The study of new double perovskites K₂AgAsX₆ (X = Cl, Br) for energy-based applications

Abstract

Halide double perovskites are the best alternative to Pb-halide perovskites. These materials play an important role in renewable energy generation. Therefore, we explore the physical properties of K₂AgAsX₆ (X = Cl, Br) double halide perovskites using full potential linearized augmented plane wave method . The structural parameters are calculated by optimization and analytical schemes. The negative values of formation energy confirm the thermodynamic stability, while Goldsmith’s tolerance factor guarantees the structural stability of both the double perovskites. The bandgaps of K₂AgAsCl₆ and K₂AgAsBr₆ are calculated as 2.10 and 1.48 eV, respectively by modified Becke and Johnson potential. Optical properties are examined in terms of the dielectric function, refractive index and absorption coefficients. The thermoelectric properties are calculated in terms of the electronic and thermal conductivities, Seebeck coefficients, power factor and figure of merit. Our study suggests the K₂AgAsX₆ perovskites for energy-related applications.

KEYWORDS:

• Halide double perovskites
• density functional theory
• renewable energy
• optical properties
• thermoelectric properties

1. Introduction

To understand technological applications, such as solar panel manufacturing, photonic sensors, thermoelectric generators, luminescence, etc., it is compulsory to evaluate the performance of materials and their native properties [1–4]. Lead-free perovskite compounds, with the stoichiometric formula of ABX₃, are known to be versatile materials. Where an A-site cation can be an element from the s/p block, B is a cation mostly from d/f block elements, and X is an anion (halogen or oxygen) [5,6]. Due to their flexible structure, perovskites easily tolerate the modification/tailoring in the composition to have improved magnetic, electronic, optical and thermoelectric properties [7–10]. However, substituting half of the B cations with some allowable B'-elements results in the shape of double perovskite A₂BB^/X₆. The exchange coupling between B and B’ cations results in remarkable and feasible properties [11,12].

Double perovskites are multipurpose materials. They have a wide range of sustainable and renewable applications because of their surprising stability and electronic structure [13–20]. The distinctive features, such as hole and electron transport, high mobility and long diffusion lengths of the charge carrier, tunable bandgaps and stimulus-based variation in the properties, are the fundamentals of the notable performance of halide double perovskites [21–24].

Within A₂BB^/X₆, the Ag-containing halide double perovskites had excellent thermoelectric and optoelectronic properties. Saeed et al. [25] investigated Cs₂AgCrZ₆ (Z = Cl, Br, and I) through the density functional theory and recommended these materials for thermoelectric applications. Lozhkina et al. [26] carried out research on Cs₂BiAgBr₆ and reported it as an indirect bandgap (Eg = 1.728 eV) compound. Filip et al. [27] also confirmed the indirect band semiconducting nature of Cs₂BiAgBr₆ along with Cs₂BiAgCl₆ through their experiment and theory. Bhorde et al. [28] suggested Rb₂AgBiI₆ for solar cell applications because of its excellent optical properties. Mathew et al. [29] recommended Cs₂AgInCl₆ (Eg = 1.1 eV) for optoelectronic properties. Nazir et al. [30] reported the effect of anion replacement in Rb₂AgAsZ₆ (Z = Cl, Br, I) for thermoelectric and solar cell applications. They calculated the bandgaps of Rb₂AgAsCl₆, Rb₂AgAsBr₆ and Rb₂AgAsI₆ as 2.21, 1.50 and 0.52 eV, respectively. Saha et al. [31] studied double perovskite materials for photovoltaic applications through machine learning. They found the bandgap of K₂AgAsCl₆ as 1.1805eV. Besides this study, there are no investigations on K₂AgAsX₆ (X = Cl, Br) double perovskite compounds. Therefore, it is required to explore the physical properties of these important compounds.

In this article, we apply the full potential linearized augmented plane wave method (FP-LAPW) [32] within the framework of the density functional (DFT) theory and the classical Boltzmann theory [33] for the calculation of physical properties of K₂AgAsX₆ (X = Cl, Br) halide double perovskites. The present work may provide important information for further research at both theoretical and experimental levels to ascertain both the K₂AgAsX₆ for applications in energy-based technologies.

2. Method of calculations

The double perovskites K₂AgAsX₆ (X = Cl, Br) crystallize in cubic structures with the space group Fm-3 m (# 225). Where the K atom occupies (0.25, 0.25, 0.25) functional coordinates and 8c Wyckoff site, the Ag atom is located at (0, 0, 0,) with 4a Wyckoff site, As atom is coordinated at (0.5, 0.5, 0.5) with the Wyckoff position of 4b, and X anion occupies (0.25, 0, 0) position with the Wyckoff site of 24e. To manipulate both the perovskites K₂AgAsX₆, the Wien2k computational code, based on the FP-LAPW [32] method of DFT [34], was used. The exchange-correlation potential was treated with a generalized gradient approximation of Wu and Cohen [35] and modified Becke–Johnson schemes [36]. The relaxation of relative atomic sites, shape and size was completed with energy 10⁻⁴ Ry, while the convergence of charge was attained at 0.001 e. Furthermore, a fine dense mesh of 1000 k-points was used for the calculation of structural parameters, band structures, the density of states and optical properties. BoltzTraP code [26] was considered for the calculation of thermoelectric properties.

3. Results and discussion

3.1. Structural properties

Figure 1 shows the crystal structure of the K₂AgAsX₆ double perovskites compounds. To explore these structures, the unit cells were first optimized by an energy minimization process and then by the relaxation of internal parameters. Afterwards, in the ground state, the lattice constants of the double perovskites were determined with the help of Murnaghan’s equation of state [37]. The calculated values of the lattice parameters are given in Table 1. K₂AgAsBr₆ has a larger lattice constant than K₂AgAsCl₆ due to its higher ionic size. However, the bulk modulus of the compounds changes inversely with the anion variation from Cl to Br. The related compounds [30] also show the same behaviour as shown in Table 1. The tolerance factor [38] of the compounds is around 0.9 which indicates the compounds are stable in the cubic phase. For further confirmation, the formation energy of the perovskites was calculated through the relation in Equation (1) [39]. Its negative values (Table 1) confirm the stability of the compounds in the cubic phase [40–42]. (1) $\begin{array}{r}{H}_f=E_{(K_2\mathrm{AgAs}{X}_6)}-(2E_K+E_{\mathrm{Ag}}+E_{\mathrm{As}}+6E_X)\end{array}$(1)

Figure 1. Crystal strucutre of K₂AgAsX₆ (X = Cl, Br).

Table 1. The computed parameters for K₂AgAsCl₆ and K₂AgAsBr₆ along with already reported [30] parametres of Rb₂AgAsCl₆ and Rb₂AgAsBr₆.

Parameter	K2AgAsCl6 Present	Rb2AgAsCl6 [30]	K2AgAsBr6 Present	Rb2AgAsBr6 [30]
Lattice constant ao(Å)	10.41	10.48	10.96	11.10
Bulk modulus Bo (GPa)	31.47	29.84	25.92	27.98
Formation energy Hf (eV)	−3.10	−1.52	−2.50	−0.96
Band gap Eg(eV)	2.10	2.21	1.48	1.50
	1.1805eV [31]
Tolerance factor Tf	0.89	0.93	0.91	0.92
Static refractive index n(0)	1.91	1.92	2.16	2.16
Static dielectric constant ϵ1(0)	3.67	3.72	4.70	4.68
Reflectivity R (0)	0.098	0.100	0.135	0.135

3.2. Electronic properties

The energy bandgap of a material is its critical parameter in deciding its use in energy-harvesting applications [43–45]. In the present work, the energy band structures and total density of states (TDOS) of the compounds K₂AgAsX₆ (X = Cl, Br) have been presented in Figure 2. TDOS provides the value of the bandgap, while the band structure also explores the nature of the bandgap. The figure makes it clear that both the predicted perovskites have energy bandgaps of indirect nature (X – L). The values of these bandgaps decrease by changing the anion (X) from Cl to Br while lying in the visible and near-infrared regions for K₂AgAsCl₆ and K₂AgAsBr₆, respectively. The bandgaps for other Ag-containing double perovskites have been also reported in this range [26,28,30]. Furthermore, the variation in bandgaps with anion change is also observed in different reports [25,46,47].

Figure 2. Band structures and total density (TDOS) of (a) K₂AgAsCl₆ and (b) K₂AgAsBr₆

The identification of different energy bands in the bandstructure can be performed by determining the partial density of states. Figure 3 shows the partial density of states (PDOS) plotted as a function of energy. The valance band below the Fermi level shows the high p-d hybridization between the p state of halogen with the cations. Therefore, the covalent bond character is dominant in these materials. In the conduction band s-state character is dominated. In these materials, p/d to s transitions from valance to conduction will be dominant when interacting with photons.

Figure 3. The partial density of states of (a) K₂AgAsCl₆ and (b) K₂AgAsBr₆.

3.3. Optical properties

In this section, we explain the optical properties of K₂AgAsX₆ (X = Cl, Br). These properties are determined through some optical parameters for which the relations are given in [14–16,48]. Figure 4(a) depicts the computed real part of the dielectric function (ε₁(ω)) for both K₂AgAsX₆ double perovskites. ε₁(ω) reveals the limit to which a compound polarizes when electromagnetic radiations fall on it. The values of this function start from a static limit (ε₁(0)). ε₁(0) for K₂AgAsBr₆ is large than K₂AgAsCl₆ because of its small bandgap. Also, the peak value of K₂AgAsBr₆ has a larger value (8.4) than K₂AgAsCl₆ (6.51). Similar bahaviour is also observed for other double perovskites [49,50].

Figure 4. Calculated (a) real $({\epsilon }_1(\omega ))$ and (b) imaginary $({\epsilon }_2(\omega ))$ parts of dielectric function, (c) refractive index $(n(\omega ))$ and (d) absorption coefficient $(\alpha (\omega ))$ for K₂AgAsCl₆ and K₂AgAsBr₆.

The imaginary part of the dielectric function (ε₂(ω)) is shown in Figure 4(b). ε₂(ω) gives information on the absorption of light by a material. The ε₂(ω) threshold points are 2.7 and 2 eV for K₂AgAsCl₆ and K₂AgAsBr₆, respectively. The spectra for both compounds increase sharply beyond the threshold points. The K₂AgAsBr₆ and K₂AgAsCl₆ show maximum peaks at around 3.5 and 4 eV, respectively with one minor peak below these. The maximum peaks originated due to the parallel bands in the valence and conduction bands. This enhances the joint DOS factor [51]. In the energy region of maximum peaks, pd-hybridized state electrons from the valence band make transitions to the s or p unoccupied states in the conduction band. In addition, the maximum peak shifts to the visible region by the replacement of Cl with Br. This makes the double perovskite compound K₂AgAsBr₆ more active for solar cell applications than K₂AgAsCl₆.

The refractive index of any optical medium is an important design parameter for device fabrication. In the present work, the refractive indexes of the compounds are also calculated and plotted in Figure 4(c). The static refractive index depicts the low-frequency response of a material. Usually, it varies inversely with the energy bandgap [52]. It is seen from the figure that K₂AgAsBr₆ has a higher static refractive index than K₂AgAsCl₆ due to its lower energy gap. The higher value of K₂AgAsBr₆ dictates that the speed of photons will be smaller in these compounds than in K₂AgAsCl₆ in the low-frequency range. The refractive index attains maximum value in the visible region for the compounds which indicates the usefulness of the current compounds for optoelectronic applications. The replacement of Br in place of Cl for the compounds significantly changes the optical response; the refractive index peak becomes prominent and also shifted to lower energies.

Materials’ absorption strength per unit length is defined by the absorption coefficient. The absorption coefficient for the compounds is shown in Figure 4(d). The absorption started from the threshold point is also known as the absorption edge. This matches exactly with the direct electronic transition energy for the compounds. Comparatively, K₂AgAsBr₆ shows a more prominent absorption per unit length of the materials than K₂AgAsCl₆ in the visible region. A major absorption peak is absorbed above the blue band in the ultraviolet region.

3.4 . Thermoelectric properties

The conversion of heat energy to electrical energy through thermoelectric generators is an important process of renewable and clean energy. The performance of thermoelectric materials can be judged through the figure of merit (ZT = σS²T/κ), where σ is the electrical conductivity, S is the Seebeck coefficient, T is the temperature and κ is the thermal conductivity [53–56]. For K₂AgAsCl₆ and K₂AgAsBr₆, all the respective parameters and ZT along power factor are calculated and are presented in Figure 5(a–d), and Figure 6 shows the temperature range 0–800 K. It has been noted the values of σ/τ (τ is the relaxation time) increase linearly for both the studied double perovskites to 1.4 × 10¹⁹ 1/Ωms at 800 K, as shown in Figure 5(a). However, the σ/τ for K₂AgAsBr₆ is a little greater than K₂AgAsCl₆ because of the large atomic radius of the Br atom than the Cl atom. Furthermore, a similar trend of increasing values of κ_e/τ has been found. Its value is noted at about 5.0 × 10¹⁴ W/mKs at 800 K for both the K₂AgAsX₆ compounds (See Figure 5(b)). Overall, the ratio of κ_e/τ to σ/τ has ultralow values (10⁻⁵) which show the studied materials are important for thermoelectric applications [57,58].

Figure 5. (a) electronic conductivity (σ/τ) (b) thermal conductivity (κ_e/τ) (c) Seebeck coefficients (S) and (d) Power factor (S²σ/τ) as a function of temperature for K₂AgAsX₆ (X = Cl, Br).

Figure 6. Temperature-dependent Figure of merit (ZT) for K₂AgAsX₆ (X = Cl, Br).

The potential gradient between different contacts of thermoelectric materials has been illustrated by the Seebeck coefficient. The calculated values of S are presented in Figure 5(c) which shows the monotonically increase in values up to 400 K then this increase reduces with a further increase in temperature. However, the values in mV/K are more than the 200 limits of best thermoelectric material materials. This limit is very essential for thermoelectric applications [59–61]. The performance of thermoelectric materials is also analyzed by power factor which is the product of σ/τ and the square of S represented as σS²/τ. Its values increase from zero to about 4.2 x10¹¹ W/mK²s, as shown in Figure 5(d). However, the K₂AgAsCl₆ has little large values of PF than K₂AgAsBr₆ because of the greater values of S.

Finally, the figure of merit is calculated by the relation described at the start of this section and presented in Figure 6. Its values decrease from 0.8 and 0.9 for K₂AgAsCl₆ and K₂AgAsBr₆ to 0.25 with the increase in temperature from zero to 800 K. Therefore, the large values at low temperature and room temperature make them potential materials for thermoelectric generators and thermoelectric coolers.

4. Conclusions

Density functional theory is applied for the calculation of structural, electronic, optical and thermoelectric properties of halide double perovskites K₂AgAsX₆ (X = Cl, Br). Both compounds are found thermodynamically stable in the cubic phase. The structural parameters are calculated for reference data for future studies. The band gaps are calculated within the visible region for both compounds. Within the valence band, the density of states explores the high p-d hybridization between the p state of halogen and the d state of the cations. The peak values of the real part of the dielectric function and refractive index are observed to increase with a decrease in the bandgap. For K₂AgAsBr₆, maximum absorption is reported in the visible region of electromagnetic spectrum. The ratio of κ_e/τ to σ/τ has ultralow values (10⁻⁵) for both compounds. Large values of the figure of merit (ZT) make K₂AgAsX₆ materials potential candidates for low-temperature thermoelectric generators. The overall calculations of the properties support the main theme of the present study for renewable green energy.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was funded by the Researchers Supporting Project Number (RSP2023R265) King Saud University, Riyadh, Saudi Arabia.