Computational Exploration of Cs2LiMoX6 (X=Cl, I) Halide Double Perovskites: Unveiling Energy Storage Potentials

doi:10.21203/rs.3.rs-4109669/v1

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Computational Exploration of Cs2LiMoX6 (X=Cl, I) Halide Double Perovskites: Unveiling Energy Storage Potentials

https://doi.org/10.21203/rs.3.rs-4109669/v1

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Density functional theory (DFT) simulations were conducted to investigate the physical characteristics of materials Cs₂LiMoCl₆ and Cs₂LiMoI₆. The magnetic and electronic features were examined using the Perdew, Burke and Ernzerhof generalized-gradient approximation (PBE-GGA). Confirmation of the semiconductor behavior was attained through spin-resolved density of state (DOS) and band structure (BS) plots. In this investigation, the computed band gap (E_g) values for Cs₂LiMoI₆ are identified as 0.96 eV in the spin-down channel and 1.76 eV in the spin-up channel. Likewise, for Cs₂LiMoCl₆, the E_g is determined to be 3.35 eV in the spin-down channel and 1.63 eV in the spin-up channel. Exchange energies and crystal field splitting were estimated, indicating magnetic characteristics, with magnetic moments (µ_B) of 3.02436 µ_B and 3.00332 µB for Cs₂LiMoCl₆ and Cs₂LiMoI₆, respectively. The study also explored optical properties and the peak values of σ(ω) are observed to be 4631 (Ω cm)⁻¹ and 3618 (Ω cm)⁻¹ at 6.24 eV and 8 eV for Cs₂LiMoI₆ and Cs₂LiMoCl₆, respectively signifying its suitable nature to UV light region. Overall, these findings suggest the suitability of both materials for photovoltaics and other related applications.

DFT

halide double perovskites

Optoelectronic

semiconductor

The exceptional properties of halide perovskites (HPs), such as their high absorption coefficients, enhanced carrier mobility, and efficient luminescence, have garnered significant attention[1]. Particularly, halide perovskite solar cells have achieved a photoelectric conversion rate exceeding 25%, rivaling established thin film solar cells [2–4]. They differ from conventional semiconductors in that they have unique benefits such as a configurable band gap, a long lifespan, excellent fault tolerance, and simple synthesis. Taking advantage of these features, HPs have emerged as a key player in the optoelectronics industry, finding use in solar photovoltaic cells, LED photodetectors, laser devices, and other applications [5, 6]. As the third generation of solar converters, photovoltaic perovskite systems have emerged as highly promising and active materials in recent years [7].

However, the toxicity of lead and the material's instability under ambient circumstances are the two main obstacles that significantly limit its applicability in practical applications[8, 9]. An efficient method to obtain Pb free perovskites involves the substitution of two Pb2 + cations with two metal cations, one being monovalent [B (I)] and the other trivalent [ B (III)]. This substitution results in the formation of A₂B(I)B(III)X₆ perovskites, characterized by a stable cubic structure [10, 11].

Researchers are interested in studying lead-free cubic compounds because recent academic studies based on DFT have shown that the cubic crystal structure of these compounds indicates superior stability and best optoelectronic applications. After investigating the variations in the optical characteristics of A₂CuSbX₆ (where X = Cl, Br and A = Cs, Rb, K), Tang et al. [12] concluded that K₂CuSbCl₆ is a promising option for solar cells.. Additionally, DFT was utilized by Saeed et al. to study Cs₂XBBr₆ (X = Li, Na and B = In, Ga, and Al). The calculated band gaps (E_g) for Cs₂NaGaBr₆ and Cs₂LiGaBr₆ were computed as 0.45 eV and 0.731 eV, correspondingly. In contrast, the remaining materials exhibited band gaps (E_g) larger than 1.4 eV[13].

Our emphasis on Pb-free halide double perovskites (HDPs) Cs₂LiMoX₆ (X = Cl, I) is rooted in their amazing optoelectronic properties and unrealized potential in the realm of unexplored research. Both materials serve as a blank canvas for scientific inquiry, inspiring us to crack their mysteries and progress the field of materials research. We venture into this uncharted territory, motivated by the thrill of discovery and the potential for revolutionary breakthroughs.

The full-potential-linearized-augmented-plane wave (FP-LAPW) method[14], instigated using the WIEN2K code[15] based on DFT, is employed to unravel the optical response and structural features of Cs₂LiMoX₆ (X = Cl, I) compounds. The muffin tin radius (R_MT) is set to 2.5 for Cs, Li, I and 2.41 bohr for Mo in Cs₂LiMoI₆, while in Cs₂LiMoCl₆, the R_MT values are set to 2.5, 2.12, 2.28, 2.06 for Cs, Li, Mo and Cl, respectively ensuring zero leakage current[16]. Key parameters, such as the plane-wave factor (R_MT × K_MAX) set to 7 with K_MAX representing the uppermost plane wave-vector value, and G_max to 12 for charge-density truncation, contribute to the precision of computations. A total of 1000 K-points in the first Brillouin Zone (BZ) and an angular-momentum value of l_max = 10 in the spherical section are employed for achieving self-consistency[17].

3.1. Structural Properties

The materials Cs₂LiMoX₆ (X = Cl, I) disclose a cubic form structure characterized by the space group Fm-3m (#225). The Li and Mo cations are surrounded by six halide ions (I⁻ and Cl⁻) in the center of octahedra, creating MoX₆ octahedral complex. Fig. depicts the optimization and the organization of these substances in a crystalline configuration, wherein octahedral complexes have vertices with the Cs cation placed at the core of the cube-octahedral [18]. In the unit cell, the Cs atom is located at (3/4, 0.25, 0.25), the Li atom at (0, 0, 0), the Mo atom at (0.5, 0, 0), and the X (I and Cl) anion at (0.75, 0, 0). For gauging the structural robustness or extent of alteration in Cs₂LiMoX₆ (X = Cl, I), Goldschmidt's tolerance factor (τ) is utilized, and it is determined using the following expression [19].

$${\tau }=\frac{0.707({r}_{Cs}+{r}_{Cl/I})}{({r}_{avg}+{r}_{Cl/I})}$$

In this context, the symbols r_Cs, and r_X denote the respective atomic radii of Cs and X = Cl, I atoms and r_avg is the average ionic radius of Li and Mo. Fedorovskiy et al. stated that a τ falling within the range of 0.7 ≪ 1.2 is permissible for the generation of stable crystal structures[20]. The calculated τ values are 0.85 and 0.88 for Cs₂LiMoI₆ and Cs₂LiMoCl₆, respectively. As such, both compounds exhibit stable cubic structures, with their tolerance factor (τ) values situated within the acceptable range (refer to Table 1). Additionally, we assessed the stability of the materials by computing the formation enthalpy (ΔH) using the expression[21]:

$$\varDelta H={E}_{\text{C}\text{s}2\text{L}\text{i}\text{M}\text{o}\text{X}6}-a{E}_{Cs}-b{E}_{Li}-c{E}_{Mo}-d{E}_{X}$$

Here, E_Cs2LiMoX6 represents the total formation energy of Cs₂LiMoX₆ (X = Cl, I), while E_Cs, E_Li, E_Mo, and E_X denote the formation energies of the individual element and a, b, c and d are the number of atoms of respective element. The ΔH values are calculated as -3.948 eV and − 2.168 eV for Cs₂LiMoI₆ and Cs₂LiMoCl₆, respectively. The indication of the thermodynamic steadiness of the under-study materials is underscored by the existence of values with minus sign for their ΔH[22], as outlined in Table 1.

Table 1

Calculated values of lattice constant (Å), bulk modulus B (GPa), pressure derivative of bulk modulus Bp (GPa), tolerance factor (τ), and ground state energies E₀(R_y) of stable state of cubic Cs₂LiMoX₆ (X = Cl, I).
Parameters	Cs₂LiMoI₆	Cs₂LiMoCl₆
Lattice constant (Å)	11.7813	10.3649
Bulk modulus (GPa)	20.9476	33.7648
Pressure derivative (Bʹ)	5.1133	3.7694
Volume(a.u.)³	2758.7638	1878.5071
Ground state energy E₀(Ry)	-124704.7764	-44814.4987
Tolerance factor $\tau$	0.85	0.88

Utilizing the Murnaghan equation of state[23], the structural parameters comprising the equilibrium lattice parameter, bulk modulus (B), bulk modulus derivative (B′), volume at the ground state (V₀), and ground state energy (E₀) are optimized.

$$E\left(V\right)=\frac{9{B}_{0}}{16}{V}_{0}\left[{\left\{{\left(\frac{{V}_{0}}{V}\right)}^{2/3}-1\right\}}^{2}{Bꞌ}_{0}+{\left\{{\left(\frac{{V}_{0}}{V}\right)}^{\frac{2}{3}}-1\right\}}^{2}{\left\{6-4{\left(\frac{{V}_{0}}{V}\right)}^{2}\right\}}^{\frac{1}{3}}\right]{+E}_{0}$$

Through a volume optimization procedure for each compound, illustrated in Fig. 1 the total energy versus the volume of the unit cell. By incorporating this information into the equation, the structural factors (a, B, B′, E₀, and V₀) are determined, as presented in Table 1.

3.2. Electronic Properties

The understanding of carrier transport mechanisms is greatly prejudiced by the electronic properties of perovskites, which facilitates the differentiation between metals, semiconductors, and insulators through the analysis of E_g[24]. These electronic characteristics have far-reaching implications on other properties, including optical and thermoelectric aspects, shaping the suitability of materials for diverse industrial and commercial applications.

Utilizing the PBE-GGA approach, we have computed the electronic BS of Cs₂LiMoI₆ and Cs₂LiMoCl₆ along the highly symmetrical path W-L-Γ-X-W-K, as depicted in Fig. 2. In this study, the calculated E_g values for Cs₂LiMoI₆ are determined to be 0.96 eV in the spin-down channel and 1.76 eV in the spin-up channel. Correspondingly, for Cs₂LiMoCl₆, the E_g is found to be 3.35 eV in the spin-down channel and 1.63 eV in the spin-up channel. Notably, the E_g for these compounds are direct (at the X-point), enhancing their appeal for potential use in solar cells. The other similar studies also reported E_g in this range like Cs₂GeVM₆ (M = Cl, Br, I) which exhibit minimal bandgaps, falling within the range of 2 to 3 eV, and suggested suitable for optoelectronic applications in both the visible and UV regions[25].

Furthermore, we conducted calculations for DOS and projected DOS (PDOS) to offer a comprehensive understanding of the orbital and elemental contributions to the electronic structures. In this study, Fig. 3–5 display the total DOS and PDOS for elapsolites Cs₂LiMoCl₆ and Cs₂LiMo₆, respectively, presenting total, element-wise, and orbital-wise dispersions. In Fig. 5, Cs-s, Li-p and Cs-p orbitals notably shows dispersion in the valence band (VB) in the energy range − 5 eV to -2 eV. However, larger influence is seen near the E_F from Mo-d-t₂g. In conduction band (CB), less dispersion is seen for both compounds with large involvement from Li-p and Li-s orbitals near 3 eV.

Conversely, for Cs₂LiMoI₆, orbitals actively participate in the conduction band. In Fig. 4, it is evident that Mo-d-t₂g and Mo-d-e-g, make significant contributions near the E_F in the VB, and I-s and I-p show dispersion in energy range of -4 eV to -1 eV. While Li-p and Li-s are prominently involved in the conduction band for Cs₂LiMoI₆. The fundamental physics responsible for the narrow E_g can be elucidated by considering the presence of dispersed spherical orbitals (Mo-d-t₂g and Mo-d-e-g) at the conduction band minimum. Due to overlapping of halide orbits caused by this presence, extremely dispersive bands are produced. The close proximity of the valence band maxima and conduction band minima is a consequence of the vastly diffused nature of these bands, ultimately creating slight E_g.

The bonding nature becomes evident through electron density plots, as illustrated in Fig. 6. In Cs₂LiMoCl₆, covalent bonding is observed among Cs, Li, and Mo atoms. Similarly, in Cs₂LiMoI₆, the same covalent character is observed between Cs, Li, and Mo atoms. In general, both Cs₂LiMoCl₆ and Cs₂LiMoI₆ exhibit a covalent bonding nature among their constituent atoms, with specific ionic contributions in interactions involving Cs, Li, Mo, and other atoms as identified.

3.3. Magnetic Properties

Magnetic characteristics have been explored through spin dependent computations. The total magnetic moment (µ_B) of Cs₂LiMoCl₆ is found as 3.02436 µ_B which is slightly higher than that of Cs₂LiMoI₆ which is 3.00332 µ_B, indicating a more pronounced magnetic behavior in Cs₂LiMoCl₆. The confirmation of the ferromagnetic nature in both substances is evidenced by values that represent integer multiples of the total µ_B[26]. The Mo-d-t2g orbitals are the key factors determining the magnetic behavior in both perovskites. The sign of µ_B functions as an indicator for the magnetic orientation of atoms. A negative µ_B implies ferrimagnetic or anti-ferromagnetic characteristics, whereas a positive µ_B defines the arrangement of atoms in the respective direction[27]. Detailed information on total, partial, and interstitial µ_B for both perovskites is provided in Table 2.

Table 2

Computed interstitial, individual and total magnetic moments of Cs₂LiMoX₆ (X = Cl, I)
Compounds	Cs (µ_B)	Li (µ_B)	Mo (µ_B)	Cl/I	Interstitial µ_B	Total µ_B
Cs₂LiMoI₆	0.00263	-0.00890	2.26185	0.01214	0.67228	3.00332
Cs₂LiMoCl₆	-0.00106	0.00059	2.18821	0.02714	0.67481	3.02436

Table 3

Computed optical parameters for Cs₂LiMoX₆ (X = Cl, I)
Compounds	ε₁(0)	n(0)	R(0)
Cs₂LiMoI₆	4.84	7.33	0.14
Cs₂LiMoCl₆	3.20	5.39	0.08

3.4. Optical Properties

The efficiency of photovoltaic devices is a crucial condition in optoelectronics, assessing the suitability of these gadgets for use in photovoltaic cell production dedicated to energy scavenging applications. In this context, the dielectric function ɛ(ω), as defined by ɛ(ω) = ɛ₁(ω)+ ɛ₂(ω)[19, 28], holds significance as a complex function determining how a photovoltaic material responds to an incoming electromagnetic (EM) radiation. Various other optical parameters, including the absorption coefficient α(ω), refractive index n(ω), reflectivity R(ω), extinction coefficient k(ω), optical conductivity σ(ω), and energy loss function L(ω) can be derived from the real ɛ₁(ω) and imaginary ɛ₂(ω) parts of the ɛ(ω).

The graphed figures in the energy range of 0–8 eV illustrate the computed optical parameters mentioned earlier. Within these figures (Figs. 7 and 8), ɛ₁(ω) conveys details related to dispersion, while ɛ₂(ω) provides insights into absorption characteristics. Both ɛ₁(ω) and ɛ₂(ω) exhibit nearly identical patterns for Cs₂LiMoI₆ and Cs₂LiMoCl₆, as depicted in Fig. 7(a) and 7(b), owing to their analogous electronic BS.

The ɛ₁(ω) parameter serves to describe the extent of Photon scattering and the propagation speed, which, in turn, relies on the maximum dispersal of light[29]. As ω approaches 0, the values of ɛ₁(ω) are approximately 4.84 and 3.20 for Cs₂LiMoI₆ and Cs₂LiMoCl₆, correspondingly, as indicated in Fig. 7(a). Various investigators have delved into the static dielectric features of analogous compounds. HDP composites, namely M₂NaInI₆ (where M = Rb, Cs), exhibit ε1(0) values of approximately 3.8 and 4.03, respectively[30]. Similarly, the M₂AgCrBr₆ compounds (where M = Cs, K, Rb) demonstrate ε1(0) values of around 6.1, 5.4, and 5.8 [31].Notably, Penn's model is affirmed in this context, confirming the contrary relationship between the static dielectric constant, represented by ɛ₁(0) and the band gap E_g.[32]

The ɛ₂(ω) spectrum shows linear increase initially with initial peaks at 2.52 eV and 4.27 eV for Cs₂LiMoI₆ and Cs₂LiMoCl₆, respectively and then fluctuation is seen. The ɛ₂(ω) component, indicative of electronic shifts from the VB to the CB, exhibits protuberant peaks at 6.21 eV for Cs₂LiMoI₆ and 8 eV for Cs₂LiMoCl₆, as demonstrated in Fig. 7(b). Analyzing the α(ω), a key parameter for discerning a material's suitability for solar cell applications, reveals that both compounds have substantial values across a wide range of energies. Notably, Fig. 8(a) highlights significant optical transitions occurring at approximately 8 eV for both Cs₂LiMoI₆ and Cs₂LiMoCl₆, corresponding to the Ultraviolet (UV) spectrum.

The refractive index n(ω), an essential parameter for determining material transparency or opacity in optical investigations, follows a movement akin to that of ɛ₂(ω), as depicted in Fig. 8(d). The expression for the complex refractive index, denoted as n’(ω), is as follows [19]

$$n{\prime }\left({\omega }\right)= \text{n}\left({\omega }\right)+i\text{k}\left({\omega }\right)$$

The variation in n(ω) is directly associated with bonding characteristics of perovskites. As a general trend, ionic compounds typically demonstrate minor values of n(ω) in contrast to covalently bonded perovskites. This discrepancy arises from the distinctive electron-sharing characteristics of covalent bonding, where more electrons are shared. In covalent compounds, the greater electron distribution increases the probability of photon-electron interactions. As a result, photons experience a more pronounced slowing down within covalently bonded structures, distinguishing them from their ionic counterparts [33]. When ω approaches 0, the static refractive index values, denoted as n(0), are 7.33 and 5.39 for Cs₂LiMoI₆ and Cs₂LiMoCl₆, respectively. These n(0) values conform to the relation $n\left(0\right)= \sqrt{\epsilon \left(0\right)}$. Additional prominent peaks for n(ω) occur at 2.38, 4.74 and 5.84 eV for Cs₂LiMoI₆ and at 3.96 eV, 5.48 eV, and 6.25 eV for Cs₂LiMoCl₆.

An additional optical parameter is the extinction coefficient, denoted as k(ω), which is directly associated with α(ω). This connection is expressed through the relationship[34] α(ω) = $\frac{4\pi k\left(\omega \right)}{{\lambda }}$, as illustrated in Fig. 7(d). k(ω) serves as a measure of the attenuation of incident photons (k ˃ 0) within the studied alloys, attributed to absorption and scattering. Importantly, it is analogous to the imaginary part because both are interconnected through Kramers–Kronig relations [52]. The behavior of k(ω) can be elucidated using the following formula:

$$k\left(\omega \right)=\frac{1}{\sqrt{2}}{\left.\left({\left.\left({\epsilon }_{1}^{2}\left(\omega \right)+{\epsilon }_{2}^{2}\left(\omega \right) \right.\right)}^{\frac{1}{2}}- {\epsilon }_{1}\left(\omega \right)\right.\right)}^{\frac{1}{2}}$$

The k(ω) spectrum shows fluctuating trend and the maximum values appeared at 6.97 eV and 8 eV for Cs₂LiMoI₆ and Cs₂LiMoCl₆, correspondingly. The optical conductivity, denoted as σ(ω), delineates the passage of photons released via photoelectric effect in a material. In the existence of intense electromagnetic (EM) rays, it elucidates the rupture of bonds [49]. Given that σ(ω) discloses free carriers produced upon the absorption of EM light and there is a close interconnection between σ(ω) and α(ω). Notably, the peak values of σ(ω) reach 4631 (Ω cm)⁻¹ and 3618 (Ω cm)⁻¹ at 6.24 eV and 8 eV for Cs₂LiMoI₆ and Cs₂LiMoCl₆, respectively (refer to Fig. 7(c)). σ(ω) can be computed as

$$\sigma \left({\omega }\right)=\frac{2{W}_{cv}ħ{\omega }}{{\underset{E}{\to }}^{2}}$$

Figure 8(b) portrays the reflectivity R(ω), a significant parameter indicating the proportion of EM light reflected at a specific energy[35]. Primarily, the R(ω) values were significant, specifically 0.14 and 0.08 at ω = 0 for Cs₂LiMoI₆ and Cs₂LiMoCl₆, respectively. As the energy rises, R(ω) experiences an upward trend. The R(ω) value is present at 0 eV due to the lattice vibrations occurring within the unit cell. The maximum reflectance is shown at 6.26 eV and 4.13 eV for Cs₂LiMoI₆ and Cs₂LiMoCl₆, respectively. R (ω) can be computed by using the given relation [35, 36]

$$R=\frac{{(n-1)}^{2}+{k}^{2}}{{(n+1)}^{2}+{k}^{2}}=\left|\frac{nˊ-1}{nˊ+1}\right|$$

The L(ω), depicted in Fig. 7(d), measures the reduction in photon energy as it traverses the material. The peaks are computed at 6.71 eV and 7.64 eV for Cs₂LiMoI₆ and Cs₂LiMoCl₆, correspondingly (see Fig. 8(c)). The E_g of a perovskite influences the energy levels of electronic shifts, impacting the absorption of light and resulting dielectric attenuation in the energy range. Compounds with larger E_g in the relevant energy range may exhibit larger energy electronic shifts and potentially higher L(ω). Notably, the compounds under investigation exhibit small E_g, which are associated with reduced E_g. The E_g can also be determined using ɛ₂(ω) and L(ω), and parallelized with those calculated from the BS[37].

Utilizing first-principles calculations, we explored the structural, optoelectronic, and magnetic features of double perovskites Cs₂LiMoX₆ (X = Cl, I). Both Cs₂LiMoI₆ and Cs₂LiMoCl₆ exhibited stability in a cubic lattice, with τ of 0.88 and 0.85, respectively. The BS reveals a direct band, while DOS illustrate the contribution of various states, portraying Cs₂LiMoX₆ (X = Cl, I) as semiconductors. Analysis of dielectric constant, n(ω), σ(ω), R(ω), α(ω), and k(ω)suggests the possible suitability of both perovskites for optoelectronic gadgets, particularly photovoltaic cells. In the energy range from zero to the E_g value, both compounds exhibit remarkably low reflectivity, making them promising candidates for lenses production within this energy range. Their maximum absorption and low reflectivity in the UV region further highlight their potential in optoelectronic applications.

The Author Contribution Declaration

The authors confirm their contribution to the manuscript as follows: study conception and design: Nasrullah; data collection: Muhammad Sajid; analysis and interpretation of results: Mubashir Nazar; analytical expressions, draft manuscript preparation, analysis and interpretation of results and wrote the main manuscript: Rasheed Ahmad Khera. All authors reviewed the results and approved.

Funding

The authors extend their appreciation to the Researchers by Supporting, University of Agriculture, Faisalabad.

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Acknowledgments

The authors acknowledge the technical and financial support from Department of Chemistry, University of Agriculture (UAF), Faisalabad 38000, Pakistan.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Computational Exploration of Cs2LiMoX6 (X=Cl, I) Halide Double Perovskites: Unveiling Energy Storage Potentials

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Abstract

Figures

1. Introduction

2. Computational Method

3. Results and Discussion

3.1. Structural Properties

3.2. Electronic Properties

3.3. Magnetic Properties

3.4. Optical Properties

4. Conclusions

Declarations

References

Additional Declarations

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