Structural properties and new phase transitions of silver iodide using the FP-LMTO method H.Rekab-Djabri1,2, S.Louhibi-Fasla1,* de Micro et de Nanophysique LaMiN – ENP d’ORAN, BP 1523, El M’Naouer, 31000, Algérie de SNVST, University AKLI Mohand-Oulhadj -BOUIRAE-Mail:
[email protected] 1Laboratoire 2Faculté
Abstract: We report first principles calculations of structural and electronic, properties of AgI compound in zinc blende(B3), CsCl(B2), rocksalt(B3), wirtzait(B4), NiAs(B8_1), PbO(B10), HCP(A3) and βSn(A5) structures employing the density functional theory (DFT) within the local density approximation (LDA) and the generalized gradient approximation (GGA). We employ the full potential linear muffin-tin orbitals (FP-LMTO) as implemented in the Lmtart code. Results are given for lattice parameters, bulk modulus and its first derivatives in the differents structures. The most important result in this work, the prediction of the possibility of two phase transitions; the firste ; from cubic rocksalt (NaCl)→ hexagonal HCP(A3) (55.58 GPa) and the second ; from rocksalt (NaCl)→ CsCl (B2) (68.78GPa) for AgBr. Keywords: FP-LMTO, Structural Properties, Electronic Properties, AgI; 1.Introduction The silver halides in particular the silver Iodide AgI, they have different applications in photographic processes [1,2], holography [3], photo and electro chemistry [4], catalysis [5-6], as liquid semiconductors [7], etc. In photochemical applications. AgI crystallize in the rock salt structure at room temperature. However their electronic structure is more complicated than the alkali halides. As Kunz [8]. Many investigations different of physical properties of the binary compounds under hydrostatic pressure have been an active topic of research in condensed matter over the past few years. At high pressures semiconductors study is an exceptionally good tool in understanding their optoelectronic properties but these studies have been scarcely used in the investigation of AgI, as compared to other I–VII semiconductors. At the end of last decade Hull and Keen [15] performed X-ray diffraction (XRD) studies of AgBr, AgCl and AgI correspond to the rocksalt structure and they exhibit transitions to cesium chloride and/or other phases upon the influence of external pressure. Theorical, calculations has been realized [24] in three main structures (B2, B1 and B3) for AgCl, four structures (B1, B2, B3 and B8_1) for AgBr, and five geometries (B1, B2, B3, B8_1 and B4) 1
for AgI. Using the density functional theory (DFT), within the local density approximation (LDA). Other First principles total energy calculations were performed by H. Rekab Djabri and S. Fasla [18], in one structure (NaCl), using the GGA and LDA approximations. The results were in general in good agreement with experiments. In this work we have employed the first-principles total energy calculations to investigate systematically the structural properties and phase transitions of AgI under high-pressure. Several possible structural phases for AgI including rocksalt (B1), CsCl (B2), zincblend(B3), wurtzite(B4), NiAs(B81), HCP(A3), βSn(A5), and PbO (B10) structures Fig .1., have been considered in our calculations. After abrief description of the calculation details, we present the main results of this work, structural parameters of these eight phases of AgI, as well as high-pressure induced phase transitions. Also the reported calculations provide new structural and electronic results from first principle for these compound. Finally, abrief summary is given. 2.Détails de calcul The calculations presented in this work were performed by FP-LMTO method as implemented in the LMTART code [8] within the framework of density functional theory (DFT) [10,11]. The Perdew [12] parameterization scheme was used for the exchange-correlation potential within the local density approximation (LDA) with and without generalized gradient approximation (GGA). In all cases, the maximal angular momentum for the expansion of the charge density and the potential in spherical harmonics was fixed to lmax=6. The muffin-tin radius (RMT) values, number of plane waves (PW) and the total cut-off/ energies used in our calculation, are listed in Table 1. The rocksalt, CsCl, zinc blendand structures have cubic symmetry, so, unit cell volume depends on one parameter only, the lattice constant. For wurtzite(B4), NiAs(B8-1), PbO(B10), HCP(A3), and βSn(A5) phases having hexagonal symmetry, we had to optimize the differents lattice constants (z. a, c/a and b/a ratio) and internal parameter (u). Table 2 represents the position of atoms for each structure. Table 1. The plane wave number PW, energy cut-off (in Ry) and the muffin-tin radius (RMT) ( in a.u.) used in calculation for binary AgI.
Structure NaCl(B1) CsCl(B2) ZnS(B3) Wz(B4) NiAs(B8-1)
PbO(B10) HCP (A3) βSn (A5)
PW AgI
Ecuttot(Ry) AgI
LDA 223
GGA 183
LDA 12.6
215
215
228
228
390 136 310
RMT(u.a) Ag I
GGA 13.3
LDA 2.29
GGA 2.769
LDA 2.972
GGA 3.039
11.1
11
2.41
2.15
2.01
2.3
11
14.3
2.32
2.31
3.02
2.40
390 136 310
9.1 21.7 9.82
12.4 33.1 13.8
2.36 2.63 2.80
2.36 2.77 2.31
2.83 1.84 2.78
2.43 1.93 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
2
Ag 1statom 0.0 ;0.0 ;0.0 0.0 ;0.0 ;0.0 0.0 ;0.0 ;0.0 0.0 ;0.0 ;0.0 0.0 ;0.0 ;0.0 3/4 ;1/4 ;0.0 1.2 ; 1/2√3 ;1/4 0.0 ;-1/4 ;1/8
NaCl(B1) CsCl(B2) ZnS(B3) Wz(B4) NiAs(B8-1) PbO(B10) HCP (A3) βSn (A5)
1statom 1/2;1/2 ;1/2 1/2;1/2 ;1/2 1/4;1/4 ;1/4 0.0 ;0.0 ;u 1.2 ;1/√12 ;1/4 1/4;1/4 ;0.3 1.2 ;1/2√3 ;3/4 0.0 ;1/4 ;-1/8
2ndatom
1.2 ;-1/2√3 ;1/2 0.0 ;0.0 ;1/2 1/4;3/4 ;0.0
I 2ndatom
1.2 ;-1/2√3 ;(0.5+u) 1.2 ;-1/√12 ;3/4 3/4;3/4 ;-0.3
Tableau 2: Location of atoms for each structure.
-a-
-d-
-b-
-e-
-c-
-f-
FP LMTO methode
-g-
-h-
Fig. 1. crystal structure of AgBr and AgCl in: a-NaCl(B1), b-CsCl(B2), c-ZnS(B3), d-Wirtzite(B4), e-PbO(B10), fHCP(A3), g-βSn(A5), h-NiAs(B8_1).
3
3. Result and discussion 3.a. Structural phase stability Total energy versus volume data for the rocksalt, CsCl, zinc blend, wurtzite, NiAs and PbO, structures of AgI crystal is shown in Fig. 2. NaCl(B1)
Parameters
NiAs(B8_1)
PbO(B10)
LDA
GGA
LDA
CsCl(B2) GGA
LDA
ZnS(B3) GGA
LDA
Wz(B4) GGA
LDA
GGA
LDA
GGA
LDA
HCP(A3) GGA
LDA
βSn(A5) GGA
52.24
59.12
50.44
57.84
67.64
77.28
68.16
77.85
53.30
60.12
58.15
66.03
51.42
58.20
68.76
78.67
63.11b, 73.04b 68.42ba 4.594 4.801
4.319
4.477
4.479
4.688
3.584
3.621
4.634
4.858
4.47b, 4.69b 4.599ba,4.59bc 35.45 22.80
52.81
33.39
45.60
29.42
46.63
28.09
34.86
21.62
39.7b, 26.23b 24bc 4.83 4.69
4.49
4.79
5.01
4.84
4.64
4.76
4.63
4.97
0.322
0.38
0.382
1.527
1.546
1.293
1.281
1.444
1.414
1.381
1.372
0.278
0.270
AgI V0(A˚ 3)
This Work Other work
a0 (A˚ )
Teo Exp
This Work Other work
Teo
B0
63.90b, 72.42b
5.934
3.694
6.468
6.183
3.867
5.90b, 6.16b
6.761
6.35b, 6.61b
6.47be 53.69
Teo
33.98
47.22
30.30
36.04
21.91
56.34b, 34.32b
51.47b, 31.86b
42.3b, 27.36b
4.70
4.858
4.87
24bc
Exp
This Work Other work
’
49.80b, 57.44b
Exp
This Work Other work
B0 (Gpa)
51.20b, 58.37b
4.96
4.91
5.12
Teo Exp
This Work Other work This Work Other work
u c/a
0.334
0.335ba 1.623
1.624
1.636ba,1.63bc
z
Table 3 Calculated structural parameters equilibrium lattice constants a, structural parameter z and c/a, thein ternal parameter u, and bulk modulus B0 and their first derivatives B0 for different phases analyzed for AgI using the LDA and GGA approximations. a-Ref[13] , c-Ref[14],
d-Ref[15], e-Ref[16], f-Ref[17], g-Ref[18], k-Ref[19], l-Ref[20], b-Ref[21], m-Ref[22], n-Ref[23],
o-Ref[24].
-338268,0
-337975
Total Energy (eV)
-338268,5
-338269,0
-338269,5
-338270,0
-338270,5
AgI LDA B1 B2 B3 B4 B8_1 B10 A3 A5
-337976
Total Enargy (eV)
AgI GGA B1 B2 B3 B4 B8_1 B10 A3 A5
-337977
-337978
-337979
-337980 -338271,0 35
40
45
50
55
60
65
70
Volume (A°)
75 3
80
85
90
95
100
-337981 30
35
40
45
50
55
60
Volume (A°)
65
70
75
80
85
3
Fig. 2. Variation of total energy with unit cell volume for eight possible candidate structures of AgI in the LDA and GGA approximations.
4
90
Energie and volume are per single AgI formula unit. By exploiting the curves of minimization, it follows that NaCl structure represents the most stable phase at zero pressure for the AgI in the LDA and GGA approximations. which is consistent with the T. Benmessabih result [13], we also show that the B8_1 structure is meta stable in AgI, in the two approximations LDA and GGA. Energies and volumes are per single AgI formula unit and solid curves were obtained by fitting the calculated data to the Murnaghan equation of state for each phase.
𝐄(𝐕) = 𝐄𝟎 +
𝐕𝟎 𝐁 𝐁 [𝐕 ( ) − 𝐕𝟎 ] + (𝐕 − 𝐕𝟎 ) 𝐕 𝐁́(𝐁́ − 𝟏) 𝐁́ 𝐁
(𝟏)
And: E0: represents the energy of the ground state corresponding to the volume V0, and V0 is the volume of the equilibrium. The constant of the equilibrium lattice is given by the minimum of the curve Etot (V). B: the compressibility modulus is determined by the following equation: 𝐁 = (𝐕
𝛛𝟐 𝐄 ) 𝛛𝐕 𝟐
(𝟐)
B': the derivative of the compressibility module: ́
𝝏𝑩
𝑩 = 𝝏𝑷
(𝟑)
From Fig. 2, we can see that using the LDA and GGA approximations, the lowest minimum energy corresponds to the NaCl phase. We note that the energy difference of the βSn (B8_1) / NaCl (B1) phases is only 0.00176 eV and 0.00115eV using the LDA and GGA approximations respectively. The total energy of the others phases (A3, A5, B4, B10 and B2) is much higher. •
Analysis with other work
The total energy difference between the minima of the B1 phase curve and of the B8_1 phase curve is very low for AgI material in LDA and GGA, Our results are summarized in Table 3 together with those of other ab-initio calculations and experimental works. The data shown in Table 3 for the AgBr (rocksalt phase) indicates that LDA underestimates the lattice parameter by 1.17% compared 5
to experimental value [15], and for the GGA is higher the lattice parameters by 1.50% compared with the same reference [15], whereas the calculated lattice parameters of B2, B3, B4, agree well with previous theoretical reports [13,20, 24]. To the best of our knowledge, there are no data available for structural properties of AgI in B8_1, B3, B5 and B10 phases. 3.b. Structural phase transition In this part we are interested only for transitions with the GGA approximation. Or there are two possible transitions. FIG. 3 shows the enthalpy differences for the phases B2 and A3 as a function of the pressure with respect to B1. From this figure we conclude: For the AgBr material and with the GGA predicts a transition from the B1 structure to the B2 structure at about 37.66 GPa. Above the B1→B2 transition, the B1 structure remains stable over a wide pressure range until a transition (B1→A3) into the Hexagonal HCP-type A3 structure is achieved at pressures around 90.55 GPa. For the AgCl in the GGA, the B1→B2 transition is predicted at a pressure of 18.11GPa we find also no evidence from and to B3, B4, B10, A5 and B8-1 phase transition. The calculated values of Pt and the transition volume are listed in Table 4. To the best of our knowledge there are no experimental or theoretical results in literature to compare our results for the pressures.
Phases
Volume Pression(GPa) AgBr V (A°)3
B1→B2 B1→A3 A3→B2
Transition pressure
VB1 50.322 VB2 47.154 VB1 50.322 VA3 48.34 VB2 47.154 VA3 48.34
AgI Other works Teo Exp
reduct (%)
Present work
6.295
55.58
/
/
3.974
68.78
/
/
2.453
95.03
/
/
Table 4 Calculated values of the transition pressure Pt and transition volumes for AgI using the GGA approximation..
6
AgI GGA B1 B2 A3
0,5
-1,0 -1,5
95.03GPa
-0,5
68.78GPa
0,0
55.58GPa
Enthalpy difference (eV/atom))
1,0
-2,0 -2,5 0
50
100
150
200
250
Pressure(GPa)
Fig. 3. Variation of the enthalpy differences H (Ry) versus pressure(GPa) for CsCl(B2) and (A3) phases of AgI. The reference Gibbs free energy in set for the rocksalt phase (B1).
4. Electronic band structures Using the lattice constants calculated at equilibrium state for the studied AgI material, the electronic band structures corresponding to high symmetry points are obtained. A Fermi level (EF) is chosen to locate at 0eV and coincides with the top of the valence band. Figs.4. and show the band structure of our materials, in the rocksalt using the LDA and GGA approximations. Our results for the AgI are compared with the experiment and theoretical works in the table (5). The valence band maximum occur at X and the conduction band minimum occur at L for Rocsalt structure, so these materials are predicted to have indirect band gap in this structure using the LDA and GGA approximations. The band gap for RS-AgI-LDA is 0.685eV which is in good agreement with T. Benmessabih and al. results (0.681 eV) [13].
AgI
Phase
Nature of gap
B1
X→ L
Présent work
Type
LDA 1.019
Indirect
GGA 1.117
Other works LDA /
GGA 0.710a
Table 5 The gap energetic calculated for AgBr and AgCl in rocksalt structure using the LDA and GGA approximations.
a-ref ]13[,
7
Fig.4. band structure of AgI, in Rocsalt structre using the LDA ang GGA approximations
5. Conclusion In
this work, we have studied AgI in the rocksalt NaCl(B1),
CsCl (B2), zincblend(B3),
wurtzite(B4), HCP(A3), PbO(B10), NiAs(B8-1) and βSn (A5) structures by the ab-initio FP-LMTO method within the local density approximation(LDA) and the gradiant generalized approximation (GGA). The ground state properties such as the equilibrium lattice parameter and the bulk modulus and its pressure derivative were determined and compared with other available experimental and the oretical data. Our most important result is that concerned with the possibility of phase transition from NaCl to CsCl and to HCP using the GGA approximation at lower pressures (55.58, 68.78 GPa, respectively). Our results show that AgI have indirect gap (X, L) in zinc blende structure using the LDA and GGA approximations.
8
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