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

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.


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][2][3][4].Lead-free perovskite compounds, with the stoichiometric formula of ABX 3 , 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][8][9][10].However, substituting half of the B cations with some allowable B'-elements results in the shape of double perovskite A 2 BB / X 6 .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][14][15][16][17][18][19][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][22][23][24].
Within A 2 BB / X 6 , the Ag-containing halide double perovskites had excellent thermoelectric and optoelectronic properties.Saeed et al. [25] investigated Cs 2 AgCrZ 6 (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 Cs 2 BiAgBr 6 and reported it as an indirect bandgap (Eg = 1.728 eV) compound.Filip et al. [27] also confirmed the indirect band semiconducting nature of Cs 2 BiAgBr 6 along with Cs 2 BiAgCl 6 through their experiment and theory.Bhorde et al. [28] suggested Rb 2 AgBiI 6 for solar cell applications because of its excellent optical properties.Mathew et al. [29] recommended Cs 2 AgInCl 6 (Eg = 1.1 eV) for optoelectronic properties.Nazir et al. [30] reported the effect of anion replacement in Rb 2 AgAsZ 6 (Z = Cl, Br, I) for thermoelectric and solar cell applications.They calculated the bandgaps of Rb 2 AgAsCl 6 , Rb 2 AgAsBr 6 and Rb 2 AgAsI 6 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 K 2 AgAsCl 6 as 1.1805eV.Besides this study, there are no investigations on K 2 AgAsX 6 (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 K 2 AgAsX 6 (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 K 2 AgAsX 6 for applications in energy-based technologies.

Method of calculations
The double perovskites K 2 AgAsX 6 (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 K 2 AgAsX 6 , 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.

Structural properties
Figure 1 shows the crystal structure of the K 2 AgAsX 6 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.K 2 AgAsBr 6 has a larger lattice constant than K 2 AgAsCl 6 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][41][42].

Electronic properties
The energy bandgap of a material is its critical parameter in deciding its use in energy-harvesting applications [43][44][45].In the present work, the energy band structures and total density of states (TDOS) of the compounds K 2 AgAsX 6 (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 K 2 AgAsCl 6 and K 2 AgAsBr 6 , respectively.The bandgaps for other Agcontaining 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].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 sstate character is dominated.In these materials, p/d to s transitions from valance to conduction will be dominant when interacting with photons.

Optical properties
In this section, we explain the optical properties of K 2 AgAsX 6 (X = Cl, Br).These properties are determined through some optical parameters for which the relations are given in [14][15][16]48].Figure 4(a) depicts the computed real part of the dielectric function (ε 1 (ω)) for  both K 2 AgAsX 6 double perovskites.ε 1 (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 (ε 1 (0)).ε 1 (0) for K 2 AgAsBr 6 is large than K 2 AgAsCl 6 because of its small bandgap.Also, the peak value of K 2 AgAsBr 6 has a larger value (8.4) than K 2 AgAsCl 6 (6.51).Similar bahaviour is also observed for other double perovskites [49,50].The imaginary part of the dielectric function (ε 2 (ω)) is shown in Figure 4(b).ε 2 (ω) gives information on the absorption of light by a material.The ε 2 (ω) threshold points are 2.7 and 2 eV for K 2 AgAsCl 6 and K 2 AgAsBr 6 , respectively.The spectra for both compounds increase sharply beyond the threshold points.The K 2 AgAsBr 6 and K 2 AgAsCl 6 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 K 2 AgAsBr 6 more active for solar cell applications than K 2 AgAsCl 6 .
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 K 2 AgAsBr 6 has a higher static refractive index than K 2 AgAsCl 6 due to its lower energy gap.The higher value of K 2 AgAsBr 6 dictates that the speed of photons will be smaller in these compounds than in K 2 AgAsCl 6 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, K 2 AgAsBr 6 shows a more prominent absorption per unit length of the materials than K 2 AgAsCl 6 in the visible region.A major absorption peak is absorbed above the blue band in the ultraviolet region.

. 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 = σ S 2 T/κ), where σ is the electrical conductivity, S is the Seebeck coefficient, T is the temperature and κ is the thermal conductivity [53][54][55][56].For K 2 AgAsCl 6 and K 2 AgAsBr 6 , 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 × 10 19 1/ ms at 800 K, as shown in Figure 5(a).However, the σ /τ for K 2 AgAsBr 6 is a little greater than K 2 AgAsCl 6 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 × 10 14 W/mKs at 800 K for both the K 2 AgAsX 6 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].
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][60][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 σ S 2 /τ .Its values increase from zero to about 4.2 x10 11 W/mK 2 s, as shown in Figure 5(d).However, the K 2 AgAsCl 6 has little large values of PF than K 2 AgAsBr 6 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 K 2 AgAsCl 6 and K 2 AgAsBr 6 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.

Conclusions
Density functional theory is applied for the calculation of structural, electronic, optical and thermoelectric properties of halide double perovskites K 2 AgAsX 6 (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 K 2 AgAsBr 6 , 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 K 2 AgAsX 6 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.