (FP-LAPW + lo) approach based on DFT, that the zinc-blende (B3) phase is slightly lower in energy than the wurtzite (B4) phase, and that it transforms to rock-salt (B1) structure at pressure of around 4.19 GPa, while Boukhtouta et al. [21] found that the rock-salt (B1) phase transforms to the eightfold coordinated CsCl-type structure (B2) at pressure of about 45.05 GPa. In this work we have employed the first-principles total energy calculations to investigate systematically the structural properties and the phase transitions of AgI under high-pressure. Several possible structural phases of AgI including rock-salt (B1), CsCl (B2), zinc-blende (B3), wurtzite (B4), NiAs (B81), HCP (A3), β-Sn (A5), and PbO (B10) structures have been considered in our calculations. The rest of the paper is organized as follows. After a brief description of the computational details in sec.2, we present the main results of this work: structural parameters of eight phases of AgI, as well as high-pressure induced phase transitions, in sec. 3. Finally, brief conclusions are given in sec. 4. 2. Computational Details The calculations presented in this work were performed using FP-LMTO method as implemented in the LMTART code [22] within the framework of density functional theory (DFT) [23, 24]. For the electron-electron interaction, in the total energy calculations, we used both, the local density approximation (LDA) for exchange correlation potential, as parameterized by Perdew et al. [25] and also the generalized gradient approximation (GGA) in the form proposed by Perdew-BurkeErnzerhof (PBE) scheme [26]. The crystal potential and the electron charge density within muffintin (MT) spheres were expanded using spherical harmonics up to lmax = 6. Table 1 contains the parameters used in the present calculations; the kinetic energy necessary to ensure the convergence 3

(Ecutoff), the number of plane waves (NPLW) used, and the radius of the muffin-tin (RMT) spheres, for each of the eight crystal structure that were studied.

Table 1. The plane wave number NPLW, energy cut-off (in Ry) and the muffin-tin radius (RMT) (in a.u.) used in calculation for binary AgI. NPLW AgI LDA GGA

Ecut (Ry) AgI LDA GGA

LDA

GGA

LDA

GGA

NaCl (B1)

223

183

12.6

13.3

2.29

2.769

2.972

3.039

CsCl (B2)

215

215

11.1

11

2.41

2.15

2.01

2.3

ZnS (B3)

228

228

11

14.3

2.32

2.31

3.02

2.40

Wz (B4)

390

390

9.1

12.4

2.36

2.36

2.83

2.43

NiAs (B81)

136

136

21.7

33.1

2.63

2.77

1.84

1.93

PbO (B10)

310

310

9.82

13.8

2.80

2.31

2.78

2.41

136

136

21.7

33.1

2.63

2.77

1.84

1.93

310

310

9.82

13.8

2.80

2.31

2.78

2.41

Structure

HCP (A3) βSn (A5)

RMT (u.a) Ag

I

The NaCl (B1), CsCl (B2), and ZnS (B3) structures, see Fig. 1(a, b and c) have cubic symmetry, where the unit cell volume depends on one parameter only which is the lattice constant a. Other structures, namely wurtzite (B4), NiAs (B81), PbO (B10), HCP (A3), and β-Sn (A5), shown in Fig. 1(d, e, f, g, and h) have a hexagonal symmetry, so the unit cell volume in these structures depends on different lattice constants (z, a, c/a ratio and internal parameter u), all of them should be optimized. The position of silver (Ag) and Iodine (I) atoms in each of the above structures of AgI compound are listed in Table 2.

4

a)

e)

b)

f)

c)

d)

g)

h)

Fig.1. Crystal structure of AgI in a) NaCl (B1), b) CsCl (B2), c) ZnS (B3), d) Wurtzite (B4), e) PbO (B10), f) HCP (A3), g) βSn (A5) and h) NiAs (B81). Silver (Ag) atom is in red colour, while Iodine (I) atom is in green colour.

These structures have the following space groups: B1: Fm3 m , B2: Pm3 m , B3: F4 3m , B4: P6 3 mc , B10: P4/nmm , A3: P6 3 / mmc , A5: I 41 / amd and B81: P6 3 / mmc

5

Table 2. Location of Silver (Ag) and Iodine (I) atoms for the eight Structures. Ag 1st atom

I 2nd atom

1st atom

2nd atom

NaCl (B1)

0.0 ;0.0 ;0.0

1/2;1/2 ;1/2

CsCl (B2)

0.0 ;0.0 ;0.0

1/2;1/2 ;1/2

ZnS (B3)

0.0 ;0.0 ;0.0

1/4;1/4 ;1/4

Wz (B4)

0.0 ;0.0 ;0.0

1.2 ;-1/2√3 ;1/2

0.0 ;0.0 ;u

NiAs (B81)

0.0 ;0.0 ;0.0

0.0 ;0.0 ;1/2

1.2 ;1/

PbO (B10)

3/4 ;1/4 ;0.0

1/4;3/4 ;0.0

1/4;1/4 ;0.3

HCP (A3)

1.2 ; 1/2√3 ;1/4

1.2 ;1/2√3 ;3/4

βSn (A5)

0.0 ;-1/4 ;1/8

0.0 ;1/4 ;-1/8

1.2 ;-1/2√3 ;(0.5+u) ;1/4

1.2 ;-1/√12 ;3/4 3/4;3/4 ;-0.3

3. Results and discussion 3.1. Equation of state parameters In ab-initio calculations, the equilibrium structural parameters can usually be predicted by calculating either the pressure as a function of unit cell volume P(V), or the energy as a function of the unit cell volume E(V) [15]. In the present work, the structural parameters of AgI semiconducting compound were obtained from E(V) for each of the eight structures considered here: NaCl (B1), CsCl (B2), ZnS (B3), Wurtzite (B4), PbO (B10), HCP (A3), βSn (A5) and NiAs (B81). The equilibrium lattice constant a0, bulk modulus B0 and pressure derivative of bulk modulus B0′ have been computed by minimizing the total energy by means of Murnaghan's equation of state (EOS), which can be expressed as in the following form [27]:

 (V / V )B0  BV + 1 − '0 0  0'  B 0 − 1  B 0 − 1 '

BV E (V ) − E (V 0 ) = 0 ' B0

(1)

where, E0 represents the energy of the ground state; the minimum of the Etot (V) curve, that corresponds to the equilibrium unit cell volume V0. The equilibrium lattice constant, a, is calculated from V0. B0 is the equilibrium bulk modulus (1/compressibility), and it is determined by the following equation:

 ∂2E B 0 =  V 2  ∂V

  

(2)

6

B0' (B0' = ∂B/∂P, at P = 0) is the pressure derivative of the bulk modulus B0. The calculated and fitted Etot as a function of volume of all structures are shown in Fig.2, for both LDA and GGA calculations .

-337975

AgI LDA B1 B2 B3 B4 B8_1 B10 A3 A5

Total Enargy (eV)

-337976

-337977

-337978

-337979

-337980

-337981 30

35

40

45

50

55

60

Volume (A°)

65

70

75

80

85

90

3

-338268,0

AgI GGA B1 B2 B3 B4 B8_1 B10 A3 A5

Total Energy (eV)

-338268,5

-338269,0

-338269,5

-338270,0

-338270,5

-338271,0 35

40

45

50

55

60

65

70

Volume (A°)

75

3

80

85

90

95 100

Fig.2 Total energy per single AgI formula unit versus volume for eight phases of AgI in both LDA and GGA approximations.

7

It is obvious from Fig. 2, that the total energies calculated using GGA approximation are lower than those calculated using LDA approximations. The total energy of B1 phase calculated at equilibrium within LDA approximation is smaller than those of B81, B10, B3, A5, B4, B2 and A3 by about 1.68, 1.7, 19.6, 24.97, 49.4, 56.5 meV respectively. While using GGA approximation, the total energy of B1 calculated at equilibrium is smaller than the energies of B81, B3, A5, B4, B2, B10 and A3 by about 0.65, 4.22, 5.22, 9.65, 43.27, 78.01, 95.67 meV respectively. This means that the B1 phase is more stable than all other phases at ambient conditions Table 3. Calculated structural parameters (equilibrium lattice constants a, structural parameter c/a and the internal parameter u), bulk modulus B0 and the first pressure derivatives B0’ for B1, B2, B3 and B4 phases for AgI using both LDA and GGA approximations. Parameters

3

V0 (Å )

NaCl (B1)

This Work Other works

Theo

CsCl (B2)

ZnS (B3)

Wz (B4)

LDA

GGA

LDA

GGA

LDA

GGA

LDA

GGA

52.24

59.12

50.44

57.84

67.64

77.28

68.16

77.85

51.20a, 58.37a

49.80a, 57.44a

52.16b

63.90a, 72.42a

63.11a, 73.04a

67.64b 68.42 a,c

Exp a0 (Å)

This Work Other works

Theo

5.934

6.183

a

a

5.90 ,

6.16

3.694

3.867

This Work B0 (GPa)

Other works

6.034d 33.98

56.34a, 34.32a

47.22

30.30

51.47a, 31.86a

B0

u

Other works

4.70

4.96 b

Theo

5.106 ,

Exp

g

6.34

4.708

4.858

4.91

f

This Work

This Work Other works

a-

4.47 ,

4.599c, 4.59e

36.04

21.91

42.3a, 27.36a 24a, e

Other works c/a

4.69a

6.61

35.45

22.80

39.7a,

26.23a

40.70 b

Exp This Work

4.801

a

6.47a

57.862b

’

4.594

a

6.468 b

53.69 Theo

6.761

a

6.35 ,

5.931b Exp

6.468

4.87 5.022

24a,e 5.12

4.83

4.69

0.322

0.334

b

0.335 a, c 1.623

1.624

1.636 a,c, 1.63 a,e

Ref [18] , b-Ref [17], c-Ref [19], d-Ref [28], e-Ref [29] , f-Ref [30], g-Ref [31].

8

The results of the calculated structural parameters compared to other experimental and theoretical results are summarized in Table 3 for B1, B2, B3 and B4 phases of AgI. It is clear, from Table 3, that our data are in a good agreement with those obtained from other abinitio calculations [17-19, 29], and experimental works [28, 30, 31]. The data shown in Table 3, indicates that LDA underestimates the lattice parameter, a, by about 1.66%, 0.03% and 0.11% for B1, B3 and B4 structures respectively compared to experimental values (6.034, 6.47 and 4.599 Å) [28], while the GGA overestimates the lattice parameters by about 2.47%, 4.50% and 4.39% compared to the same experimental values [28]. This is a well known behaviour of these approximations. On the other hand, notice from Table 3, that the calculated bulk modulus is overestimated in LDA and underestimated in GGA compared to the available experimental results and the first derivative of the bulk modulus is underestimated compared to the experimental values, using both LDA and GGA. Actually the values of bulk modulus and its first derivative are more sensitive to the different values of parameters used in ab initio calculations. In order to study the effect of the position of atoms on the structural properties of AgI, four other phases: PbO (B10), HCP (A3), βSn (A5) and NiAs (B81) are investigated. To the best of our knowledge, there are no other ab-initio calculations or experimental data exist in the literature concerning the structural parameters for AgI in B10, A3, A5 and B81 phases, so our results for these phases are predictions and may serve as a reference for future works.. Our results for the previous phases are summarized in Table 4.

9

Table 4. Calculated structural parameters equilibrium (lattice constants a structural parameter z and c/a, the internal parameter u), bulk modulus B0 and their first pressure derivatives B0’ for PbO (B10), HCP (A3), βSn (A5) and NiAs (B81) phases for AgI using both LDA and GGA approximations. Parameters V0 (Å3) a0 (Å)

NiAs (B81)

PbO (B10)

HCP (A3)

βSn (A5)

LDA

GGA

LDA

GGA

LDA

GGA

LDA

GGA

53.30

60.12

58.15

66.03

51.42

58.20

68.76

78.67

4.477

4.479

4.688

3.584

3.621

4.634

4.858

4.319

B0 (GPa)

52.81

33.39

45.60

29.42

46.63

28.09

34.86

21.62

B0’

4.49

4.79

5.01

4.84

4.64

4.76

4.63

4.97

u

0.38

0.382

c/a

1.527

1.546

1.293

1.281

1.444

1.414

1.381

1.372

0.278

0.270

z 3.2. Structural phase transition

Many of the physical properties of compounds and alloys are strongly affected by the concentration of elements in the solid [32]–and hence, these properties are expected to change when the structure changes–as well as temperature and pressure [33-35]. This is an important reason why many researches focus on phase transition of compounds and alloys. In general, there are three approaches which are usually used to study the structural phase transition under pressure. The first approach is based on dynamic calculations (phonons) at different pressures. The second approach depends on thermodynamic calculations (Gibb's free energy or enthalpy), and the last one based on generalized stability criteria [15]. In this part of the present work, we used the second approach to study phase transitions between the B1, B2 and A3 phases of AgI binary compound under high pressures, using GGA approximation only. In this approach, to estimate the pressure values for the structural phase transition, Pt, we calculated the Gibb's free energies, G = Etot+PV-TS for the different phases, which in fact equals the enthalpy, H=Etot+PV, at T=0 K where we perform our calculations. Then we ploted the difference between the enthalpy of the B1 phase and each of the other phases as a function of pressure, as shown in Fig. 3

10

Fig. 3 predicts three transitions at the intersection points (equal enthalpies) of the curves. The first transition is from B1 structure to B2 structure at about 55.58 GPa. Above the B1→B2 transition, the B2 structure remains stable over a wide pressure range until a transition into the hexagonal close packed HCP-type (A3) structure, (B2→A3), is achieved at a pressure of about 95.03 GPa. Our calculated pressure of 55.58 GPa for the B1→B2 transition is in reasonable agreement with the previous theoretical values: 45.05 GPa and 49 GPa obtained by Boukhtouta et al. [21] and Nunes and Allen [36], respectively. To the best of our knowledge, there are no experimental results in the literature on the B1→B2 pressure phase transition for AgI semiconducting compound. The third transition appeared in Fig. 3 is the B1→A3 transition at a pressure of 68.78 GPa.

-338373

AgI GGA B1 B2 A3

Enthalpy (Ry)

-338375

-338377

-338379

P(B1 to B2) = 55.58 GPa

-338381

P(B1 to A3) = 68.78 GPa P(B2 to A3) = 95.03 GPa

-338383 50

55

60

65

70

75

80

85

90

95

100

Pressure(GPa)

Fig. 3. Enthalpy H (Ry) versus pressure (GPa) for CsCl (B2) and (A3) phases of AgI.

4. Conclusion In this work, we have studied the equilibrium structural parameters of AgI in the NaCl (B1), CsCl (B2), zinc-blende (B3), wurtzite (B4), HCP(A3), PbO (B10), NiAs (B81) and β-Sn (A5) structures using ab-initio FP-LMTO method, within both the local density approximation (LDA) and the 11

gradient generalized approximation (GGA). The ground state properties, such as the equilibrium lattice parameters, the bulk modulus and its pressure derivative were calculated. Our obtained results are in good agreement compared to the available experimental and other theoretical data of the literature. Total energy calculations showed that the B1 phase is the more stable at ambient conditions. Due to the lack of both experimental and theoretical data regarding B10, A3, A5 and B81 phases, our results of the structural parameters for these phases are predictions and may serve as a reference for future works. Another important result is that concerned with the possibility of phase transition from NaCl-type (B1) to CsCl-type (B2), then from B2 to the hexagonal close packed HCP-type (A3) structure, respectively. The pressures of the phase transitions were found to be at 55.58 and 95.03 GPa, respectively, in reasonable agreement with other theoretical results. Reference [1] S. Dahne, J. Photogr. Sci. 38 (1990) 66. [2] H. Kanzaki, Photogr. Sci. Eng. 24 (1980) 219. [3] E. Aprà, E. Stefanovich, R. Dovesi, C. Roetti, Chem. Phys. Lett. 186 (1991) 329. [4] S. Gu, B. Li, C. Zhao, Y. Xu, X. Qian, G. Chen, J. Alloys. Compd. 509 (2011) 5677. [5] M. Zhu, P. Chen, M. Liu, ACS Nano. 5 (2011) 4529. [6] J.E. Enderby, A.C. Barnes, Rep. Prog. Phys. 53 (1990) 85. [7] J. M. Kim, B.S. Choi, S. Kim II, J.M. Kim, H.I. Bjelkhagen, N.J. Phillips, Appl. Opt. 40 (2001) 622. [8] A. B. Kunz, Phys. Rev. B 26 (1982) 2070. [9] N. Bioud, K. Kassali, N. Bouarissa, J. Electron. Mater. 46 (2017) 2521. [10] S. Daoud, N. Bioud, N. Bouarissa, Mater. Sci. Semicond. Process. 31(2015) 124. [11] N. Lebga, S. Daoud, X.W. Sun, N. Bioud, A. Latreche, J. Electron. Mater. 47 (2017) 4030. [12] S. Daoud, N. Bouarissa, N. Bioud, P. K. Saini, Chem. Phys. 525 (2019) 110399. [13] H. Algarni, O. A. Al-Hagan, N. Bouarissa, M. A. Khan, T. F. Alhuwaymel, Infrared Phys. Technol. 86 (2017) 176. [14] N. Bouarissa, S. Saib, M. Boucenna, F. Mezrag, Comput. Condens. Matter. 18 (2018) 951. [15] S. Daoud, N. Bioud, N. Lebga, Chin. J. Phys. 57 (2019) 165. [16] N. Bioud, K. Kassali, X.W. Sun, T. Song, R. Khenata, S. Bin-Omran, Mater. Chem. Phys. 203 (2018) 362. [17] S. Hull, D.A. Keen, Phys. Rev. B 59 (1998) 750. 12

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Declaration of interests ☒ 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. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: