First-Principles Investigation of Diverse Properties of X₂CaTa₂O₇ (X = Li, Na, K, and Rb) Ruddlesden–Popper Compounds for Photovoltaic Applications

Abstract

For the first time, we explored the optical, electronic, mechanical, and structural properties of the Ruddlesden–Popper phase family member X₂CaTa₂O₇ (X = Li, Na, K, and Rb) by using density functional theory (DFT) with the Perdew–Burke–Ernzerhof (PBE) function in the generalized gradient approximation (GGA) framework. These materials show promising potential for energy conversion applications. Detailed investigations into structural parameters, band gaps, total and partial densities of states, and optical and mechanical properties demonstrate their suitability for photovoltaic technologies. The calculated electronic band gap structures and density of states demonstrate that X₂CaTa₂O₇ (X = Li, Na, K, and Rb) are semiconductors in nature with band gaps ranging from 1.52 eV to 3.02 eV. Measurements demonstrate substantial contributions from O-2p⁴, Ca-4p⁴, and Ta-4f¹⁴ orbitals to the electronic structures of the compounds. Moreover, the optical characteristics, like the reflectivity, absorption coefficients (10⁵ cm⁻¹), dielectric functions (8.5), refractive index (2–3), and optical conductivity (4–6 fs⁻¹), highlight the abilities of these compounds for optoelectronic and photovoltaic devices. Additionally, the mechanical properties measurements of the compounds show that they are capable for flexible electronic applications as well. This manuscript provides good insights into the design and development of the compounds capable for next-generation photovoltaic devices.

1. Introduction

Recently, photovoltaic (PV) applications have gained significant attention from researchers and the scientific community. The introduction of novelty and versatility has made them prominent in energy applications, ranging from large-scale utility power generation to powering satellites in orbit and even solar systems installed in homes. Additionally, photovoltaic cells have shown advancements in specific industries like solar desalination systems and solar-powered cars [1]. Perovskite-based materials are considered the best among the materials for emerging PV technologies and have been the focus of considerable research due to their excellent optoelectronic features, including tunable energy band gaps, a broad absorption spectrum, and dominant point-defect behavior, all of which make them especially suited for solar cell applications. Researchers have been motivated to increase the efficiency and performance of PV devices due to their wide range of applications and undeniable advantages [2,3,4]. Recently, Ruddlesden–Popper perovskites (RPPs) have shown interesting features like high Curie temperature (TC), high resistivity, and low conductivity. RPPs contain a special structure of cations with alternating 2D perovskite layers. Dion–Jacobson and Aurivillius materials, with special properties, exhibit similar complicated architectures [5,6,7,8]. [A_n−1A′₂B_nO_3n+1] is the general formula for RPPs, where n is the number of perovskite layers aligned along the [001] crystallographic direction. RPPs are an interesting option for future-oriented solar systems because of the intriguing features that this structural configuration provides [9,10].

There exist many experimental-based studies on RPP family members but very limited articles are available on theoretical investigations in the literature that we surveyed. Liang et al. [11] reported the synthesis and characterization of a two-layer RPP-based Li₂CaTa₂O₇ compound and revealed its crystal structure within the Fmmm space group. The material exhibited UV light absorption and demonstrated significant photocatalytic activity by degrading RhB molecules under visible light at room temperature. Galven et al. [12] reported on the RPP-based Li₂CaTa₂O₇ compound, with its exceptional photocatalytic water-splitting properties, and that it exhibited two continuous structural phase transitions at ~220 °C and ~660 °C. Detailed characterization through X-ray and neutron diffraction, TEM, SHG, and Raman spectroscopy revealed symmetry changes from Pna2₁ to Pnma to Cmcm, driven by octahedral tilting dynamics. Wang et al. [13] measured the interlayer spacing of the compound and the AC impedance of the Li⁺ ion-deposited H₂CaTa₂O₇ compound and compared it with bare Li₂CaTa₂O₇. Tefaghi et al. [14] demonstrated an efficient microwave-assisted method for modifying layered oxide perovskites, achieving rapid cation exchange, grafting, and intercalation reactions. Double- and triple-layered RPPs undergo proton exchange within hours, significantly reducing reaction times compared to conventional methods. This approach enables the swift synthesis of organic–inorganic hybrids, with variations in behavior observed between double- and triple-layered hosts. Hasin et al. [15] explored the intriguing competition between ferroelectric and antiferroelectric states in the Li-based layered perovskite Li₂AB₂O₇ (A = Ca, Sr; B = Nb, Ta), driven by coupled octahedral rotations and (anti)polar instabilities. Through the DFT and group theory, they unveiled the mechanisms governing phase transitions, revealing low-energy barriers and strain-induced tunability. Murat et al. [16] explored the electronic and optical properties of Li₂CaTa₂O₇, an RPP material using first-principles methods. They verified that it is a semiconductor by looking at its direct band gap, which narrows as temperatures rise because of structural features.

The investigation of RPPs has explored new developments in materials science and provided encouraging information about their possible uses. In this work, we investigated the mechanical, optical, electrical, and structural properties of these multifunctional materials, emphasizing the replacement of elements. We initiated our analysis by systematically replacing Li with other alkali metals like Na, K, and Rb in the basic unit cell of Li₂CaTa₂O₇. The changes in material properties that occurred due to these substitutions were investigated by utilizing the PBE function in the GGA framework. The material with the best optoelectronic and mechanical performance is highlighted in a comparative analysis, highlighting its utilization in photovoltaic applications.

2. Methodology

The Cambridge Sequential Total Energy Package (CASTEP) code, which is based on the DFT, was used in the present research to carry out calculations based on first principles [17]. Ultrasoft pseudopotentials that were On-the-Fly-Generated (OTFG) were used to take into consideration the interaction among valence and core electrons. The exchange-correlation effects were taken into consideration using the PBE function in the GGA framework. For each calculation, a consistent 400 eV plane-wave cutoff energy was used [18,19]. A 7 × 7 × 2 grid and the Monkhorst–Pack [20] scheme with k-point sampling was utilized for structural optimization and band structure investigation. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm was used to determine the ground state of the system [21]. A threshold of 5 × 10⁻⁶ eV/atom for the total energy difference, a maximum Hellmann–Feynman force of 0.01 eV/Å, and a maximum ionic displacement of 5 × 10⁻⁴ Å were used to determine the convergence conditions. The lattice constants for each of the four structures were obtained by thoroughly optimizing the input structures using all of these parameters. The optoelectronic characteristics were then examined using the structural parameters that were obtained. In addition, the Forcite module’s constant strain approach was used to evaluate the elastic qualities of orthorhombic materials [22,23].

3. Results and Discussion

3.1. Structural Properties

The compound Li₂CaTa₂O₇, which possesses an orthorhombic structure with a Pnma space group, is demonstrated in Figure 1a. Five oxygen atoms (O²⁻) coordinate with lithium ions (Li⁺) to form deformed LiO₅ trigonal bipyramids. These bipyramids share corners with four additional LiO₅ trigonal bipyramids and two TaO₆ octahedra. They also have four LiO₅ bipyramids and two TaO₆ octahedra connected by edges. When calcium ions (Ca²⁺) form a connection with eight oxygen atoms, they take on an eight-coordinate configuration. In the meantime, six oxygen atoms encircle tantalum ions (Ta⁵⁺), creating TaO₆ octahedra. These interlinked octahedra share corners with two LiO₅ bipyramids and five identical TaO₆ units. They also have edges in common with two LiO₅ bipyramids. There are four different oxygen sites in the structure. At the first site, oxygen forms a connection with one Li⁺, one Ca²⁺, and two Ta⁵⁺ ions in a four-coordinate framework. Two Ca²⁺ and two Ta²⁺ ions combine with oxygen to form a four-coordinate connection in the second position. Deformed Ca₂Ta₂ tetrahedra are generated at the third site by oxygen atoms, sharing corners with two Li₄Ta trigonal bipyramids and two similar tetrahedra. When oxygen forms connections with four Li⁺ ions and one Ta⁵⁺ ion, the fourth site results in distorted Li₄Ta bipyramids. By interacting with each other by corner and edge sharing, such bipyramids contribute to the complex crystal architecture.

Our obtained lattice parameters for Li₂CaTa₂O₇ are closely related to reported lattice parameters (a = 5.51 Å; b = 5.46 Å; and c = 18.24 Å) [11]. The general formula for this RPP is À₂(A_n−1B_nO_3n+1) with n = 2, which lies in the space group Pnma (62). Here lies one transition metal, Ta, with two A cations in this general formula, one of which is divalent, which in our case is Ca. The other is monovalent, which can be Li, Na, K, and Rb. Substituting all these in general formulae and optimizing, we obtain four different structures: one is Li₂CaTa₂O₇ and others are Na₂CaTa₂O₇, K₂CaTa₂O₇, and Rb₂CaTa₂O₇. To the best of our knowledge, there are no experimental or theoretical data on lattice parameters present other than for Li₂CaTa₂O_7. The lattice parameters of all these compounds are mentioned in

Table 1. Lattice parameters of X₂CaTa₂O₇ (X = Li, Na, K, and Rb) compounds after optimization of their structures.

Compound	a (Å)	b (Å)	c (Å)	α = β = γ
Li2CaTa2O7	5.52	5.46	18.16	90°
Na2CaTa2O7	5.63	5.71	20.02	90°
K2CaTa2O7	5.89	5.66	20.82	90°
Rb2CaTa2O7	6.44	6.11	20.81	90°

and also demonstrated in Figure 1b. All these structures were obtained after optimization in the orthorhombic geometry of the Pnma space group.

If we look at the lattice parameters, it is concluded that by substituting the monovalent atom in the given structures, structure expands in order from Li to Rb; one of the main reasons behind this is the ionic radius of all these compounds. Li has the lowest ionic radius as compared to all others and Rb has the highest ionic radius among all radii. So, in conclusion, Rb₂CaTa₂O₇ has the highest lattice parameters among all compounds.

3.2. Electronic Properties

3.2.1. Band Structures

A semiconductor’s ability to absorb light in solar cells is largely dependent on its band gap. After geometrical optimization, the GGA-PBE approach was used to precisely evaluate these materials’ electrical characteristics. Li₂CaTa₂O₇ has a calculated band gap of 3.02 eV; however, the band gap values for Na₂CaTa₂O₇, K₂CaTa₂O₇, and Rb₂CaTa₂O₇ are 3.06 eV, 2.44 eV, and 1.52 eV, respectively. The achieved outcomes show that the band gaps of X₂CaTa₂O₇ compounds are appropriate to be utilized in solar cell devices. In addition, the band structure examination of all compounds also shows that the conduction band minimum (CBM) and valence band maximum (VBM) are dependent on X elements and their positions (Figure 2). The calculated outcomes show that the compounds contain direct band gaps and are semiconductors in nature with suitable behavior for optical devices.

3.2.2. Total Density of States (TDOS)

Figure 3 compares the total density of states (TDOS) for X₂CaTa₂O₇ (X = Li, Na, K and Rb) compounds to provide a better understanding of the electronic contributions. The TDOS illustrates the overall contribution of various states within both the conduction and valence bands, aligning with the corresponding band structures of Li₂CaTa₂O₇, Na₂CaTa₂O₇, K₂CaTa₂O₇, and Rb₂CaTa₂O₇. One of the highest peaks which is present in valence band of each of the materials is due to the existence of Ta-4f¹⁴. Close to the Fermi level, there exists O-2p⁴, and in the valence band, there exists Ca-4d⁴, in the case of the density of states of these materials.

3.2.3. Partial Density of States (PDOS)

➢

Li₂CaTa₂O₇

In the VB, Li atoms contribute more as compared to Ca, Ta, and O atoms, as shown in Figure 4a. Ta, Ca, and O atoms show just a minute portion of contribution in the VB. The Ta-4f¹⁴ state exhibits one of the most prominent peaks, while Ca-3p⁶ and O-2p⁴ contribute significantly to the second sub-band of the valence band. Additionally, Ca-3p⁶ plays a noticeable role. Beyond this point, there are no electronic states present between 0 and 3.1 eV, which represents the energy band gap of the material. In the CB, the contributions of Li-2s¹ and Ca-4d⁴ are more while the contribution of Ta-4f¹⁴ and O-2p⁴ is very little.

➢

Na₂CaTa₂O₇

In Figure 4b, the O-2p⁴ state shows more contribution while Na-2p⁶, Ca-3p⁶, and Ta-4f¹⁴ show little significance in the VB. The material’s semiconductor characteristics can be predicted because of the ample space between the VB and CB. Ca-4d⁴ makes a greater contribution than Na-2p⁶, Ta-4f¹⁴, and O-2p⁴ in the CB. Specifically, the states Ca-4d⁴ and Na-2p⁶ exert significant effects, whereas the other state has negligible presence.

➢

K₂CaTa₂O₇

The PDOS plot of K₂CaTa₂O₇ is displayed in Figure 4c. O-2p⁴ and K-3p⁶ atoms clearly dominate the VB, while Ca-3p⁶ and Ta-4f¹⁴ show a minimal contribution. The presence of the forbidden energy gap shows the compound’s potential as a semiconductor. In the CB, K-4s¹, K-3p⁶, and Ca-4d⁴ show a greater presence but Ta-4f¹⁴ and O-2p⁴ show just a minute portion of contribution. A tiny percentage of the K-3s² and Ca-4d⁴ states hybridize with K-3p⁶ to affect the CB in the PDOS.

➢

Rb₂CaTa₂O₇

In Figure 4d, Rb-4p⁶ shows a significant influence in the VB, while the contribution of O-2p⁴ is little, and Ta-4f¹⁴ and Ca-4d⁴ show just a minute contribution in the VB. In the CB, Rb-4s², Rb-4p⁶, and Ca-4d⁴ make up the majority of the contributions, while O-2p⁴ shows a minor contribution and Ta has no presence in the CB.

3.3. Optical Properties

To gain a deeper understanding of how materials are used in various applications, it is essential to consider their optical properties. One key aspect of this is the dielectric function, which describes how a material interacts with electromagnetic waves as follows [24]:

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

(1)

The dielectric function plays a vital role in defining the optical characteristics of any uniform material. Its imaginary component, ε₂(ω), is derived from the momentum matrix elements connecting the occupied and unoccupied electronic states. This value is computed directly using Equations (2) and (3) [24]:

$${\epsilon }_2\left(\omega \right)={\displaystyle \frac{4{\pi }^2{e}^2}{m^2{\omega }^{2}V}}\sum {\int }_{Bz}{\left|⟨{\psi }_k^v\left|\overrightarrow{p_i}\right|{\psi }_k^C⟩\right|}^2\delta (E_{{\psi }_k^c}-E_{{\psi }_k^v}-ħ\omega )$$

(2)

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

(3)

The dielectric function, ε(ω), consists of two main contributions: interband and intraband transitions. The real part, ε₁(ω), can be determined from the imaginary part, ε₂(ω), using the Kramers–Kronig relation. By knowing both ε₁(ω) and ε₂(ω), various essential optical properties can be derived, including the refractive index (n(ω)), extinction coefficient (k(ω)), energy loss function (L(ω)), absorption spectrum (α(ω)), reflectivity (R(ω)), and optical conductivity (σ(ω)). These properties can be computed using the corresponding mathematical expressions given in Equations (4)–(7) [25,26,27,28]:

$$n\left(\omega \right)={\left\{{\displaystyle \frac{{\epsilon }_1\left(\omega \right)}{2}}+{\displaystyle \frac{\sqrt{{\epsilon }_1^2\left(\omega \right)+{\epsilon }_2^2\left(\omega \right)}}{2}}\right\}}^{{\displaystyle \frac{1}{2}}}$$

(4)

$$L\left(\omega \right)=-{\displaystyle \frac{{\epsilon }_2\left(\omega \right)}{{\epsilon }_1^2\left(\omega \right)+{\epsilon }_2^2\left(\omega \right)}}$$

(5)

$$\alpha (\omega )={\displaystyle \frac{2k\omega }{c}}$$

(6)

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

(7)

Figure 5 and Figure 6 illustrate the optical characteristics of X₂CaTa₂O₇ for photon energies up to 15 eV, considering polarization along the [100] direction.

It is shown in Figure 5a that there is a single individual peak in the real parts of the dielectric function ${\epsilon }_1\left(\omega \right)$ for all the materials. These peaks exist in the ultraviolet region with peak values of 8.08, 8.11, 8.37, and 8.51, respectively, for the materials, with Rb₂CaTa₂O₇ demonstrating the highest peak value for the real dielectric function. Threshold values for the real dielectric function lie in range of 4.98 to 6.03 at minimal energy, and at higher energy values, there lie the lowest values, with 0.29 for Li₂CaTa₂O₇.

Similar behavior can be observed for the refractive index shown in Figure 5c; these peaks also lie in the ultraviolet region for X₂CaTa₂O₇ with the highest peak value of ~2.95 for Rb₂CaTa₂O₇. On the other hand, Li₂CaTa₂O₇ and Na₂CaTa₂O₇ share the same peak values of 2.88 in this region, and 2.93 is the n(ω) peak value of K₂CaTa₂O₇. For all the compounds, the threshold values are 2.23, 2.23, 2.3, and 2.45 for Li₂CaTa₂O₇, Na₂CaTa₂O₇, K₂CaTa₂O₇, and Rb₂CaTa₂O₇, respectively, at minimal energy values.

The imaginary parts of the dielectric constant ${\epsilon }_2\left(\omega \right)$ and extinction coefficient k(ω) show similar trends, starting from the threshold values and moving towards their peak values. The imaginary part of the dielectric function is shown in Figure 5b. In Figure 5c, the peak values are 5.33, 5.29, and 5.22 for Li₂CaTa₂O₇, Na₂CaTa₂O₇, and K₂CaTa₂O₇, respectively, with the highest peak value of 5.49 for Rb₂CaTa₂O₇. Similarly, extinction coefficients are shown in Figure 5d; the highest peak value is 1.22 for Rb₂CaTa₂O₇, and the other peak values are 1.18, 1.19, and 1.16 for Li₂CaTa₂O₇, Na₂CaTa₂O₇, and K₂CaTa₂O₇, respectively. From 0 eV to 3.1 eV, no values exist for these two properties, showing the corresponding band gaps of Li₂CaTa₂O₇, Na₂CaTa₂O₇, K₂CaTa₂O₇, and Rb₂CaTa₂O₇.

Reflectivity is another important parameter in optical properties, which is presented in Figure 6a. Results indicate that the reflectivity R(ω) at zero energy for Li₂CaTa₂O₇ starts at 0.15, while for Na₂CaTa₂O₇, K₂CaTa₂O₇, and Rb₂CaTa₂O₇, the values at zero energy are 0.16, 0.17, and 0.18, respectively. A remarkable peak value of 0.27 can be seen for Rb₂CaTa₂O₇ around energy of 4.66 eV. The other peak values of Li₂CaTa₂O₇, Na₂CaTa₂O₇, and K₂CaTa₂O₇ are 0.26 at 4.68 eV, 0.25 at 4.65 eV, and 0.26 at 4.54 eV, respectively.

The absorption coefficient plays a crucial role in determining the efficiency of solar energy conversion, as it indicates how deeply light of a specific wavelength can penetrate a material before being absorbed. Figure 6b presents the absorption spectra of X₂CaTa₂O₇ along the [100] direction. The spectra begin beyond the energy range of 0 eV to 3.1 eV, highlighting the energy band gap within this region for all the studied materials. This observation confirms the semiconducting nature of these compounds. Additionally, the absorption spectra exhibit prominent peaks at higher energy levels, specifically between 11.3 eV and 14.5 eV, with peak absorption values reaching approximately to 10⁵ cm⁻¹.

Figure 6c illustrates the variation in conductivity with photon energy for these compounds. As observed, conductivity begins around 3.1 eV, which corresponds to the band gap characteristic of their semiconducting nature. Additionally, the computed optical conductivity exhibits a peak within the examined energy range. The highest conductivity values are found between 10.7 eV and 11.6 eV, which are 4.62 fs⁻¹, 4.15 fs⁻¹, 4.53 fs⁻¹, and 5.66 fs⁻¹ for Rb₂CaTa₂O₇, Li₂CaTa₂O₇, Na₂CaTa₂O₇, and K₂CaTa₂O₇, respectively.

Figure 6d illustrates the energy loss function of X₂CaTa₂O₇ as a function of photon energy. This function represents the energy lost by a fast-moving electron as it passes through the material. The loss function is primarily determined by the bulk plasma frequency (ω_p), which is identified at the point where the real part of the dielectric function (ε₁ω) equals zero and the imaginary part (ε₂ω) is less than one [29]. It is observed that the prominent peaks are found in the range of 14 eV to 15 eV, which shows that reflectance decreases quickly. Therefore, when the incident photon energy surpasses this value, this material becomes more transparent.

3.4. Mechanical Properties

For each composition of X₂CaTa₂O₇ (X = Li, Na, K, and Rb), the elastic stiffness constants (C_ij) are measured and plotted in Figure 7a. These stiffness constants are used to compute the Poisson ratio (v), shear modulus of elasticity (G), bulk modulus of elasticity (B), and Young modulus of elasticity (E). As this is the first attempt to calculate the mechanical properties of this class (RPP family) of materials, there is no review of the literature available to compare our calculations. For orthorhombic compounds, there are nine independent elastic constants which are required to satisfy the following Born stability criteria [30].

$$C_{11}>0,C_{22}>0,C_{33}>0,C_{44}>0,C_{55}>0,C_{66}>0$$

(8)

$$C_{11}+C_{22}-2C_{12}>0$$

(9)

$$C_{11}+C_{33}-2C_{13}>0$$

(10)

$$C_{22}+C_{33}-2C_{23}>0$$

(11)

$$C_{11}+C_{22}+C_{33}+2C_{12}+2C_{13}+2C_{23}>0$$

(12)

From all the calculated values of the elastic constants (

Table 2. Elastic constant, C_ij, and calculated values of bulk modulus, B, shear modulus, G, Young’s modulus, E, Pugh’s ratio (B/G), Frantesvich’s ratio (G/B), and Poisson’s ratio (v) for X₂CaTa₂O₇ (X = Li, Na, K, and Rb).

Name	Li2CaTa2O7	Na2CaTa2O7	K2CaTa2O7	Rb2CaTa2O7
C11	122.1879	164.0388	282.3363	382.8475
C22	113.0975	161.0484	292.0578	302.5688
C33	155.7685	143.507	259.8871	381.9728
C44	18.2948	54.566	89.4783	90.5571
C55	16.3707	62.7448	91.012	101.3848
C66	41.6563	44.4796	89.7577	82.469
C12	75.3125	143.8251	251.8643	304.622
C13	112.5409	146.7116	204.1605	296.6557
C23	114.5335	150.7923	200.5333	288.449
B	97.2951	153.4672	220.6509	278.9065
G	17.7561	17.0879	50.8638	38.421
E	50.2	49.44	141.71	110.21
B/G	5.48	8.9	4.3	7.25
G/B	0.18	0.11	0.23	0.13
v	0.41	0.45	0.39	0.43

), it is seen that these stability criteria are satisfied for X₂CaTa₂O₇ compounds that are mechanically stable.

The mechanical properties of compounds are typically characterized by their polycrystalline elastic constants, which include the bulk modulus, the shear modulus, Young’s modulus, and Poisson’s ratio. Among these, Young’s modulus and Poisson’s ratio [31] play a crucial role and are defined by Equations (13) and (14):

Young’s modulus:

$$E={\displaystyle \frac{9BG}{3B+G}}$$

(13)

Poisson’s ratio:

$$\nu ={\displaystyle \frac{3B_H-2G_H}{2\left(3B_H+G_H\right)}}$$

(14)

In Figure 7b, in the calculated values for the moduli, Rb₂CaTa₂O₇ displays the highest values in the bulk modulus, the shear modulus, and Young’s modulus as compared to others. In Figure 7c, the B/G ratio and Poisson’s ratio are also calculated to investigate the ductile and brittle nature of the materials. It is reported that the material behaves with a ductile nature if the B/G ratio goes beyond 1.75 [30]; otherwise, it is brittle. In Figure 7d, the compounds’ shear modulus has a high resistance to deformation and also has a significant impact on their stability. When G is smaller than B, it indicates that the compounds are highly resistive to volumetric compression as compared to shear deformation. Such outcomes are important to provide the better idea that the compounds under study are mechanically stable enough to be utilized for solar energy storage devices in fatigue conditions.

4. Conclusions

In this work, we calculated the electronic, structural, mechanical, and optical properties of the RPP-family-based X₂CaTa₂O₇ (X = Li, Na, K, and Rb) compounds by using CASTEP. All calculations were conducted using the PBE function within the GGA framework. The band gaps of the X₂CaTa₂O₇ compounds show a semiconducting nature and are ideal for photovoltaic applications. Rb₂CaTa₂O₇ shows a direct band gap value of 1.52 eV while the Li₂CaTa₂O₇, Na₂CaTa₂O₇, and K₂CaTa₂O₇ compounds show indirect band gap values of 3.02eV, 3.06eV, and 2.44eV, respectively. Their optical properties, such as reflectivity, absorption spectra, and dielectric functions, underscore the potential of these materials for optoelectronic applications, particularly in enhancing photovoltaic performance. All these compounds demonstrate B/G ratios greater than 1.75 and G/B ratios less than 0.571, suggesting that they exhibit ductile behavior. This work provides valuable insights into the design and development of next-generation photovoltaic devices, paving the way for innovative strategies to achieve high efficiency.