Insight into the Structural, Mechanical and Optoelectronic Properties of Ternary Cubic Barium-Based BaMCl₃ (M = Ag, Cu) Chloroperovskites Compounds

Abstract

Prediction of new materials is crucial for the advancement of technology. Here, in this research work, the first-principle computation has been conducted utilizing the WIEN2K package to probe the structural, electronic, mechanical, and optical properties of barium-based chloroperovskites BaMCl₃ (M = Ag, Cu) compounds. The optimized lattice constants are calculated for both compounds which are 9.90 Bohr for BaAgCl₃ and 9.38 Bohr for BaCuCl₃. To obtain better and more precise results for the electronic band’s structure, TDOS and PDOS (total and partial density of states), and the TB-mBJ potential approximation are employed. The indirect band gap (R–Γ) is found for both compounds having values of 1.173 eV and 2.30 eV for BaCuCl₃ and BaAgCl₃, respectively, which depicts its semiconducting nature. The calculation of elastic properties is conducted with IRelast code. The Cauchy pressure, Bulk modulus, Young’s modulus, Shear modulus, anisotropic ratio, Kleinman parameters, and Poisson’s ratio are calculated from the obtained elastic constants. The computation of elastic parameters indicates that the interested chloroperovskites are anisotropic, mechanically stable, hard to scratch, and ductile. From 0 eV to 40 eV incident photon energy ranges, the various optical parameter such as refractive index, absorption coefficient, dielectric function, reflectivity, extinction coefficient, and optical conductivity are analyzed. These compounds absorb maximum light within 5 to 25 eV incident photon energy. Hence, these materials are good light absorbers, therefore, they can be used in optoelectronic devices for high-frequency applications.

1. Introduction

As the population of the world is growing drastically, the energy crises are catching increasing day by day. It proves the importance of energy in the field of economic growth and a higher standard of living [1]. The careless usage of energy creates a gap between the required and supply of energy, which ultimately affects nearly all economic fields. To overcome the energy gap, human beings need cheaper and environmentally friendly renewable energy sources [2]; among these sources, solar energy is the most economical and eco-friendly [3]. We can use solar energy directly (heating and warming objects) and indirectly (converting it to electrical energy by using certain devices). The device (solar cell) is primarily based on the rule of activation of electrons through solar light creating electron-hole pairs, ultimately giving the electricity [4]. In the past, solar cells were mostly fabricated from Si-based materials. However, at present, the researcher is working on Perovskite-based solar cells to enhance power-converting efficiency and minimize power loss [5,6]. In 1839 Gustav Rose, a German scientist, discovered CaTiO₃, a new kind of material exhibiting the structure ABX₃ in the Ural mountain region; it was named after Lev von Perovski (Russian mineralogist) as “Perovskites” [7]. Perovskite materials are attracting the researcher’s attention because of their versatile structure and distinctive electromagnetic, elastic, thermal, optical, and electronic behaviour [8,9]. The hybrid halide CH₃NH₃PbBr₃ and CH₃NH₃PbI₃ perovskite materials were first used in 2009 in the dye-sensitized solar cells industry, delivering excellent power conversion efficiency [10]. Currently, CsRhCl₃ and CsBeCl₃ are being studied by Umar Ayaz Khan et al. [11], who described that both materials are mechanically and structurally stable and a paramagnetic, and ductile nature is recorded for these materials. ASnO₃ (A = Sr, Ca, and Ba) was investigated by Djellal Cherrad et al. [12] who noted the indirect band gap (R–G) confirming their semiconducting nature and proposed that these compounds can be excellent materials for shielding devices in ultra-violet radiations range because of its high reflectivity. Kashif Murad et al. predicted some physical properties in their work that both BaAgCl₃ and BaCuCl₃ ternary chloroperovskites compounds are stable [13]. Their work is limited to predicting the stability and some physical properties. The stability of these chloroperovskites materials is also reported by Gómez-Peralta et al. [14]. We have computed precisely and accurately the structural, phonons dynamical stability, elastic, electronic, and optical properties of the selected ternary chloroperovskites compounds and we are assured of our outcomes. Our investigations will provide a pathway for the experimentalist to verify it experimentally. These BaMCl₃ (M = Ag, Cu) compounds are interesting materials for the applications of optoelectronics and many modern technologies. Here, we explored the diverse properties such as the structural, phonon dynamical stability, electronic, optical, and elastic properties of BaXCl₃ (M = Ag, Cu) through DFT within the WIEN2K package (WIEN2K 18.02, Creater Peter Blaha, Vienna Austria). Structural properties of both the materials are carried out from the optimization curve bulk modulus and tolerance factor, while the electronic properties are explored from band gap and DOS. The elastic properties are computed from the elastic constant. The refractive index, reflectivity, absorption coefficient, optical conductivity, and extinction coefficient, are studied for optical properties.

2. Computational Methodologies

The first-principle computations perform precise investigations and are increasingly capable of calculating material properties at the atomic/electronic level. This research is conducted using the DFT approach executed within the WIEN2K simulation code [15]. The volume of the unit cell is disintegrated into two portions: (1) The sphere of non-intersecting muffin-tin radius (RMT) centered at the nuclear positions and (2) the interstitial sphere. The electronic density and the exchange-correlation potential are extended into combinations of spherical harmonics time’s radial functions within the MT spheres and Fourier expansions in the interstitial position. The values of RMT are picked for constituent atoms so that there is no overlapping within the RMT. The RMTs values for the constituent atoms are 2.5, 1.78, and 1.92 atomic units for “Ba”, and “M” where (M = Ag and Cu), and “Cl”, respectively. The determination of the electronic structure of solid crystal density functional theory (DFT) approach has proved itself to be one of the most efficient techniques [16,17]. Here, the full-potential linearized augmented plane wave (FP-LAPW) approach [18] inside the frame of DFT is used to compute the electronic and optical structure. Kohn-sham’s equations are consistently solved for obtaining the total energies within TB-mBJ approximation [19,20,21]. The structural parameters are computed by fitting the unit cell volume vs. unit cell energy through the Birch–Murnaghan equation of state [22]. The TB-mBJ potential approximation is applied to calculate the electronic properties of both compounds [23]. Elastic constants are obtained through the IRelast package from which the diverse mechanical parameters are investigated. From ε(ω) = ${\mathsf{\epsilon }}_1$(ω) + i${\mathsf{\epsilon }}_2$(ω) (complex dielectric function), we have determined the optical character of both compounds in which ε₁(ω) shows the real and ${\mathsf{\epsilon }}_2$(ω) represent an imaginary part. The ${\mathsf{\epsilon }}_2$(ω) was computed from the momentum matrix of unoccupied and occupied wave functions, while the ${\mathsf{\epsilon }}_1$(ω) is achieved from ${\mathsf{\epsilon }}_2$(ω) through Kramers–Kronig relations [24,25]. The expression of the lattice harmonics angular momentum cuts at l_max = 10 and up to G_max = 14 Bohr⁻¹, the Fourier expansion runs, while the wave function in the interstitial regions is described by plane wave expansions. The cut-off value of K_max displays the determined number of plane waves and depends on the parameter of R_MT × K_max = 6.5 (in these investigations) and 2000 k-points are taken to obtain the precise result.

3. Structural Properties

Herein, the investigated compounds BaMCl₃ (M = Ag, Cu) crystallize into the ideal cubic structure of perovskite having space group (#221). The unit cell contains one molecule of BaMCl₃. The constituent atom lies at positions (0, 0, 0), (0.5, 0.5, 0.5), and (0, 0.5, 0.5) for Ba, M, and Cl, respectively. The crystal structures are displayed in Figure 1.

To measure the thermodynamic stability and synthesizability, the enthalpy of formation is computed through formulas:

H = E + PV

(1)

For both compounds, the “H” values are negative. The negative values of enthalpy for both compounds signify the thermodynamic stability and the formation of the interested compound [26]. Furthermore, to investigate the structural stability, the Goldschmidt tolerance factor is computed from the ionic radii [27]. By using the volume optimization graph, the lattice parameters are computed at minimum energy and the calculated values are present in

Table 1. The optimized crystal structural parameters comprising lattice constant (in Bohr), Bulk modulus (in GPa), ground state volume in (Bohr)³, B^/ (the derivative of Bulk modulus in GPa), ground state energy E₀ in Ry and the tolerance factor τ.

Structural Parameters	BaAgCl3	BaCuCl3
Lattice constant (Bohr)	9.90	9.38
Bulk modulus (B)	34.19	43.03
Ground state volume (V0)	968.2	820.78
Bulk modulus derivative (B/)	5.52	7.66
Ground state energy (E0)	−29,682.92	−22,358.39
Tolerance factor (τ)	0.93	0.97

. The optimized volume versus energy curve is plotted in Figure 2. Table 1 clarifies that with an increase in the lattice constant, the bulk modulus decreases indicating the hardness of BaAgCl₃ is more than BaCuCl₃.

From the above presented optimized structural parameters, it is concluded that both the materials BaMCl₃ (M = Ag, and Cu) are structurally stable and optimized.

Phonon Properties

Phonons are a crucial component of dynamic behaviors and thermal characteristics, which are the main aspects of the fundamental problems of materials science. The phonon dispersion band structure of cubic ternary BaAgCl₃ and BaCuCl₃ are investigated using the WIEN2K package within the frequency range from 0 THz up to 16 THz, as depicted in Figure 3. It can be seen from Figure 3 that the phonon dispersion curves for both materials are positive and there are no negative values of dispersion curves (imaginary phonon frequencies). The positive dispersion curves confirm the phonon dynamical stability of both compounds.

4. Electronic Properties

The fitted band structures and densities of states (DOS) within the energy range from −8 eV to 8 eV are conducted for the computation of electronic properties of BaAgCl₃ and BaCuCl₃ ternary chloroperovskites. The TB-mBJ approximation is applied to investigate the band structures of both ternary BaAgCl₃ and BaCuCl₃ chloroperovskites compounds, shown in Figure 4. The Fermi energy level (E_F) separates the valence and conduction states. Valance band maxima and conduction band minima appear at the different symmetry points, i.e., from R–Γ, and hence, possess the indirect band gap with values 1.173 eV and 2.30 eV for BaCuCl₃ and BaAgCl₃, respectively. The BaAgCl₃ possesses a higher band gap than BaCuCl₃ due to the high electronegativity of Ag than Cu.

TDOS and PDOS for BaCuCl₃ and BaAgCl₃ are plotted in Figure 5a,b, respectively, to analyze the impact of different electronic states in valence and conduction bands. Figure 5a clarifies that the valance band of BaCuCl₃ consists of Cl p-orbital from −4.5 to −8 eV have high contribution and p, d-orbital from −1.5 to 0 eV energy have little contribution and Cu d-orbital contribute from energy 0 to −2 eV, while Ba has no contribution to the valance band. In the conduction band, Ba-d and f orbitals from 2 to 6 eV, Cu s-p orbital contribute in the range of 4 up to 6 eV, while s, p, d-orbitals of “Cl” contribute from 2 up to 8 eV. Figure 5b clarifies that the valance band of BaAgCl₃ mainly consists of Cl-p, and Ag-d orbital from 0 to −6 eV, while “Ba” has no contribution to the valance band. In the conduction band Ag-s, Ba-d, f, and p, d-orbitals of Cl mainly contribute from energy 2 up to 6 eV. The band structures and DOS indicate the existence of a band gap between the conduction and valance bands in both compounds justifying that these compounds are semiconductors in nature.

5. Elastic Properties

The mechanical properties of a material are interrelated to essential solid-state phenomena including inter-atomic bonding, phonon spectra, and equation of state that play a vital role in structural stability and resistance to external forces. Many mechanical properties such as fracture toughness, ductility, brittleness, thermo-elastic stress, sound velocities, internal strain, etc., can be explained through elastics constants [28,29,30]. Herein, the elastic constants are investigated through the IRelast package developed by J. Murtaza [31]. As both compounds are FCC, the elastics constants C₁₁, C₁₂, and C₄₄ are sufficient to explain their elastics characteristics. The investigated elastics constants C₁₁, C₁₂, and C₄₄ are present in

Table 2. The computed elastic parameters including the cubic elastic constants (C₁₁, C₁₂, and C₄₄ in GPa), the Bulk modulus “B” (in GPa), anisotropy factor “A”, Shear modulus “G” (in GPa), Young’s modulus “E” (in GPa), Poisons ration “υ” and the Pugh ratio (B/G) and the Kleinman parameter (ζ).

Compounds	C11	C12	C44	B	A	G	E	υ	B/G	ζ
BaAgCl3	89.42	25.31	3.35	46.68	0.10	4.80	13.9	0.66	9.73	0.793
BaCuCl3	105.16	40.6	19.93	62.12	0.61	15	2.00	0.74	4.14	0.878

.

For structure stability, the elastics constants should satisfy the Born stability criteria which are

C₁₁ − C₁₂ > 0, C₄₄ > 0, C₁₁ + 2C₁₂ > 0

(2)

Based on our calculated elastics constant we can conclude that both compounds are structurally stable and resist elastic deformation [32]. Bulk modulus, Young’s modulus, Shear modulus, anisotropic ratio, Poisson’s ratio, and Kleinman parameters are other essential mechanical properties of solids for industrial applications. Table 2 clarifies that the value of bulk modulus “B” is higher for BaAgCl₃ than BaCuCl₃, showing that BaCuCl₃ is more compressible than BaAgcl₃ when they are compressed from all sides. The value of “B” depends upon the lattice constant of the compound, and similarly, the bulk modulus and volume are inversely proportional to each other. Our calculated result is in agreement with this literature [20,21]. Cauchy pressure (C₁₂ − C₄₄), Poisson’s ratio, and Pugh ratio predict the brittle (ductile) nature of the material. If the value of Cauchy’s pressure is negative (positive) the material will be brittle (ductile). For the investigated compounds the value is positive hence both are ductile. Pugh’s criteria suggest that material will be brittle if the B/G value is smaller than 1.75 and ductile for the value of B/G is greater than 1.75 [33,34]. For a Poisson’s ratio greater (smaller) than 0.26, the material will be ductile (brittle). From Table 2, the Pugh’s ratio and Poisson ratio is greater than 1.75 and 0.26 for BaAgCl₃ than BaCuCl₃, respectively, hence both compounds are ductile [35]. Cauchy’s pressure also defines the bonding nature of the material. For the ionic nature of the material, the material will have a positive value of Cauchy’s pressure and a negative for covalent bonding [36,37]. The anisotropic ratio (A) is applied to determine the degree of elastic anisotropy in a solid material. An ideal isotropic system has an anisotropic ratio of one. When the value is “A” rather than unity, the material is said to be elastically anisotropic, meaning its elastic characteristics vary in different directions. The calculated value of “A” is not equal to “1” which is presented in Table 2, hence the compounds are anisotropic [38]. Another important parameter that describes bond stretching and bond bending is the Kleinman parameter (ζ). The zero value of the Kleinman parameter (ζ) indicates the minimum bond bending and when its value is 1, it shows minimum bond stretching. Table 2 clarifies that the value of ζ for BaCuCl₃ is 0.878 and that for BaAgCl₃ is 0.793, reflecting that the bond stretching of the selected compound is minimal [37,39].

6. Optical Properties

Herein, the parameters in optical properties are explored which include the dielectric function, optical conductivity, reflectivity, absorption coefficient, and refractive index of halide perovskite in the energy range from 0 to 40 eV. The complex dielectric function described the optical properties of the material. According to Ehrenreich and Cohen’s equation [40], the dielectric can be written as:

$$\mathsf{\epsilon }(\mathbf{\omega })={\mathsf{\epsilon }}_1(\mathbf{\omega })+\mathit{i}{\mathsf{\epsilon }}_2\left(\mathbf{\omega }\right)$$

(3)

Here, the ${\mathsf{\epsilon }}_1$ (ω) displays the real part and ${\mathsf{\epsilon }}_2$ (ω) shows an imaginary component of the dielectric function and they can be determined from the following equations [25,41]:

$${\mathsf{\epsilon }}_1\left(\mathsf{\omega }\right)=1+\frac{2}{\pi }P {{\displaystyle \int }}_0^{\infty }\frac{{\mathsf{\omega }}^{\prime }{\mathsf{\epsilon }}_2\left({\mathsf{\omega }}^{\prime }\right)}{{{\mathsf{\omega }}^{\prime }}^2-{\mathsf{\omega }}^2}\mathrm{d}{\mathsf{\omega }}^{\prime }$$

(4)

$${\mathsf{\epsilon }}_2\left(\mathsf{\omega }\right)=\frac{8}{2\pi {\mathsf{\omega }}^2}{{\displaystyle \sum }}_{{nn}^{\prime }}{\displaystyle \int } {|p_{{nn}^{\prime }} \left(k\right)|}^2\frac{d{S}_k}{\nabla {\mathsf{\omega }}_{{nn}^{\prime }} \left(ks\right)}$$

(5)

The dispersive behavior of compounds can be determined from the real component of the dielectric function whereas, the imaginary component gives information about the absorption of light [42,43]. Other optical parameters such as absorption coefficient, refractive index, optical conductivity, extension coefficient, and reflectivity can be described from the real and imaginary parts of the dielectric function. Figure 6a depicts the real part of the function and the values of ${\mathsf{\epsilon }}_1\left(\mathsf{\omega }\right)$ at zero frequency are 3.8 and 4.48 for BaAgcl₃ and BaCuCl₃, respectively. The greater value of BaCuCl₃ indicates a smaller band gap as compared to BaAgCl₃. The maximum peaks of the real part approach 6.79 at 4.50 eV for BaAgCl₃ and 6.009 at 5.8 eV for BaCuCl₃. The minima of the real part are about the same at 18.1 ev of value −2.1, indicating its metallic behavior. The obtained curved for the imagery part of the function is plotted in Figure 6b.

It can be observed that the peak starts from 2.1 and 2.3 for BaAgCl₃ and BaCuCl₃, respectively, which means that the photon absorption starts from this energy range and the photons having less energy than these values are not able to be used for the transition of electrons from the valance to the conduction band. Moreover, the maximum peak reached 5.23 at 5.79 eV and 5.4 at 6.4 eV for BaAgCl₃ and BaCuCl₃, respectively. The indirect band gap and band-to-band transition are confirmed by the fluctuating peaks.

6.1. Extension Coefficient and Refractive Index

Utilizing the following expression the extension coefficient and refractive index are calculated.

$$\mathrm{k}(\mathsf{\omega })={\left[\frac{\sqrt{{\mathsf{\epsilon }}_1{}^2\left(\mathsf{\omega }\right)+{\mathsf{\epsilon }}_2{}^2\left(\mathsf{\omega }\right)}}{2}-\frac{{\mathsf{\epsilon }}_1\left(\mathsf{\omega }\right)}{2}\right]}^{1/2}$$

(6)

$$\mathit{n}(\mathsf{\omega })={\left[\frac{\sqrt{{\mathsf{\epsilon }}_1{}^2\left(\mathsf{\omega }\right)+{\mathsf{\epsilon }}_2{}^2\left(\mathsf{\omega }\right)}}{2}+\frac{{\mathsf{\epsilon }}_1\left(\mathsf{\omega }\right)}{2}\right]}^{1/2}$$

(7)

On the bases of the refractive index of the material, one can judge its application in optical devices. Materials having a high refractive index can be used in a photovoltaic cell. In Figure 7 the refractive index and extension coefficient are plotted. From Figure 7, it is noted that the value of (0) is 1.96 and 2.12 for BaAgCl₃ and BaCuCl₃, respectively.

The maximum values of n(0) for BaAgCl₃ and BaCuCl₃ are 2.63 at 4.64 eV, and 2.56 at 5.98 eV, respectively. The photon and electrons of compounds will interact with each other and after an interaction; the photon will slow down because of a refractive index value greater than 1.

6.2. Reflectivity

The numerical value of reflectivity R(ω) can be calculated from the refractive index and extension coefficient through the following expression:

$$\mathrm{R}(\mathsf{\omega })=\frac{{\left(1-n\right)}^2+k^2}{{\left(1+n\right)}^2+k^2}$$

(8)

The obtained spectra for reflectivity are plotted in Figure 8.

The value of reflectivity at zero energy is 0.106 and 0.12 for BaAgCl₃ and BaCuCl₃, respectively. The materials are more reflective in the energy range of 16 eV to 25 eV. The highest peak is found at 0.524 at 18.17 eV for BaAgCl₃ while for BaCuCl₃ the highest peak is 0.566 at 18.4 eV.

6.3. Absorption Coefficient

A material’s ability to transmit light of a specific wavelength for a certain distance before it is absorbed depends on its absorption coefficient. Using the following expression, the I (ω) can be determined:

$$I(\mathsf{\omega })=\frac{4\pi k}{\lambda }$$

(9)

Whereas, λ and k are the wavelength and extinction coefficient. The absorption coefficient shows the absorption of photons per unit length by material. The absorbed photon transmits the electron from the valance to the conduction band by giving them suitable energy. The spectra of the absorption coefficient are shown in Figure 9. From Figure 9 it is noted that this material absorbs energy in the range of 5 to 25 eV.

Hence, these materials are good light absorbers; therefore, they can be used in optoelectronic devices. From the absorption coefficient spectra, it can also be observed that BaCuCl₃ is a good absorber as compared to BaAgCl₃. The highest peak is found for BaCuCl₃ to be 296 at 18.3 eV while for BaAgCl₃ it is noted at 300 at 18.17 eV.

6.4. Optical Conductivity

By using the following expression we can calculate the optical conductivity

$$\mathsf{\sigma }\left(\mathsf{\omega }\right)=\frac{2\mathrm{ħ}\mathsf{\omega }}{E_0}$$

(10)

Whereas, “ω” is the incident frequency of the photon and E₀ is the photon energy. The obtained spectra for optical conductivity are presented in Figure 10, indicating that BaCuCl₃ is more optical conductive as compared to BaAgCl₃.

The maximum value of optical conductivity is found at 10,200 at 17.25 eV and 10,700 at 17.13 eV, respectively. The materials show conductance in the 5 eV to 20 eV energy range.

7. Conclusions

The structural, electronic, mechanical, and optical properties of BaAgCl₃ and BaCuCl₃ are explored for the first time through density functional theory. The structural properties reveal that BaAgCl₃ and BaCuCl₃ have stable structures and the negative enthalpy conforms to their formation. The electronic structure shows its semi-conducting nature with an indirect band gap (R–Γ) of value 1.173 eV and 2.30 eV for BaCuCl₃ and BaAgCl₃, respectively. It is found that BaCuCl₃ is more compressible than BaAgCl_3. Furthermore, the study of elastic properties reveals that both compounds are ductile, anisotropic, and possess an ionic bonding nature. Various spectrums of optical parameters are studied and from the optical spectrum, the indirect band gap and band-to-band transition is conformed for both compounds. Moreover, these compounds absorb light within 5 to 25 eV incident photon energy. Hence, these materials are good light absorbers; therefore, they can be used in optoelectronic devices.