First principles insight into the structural, electronic, optical and thermodynamic properties of CsPb2Br5 compound

Chemical Physics 533 (2020) 110704

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First principles insight into the structural, electronic, optical and thermodynamic properties of CsPb2Br5 compound

T

D.M. Hoata,b, , Mosayeb Naseric, R. Ponce-Pérezd, J.F. Rivas-Silvae, Gregorio H. Cocoletzie ⁎

a

Computational Laboratory for Advanced Materials and Structures, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam c Department of Physics, Kermanshah Branch, Islamic Azad University, P.O. Box 6718997551, Kermanshah, Iran d Universidad Nacional Autónoma de México, Centro de Nanociencias y Nanotecnología, Apartado Postal 14, Ensenada, Baja California, Código Postal 22800, Mexico e Benemérita Universidad Autónoma de Puebla, Instituto de Física, Apartado Postal J-48, Puebla 72570, Mexico b

ARTICLE INFO

ABSTRACT

Keywords: First-principles CsPb2Br5 compound Structural properties Electronic properties Optical properties Thermodynamic properties

The ternary CsPb2Br5 compound is a promising candidate for optoelectronic applications, however, its electronic properties are not well understood yet. In this work, the structural, electronic, optical and thermodynamic properties have been systematically examined using first-principles calculations. The exchange-correlation potentials are included in the calculations through the generalized gradient approximation (GGA-PBESol) and Tran-Blaha modified Becke-Johnson exchange (mBJ) potential. Obtained structural parameters match well with the experimental data. The CsPb2Br5 compound is an indirect semiconductor with a band gap of 3.589 eV predicted by mBJ potential. A wide absorption band in the ultraviolet region with very high absorption coefficient was observed for the ternary at hand. Finally, the thermodynamic behaviors of CsPb2Br5 are also computed using the Debye quasi-harmonic model. Properties are investigated as a function of pressure up to 25 GPa under different temperatures, and discussed in details.

1. Introduction In recent years, solution process halide based materials have been extensively investigated due to their potential applicability in optoelectronic devices resulting from their extremely interesting physical and chemical properties such as tunable electronic properties, high absorption coefficient and long diffusion length of charge carriers [1–4]. It shall be mention that the hybrid organic–inorganic CH3NH3PbX3 (X = Cl, Br, and I) perovskites are of the most promising materials for applications in solar cells with a power conversion efficiency as high as up to 22.1% [5]. However, the low stability under working conditions has limited its practical applications. In this regard, Cesium Lead Halide based all-inorganic perovskites (CsPbX3, X = Cl, Br and I) have emerged as promising alternatives due to their higher chemical stability, intriguing electronic and photoluminescent properties [6–8]. Recently, other compound belonging to Cs-Pb-Br family, namely CsPb2Br5, has also attracted attention of the researcher. In general, this compound is formed during the synthesis of the perovskite CsPbBr3 as a secondary. The first CsPb2Br5 successful preparation was realized by I.

Y. Kuznetsova et al. [9]. Such mentioned work has motivated a huge interest in synthesizing and characterizing the optical properties of this ternary. Experimental works have demonstrated that the CsPb2Br5 compound is a promising candidate for lasing and light-emiting applications [10,4,11–13]. Theoretically, electronic properties of the ternary CsPb2Br5 have been investigated by some research groups. For examples, Li et al. [10] determined a band gap value of 2.979 eV from DFT calculations. Later, Dursun et al. [12] also investigated the electronic band structure of the compound at hand using DFT calculations and obtained an indirect band gap of 3.1 eV. More recently, a band gap of 3.72 eV was determined by Jin et al. [14] using first-principles calculations in combination with hybrid HSE06 functional. Such mentioned results show a disagreement and an accurate calculation of the electronic band gap is still needed in order to understand deeply the optical properties of CsPb2Br5 compound. Therefore, we consider necessary to carry out a systematic investigation on the electronic and optical properties of the CsPb2Br5 compound. Herein, we present results of the comprehensive study on the structural, electronic, optical and thermodynamic properties of the

Corresponding author at: Computational Laboratory for Advanced Materials and Structures, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam. E-mail addresses: [email protected] (D.M. Hoat), [email protected] (M. Naseri), [email protected] (R. Ponce-Pérez), [email protected] (G.H. Cocoletzi). ⁎

https://doi.org/10.1016/j.chemphys.2020.110704 Received 21 November 2019; Received in revised form 30 January 2020; Accepted 3 February 2020 Available online 10 February 2020 0301-0104/ © 2020 Elsevier B.V. All rights reserved.

Chemical Physics 533 (2020) 110704

D.M. Hoat, et al.

ternary CsPb2Br5 compound. Studies are done theoretically based on the density functional theory (DFT) and Debye quasi-harmonic model. Obtained results assert that the CsPb2Br5 compound is an indirect semiconductor with a band gap of 3.589 eV and it has a wide absorption band in the ultraviolet region with very high absorption coefficient up to 2.21 (× 106 /cm). Results suggest that the studied compound is very promising absorber to be used in optoelectronic devices. Calculations are performed using the full-potential linearized augmented plane-wave, the main used parameters are given in Section 2. The obtained results are presented in Section 3 and they are also discussed in details. Finally, in Section 4, we present a conclusion of the remarkable results of the work. 2. Computational details Structural, electronic and optical properties of the CsPb2Br5 compound have been investigated using the WIEN2k package [15]. The fullpotential linearized augmented plane-wave (FP-LAPW) method is applied to solve the self-consistent Kohn-Sham equations [16]. The exchange-correlation potentials were treated with the revised PerdewBurke-Ernzerhof generalized gradient approximation for the densely packed solids and their surfaces (GGA-PBESol) [17]. Theoretical experiences have demonstrated that the local density approximation (LDA) and GGA can describe very well the ground state properties of materials, however, they make no good calculation of the electronic band gap (as compared with the experimental results). To overcome this deficiency, some approaches have been proposed such as the DFT + U theory to treat the highly correlated electrons [18,19], hybrid functionals [20] or the low computational cost and efficient Tran-Blaha modified Becke-Johnson exchange potential (mBJ). mBJ can improve considerably the electronic band gap calculation of solids providing very accurate results [21–23], therefore, in this work it is used to compute the electronic and optical properties of the ternary at hand. In the interstitial regions, the energy cut-off for plane-wave expansion is selected to be RMT Kmax = 7 , where RMT is the smallest muffin-tin radius and Kmax is the largest K-vector. Whereas, the maximum quantum number for the spherical harmonics within the atomic spheres is set to lmax = 10 . 1000 k-points are employed for the Brillouin zone sampling. For the structural optimization, the constituent atoms are freely relaxed until the forces are smaller than 1 × 10 3 Ryd. The self-consistent iterations are repeated until the energy difference between two consecutive cycles are smaller than 1 × 10 4 Ry.

Fig. 1. Crystal structure of CsPb2Br5 compound. Table 1 Calculated structural parameters of CsPb2Br5 compound along with previous theoretical and experimental results.

Present Theory Expt

3. Results and discussion

a (Å)

c (Å)

xPb

yPb

xBr2

yBr2

zBr2

8.3707 8.46a 8.60b 8.58c 8.483d 8.490e 8.4926f

15.4130 15.95a 15.90b 16.10c 15.250d 15.197e 15.1974f

0.3355

0.8355

0.1527

0.6527

0.1262

0.329f

0.829f

0.152f

0.653f

0.131f

a

Ref. [11], bRef. [13], cRef. [14], dRef. [10], eRef. [12], fRef. [24].

3.1. Structural properties

E (V )

The ternary CsPb2Br5 compound has been reported to crystallize in a tetragonal structure, space group I4/mcm (No. 140), where Cs, Pb, Br1 and Br2 atoms are positioned at (0.5; 0.5; 0.25), ( xPb;yPb ; 0), (0.5; 0.5; 0) and ( xBr 2;yBr 2 ;zBr 2 ), respectively. The crystal structure is displayed in Fig. 1. We start the structural optimization by freely relaxing all the atoms within the unit cell. Results are given in Table 1. According to our calculations, the energetically favorable positions of Cs, Pb, Br1 and Br2 are (0.5; 0.5; 0.25), (0.3355; 0.8355; 0), (0.5; 0.5; 0) and (0.1527; 0.6527; 0.1262), respectively. These are in very good agreement with the experimental results, namely, (0.5; 0.5; 0.25), (0.329; 0.829; 0), (0.5; 0.5; 0) and (0.152; 0.653; 0.131) [24], respectively. In order to optimize the unit cell geometry, the volume and c /a ratio are computed using the Birch-Murnaghan equation of state [25] and fifth-order equation, respectively. Birch-Murnaghan equation of state is formulated by:

= E0 +

9V0 B 16

V0 V

2/3

3

1 B +

V0 V

2/3

2

1

6

4

V0 V

2/3

(1) where V0 refers to the experimental volume, B is the bulk modulus and it dP is given by B = V dV and B is the derivative of bulk modulus. Here the dE

pressure is determined by P = dV . Calculated values of lattice parameters are a = 8.3707 (Å) and c = 15.4130 (Å). Taking the experimental results reported by Maity et al. [24] for comparison, these values present very small difference of the order of −1.43% and 1.42%, respectively. Additionally, they also match well with previous DFT calculations (See Table 1). The accuracy of the obtained structural optimization results confirms the reliability of the methodology and computational parameters used in this work.

2

Chemical Physics 533 (2020) 110704

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Fig. 2. Self-consistent band structure of CsPb2Br5 compound calculated with PBESol (left panel) and mBJ (right panel) potentials.

3.2. Electronic properties In order to systematically investigate the electronic structure of the ternary CsPb2Br5 compound, we have calculated its electronic band structure and density of states (total and partial) using the optimized structure using both PBESol and mBJ potentials. In all cases, the Fermi level is set at 0 eV and the considered energy range goes from −4 to 6 eV. Fig. 2 shows the band structures of the CsPb2Br5 compound X Y along the high symmetry directions Z N P Y1 Z in the first Brillouin zone calculated by 1 PBESol and mBJ potentials. Note that both employed potentials predict that the considered ternary has an indirect band gap as the valence band maximum is found in direction, while the conduction band minimum is located at Z point. It is worth mentioning that the lowest point of the conduction band at point is only 0.03(0.02) eV above of that at Z point as calculated using the PBESol(mBJ) potential. PBESol provides a band gap value of 2.964 eV, which is in very good agreement with previous results such as 2.979 eV [10], 3.1 eV [12], 3.08 eV [14]. Whereas that obtained with the use of the mBJ potential is 3.589 eV, which is larger than the result of standard functional PBESol. Recall that the band gap of solids is frequently underestimated by GGA and LDA functionals. Additionally, it only differs of the order of 3.52% from the result of hybrid HSE06 functional (3.72 eV – [14]). Despite the fact that no experimental band gap of the ternary CsPb2Br5 compound has been reported, we believe that 3.589 eV is more reasonable than 2.964 eV, therefore, only the results of mBJ potential are presented in the rest of the paper. For better understanding on the contribution of each constituent atom to the band structure, the total and partial density of states (TDOS and PDOS) are calculated and the obtained results are plotted in Fig. 3. Following the figure, it can be noted that in the considered energy range the valence band is mainly formed by the Br atoms, while the Pb electronic states dominate the conduction band. In CsPb2Br5 compound, Cs, Pb and Br have oxidation states of +1, +2 and −1, respectively. The electronic configurations of Cs+1, Pb+2 and Br−1 ions are [Xe], [Xe]4f 14 5d106s 2 and [Ar]3d10 4s 2 4p6 , respectively. PDOS spectra indicate clearly that the valence band from −3.1 to 0 eV is dominated by the occupied Br-4p state. However, a significant contribution from the 6s electrons to the upper part from −1.85 eV is also noted. Whereas, the conduction band is built mainly by the unoccupied Pb-6p orbital.

Fig. 3. Total and partial density of states of CsPb2Br5 compound calculated with mBJ potential.

3.3. Optical properties In order to investigate the optical properties of CsPb2Br5 it is required determining its complex dielectric function ( ) = 1 ( ) + 2 ( ) . Firstly, the imaginary part is determined through the matrix elements of the momentum states between valence band and conduction band as follows [26]:

3

Chemical Physics 533 (2020) 110704

D.M. Hoat, et al.

2(

)=

Ve 2 2 m2 (E k n

d3k

2

| k n|p| k n |2 f ( k n)[1

Ekn

2

)=1+

n = 4.048

nn

(2)

)

Using the Kramers–Kronig dispersion relation, the real part derived from the imaginary part as follows [27]: 1(

Revindra model [31]:

f ( k n )]

2(

)

d

2

0

1(

Moss model [32,33]:

) is

n=

From the dielectric function, some related optical properties as refractive index n ( ) , reflectivity R ( ) , absorption coefficient ( ) and energy loss function L ( ) can be computed as follow [28–30]:

(

n( ) =

2 1

+

2 1/2 2)

+

1

R( ) =

( )=

L( ) =

(n 1) 2 + k 2 (n + 1) 2 + k 2

(5)

2k c

(6)

Im (

1)

=

2 2 1

+

n=

(7)

2 2

Because of the tetragonal symmetry, the optical response of the compound shows isotropy displaying similar behaviors along the x and y directions. Therefore, in this work, we only study the optical properties of the CsPb2Br5 compound considering light polarized along the x axis (E//x or E||) and z axis (E//z or E ). Important optical parameters are given in Table 2. The polarizability of a material under electromagnetic radiation is associated to the real part 1 ( ) of the dielectric function. Fig. 4a shows 1 ( ) of CsPb2Br5 compound as a function of energy. The calculated static dielectric constant 1 (0) is 4.507 and 4.136 in the case of E//x and E//z, respectively. Results show an increasing trend of 1 ( ) up to around 4.6 eV to reach its maximum value of 9.563 (at 4.585 eV) for E|| and 8.905 (at 4.613 eV) for E . After that this parameter decreases considerably. Fig. 4b shows the variation of the imaginary part 2 ( ) of CsPb2Br5 compound as a function of energy. The threshold point of 2 ( ) is found near the electronic band gap, that is 3.589 eV. The 2 ( ) value depends on the overlapping of the involved states. From the figure, it can be seen a well pronounced peak for each case. Specifically, the highest value of this parameter is 9.304 for E//x and 10.224 for E// z, which occurs at energy of 5.429 and 5.401 eV, respectively. However, 2 ( ) has also significant values in the energy range from 7.5 to 17.5 eV. Energy-dependence of the refractive index n( ) of CsPb2Br5 compound is illustrated in Fig. 4c. At zero frequency, 2 ( ) is negligible for semiconductors, thus, the static refractive index n(0) can be calculated by n (0) = 1 (0) (see Eq. (4)). The n(0) value of the ternary at hand is 2.123 and 2.304 in the case of incident light polarized in the x- and zdirection, respectively. Empirically, some models have been proposed to determine the refractive index of solids from their band gap, such as, Table 2 Calculated optical parameters of CsPb2Br5 compound.

1 (0) max ( 1 max ( 2

)

) n (0) nmax ( ) R (0) (%) Rmax ( ) (%)

max ( ) (× 10 4 /cm) Lmax ( )

108 Eg

(9)

1+

13.6 Eg + 3.4

2

(10)

Substituting the band gap of 3.589 eV in the equations, we may obtain the refractive index of 1.823, 2.342 and 2.188, respectively. As it is noted, FP-LAPW results are greater than that obtained by Revindra model, however, yielding a better match with the other two models’ results, confirming the reliability of our results. From zero energy up to 1.5 eV, n( ) increases slightly, the increasing rate becomes considerably larger at higher energies. The largest values of this parameter are found around energy of 5 eV. The maximum value is 3.209 for E//x and 3.176 for E//z, which occur when the incident light energies are 4.721 and 5.293 eV, respectively. Beyond these energies, n( ) show a significant decreasing behavior. The CsPb2Br5 compound possesses refractive index smaller than unity in the energy range from 6.725 to 7.656 eV and from 7.207 to 7.638 eV in the case of E//x and E//z, respectively. Similar situation takes place beyond 15 eV. In Fig. 4d, the reflectivity of CsPb2Br5 compound is plotted as a function of energy. The spectra show clearly that the reflectivity is greater than 5% in most of the considered energy range, except in the energy window [7.668 to 7.992 eV] for E|| and [7.597 to 7.904 eV] for E , and also beyond 24 eV. At zero frequency, the reflectivity R(0) value is 12.930% and 11.611% for E//x and E//z, respectively. Peaks are obtained at energies of 6.5, 12, 15.5 and 22 eV. The maxima reflectivities are 40.656% at 15.388 eV and 37.534% at 5.672 eV in the case of x- and z-polarization, respectively. The absorption coefficient spectra of CsPB2Br5 compound are exhibited in Fig. 4e. From the figure, it can be seen that no photons with energy smaller than 3.589 eV are absorbed by the studied material. This is because no sufficient energy is available to excite electrons from the valence band to the conduction band. CsPb2Br5 has wide absorption band with the most intense absorption is manifested at high energies in the ultraviolet regime from 10 to 22.5 eV, where the absorption coefficient maxima are 221.064 (× 10 4 /cm) at 15.116 eV and 200.650 (× 10 4 /cm) at 15.143 eV for E//x and E//z, respectively. Otherwise, a small absorption band is also seen in the near ultraviolet region around 6 eV for incident light polarized in both directions. The spectra of energy loss function of CsPb2Br5 compound as a function of energy are given in Fig. 4f. This important optical parameter represents the energy loss of a fast electron, and in the energy range considered in this work (lower than 50 eV), the energy loss is mainly due to the plasmon excitations in the material. The dominant peak is associated to the plasma resonance of the material and the corresponding frequency is the plasma frequency. In our case, the most pronounced peaks are found at energies of 22.327 and 22.354 eV, in the case of E//x and E//z, respectively, with the maxima values of L( ) being 3.246 and 3.396, respectively.

(4)

2

4

and Herve and Vandamme model [34]:

(3)

2

(8)

0.62Eg

x-Polarization

z-Polarization

4.507 9.563

4.136 8.905

3.4. Thermodynamic properties

2.123 3.209 12.930 40.656 221.064

2.304 3.176 11.611 37.534 200.650

Thermodynamic properties of the ternary CsPb2Br5 compound are evaluated using the GIBBS2 code [35], an implementation of the Debye quasi-harmonic model, which has been widely employed to determine the thermodynamic properties of solids [36]. The non-equilibrium Gibbs function is given by [35]:

9.304

3.246

10.224

3.396

G (V , P , T ) = E (V ) + PV + Avib [ (V );T ] 4

(11)

Chemical Physics 533 (2020) 110704

D.M. Hoat, et al.

Fig. 4. (a) Real and (b) Imaginary part of dielectric function; (c) Refractive index; (d) Reflectivity; (e) Absorption coefficient and (f) Energy loss function of CsPb2Br5 compound.

here the Debye temperature

=

(V ) is calculated by:

1 1 h BS (6n 2V 2 ) 3 f ( ) kB M

(12)

where M is molecular mass and f ( ):

2 1+ f( )= 3 2 31 2

3 2

11+ + 31

is Poisson’s ratio, and the function 1

3 2

1 3

(13)

while the vibrational Helmholtz free energy Avib as a function of the Debye temperature is computed as follows [35,37]:

Avib [ (V );T ] = nkB T

(

9 + 3ln 1 8T

e

T

)

D

T

(14)

where the Debye integral takes the following form [35,37,38]:

D (y ) =

3 y3

x3

y 0

ex

1

dx

Fig. 5. Bulk modulus of CsPb2Br5 compound as a function of pressure at different temperatures.

(15)

When minimizing the Gibbs energy as a function of volume, the heat capacities and thermal expansion coefficient are given by:

CV = 3nkB 4D CP = CV (1 +

=

T

3( / T ) e /T 1

T)

CV BT V

characterize the resistance to contraction of materials; however, it has been demonstrated that the resistance is proportional to the bulk modulus. Therefore, bulk modulus has been widely employed to study qualitatively the capability of materials to resist the contraction. It can be noted that at a given temperature, the bulk modulus of the studied compound increases nearly linearly with the pressure. Whereas at fixed pressure, this parameter decreases slightly when temperature rises. Results suggest that the resistance to contraction of CsPb2Br5 compound increases with pressures and decreases with temperature, obeying the well-known inverse relation between the volume and resistance of materials. In the considered range of temperature and pressure, it seem that the pressure is more determinant on bulk modulus than temperature. For example, at 0 GPa bulk modulus value only decreases of the order of 52.222% from 0 K to 900 K, however, it increases as much as of the order of 401.064% when pressure rises from 0 GPa to 25 GPa at

(16) (17) (18)

where Grüneisen parameter defined as:

=

d ln (V ) d lnV

(19)

The bulk modulus of ternary CsPb2Br5 compound is plotted as a function of pressure at different temperatures 0, 300, 600 and 900 K in Fig. 5. It shall be mentioned that the bulk modulus does not 5

Chemical Physics 533 (2020) 110704

D.M. Hoat, et al.

Fig. 6. (a) Isochoric and (b) Isobaric heat capacity of CsPb2Br5 compound as a function of pressure at different temperatures.

room temperature. Lattice vibrations are significant to study physical properties of materials, and the vibrational properties of materials are associated to their heat capacity. Fig. 6a displays the isochoric heat capacity CV of CsPb2Br5 compound as a function of pressure at different temperatures 0, 300, 600 and 900 K. From the figure, one can see that at fixed temperature CV decreases as the pressure rises, it is clearly noted that at higher temperature, the decreasing rate becomes smaller. Specifically, CV decreases of the order of 5.099%, 1.339% and 0.613% at temperatures of 300, 600 and 900 K, respectively. On the other hand, at a given pressure, CV increases with temperature with variations becoming faster at high pressures. For example, at pressure of 0 and 25 GPa, CV increases of the order of 1.475% and 6.271%, respectively, when the temperature is raised from 300 to 900 K. It seems that constant pressure, CV tends to a saturation value, which is also known as DulongPetit limit, suggesting that all the phonon modes can be excited at high temperature. Fig. 6b shows the plots of the isobaric heat capacity CP of ternary CsPb2Br5 compound as a function of pressure at several temperatures 300, 600 and 900 K. In general, CP shows a similar behavior as compared with CV, however, it has no saturation limit as temperature increases as for CV. The plot profiles indicate that the temperature plays a more important role on the variation of heat capacities than pressure. Debye temperature is closely related to the elastic and thermal properties of materials. In Fig. 7, the Debye temperature of ternary CsPb2Br5 compound is plotted as a function of pressure at temperatures of 0, 300, 600 and 900 K. It can be seen that at given pressure, Debye temperature shows an inverse relation with temperature, whereas an

opposite trend is observed when varying pressure. Specifically, this parameter increases considerably with rising pressure, however, it seems that the increasing rate becomes slightly smaller at high pressures. In the considered ranges, it is obvious that the pressure is more important than temperature on the variation of Debye temperature. For example, at fixed pressure of 0 GPa, it decreases of the order of 23.388% from 0 to 900 K, while increases as much as of the order of 108.839% from 0 to 25 GPa at room temperature. In general, the thermodynamic properties of materials are related to their lattice vibrations, and the alterations of vibrations under high temperatures and pressures are associated to the Grüneisen parameter. Fig. 8 displays the curves of Grüneisen parameter of CsPb2Br5 compound as a function of pressure at various temperatures 0, 300, 600 and 900 K. It can be noted that this parameter increases with temperature and decreases with pressure, indicating the enhancement and reduction of vibrations strength, respectively. Clearly, according to the pressure increase, the increasing rate of this parameter becomes considerably smaller. For example, it increases of the order of 18.177% in the absence of pressure and 0.836% at 25 GPa if rising temperature from 0 to 900 K. Thermal expansion coefficient of materials is a very important thermodynamic parameter, being significant for both experimental and theoretical studies. It represents the variation of material volume under temperature effect. Fig. 9 shows the thermal expansion coefficient of ternary CsPb2Br5 compound as a function of pressure at temperatures 300, 600 and 900 K. Note that this parameter behaves similarly to the is Grüneisen parameter. At small pressures the thermal expansion

Fig. 7. Debye temperature of CsPb2Br5 compound as a function of pressure at different temperatures.

Fig. 8. Grüneisen parameter of CsPb2Br5 compound as a function of pressure at different temperatures. 6

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Fig. 9. Thermal expansion coefficient of CsPb2Br5 compound as a function of pressure at different temperatures.

highly affected by the change in temperature, in contrast as the pressure is raised the temperature makes almost no changes in . 4. Conclusions In this paper, the full-potential linearized augmented plane wave approach and Debye quasi-harmonic model have been used to study systematically the structural, electronic, optical and thermodynamic properties of the ternary CsPb2Br5 compound. Remarkable results are summarized as follows:

• CsPb Br • • • •

Z , whose value 2 5 compound has an indirect band gap is 2.964 and 3.589 eV obtained by PBESol and mBJ theories, respectively. Valence band and conduction band are dominated mainly by the Br4p and Pb-6p, respectively. Optical properties show a significant anisotropy. The CsPb2Br5 compound has a wide absorption band gap in the ultraviolet region with strongest absorption in the high energies zone around 15 eV. The volume variation under effects of temperature and pressure generates the opposite role of these two factors on the compound thermodynamic properties.

We hope that results reported here will be useful for designing the applications of the CsPb2Br5 compound in optoelectronic devices working under different conditions of temperature and pressure. CRediT authorship contribution statement D.M. Hoat: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing. Mosayeb Naseri: Formal analysis, Investigation, Methodology. R. Ponce-Pérez: Formal analysis, Investigation, Methodology. J.F. Rivas-Silva: Data curation, Formal analysis, Methodology, Software. Gregorio H. Cocoletzi: Data curation, Formal analysis, Methodology, Software, Validation, Writing - review & editing. Declaration of Competing Interest 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. 7

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