The First-Principles Investigation of Structural Stability, Mechanical, Vibrational, Thermodynamic, and Optical Properties of CaHfS<sub>3</sub> for Optoelectronic Application

Kassa, Mulugetta; Debelo, Nebiyu; Woldemariam, Menberu

doi:https://doi.org/10.1155/2023/9332399

Advances in Condensed Matter Physics

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Abstract Introduction Results and Discussion Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 9332399 | https://doi.org/10.1155/2023/9332399

The First-Principles Investigation of Structural Stability, Mechanical, Vibrational, Thermodynamic, and Optical Properties of CaHfS₃ for Optoelectronic Application

Mulugetta Kassa,¹Nebiyu Debelo,¹and Menberu Woldemariam¹

Academic Editor: Golam M. Bhuiyan

Received01 Dec 2022

Revised03 Feb 2023

Accepted10 Feb 2023

Published23 Feb 2023

Abstract

In this study, the structural, electronic, elastic, phonon vibration, thermodynamic features, and optical properties of the orthorhombic phase of (space group Pnma) were examined by first-principles calculations utilizing the plane wave ultrasoft pseudopotentials in generalized gradient approximations (GGAs) and with Hubbard on-site correction (DFT + U). To improve the value of the band gap, the exchange correlation potential is also approximated with Hubbard correction (GGA + U). The equilibrium state properties such as lattice parameters, unit cell volume, bulk modulus, and its derivative were calculated and are in good agreement with the existing data. The mechanical properties such as bulk modulus, shear modulus, Young’s modulus, and elastic anisotropy were determined from the obtained elastic constants. The ratio of bulk modulus to shear modulus confirms that the orthorhombic phase of is a ductile material. In addition, the longitudinal sound velocity, transverse sound velocity, and Debye temperature for have been computed. The absence of negative frequencies in the phonon dispersion curve and the phonon density of states confirm that in the orthorhombic phase is dynamically stable. The thermodynamic parameters such as free energy, entropy, and heat capacity were examined with variations in temperature. Finally, the absorption coefficient, dielectric constant, energy loss function, reflectivity, and refractive index are discussed in detail in the spectral range 0–1.6 Ry (21.77 eV). The polarizations along (100), (010), and (001) directions significantly show different optical responses.

1. Introduction

Perovskite materials recently have attracted the interest of scientists and engineers due to their numerous potential advantages. Perovskite materials are crystals that have a chemical formula or equivalent crystal structure, where A and B are two cations (very different sizes or different valences) and X is the anion that bonds with both [1]. These materials could have a significant impact on a variety of fields, including energy production, information storage, and solar cell manufacturing. In the past decades, due to their possible applications in many industrial and engineering domains [2], perovskite materials with different compositions and structures have attracted much attention. These perovskite material classes have been recognized as semiconductors for photovoltaic and optoelectronic applications, such as photo-detection and light-emitting devices [2], in addition to being used mainly for dielectric applications, such as piezoelectric and ferroelectrics [3]. The most commonly used perovskite materials for photovoltaics and optoelectronics are hybrid organic-inorganic metal halide-based materials as light-absorbing active layers [4]. In 1970, Weber studied the synthesis and physical properties of -CH₃NH₃PbX₃ (X = Cl, Br, l) organometallic lead halide perovskite [5]. During this time, the organometallic lead halide perovskites have emerged as a candidate and promising for light harvesting in the solar cell as reported in 2009 [6], for which the efficiency reached 22.7% in 2018 [7], starting from 3.8% in 2009 [6]. However, this category of hybrid perovskite materials suffers from long-term instability in ambient air due to the hygroscopic amine cations as well as from the presence of lead toxicity [8], which has slowed down their industrial application and commercialization. To address the stability and toxicity issues of halide perovskites, it is promising to use the synthesized chalcogenide perovskites as an alternative family of materials to replace halide perovskites for photovoltaic and other optoelectronic applications [9]. To date, chalcogenide perovskites having similar kinds of optoelectronic properties have received attention due to their promising photovoltaic and thermoelectric properties, with initial studies conducted on oxide perovskites that have good band gaps for optical absorption [10]. Recently, because of their advantages of being abundant on Earth, having a low impact on the environment, and having good thermal and aqueous stability for applications in photovoltaic and optoelectronic applications, chalcogenides perovskites are the subject of research investigation [10].

Chalcogenide perovskites assume an ABX₃ configuration with A, and B are elements with a combined valence of 6 (with different valences), while X is typically S or Se [11, 12]. These materials are found to be belonging to a new class of ionic semiconductors [11]. Mostly, a family of chalcogenide and oxy-sulfide perovskite compounds including BaZrS₃, BaHfS₃, BaTiS₃, CaZrS₃, CaHfS₃, SrZrS₃, SrHfS₃, SrTiS₃, and BaZr (O_xS_1-x)₃ have been identified and studied [1, 13–15]. Due to their predicted strong iconicity, they may display special physical characteristics that are free of deep level flaws, and advantageous for energy harvesting and other optoelectronic applications.

For the past few years, theoretical calculations based on the density functional theory (DFT) have been used to reveal and predict the structural, mechanical, electronic, optical, and thermal properties of crystals. CaHfS₃, which is the focus of this work, is a family of chalcogenide perovskite crystal material that has been considered theoretically for optoelectronic applications in this study. CaHfS₃ has been classified as a promising and attractive chalcogenide ionic semiconductor for optoelectronics and photovoltaic applications [11, 12, 16]. On the other hand there is limited knowledge on the physical properties of this material in both theoretical and experimental aspects. To the best of our knowledge, the structural, elastic, electronic, phonon dispersion, and thermodynamic properties of CaHfS₃ are not yet well investigated from computational perspective for optoelectronic application. Moreover, investigation of mechanical properties, phonon dispersion, and thermodynamic properties of CaHfS₃ using the first principle computational methods remains unexplored. In this paper, the structural, elastic, electronic, and phonon dispersion relation and thermal properties of CaHfS₃ are carefully examined. The electronic properties are calculated by considering GGA-PBE [17] and with the Hubbard correction GGA + U [18] for exchange correlation potential using Quantum Espresso Package (QE). In addition to this, phonon dispersion and the thermodynamic properties are studied using a 1 × 1 × 2 (in x, y, and z direction, respectively) supercell containing 40 atoms as in [19] with density functional perturbation theory (DFPT) as implemented in Quantum Espresso. Furthermore, implementing time-dependent density functional perturbation theory (TD-DFPT), optical properties are estimated. Finally with these predictable properties, these materials are particularly attractive for photovoltaic and optoelectronic applications and therefore call for experimental verification.

2. Computational Details

In this work, the first principle computations were carried out in the Quantum Espresso (QE) software package [20] based on the density functional theory (DFT) as implemented within the generalized gradient approximation (GGA) functional [17] and with the Hubbard correction GGA + U [18]. The effective Hubbard parameter (U_eff) was calculated iteratively for Hf-d orbitals using a linear response formalism, utilizing DFPT with the orthoatomic projection method [21, 22] (calculated value of = 2.2167). For this study, a cell with 20 atoms (4-Ca, 4-Hf, and 12-S) in orthorhombic phase for structural, elastic, and electronic property calculations were used. The ultrasoft pseudopotentials (US-PP) obtained from standard solid-state pseudopotential (SSSP) libraries [23] were used to treat the interaction of the electrons with the ion cores as in [24]. The corresponding valence electrons considered for the calculations are Ca-[Ar] 4s², Hf-[Xe] 4f¹⁴ 5d² 6s², and S-[Ne] 3s² 3p⁴. The convergence of energy, force, and cell pressure with respect to the plane-wave cutoff and k-points mesh, were carefully tested. Crystal structure optimization was conducted using a plane wave cutoff energy of 55 Ry, density cutoff energy 220 Ry and the Brillouin zone with a 3 × 3 × 3 Monk horst-Packk-point grid [25] based on the convergence criteria (energy 10⁻⁴ Ry), (force 10⁻³ Ry/Bohr), and (cell pressure 0.5 kbar) with the help of Brayden-Fletcher-Goldfarb-Shannon (BFGS) method [26]. Using the optimized structure, the elastic properties were calculated by density functional theory (DFT) within Quantum Espresso package [20]. In addition, the thermal properties were calculated with the help of density functional perturbation theory (DFPT) within a Quantum Espresso package [19]. For the study of phonon dispersion relations and thermodynamic properties of CaHfS₃, a supercell of 1 × 1 × 2 in x, y, and z directions with 40 atoms was generated and utilized in calculations. Finally, the optical properties were investigated with the help of time-dependent density functional perturbation theory (TD-DFPT) as implemented in Quantum Espresso package.

3. Results and Discussion

3.1. Crystal Structure

The crystal structure of a material describes the arrangement of the atoms or molecules in a unit cell in three dimensions. The structure is described in terms of the symmetry elements present and the atomic positions relative to each other. The symmetry elements can be translational, rotational, or reflective. The most common crystal structures are based on the cubic, hexagonal, and tetragonal crystal systems. Most of the materials’ properties are governed by their crystal structures. The equilibrium lattice constant is a fundamental part of the structural information related to crystal structures. In this study, CaHfS₃ crystals in the orthorhombic crystal system of space group Pnma (62) and point group (mmm) with the crystallographic structure GdFeO₃-type were considered, as shown in Figure 1.

The structural stability is determined with the help of Goldschmidt tolerance factor (τ) using the ionic radius of Ca⁺², Hf⁺⁴, and S⁻² [27]. The calculated value of tolerance factor (τ) is found to be 0.83 lies, which within a distorted perovskite range , indicating that CaHfS₃ stability is defined, and Pnma symmetry is observed.

Here, structural optimization was performed for CaHfS₃ using the cutoff energy and k-point grid size values that were estimated from the convergence test with GGA-PBE and GGA + U approximations. From this, the optimized equilibrium lattice constants were found to be a = 6.561, b = 7.015, and c = 9.592 angstrom with GGA-PBE and a = 6.581, b = 7.039, and c = 9.627 angstrom with GGA + U approximations. These values are in good agreement with the theoretical and experimental values, as summarized in Table 1. Furthermore, the static lattice potential corresponding to total energy was calculated using a series of strained lattices. These results allow for the calculation of the equilibrium unit cell volume, bulk modulus, and its pressure derivative. A sequence of volume-dependent total energy calculations can be fitted to an equation of state consistent with Murnaghan [32].where is an equilibrium bulk modulus that effectively measures the curvature of the energy versus volume curve about the relaxed volume and is the derivative of the bulk modulus. The calculated values of lattice constant, bulk modulus, volume, and pressure derivatives of bulk modulus from the equation of states are summarized in Table 1. The values obtained with respect to GGA + U approximations results in an increment of the lattice constants and volume, but in decrement of bulk modulus and its derivative.

3.2. Elastic Properties

Elastic properties play a vital role in the governing of a material’s properties and behavior. This is due to the fact that elasticity is one of the most important properties of a material. Elasticity is a measure of how much a material will change in size when subjected to a force. This can be important in many fields, such as engineering and physics. Due to their relationship to mechanical properties of the material, such as elastic moduli, Poisson’s ratio, and elastic anisotropy factor, crystals elastic constants provide key knowledge for the study of mechanical properties of materials. Calculations of the stresses produced by slight deformations of the equilibrium primitive cell led to the determination of the complete elastic constant tensor. Starting from the generalized form of Hooke’s law, the elastic constant tensors are given by [33]where stands for the Helmholtz free energy, and are the applied stress and Eulerian strain tensors, and stands for the coordinates. Moreover, in orthorhombic symmetry system of Laue class D_2h (mmm) group, there are nine independent elastic constants that should satisfy the well-known Born stability criteria [34];

In this study, the calculated elastic constants C_ij, bulk moduli as well as the shear modulus are shown in Tables 2 and 3. From Table 2, we can find that , C₁₁ > C₁₂, and 2C₁₃ < (C₁₁ + C₃₃), which shows that our results satisfy the required born mechanical stability conditions for CaHfS₃. Moreover, using the Voigt-Reuss-Hill (VRH) average approximation, mechanical parameters such as the Young’s modulus (E), Poisson’s ratio , and shear modulus (G) are computed from the calculated elastic constants as [35]where and are the Reuss bulk and shear moduli, and and correspond to the Voigt bulk and shear moduli. The Voigt bound values for orthorhombic crystals are obtained using the elastic constant matrix as [36]:

Also, the Reuss bound values obtained from the Elastic compliances are

Moreover, the Young’s modulus (E) and Poisson’s ratio are given by [36, 37]

The elastic constants and calculated mechanical properties such as bulk modulus (B), Young’s modulus (E), Poisson’s ratio (η), and shear modulus (G) from the elastic constant using the Voigt-Reuss-Hill (VRH) average approximation [35] are shown in Table 3.

The calculated bulk modulus values from elastic constants are found to be 80.76 GPa with GGA-PBE and 73.0 GPa with GGA + U. The value calculated with GGA + U approximation is in good agreement with the value calculated from the equation of state (73.4 GPa) for CaHfS₃ as in Table 1. Furthermore, determining the ratio of B/G is important for the brittle and ductile behavior of materials during material fabrication. The ductility and brittleness of materials can be determined based on the value of the B/G ratio, according to Pugh [38]. The threshold value that distinguishes between brittleness and ductility tendencies in materials is 1.75. The material behaves ductile when B/G > 1.75; otherwise, it exhibits brittle characteristics. From Table 3, our calculated ratio for B/G value is 1.76 and 1.85 (>1.75) with GGA-PBE and GGA + U, respectively, for CaHfS₃. This indicates that CaHfS₃ in GdFeO₃-type phase is a ductile.

Poisson’s ratio (η) is another mechanical parameter that provides information about the feature of the bonding forces. In the evaluation of Poisson’s ratio, the values 0.25 and 0.5 are the lower and upper limits of the central force, respectively [37, 39]. From Table 3, the calculated Poisson’s ratio for CaHfS₃ is 0.26 and 0.34 (which is between 0.25 and 0.5) with GGA-PBE and GGA + U, respectively, indicating that the interatomic forces are central.

The universal anisotropic index is a measure to determine whether an elastic material is anisotropic or isotropic based on the contributions of its bulk and sheared moduli [40]where G_V and B_V are sheared and bulk modulus obtained from Voigt bound approximation, respectively. Similarly, G_R and B_R are sheared and bulk modulus acquired from Reuss bound approximation. The material is known to be isotropic if the value of ; otherwise, it refers to the anisotropic mechanical properties. The variation of from zero value defines the level of elastic anisotropy. Based on this, the calculated value of is 0.31 and 0.34 with GGA-PBE and GGA + U, respectively, for CaHfS₃, indicating that the CaHfS₃ was found to be anisotropic.

3.3. Debye Temperature and Speed of Sound

The Debye temperature is an important physical quantity to describe phenomena of solid-state physics which are associated with lattice vibration, elastic constants, specific heat and melting point. At low temperatures the vibrational excitations arise solely from acoustic vibrations. Hence, at low temperatures the Debye temperature calculated from elastic constants is the same as that determined from specific heat measurements. The Debye temperature can be estimated from the averaged sound velocity, , given by [41]where is Planck’s constant, is Boltzmann’s constant, is Avogadro’s number, is density, M is molecular weight, and n is the number of atoms in a formula unit and average sound velocity, iswhere and are the longitudinal and transverse sound velocity. These velocities are obtained from density, shear and bulk modulus of the material as [42]

The calculated values of longitudinal (compressional) sound velocity and transverse (shear) sound velocity and Debye temperature for CaHfS₃ is given in Table 4. Unfortunately, as our knowledge, there are no previous works available on these properties for CaHfS₃ phases. Future experimental work will test our calculated results.

3.4. Electronic Properties: Density of States (DOS) and Band Structure

In this study, the electronic band structure along the high symmetry direction of the Brillouin zone was estimated using the GGA-PBE functional and the Hubbard correction (GGA + U) for the exchange-correlation potential of CaHfS₃ as shown in Figure 2. The calculated band gap value is compared with the existing theoretical band gap values in Table 5. With the help of the approximation of GGA-PBE exchange-correlation potential, the calculated band gap value is 1.526 eV for CaHfS₃. Moreover, the band gap was calculated with the Hubbard correction for onsite interaction, yielding a band gap value of 1.86 eV, which is less than the value (2.5 eV) estimated by reference [28] using HSE06 hybrid functional. To our knowledge, there is no experimental data to compare it with the calculated values.

(a)

(b)

In addition to this, the total and partial density of states were obtained for the equilibrium states of the phases using GGA-PBE and GGA + U (on-site Hubbard correction) approximations for exchange correlation interaction of CaHfS₃ as shown in Figures 3 and 4, respectively. The result shows that for the low-lying states at the maximum valence band mostly contributed by S (2p) orbitals and minimum conduction band mainly dominated by Hf (5d) orbitals. On the other hand, the rest of the orbitals observed to have small contributions on both maximum valence and minimum conduction bands.

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(b)

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Moreover, the other important parameter calculated from the band gap is the effective masses of the electron and the hole. The effective masses can be obtained by fitting the energy of the valence band maximum (holes) and conduction band minimum (electrons) to a quadratic polynomial in the reciprocal lattice vector based on the equation

The calculated electron (hole) effective masses for CaHfS₃ along the directions are 0.67(0.47) m₀ (electron rest mass).

3.5. Phonon Vibrations

Dynamic behaviors and thermal properties, which are central topics in the core problems of materials science, are significantly influenced by phonon vibration. One of the basic elements to consider when studying the phase stability, phase transformations, and thermodynamics of these materials is the phonon frequency of crystalline structures. The phonon density of states as a function of frequency is given by [43, 44]where N is the number of unit cells in a crystal. Divided by N, is normalized so that the integral over frequency becomes , where is a number of atoms.

Moreover, considering atom specific phonon density of states projected along a unit direction vector , is defined as [44]

From the canonical distribution in statistical mechanics for phonons under the harmonic approximation, the energy of the phonon system is given aswhere and are temperature, and reduced Planck constant, respectively. Here from statistical mechanics, gives the mean phonon number distribution function.

A supercell of 1 × 1 × 2 (in x, y, and z-direction) containing 40 atoms was created to study the phonon dispersion relation for CaHfS₃, using a DFPT and DFPT + U with Quantum Espresso as implemented in [19]. It is known that a crystal constituent of 40 atoms in bulk system (three dimensions x, y, and z coordinates) has 120 degrees of freedom ( where is number of atoms). The phonon dispersion relation for frequency bands and frequency density of states were calculated and displayed as shown in Figures 5 and 6, respectively. As indicated on Figure 5, it was observed that there are three (3) acoustic branches and 117 optical branches mode of vibrations. Here also the results showed that CaHfS₃ possesses no imaginary (no negative terms) phonon frequencies mode in both DFPT and DFPT + U. Hence, it is structurally and dynamically stable which agrees with the results of the analysis of the elastic constants and Goldschmidt tolerance factor analysis.

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(b)

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3.6. Thermodynamic Properties

Thermodynamic properties of materials are one of the underlying principles of solid-state research and industry. The investigation of these properties is important in order to reveal their specific behavior when these materials are under high pressure and temperature. With the use of thermodynamic relations, a number of thermal properties, such as constant volume heat capacity C_V, Helmholtz free energy F, and entropy S, can be computed as functions of temperature as [19, 43, 45, 46]

Here also, a supercell of 1 × 1 × 2 (in x, y, and z directions) containing 40 atoms was used to study the thermodynamic properties of , using DFPT and DFPT + U with Quantum Espresso as implemented in [19]. At a limited temperature ranging from 0K to 1000 K, thermodynamic parameters such as enthalpy, free energy, entropy, and heat capacity were computed and plotted as shown in Figure 7. In this consideration, the volume and temperature are independent variables. The overall feature of the results remains the same in both DFPT and DFPT + U approximation. In Figure 7, at 0 K, it can be seen that the entropy and heat capacity values are zero, which is in agreement with the third law of thermodynamics. While, with an increase in temperature, the free energy gradually decreases while the entropy increases quickly, following the reasonable trends shown in [43, 47, 48]. As a result, the enthalpy increases linearly with the increase in temperature. The increase in enthalpy at high temperatures leads to a decrease in free energy, which is associated with defects. It is clearly observed that for the temperature below 400 K, the heat capacity increases rapidly, whereas for the temperature above 400 K, it increases slowly (almost increasing linearly) with temperature and gradually approaches the Dulong–Petit classical limit (495.35 J/K/mol) owing to the anharmonic approximations of the Debye model as observed in [39, 43, 49]. The calculated heat capacity graph is also smooth and continuous, confirming that there is no phase change occurring in CaHfS₃ up to 1000 K as in [43]. These results can be helpful for further analysis and future experimental verifications.

3.7. Optical Properties

Optical properties are the physical properties of materials that determine how the materials respond to interaction with electromagnetic radiation (photon energy), including visible light. The optical property of a material can be determined from the complex dielectric function within an independent particle formalism [50]. The imaginary part is determined from the momentum dipole transition matrix elements between the occupied and the unoccupied electronic states along the long wave length limit [51]

The dispersion of the real part of the dielectric function is computed from the imaginary part of the dielectric function by using Kramers–Kronig relations:where P represents the principal value of the integral. With the help of the real and imaginary part of the dielectric function, other optical parameters such as the refractive index , the reflectivity , the absorption coefficient , and the electron energy loss function were calculated.

In this study, the optical properties of was studied with the polarization along the X-axis (100), Y-axis (010), and Z-axis (001) within time-dependent density functional perturbation theory (TD-DFPT) as implemented in Quantum Espresso package. We investigated the optical properties including dielectric function, optical absorption and conductivity, reflectivity, refractive index as well as the extinction coefficient for the considered for the photon energy from 0 to 1.6 Ry (21.77 eV) and the details of the calculations are presented. The calculated real (dispersive) and imaginary (absorptive) parts of the dielectric functions along X-axis (100), Y-axis (010) and Z-axis (001) for are shown in Figure 8. As described in Figure 8, the peak of the real of the dielectric function is 12 at 0.21 Ry, 12.83 at 0.16 Ry and 12.01 at 0.16 Ry along (100), (010), and (001) polarization direction, respectively. The static dielectric constant is 7.93, 8.09 and 7.90 along (100), (010), and (001) polarization direction, respectively. On the other hand, the peal of the imaginary part of the dielectric function is 10.80 at 0.24 Ry, 11.35 at 0.29 Ry, and 10.94 at 0.24 Ry along (100), (010), and (001) polarization direction, respectively. Here, we can observe that the dielectric constant along (010) polarization direction shows greater value (12.83) than other directions. Overall, the predicted high dielectric constants are the desired properties for photovoltaics applications as a dielectric constant value of 10 (and greater than 10) are good enough to produce exciton binding energy value lower than 25 meV (1.84 mRy) at room temperature as in [52], which indicates that is favorable for photovoltaic devices.

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(b)

In addition to this, the reflectivity and refractive index are two important parameters necessary for photovoltaic and optoelectronic applications, are calculated and plotted as shown in Figure 9. The optical reflectivity shows a greater value (39%) at about energy of 0.30 Ry along (010) polarization direction. The static reflectivity is 22.6%, 23.0%, and 22.6% along (100), (010), and (001) polarizations direction, respectively. This implies that highest reflection occurs along Y-axis (010) polarization direction and least reflection occurs on both (100) and (001) polarization directions. The peak of the refractive index is 3.63 at 0.22 Ry, 3.61 at 0.16 Ry, and 3.60 at 0.22 Ry along (100), (010), and (001) polarization directions, respectively. The estimated refractive index exists in the range of 0.52–3.63 for

The other two important optical parameters are the optical absorption function and the energy loss function, which are calculated and plotted in Figure 10. The absorption coefficient gives important knowledge on the light harvesting ability of a material, which affects the efficiency of solar energy conversion of corresponding solar cells as a consequence. As shown in Figure 10, the energy dependence of the absorption spectrum is given. The fundamental absorption edge starts at about 0.14 Ry (1.90 eV) that corresponds to the direct transition or fundamental band gap. This originates from the transition from the S (2p) states located at the top of the valence band to the empty Hf (5d) states located at the bottom of the conduction bands. The absorption spectrum peaks are mainly found in the ultraviolet region. The loss function describes the energy loss of a fast electron traversing the material [53]. The sharp peak is associated with the collective plasma oscillation [54]. The computed energy loss function has a peak value of 2.41 at 1.44 Ry, 2.30 at 1.44 Ry, and 2.11 at 1.45 Ry along (100), (010), and (001) polarizations directions, respectively. This indicates that a plasma oscillation occurs about energy of 1.44 Ry (19.59 eV), which is far away from the peak position of absorption for .

4. Conclusion

In this study, the first-principles calculations using the Quantum Espresso software package were performed to study the structural, electrical, elastic, phonon dispersion relation, temperature-dependent thermodynamic characteristics, and optical properties of orthorhombic . The elastic characteristics of the material were computed using the optimized structure. The density functional perturbation theory (DFPT) and DFPT + U implemented in Quantum Espresso software package was also used to calculate the phonon dispersion and thermal characteristics. The optical properties were also studied with the help of time-dependent density functional perturbation theory (TD-DFPT) as implemented in Quantum Espresso package. The computed lattice parameters are a = 6.561, b = 7.015, and c = 9.592 angstrom with GGA-PBE, and a = 6.581, b = 7.039, and c = 9.627 angstrom with GGA + U approximations, and comparable to the existing theoretical and experimental results. The elastic constants of CaHfS₃ were obtained and used to calculate the mechanical parameters such as bulk modulus, shear modulus, Young’s modulus, and elastic anisotropy. The Poisson’s ratio is 0.26 (0.34) with GGA-PBE (GGA + U) and indicates that the interatomic forces are central. The value of B/G (1.76) confirms that CaHfS₃ is ductile. The calculated band gap values were 1.526 eV and 1.86 eV with respect to GGA-PBE and GGA + U approximations, respectively. The absence of imaginary (negative frequencies in the figures) frequencies in phonon dispersion curve and the phonon density of states indicate that the structure is dynamically stable. The temperature dependence of thermodynamic parameters including enthalpy, entropy, free energy, and heat capacity is calculated and analyzed. Main optical properties such as absorption coefficient, dielectric constant, energy loss function, reflectivity, and refractive index are calculated and discussed in detail in the spectral range 0–1.6 Ry (21.77 eV). The polarizations along X-axis (100), Y-axis (010), and Z-axis (001) found exhibit significantly different optical responses confirming anisotropic behavior. Optical properties also show relatively high reflectivity and absorption in the ultraviolet region. To our knowledge there is no experimental data available for comparison for elastic, thermal and optical properties. These results will be hopeful that it can inspire researchers for the future further works.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this article.

Acknowledgments

One of the authors Mulugetta Duressa Kassa expresses his gratitude and appreciation to the Department of Physics, College of Natural Sciences, Jimma University, and Arba Minch University, for providing material support. This study was funded by Jimma University, College of Natural Sciences for supporting PhD student (grant number: CNSPHYS-04-2021/2022), and also supported by a subsidy fund from Arba Minch University (under project: Gov/AMU/TH3/CNS/phy/01/14).

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Copyright © 2023 Mulugetta Kassa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Advances in Condensed Matter Physics

The First-Principles Investigation of Structural Stability, Mechanical, Vibrational, Thermodynamic, and Optical Properties of CaHfS3 for Optoelectronic Application

Abstract

1. Introduction

2. Computational Details

3. Results and Discussion

3.1. Crystal Structure

3.2. Elastic Properties

3.3. Debye Temperature and Speed of Sound

3.4. Electronic Properties: Density of States (DOS) and Band Structure

3.5. Phonon Vibrations

3.6. Thermodynamic Properties

3.7. Optical Properties

4. Conclusion

Data Availability

Conflicts of Interest

Acknowledgments

References

Copyright

The First-Principles Investigation of Structural Stability, Mechanical, Vibrational, Thermodynamic, and Optical Properties of CaHfS₃ for Optoelectronic Application