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. 2023 Feb 1;8(6):5274–5284. doi: 10.1021/acsomega.2c05845

Investigation of Structural, Mechanical, Optoelectronic, and Thermoelectric Properties of BaXF3 (X = Co, Ir) Fluoro-Perovskites: Promising Materials for Optoelectronic and Thermoelectric Applications

Shaukat Ali Khattak †,*, Mohammed Abohashrh ‡, Imtiaz Ahmad §, Mudasser Husain ∥, Irfan Ullah †, Syed Zulfiqar †, Gul Rooh †, Nasir Rahman ∥, Gulzar Khan †, Tahirzeb Khan †, Muhammad Salman Khan †, Said Karim Shah †, Vineet Tirth ⊥,#
PMCID: PMC9933232  PMID: 36816671

Abstract

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Coded within Wien2K, we carry out DFT-based calculations for investigations of the structural, elastic, optoelectronic, and thermoelectric properties of BaXF3 (X = Co, Ir) fluoro-perovskites. The Birch–Murnaghan fit to the energy-vs-volume data and formation energy shows that these fluoro-perovskites are structurally stable. The phonon calculation confirms the thermodynamic stability, while the relation between elastic constants such as C11 – C12 > 0, C11 > 0, C11 + 2C12 > 0, and B > 0 validates the mechanical stability of the compounds. BaIrF3 exhibits a strong ability to endure compressive and shear stresses. BaCoF3 shows a weaker capacity of withstanding changes in volume, attributed to a lower bulk modulus. Demonstrating a higher G-modulus of rigidity than the BaIrF3, BaCoF3 demonstrates stronger resistance to change the shape and both compounds are found to be anisotropic and brittle. The determined band structure profiles reveal that both BaCoF3 and BaIrF3 demonstrate a metallic nature. In addition, the metallic nature of BaCoF3 and BaIrF3 is reinforced by the density-of-states (DOS) study, where Co and F atoms contribute significantly to the total DOS in the valence band in the case of BaCoF3, while that of BaIrF3 is predominated by the Ba and F atoms. The computed values of ε1(0) for BaCoF3 and BaIrF3 are approximately 30 and 19, respectively, which are in line with Penn’s model. The researched materials are confirmed to be strong contenders for optoelectronics by the lack of absorption in the visible range. For their potential use in thermoelectric device applications, thermoelectric parameters such as temperature-dependent Seebeck coefficient, specific heat capacity, thermal conductivity, power factor, and figure of merit are also investigated, which show that these materials are thermally stable and promising for applications in thermoelectric devices.

1. Introduction

The new interest in cubic fluoro-perovskites (AXF3), where A and B are cations, is thanks to their promising crystal structure and significant physical characteristics. DFT investigation of different AXF3 for the determination of their band structure has been performed by Nishimatsu et al.1 utilizing the local density approximation (LDA) and pseudopotential approach.2 The research on the use of the solid solution LiBaCaSrF3 on LiSrF3 to produce light-emitting diodes was conducted by the authors, where they inferred their potential use in the development of lenses in the optical lithography steppers.3 Tran and Blaha’s modified Becke and Johnson exchange potential was exploited to study the optoelectronic characteristics of SrTiO3 and BaTiO3 at an ambient temperature while reporting results that are significantly better than those of prior first-principles studies in terms of experimental values.4 Khan et al. studied the rare earth telluride compounds, Ba2MYTe5 (M = Ga, In), where their band gaps were found to be in the range of 1.08–1.36 eV and studied the thermoelectric properties of these compounds.5 CaS was investigated where the full-potential Green’s function multiple-scattering, FLAPW, and finite-difference techniques provided similar Ca and S K-edge spectra.6 To determine which is wide and direct and optical qualities to forecast their use in the optoelectronic industry, the bonding nature, as well as the structural, electronic, chemical bonding, and optical characteristics of KCaF3, RbCaF3, and CsCaF3, has been explored.7 The optical characteristics of many systems containing rare earth were investigated, utilizing FP-LAPW GGA and GGA + U approximations.8−11 However, it was discovered that the developed modified Becke–Johnson potential (TB-mBJ) approximation is more suitable for systems without correlated electrons, primarily semiconductors and insulators. It was better from a computational cost perspective as well as in terms of the outcomes. To describe a drop in bulk modulus and the increase in lattice parameter, Murtaza et al.12 calculated the electrical and optical characteristics using the TB-mBJ approach. For use in the deep ultraviolet area, solid solutions of LiKBaMgF3 on LiBaF3 were produced.13 Experimental work on the structural phase transition in RbCdF3 has been done by Studzinski et al.14 Investigations into the cubic fluoro-perovskites, ACaF3 (where A = K, Rb, Cs), as promising candidates for core-valence luminescence (CVL), have been conducted.15 The following three factors are critical for CVL: (1) electron energy difference between the core p-states of K, Rb, and Cs and the p-states of F constituting the top of the valence band; (2) the breadth of the upper valence band; and (3) the band gap. Exploiting the ab initio approach, these investigations further rekindled interest in these systems. Cubic perovskites have been studied with a focus on their optical characteristics utilizing the full-potential linearized augmented plane wave (FP-LAPW) approach, using the generalized gradient approximation (GGA) and LDA by Babu et al.,16 Mousa et al.,17 and Li et al.18 To imply an order–disorder nature of the 193 and 50 K phase transitions, researchers analyzed the temperature dependency of structural parameters and phase transition of RbCaF3.19 However, neither the optical and electrical nor the thermoelectric characteristics of the cubic perovskites BaXF3 (X = Co, Ir) have been previously studied or determined using the TB-mBJ-based approach.20

This triggered the conduction of this study while employing the DFT-based FP-LAPW method because mBJ-based calculations are anticipated to produce significant optical qualities that would more precisely address band gaps and transitions. To get insight into these structures, we have therefore investigated their thermoelectric in addition to the optoelectronic properties.

2. Computational Details and Crystal Structure

As depicted in Figure 1, the BaXF3 (X = Co, Ir) compounds with the Pm3̅m space group crystallize in a cubic form. According to the Wyckoff coordinates, the Ba, X (Co and Ir), and fluorine are located at locations 1a (0, 0, 0), 1b (0.5, 0.5, 0.5), and 3c (0, 0.5, 0.5), respectively.21 A well-known quantum mechanical solution to the many-body issue is DFT.22 An effective technique to calculate the ground-state characteristics of materials, i.e., the DFT-based FP-LAPW approach encoded in the Wien2k code,23 was used in this work to perform the first-principles total energy calculations.24,25 The unit cell was partitioned into (I) interstitial space and (II) nonoverlapping atomic spheres (centered at the atomic sites).

Figure 1.

Figure 1

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Crystal structure of the BaIrF3 fluoro-perovskite. The BaCoF3 has a similar structure where Ir in this figure is replaced with Co.

Different basis sets are employed in these two different types of areas. The Ba, Co, and F atoms’ muffin tin (MT) radii have been set at 2.39, 1.48, and 1.89 a.u., respectively, in BaCoF3. Additionally, in the case of BaIrF3, the MT radii of the Ba, Ir, and F atoms are at 2.49, 1.69, and 1.79 a.u., respectively. Taking 1000 spatial k-points in the irreducible wedge of the Brillouin zone (BZ), integrations in the reciprocal space were carried out. The size of the basis sets made up of the plane waves is controlled by the convergence parameters, which are assumed to have a value of RMT × KMAX = 8. For consistency, GMAX is set to 11 (a.u.)−1, and convergence is accomplished with a 10–3 Ry energy tolerance. The ideal value of the lattice parameters is used to calculate the ground-state electronic structures of the present compound. We evaluated the total energies for the various volumes, which range from −10 to +10% of the experimental (theoretical) lattice parameters to determine the lattice parameters’ optimum value.26,27 Plots of the calculated findings are made using equations given in ref (28).

The most notable achievements employing the mBJ results for semiconductors were the improved band-gap results29 and the optical characteristic computations in the current FP-LAPW study using the mBJ-based approximation. The electron–hole interaction was considered using the random-phase approximation, although local field effects were not considered.30,31 Additionally, the BoltzTrap code was used to calculate the thermoelectric (TE) properties.32 The thermoelectric properties are calculated while exploiting the Onsager relations and the Boltzmann transport theory.

3. Results and Discussion

3.1. Structural and Mechanical Properties

Figure 2 displays the Birch–Murnaghan-fitted optimum energy curves for the cubic BaCoF3 and BaIrF3 fluoro-perovskites employing the TB-mBJ technique. The ground-state energy (E0), ground-state volume (V0), the structure’s bulk modulus (B0), and pressure derivative (B0′) are all predicted by these computations. The parameters associated with the point are considered the ground-state energy and volume.33−36 The materials’ ground state is found by looking into the points in the curve where the lowest energy relative to the volume is fitted with the Birch–Murnaghan equation. The ground-state volume can be utilized to calculate lattice constants. In addition to the volume optimization by the Birch–Murnaghan equation of state, the thermodynamic stability was checked by determining the formation energy (Hf) for both compounds by using eq 1

3.1. 1

where EBaXF3 and EBa, EX, and EF are the total energy of the compound and energy of Ba, X (Co, Ir), and F, respectively. The a, b, and c represent the number of Ba, X (Co, Ir), and F, respectively. The calculated formation energies for BaCoF3 and BaIrF3 are −1.48 and −19 438.68 Ry, respectively. The negative formation energies of the compounds suggest that they are thermodynamically stable where the BaIrF3 exhibits more thermodynamic stability than the BaCoF3.

Figure 2.

Figure 2

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Optimized energy vs. volume for (a) BaCoF3 and (b) BaIrF3 fluoro-perovskites.

Table 1 provides a summary of the structural parameters of BaCoF3 and BaIrF3 fluoro-perovskites.

Table 1. Structural Parameters Such As Lattice Parameter (a0), Bulk Modulus (B0), Pressure Derivative (B0′), Ground-State Energy (E0), and Formation Energy (Hf) of the BXF3 (X = Co, Ir) Fluoro-Perovskites.

structural parameter BaCoF3 BaIrF3
a0 (Å) 4.21 4.54
V0 (a.u3) 503.74 608.09
B0 (GPa) 79.79 149.90
B0′ 4.03 108.46
E0 (Ry) –19 665.07 –52 557.70
Hf (Ry) –1.48 –1.17
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The thermodynamic stability was determined by carrying out the phonon calculation, as shown in Figure 3, which exhibits no imaginary frequencies, and the only frequencies are those that are real for both BaCoF3 and BaIrF3. This suggests that both compounds demonstrate thermodynamic stability.

Figure 3.

Figure 3

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Frequency vs. energy while using phonon calculations for BaCoF3 and BaIrF3.

Furthermore, the mechanical stability of the compounds was analyzed by calculating and characterizing their elastic properties by determining the elastic constants as they demonstrate the materials’ response to the applied forces, i.e., reveal the mechanical characteristics of materials. Therefore, these constants provide information about the mechanical stability and toughness of the materials. The components of the stress tensor for tiny strains were computed at zero pressure, and the energy was put per the lattice strain, which maintained the volume constant.37 The IRelast package, built specifically for cubic systems and interfaced with WIEN2K, was used to calculate the elastic constants. There are only three independent elastic constants Cij in total for cubic structures, namely, C11, C12, and C. Various elastic parameters, of the materials, given in Table 2, were determined by using equations given in the work carried out by Khattak et al.38

Table 2. Elastic Parameters for BaCoF3 and BaIrF3: Elastic Stiffness Coefficients (C11, C12, and C44), Bulk Modulus (B), and Zener’s Constant (A)a.

elastic parameters BaCoF3 BaIrF3
C11 (GPa) 57.4 84.7
C12 (GPa) 45.7 50.0
C44 (GPa) –11.3 –22.9
B (GPa) 47.9 60.7
A –1.9 –1.3
Gv (GPa) –4.4 –6.8
GR (GPa) –8.1 –35.2
G (GPa) –6.3 –21.0
E (GPa) –19.6 –71.1
V 0.9 1.1
B/G –7.9 –2.9
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a

Gv, GR, and G are the Voigt shear modulus, Reuss shear modulus, and mean of Gv and GR, respectively. E is the elastic modulus, V is Poisson’s ratio, and B/G is the ratio of bulk to shear moduli. The elastic stiffness coefficients and other constants as well as pressure are in GPa and volume in bohr3.

The elastic constants must be related to each other for the cubic crystal mechanical stability: C11 – C12 > 0, C11 > 0, C11 + 2C12 > 0, and B > 0.39 According to Table 2, which shows that the researched materials comply with these requirements, they are inferred to be mechanically stable. BaIrF3 has greater elastic stiffness coefficients, which shows that the material has a strong ability to endure compressive as well as shear stresses, according to Table 2. BaCoF3, on the other hand, has a lower bulk modulus, which indicates a weaker capacity to withstand changes in volume. Additionally, the fact that BaCoF3 has a higher G-modulus of rigidity than BaIrF3 suggests that it has a stronger ability to resist shape change. According to the values of A, no compound is entirely isotropic. It is interesting to note that the materials’ B/G ratio is negative, which suggests the brittle nature of both compounds.40

3.2. Electronic Band Structure and Density of States

Electronic properties establish the role of materials in their technological uses and are also responsible for determining many of their physical properties, particularly thermoelectric transport properties. The approaches for computing electronic characteristics were largely introduced in the past decades owing to the DFT and improvements in programming knowledge and computing capacity. Numerous DFT-based computational algorithms may be used to properly calculate the electronic structure of materials. Scf computations have been used to analyze the electronic characteristics of materials.41−43 The two main factors that influence how the materials’ electronic properties are determined are the band structure and DOS. With the aid of the modified Becke–Johnson (mBJ) potential and the unit cell’s optimized design, the electronic characteristics of the materials were calculated together with a high symmetric point of the Brillouin zone. Figure 4 shows calculated electronic band structures of the examined compounds BaCoF3 [Figure 4a] and BaIrF3 [Figure 4b], fluoro-perovskites, which show that the minima of conduction and maxima of valence bands overlap with each other around the Fermi level. This implies that both BaCoF3 and BaIrF3 exhibit metallic behavior.

Figure 4.

Figure 4

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Band structure profile of the (a) BaCoF3 and (b) BaIrF3 fluoro-perovskites.

We further estimated the DOS, which are shown in Figures 5 and 6, to get insight into the electrical characteristics of the present structures. The results of band structures are corroborated by the total density of states (TDOS) of BaCoF3 [Figure 5] and BaIrF3 [Figure 6] fluoro-perovskites, which further confirms their metallic nature. In the case of BaCoF3 [Figure 5a], the TDOS is predominantly contributed by fluorine in the energy range lying in the valence band [between −10 and −6 eV] and around the Fermi level in the valence band cobalt dominates the contribution to the total density of states. In the conduction-band energy region, the density of states is mainly contributed by the barium. Figure 5b exhibits the total density of states for the BaCoF3 and the contribution of the partial density of states (PDOS) toward it, where the TDOS is mainly contributed by the F-p PDOS in the valence band between −9.5 and −6.5 eV, while the Co-d PDOS has the contribution near the Fermi level in the valence band. In the conduction band, the TDOS is mainly caused by the Ba-d PDOS. The contribution of all PDOS in both valence and conduction bands is overshadowed.

Figure 5.

Figure 5

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(a) Total density of states of the BaCoF3 and (b) partial density of states.

Figure 6.

Figure 6

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(a) Total density of states of the BaIrF3 and (b) partial density of states.

Figure 6a shows that the TDOS of BaIrF3 is caused majorly by the F atom in the valence band, which is maximum at −2.0 eV, while in the conduction band the Ba atom mainly contributes to the TDOS at 4.0 eV while at the other energy of the conduction band, the TDOS is lesser while fluctuating from one energy to another.

The presence of the DOS around the Fermi level also reinforces the revelation of Figure 4b, i.e., the BaIrF3 exhibits a metallic behavior, which is attributed to the PDOS of Ir and F atoms as evident from Figure 6b, where the PDOS are populated around the Fermi level. In the valence band, the F-d has the highest contribution, while it is overshadowed by the Ba-d in the conduction band. All other PDOS are hard to be noticed. This also shows that Ba-d and F-d orbitals contribute in a mixed manner to the development of the CB of BaIrF3.

3.3. Optical Properties

Exploring the emission of BaCoF3 in the infrared region, i.e., 12.39 μm, and reflectivity and transmission of BaIrF3, exhibiting the metallic nature, requires the investigation of the complex dielectric function. Complex dielectric functions, which are typically used to explain how solids behave when electromagnetic waves (EMs) are present, can be exploited to learn more about how EM waves travel through different media and how electrons and phonons interact. The ε1(ω), which is what accounts for the energy stored in any medium, can be used to extract the stored energy from the imaginary part of the dielectric function using Kramer–Kronig transformations.44 Data on band topologies, absorption behavior, and charge carrier transitions from occupied to unoccupied levels are also provided by the ε2(ω).45−47Figure 7a,b depicts the real and imaginary parts of the dielectric function for the materials under investigation. ε(ω) is utilized to determine the optical responses of the material. Because it represents the electronic aspect of the static dielectric constant and majorly depends on the band-gap value, the zero-frequency limit ε1(0) is an accurate measurement of ε1(ω). Values of ε1(0) for BaCoF3 and BaIrF3 are 29.50 and 16.13, respectively.

Figure 7.

Figure 7

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(a) Real and (b) imaginary parts of the dielectric function, (c) energy loss function, and (d) absorption coefficient for the BaCoF3 (represented by red data points) and BaIrF3 (represented by blue data points).

The ε1(0) in the BaCoF3 material reaches its maximum value at 0.01 eV, beyond which point it continues to degrade. On the other hand, the value of ε1(ω) for BaIrF3 falls after reaching a peak at 0.34 eV and moves into the negative zone. It is evident that BaCoF3 is conducting for incident photons at all energy range, while BaCoF3 turn out to be insulating for incident photons with higher energies [negative part of ε1(ω)]. Figure 7b shows how the stated compounds’ imaginary portion of the dielectric constant behaves. It is well known that the biggest determinant of the electrical behavior of crystalline materials is the photon absorption-related quantity ε2(ω) The initial peak in the ε2(ω) spectra of BaCoF3 and BaIrF3 emerges at 0.01 and 0.55, respectively, according to Figure 7b, and thereafter decreases as energy increases. These peak locations mark the change from valance to CB. Since BaCaF3 fluoro-perovskite has a direct band gap, its optical transition is also a direct band gap in nature. It is also abundantly obvious from the compounds’ PDOS that these transitions are mostly caused by the Ba-p, Co-d, and F-p. Furthermore, as each researched compound has a distinct value for its dielectric function in various dimensions, its real and imaginary parts for the present materials reveal their anisotropy. When an electron moves quickly through a medium, energy is lost. This energy loss can cause several events, including phonon and plasmon excitation, interband transition, and inner shell ionization.48 The plasma frequency is when the energy loss function reaches its highest value.32 According to the energy loss spectra shown in Figure 7c, the static level for any of the compounds demonstrates no energy loss, but the energy loss peak for BaCoF3 starts at 3.85 eV and for BaIrF3 appears at 4.55 eV. The energy loss values start increasing dramatically at a higher energy range between 10 and 14 eV for both materials. The absorption coefficient is another significant parameter employed to measure light absorption. The attenuation of light intensity and distance as it travels through the material may be measured using its spectrum, and how it behaves can be anticipated by using the dielectric function. The energy absorption spectra [Figure 7d] for both materials show that there is no absorption peak in the infrared (IR) or visible energy range, indicating that the compounds demonstrate transparency in these regions. The absorption coefficient has maximum absorption I(ω) peaks in the UV region at 10.73 and 10.70 eV, respectively. For both materials, the UV region is where intense light absorption occurs. The generation of absorption peaks results from the electrons’ interband transition. These materials present a potential for optoelectronics applications as they do not absorb light in the visible spectrum.

Reflectivity, R(ω), is a crucial factor since it evaluates a substance’s suitability for shielding application due to its antireflective coating. The reflectivity spectra of the materials under investigation are displayed in Figure 8a, where at the static level, BaCoF3 and BaIrF3 have R(ω) values of 0.72 and 0.35, respectively. After reaching a static level, reflectance drops abruptly for the BaCoF3, while it continues to increase and reaches its maximum at about 0.70 eV. In the energy ranging from 0 to 14 eV, the determined refractive index for BaCoF3 (red) and BaIrF3 (blue) is 7.84 and 4.65, at a lower energy of 0.12 and 3.82 eV, respectively, as shown in Figure 8b. The curves for b materials coincide and begin to drop with increasing energy and flatten for the rest of the energy. The fact that BaCoF3 has a greater refractive index than BaIrF3 does suggest that the photons are more delayed because of electronic polarization while passing through the former’s medium. The size of the atoms that make up the material determines the degree of electronic polarization: an Ir atom with a bigger size creates a stronger polarization, which causes higher retardation (slower velocity) of the photon inside the material and, consequently, a lower refractive index. For both materials, it falls to 0.50 at around 13.50 eV.

Figure 8.

Figure 8

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(a) Reflectivity, (b) refraction, and (c) extinction coefficient of the BaCoF3 and BaIrF3 fluoro-perovskites, represented by red and blue data points, respectively.

The extinction coefficient, k(ω), was derived to show how much light a material absorbs.

The extinction coefficients for BaCoF3 and BaIrF3, which are shown in Figure 8c as red- and blue-colored data, respectively, have maximum values of 5.70 and 3.12 at 0.15 and 0.56 eV, respectively. For both materials, the extinction coefficient drops dramatically and diminishes at higher energies while fluctuating slightly.

3.4. Thermoelectric Properties

The thermoelectricity of the compounds is investigated for energy conversion and their uses in thermoelectric refrigeration, computer cooling, and tiny detector components. The thermoelectric effect is brought about by the production of potential difference, which, in turn, results in the generation of the heat gradient. We measured the negative formation energies of −1.3 and −2.5 eV, respectively, for BaCoF3 and BaIrF3, confirming the thermodynamic stability of these materials. Thermal conductivity (κ/τ), Seebeck coefficient (S), specific heat capacity (Cv), and power factor (PF) for BaCoF3 and BaIrF3 vs temperature are studied in Figure 9a–d. The increased thermoelectric efficiency is supported by the low thermal conductivity, high electrical conductivity, and higher Seebeck value. The crucial element, the Seebeck coefficient, or thermopower, is given by the ratio of the voltage change to temperature change (S = ΔV/ΔT). Subject to the type of charge, it may have a positive or negative value: the positive value indicates holes, while the negative value indicates electrons. Figure 9a shows how the predicted Seebeck coefficient changes with temperature for the two materials BaCoF3 and BaIrF3, where the S starts to increase with the increase in temperature from 100 to 200 K, followed by a decrease in it with a further increase in the temperature from 200 to 500 K. The increase in S is attributed to a perfect concentration of the holes where the Seebeck coefficient begins to increase as the temperature increases. Since thermally stimulated electrons dominate the transport behavior, the decline in the Seebeck coefficient value is primarily attributed to this. At an ambient temperature, BaCoF3 has a larger Seebeck coefficient value than BaIrF3. In comparison to the BaCoF3 curve, the BaIrF3 curve is flatter due to a lower Seebeck coefficient and higher thermal conductivity. Figure 8a also shows that the Seebeck coefficient has negative values over the entire range of temperature, which shows that the dominant charge carriers are electrons. This suggests the n-type nature of the semiconductor. A crystal lattice’s thermal conductivity (κ/τ) quantifies the thermal current generated by the combined electron and phonon energy. The materials with a κ/τ are frequently used in applications requiring heat sinks and low-value thermal insulation. Lattice vibrations, the source of mechanical elastic waves for phonon contributions and free carriers for electron contributions, are created because of the increase in temperature. The temperature-dependent κ/τ for both materials is shown in Figure 9b. Owing to the high electron energy, BaCoF3 has a substantially steeper slope than BaIrF3. Unlike the BaIrF3, which has a maximum figure of merit (ZT) of 0.03 at a 100 K temperature and dramatically decreases with increasing temperature, BaCoF3 has a smaller ZT value, and the value does not abruptly change [Figure 9c]. However, the inset of Figure 9c illustrates the curve of the ZT for the BaCoF3. The power factor (PF), which is theoretically represented as PF = σS2/t, assesses thermoelectric efficiency without taking thermal conductivity into account in terms of the square of the Seebeck coefficient (S) and electrical conductivity (σ/τ). For both materials, the PF value reaches its maximum at 500 K, but the PF increase for BaCoF3 is more than that for BaIrF3.

Figure 9.

Figure 9

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(a) Seebeck coefficient, (b) thermal conductivity, (c) figure of merit, and (d) power factor for the BaCoF3 and BaIrF3 fluoro-perovskites, represented by red and blue data points, respectively.

The magnetic reaction of a material is described by its susceptibility. For BaCoF3, the susceptibility increases from 1.56 × 10–11 to 1.74 × 10–11 m3 mol–1 with increasing temperature from 100 to 250 K but gets saturated with a further increase in temperature [Figure 10a], which is attributed to heat effects on electron spin movement. On the other hand, for BaIrF3 material, it decreases from 1.85 × 10–11 to 1.77 × 10–11 while increasing the temperature from 100 to 208 K. This decrease is explained based on thermal effects on electron spin movement. Both charge carriers and phonons are included in the specific heat capacity (Cv) of solids. To see the Dulong–Petit behavior, the Cv vs temperature is plotted in Figure 10b, where for BaCoF3 it leads the one for BaIrF3, with the increase in temperature ranging from 50 to 250 K and gets saturated with further increasing the temperature up to 950 K at around 124. The vibrational contribution in the Cv reaches around 3R at 50 K. Since both compounds exhibit a metallic nature, the phonon contribution dominates the electronic ones at high temperatures.

Figure 10.

Figure 10

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(a) Susceptibility, (b) specific heat capacity, (c) Hall coefficient, and (d) electrical conductivity for the BaCoF3 and BaIrF3 fluoro-perovskites, represented by red and blue data points, respectively.

As demonstrated in the inset of Figure 10c, the Hall coefficient is high at low temperatures for BaIrF3 and drops exponentially with increasing temperatures from 100 to 220 K as carriers become more conductive. However, it starts increasing with a further increase in temperature like in the case of BaCoF3. A negative Hall coefficient was calculated for each of the two materials, indicating that they are both p-type conducting materials: in each of the examined materials, the holes dominate in electronic transport. Figure 10d shows that the electrical conductivity of BaCoF3 elevates with the increase in temperature while gaining saturation at higher energies, whereas BaIrF3 exhibits temperature-dependent decreases in conductivity. In the instance of BaCoF3, the increase in electrical conductivity is most likely the result of a thermal disturbance between electrons and ions.

4. Conclusions

In conclusion, the structural and thermodynamical stability and optoelectronic and thermoelectric properties of BaXF3 (X = Co, Ir) fluoro-perovskites were investigated while using the density functional theory coded within Wien2K. The structural stability of these fluoro-perovskites was confirmed by the Birch–Murnaghan fit to the energy-vs-volume data, while the thermodynamic stability was shown by the negative formation energy and phonon calculations for both compounds. The relation between elastic constants such as C11 – C12 > 0, C11 > 0, C11 + 2C12 > 0, and B > 0 revealed the mechanical stability of the compounds. With greater elastic stiffness coefficients, BaIrF3 exhibited a strong ability to endure compressive and shear stresses. BaCoF3 showed a weaker capacity of withstanding changes in volume due to a lower bulk modulus. Exhibiting a higher G-modulus of rigidity than the BaIrF3, BaCoF3 turned out to be stronger for resisting a changing shape. Both compounds demonstrated anisotropy and brittleness. The band gaps revealed the metallic nature of the BaCoF3 and BaIrF3. Furthermore, the metallic nature of BaCoF3 and BaIrF3 was also validated by the density-of-states study, where Co and F atoms contributed significantly to the TDOS in the valence band in the case of BaCoF3, while the TDOS of BaIrF3 was dominated by the Ba and F atoms. The computed values of ε1(0) for BaCoF3 and BaIrF3 are approximately 30 and 19, respectively, which were in line with Penn’s model. The researched materials were confirmed to be strong contenders for optoelectronics by the lack of absorption in the visible range. For their potential use in thermoelectric device applications, the Seebeck coefficient, specific heat capacity, thermal conductivity, power factor (PF), and figure of merit as a function of temperature were also investigated, which showed that these materials are thermally stable and preset potentiality to be used in thermoelectric devices.

Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through the Small Groups Project under grant number RGP.1/368/43. The authors would like to thank the National Research Program for Universities (NRPU), Higher Education Commission Pakistan, No. 20-8862/NRPU/R&D/HEC/2017, the National Research Program for Universities (NRPU), Higher Education Commission Pakistan, No. 20-15131/NRPU/R&D/HEC/2021, and the National Research Program for Universities (NRPU), Higher Education Commission Pakistan, No. 20-15128/NRPU/R&D/HEC/2021.

The authors declare no competing financial interest.

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