The Structural, Electronic and Elastic Properties ... - Chin. Phys. Lett.

CHIN. PHYS. LETT. Vol. 30, No. 7 (2013) 077101

The Structural, Electronic and Elastic Properties, and the Raman Spectra of Orthorhombic CaSnO3 through First Principles Calculations * A. Yangthaisong** Computational Materials and Device Physics Group, Department of Physics, Faculty of Science, Ubon Ratchathani University, Ubonratchathani 34190, Thailand

(Received 2 February 2013) First principles calculations based on the density functional theory of the electronic structure, elastic and lattice vibrational properties of orthorhombic CaSnO3 are carried out using standard functional approximation and density functional perturbation theory. The results show that CaSnO3 is an insulator with an indirect local density approximation and generalized gradient approximation gap of 3.10(2.69) eV. In addition, the Raman vibration modes of CaSnO3 are determined by the calculated phonon frequencies at the gamma point, where the prominent peaks of the Raman spectra of CaSnO3 coinciding with the calculated frequencies can be assigned.

PACS: 71.15.Mb, 36.20.Ng

DOI: 10.1088/0256-307X/30/7/077101

In recent years, perovskite alkaline earth stannate compounds such as BaSnO3 , CaSnO3 and SrSnO3 have been widely investigated due to their dielectric properties and several potential applications ranging from a high-capacity anode material for Li-ion batteries to ceramic capacitors and sensors.[1,2] These three compounds have perovskite structures, BaSnO3 has a cubic structure, whilst the structures of CaSnO3 and SrSnO3 are orthorhombic. CaSnO3 has also attracted considerable attention in the geophysics community since it is an isostructural analogue of (Mg,Fe)SiO3 perovskite, the most abundant silicate on Earth.[3] It is also worth noting that extremely high pressure-temperature conditions, such as 115 GPa at 2000 K, are required to investigate the phase transformation in Mg-silicate.[4] Hence, isostructural perovskite structures are of interest since they can be used to conduct experiments at lower pressure regarding the phase transition from the perovskite to postperovskite structure in MgSiO3 . Recently, a combination of laser-heated diamond anvil cell (LHDAC) techniques and synchrotron x-ray diffraction measurements were performed to investigate the high phase transition of CaSnO3 in a pressure range from 8 GPa to 86 GPa.[4] It is shown that the post-perovskite is formed above 40 GPa and 2000 K. It is also found that the phase transition can be quenchable to ambient conditions. An understanding of CaSnO3 analogous to MgSiO3 would make a valuable contribution to the understanding of the transition in MgSiO3 . CaSnO3 exhibits in two crystalline forms: an ordered ilmenite phase with rhombo-hedral unit cell, and an orthorhombic phase with perovskite structure (space group 𝑃 𝑏𝑛𝑚). It is worth mentioning that there are only a few studies based on first principles calculations reported for the ilmenite[5] and orthorhombic CaSnO3 .[6] For example, in the first theoretical study of the structural, electronic and optical absorption properties of orthorhombic CaSnO3 , it was suggested that CaSnO3 is a direct gap semiconductor with potential optoelectronic applications.[6] In addition, a phase transition in the CaSnO3 structure from

CdFeO3 -type perovskite to a CaIrO3 structure was predicted to occur at 12 GPa.[7] Raman spectroscopy is an experimental tool for characterization of materials via probing the elementary excitations in materials by utilizing inelastic scattering processes of monochromatic light sources such as lasers. It can be considered as an accurate and convenient technique for measuring zone-center phonons. It is also suitable for identifying the phase transition as it provides the structure modification information at microscopic level. A recent investigation employing Raman spectroscopy was performed to study the behavior of vibrational modes of CaSnO3 perovskite under high pressure.[8] It was found that CaSnO3 remains a GdFeO3 -type perovskite up to 26 GPa. It is worth noting that the assignment of Raman peaks in this study was carried out by comparing with the Raman modes of CaZrO3 and other isostructural Ca-bearing perovskites since no detailed lattice dynamic studies of CaSnO3 are available. The theoretical determination of Raman spectra is required since this can be used to associate Raman lines to specific microscopic structures. Hence, it is instructive to perform systematic investigation of the structural, electronic, dielectric, and lattice vibration properties of CaSnO3 . In this Letter, we theoretically investigate the electronic band structure, elastic, dielectric and lattice vibration properties at the zone center of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 . In addition, the Raman-active frequencies of CaSnO3 are calculated. The calculation methods used in the investigation and the predictions and discussion of the electronic structure, elastic, dielectric and lattice vibration properties of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 are given. First principles calculations are performed according to density functional theory (DFT), by using the plane wave method as implemented in the CASTEP code.[9] The atoms are represented by the normconserving pseudopotential as generated with the OPIUM[10] code, where the Ca (3𝑠, 3𝑝, 4𝑠) and O (2𝑠, 2𝑝) orbitals are considered as valence states, while the ultrasoft Vanderbilt pseudopotentials[11] are adopted

* Supported by the National Nanotechnology Center (NANOTEC), National Science and Technology Development Agency (NSTDA), Ministry of Science and Technology, Thailand, through its Computational Nanoscience Consortium (CNC). ** Corresponding author. Email: [email protected] © 2013 Chinese Physical Society and IOP Publishing Ltd

077101-1


Energy (eV)

5 4 3 2 1 0 -1 -2

Fig. 1. The calculated GGA band structure of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 along the high symmetry lines of the Brillouin zone.

In addition to electronic structure calculations, the phonon dispersion and phonon frequencies at the zone center of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 are calculated using the linear response with density functional perturbation theory (DFPT).[17,18] In addition, the Raman activities of CaSnO3 are determined using the combined DFPT and finite displacement method. In particular, the Raman activity tensor of a mode is obtained by the derivative of the dielectric permittivity tensor with respect to the mode amplitude, as explained in more detail in Ref. [18] and references therein. Here, the Raman-active vibrational modes and their frequencies of CaSnO3 are calculated and compared with recent experimental investigations. The predicted LDA (GGA) lattice constants of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 are 𝑎 = 5.4031(5.4882) Å, 𝑏 = 5.5726(5.6232) Å, 𝑐 = 7.7268(7.8314) Å, in good agreement with other theoretical results[5,6] and somewhat lower than the experiment values.[19] Figure 1 shows the calculated GGA band structure, indicating that CaSnO3 is an indirect gap (𝑆 → Γ ) material with a gap of about 2.59 eV. The LDA gap is 3.01 eV. Note that the valence band maximum (VBM) in LDA (GGA) calculations is at the 𝑆-point, while the valence band energy at the Γ -point is just 0.05 (0.07) eV lower. The LDA (GGA)

direct gap at the Γ -point is 3.10(2.64) eV. Note that there is no experimental gap of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 reported in the literature, while the relevant value for ilmenite CaSnO3 was reported to be 4.4 eV.[5] The band gaps calculated based on the LDA/GGA method are expected to underestimate the experimental values. It is worth comparing our results with the plane wave calculation reported in Ref. [6], in which the band gap of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 was predicted to be a GGA (LDA) direct gap at a Γ -point of 1.95(2.92) eV. The indirect gap (𝑇 → Γ ) of 57 meV was obtained for both the LDA and GGA results in Ref. [6]. Note that the ultrasoft Vanderbilt pseudopotentials were used for the valence states of Ca and Sn atoms, whilst that for oxygen was generated onthe-fly with a plane-wave cutoff energy of 550 eV. In fact, we also perform a similar calculation using the ultrasoft pseudopotential for all atoms, while with the parameters mentioned above, similar results to those in Ref. [6] are obtained. It can be seen that our results are consistent with those reported in Ref. [6]. In this study, the pseudopotentials used for Ca and O are generated by the designed nonlocal pseudopotential scheme of Rappe et al.,[20] with the emphasis on guaranteeing accurate valence states in unfrozen semicore potentials. For the Sn pseudopotential, nonlinear core corrections are taken into account to describe the Sn 4𝑑 electrons properly as suggested, and are described in more detail in Ref. [21]. In particular, the Sn 4𝑑 electrons are included among the valence states. Considering the LDA (GGA) lattice parameters obtained from our calculations, in comparison with the experimental values of 𝑎 = 5.5142 Å, 𝑏 = 5.6634 Å, 𝑐 = 7.8816 Å[19,22] and those calculated results reported in Ref. [6] in which 𝑎 = 5.4099(5.6086) Å, 𝑏 = 5.5887(5.7978) Å, and 𝑐 = 7.7459(8.0452) Å, it is clearly seen that our results are closer to the experimental lattice parameters of CaSnO3 . This suggests that the pseudopotentials used are reliable.

Density of states (e/eV)

to represent Sn valence shells in which Sn (4𝑑, 5𝑠, 5𝑝) are considered as valence states. The exchangecorrelation energy functional is treated with the local density approximation (LDA) given by Ceperley and Alder[10] as parameterized by Perdew and Zunger[13] or the Perdew–Burke–Ernzerhof (PBE) version of the generalized gradient approximation (GGA).[14] The plane wave basis set cutoff energy is 880 eV, and the Brillouin zone is sampled on a 6×6×4 mesh generated according to the Monkhorst–Pack scheme[15] to ensure a well converged electronic structure. Broyden– Fletcher–Goldfarb–Shanno (BFGS) minimization[16] is used to carry out the structural optimization in which atomic positions and lattice parameters are optimized simultaneously with the following threshold for the converged structure: an energy change per atom of less than 0.5 × 10−6 eV, a residual force less than 0.01 eV/Å, stress below 0.02 GPa and the displacement of atoms during geometry optimization of less than 5 × 10−4 Å.

38.0 28.5 19.0 9.5 36 27 18 9 0 1.32 0.88 0.44 0.00 21.9 14.6 7.3 0.0

(a)

Total

(b)

Ca

(c)

Sn

(d)

O

-40 -30 -20 -10

Energy (eV)

0

10

Fig. 2. The total and partial density of states (GGA) of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 .

077101-2

The PBE total and partial density of states of


CaSnO3 is shown in Fig. 2. It can be seen that the uppermost valence bands are mainly due to Sn-𝑝 states hybridized with some O-𝑝 states, suggesting that the bonding between Sn and O is ionic. The bandwidth of the valence bands is about 9.5 eV. The conduction bands are composed mainly of antibonding between Ca-𝑑 electrons and Sn-𝑝, Sn-𝑠 electrons. The response of the crystal to the external force can be determined via the elastic constants, which are directly related to the mechanical properties of the materials. The values of these constants provide invaluable information regarding the stability and stiffness of materials. For the orthorhombic crystal, there are nine independent elastic constants (𝐶𝑖𝑗 henceforth), three diagonals (𝐶11 , 𝐶22 , 𝐶33 ), three offdiagonals (𝐶12 , 𝐶13 , 𝐶23 ), and three shears (𝐶44 , 𝐶55 , 𝐶66 )𝐶𝑖𝑗 . The mechanical stability of the orthorhombic crystal requires that the nine independent elastic

constants should satisfy the following criteria:

[23]

(𝐶11 − 𝐶22 − 2𝐶12 ) > 0, (𝐶11 − 𝐶33 − 2𝐶13 ) > 0, (𝐶22 − 𝐶33 − 2𝐶23 ) > 0, 𝐶11 > 0, 𝐶22 > 0, 𝐶33 > 0, 𝐶44 > 0, 𝐶55 > 0, 𝐶66 > 0, (𝐶11 + 𝐶22 + 𝐶33 + 2𝐶12 + 2𝐶13 + 2𝐶23 ) > 0. (1) The calculated elastic constants and elastic compliance constants of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 are listed in Table 1. It can be seen that CaSnO3 can be stabilized mechanically in the 𝑃 𝑏𝑛𝑚 orthorhombic phase. The GGA (LDA) bulk modulus of orthorhombic CaSnO3 is 182.0(200.4) GPa, which is slightly higher than the experimental value that is reported to be about 162 GPa, as determined from acoustic measurements.[24]

Table 1. The calculated independent elastic constants (𝐶𝑖𝑗 ) of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 . Phase 𝑃 𝑏𝑛𝑚 (LDA) 𝑃 𝑏𝑛𝑚 (GGA)

𝐶11 340.2 325.4

𝐶22 348.11 322.9

𝐶33 347.4 318.1

𝐶44 132.9 129.3

𝐶𝑖𝑗 (GPa) 𝐶55 𝐶66 116.7 110.9 118.4 100.1

𝐶12 130.9 108.3

𝐶13 132.0 116.4

𝐶23 121.2 111.4

Table 2. The LDA (GGA) elastic constants for polycrystalline CaSnO3 . Parameters Bulk modulus(GPa) Shear modulus(Lame Mu, GPa) Lame lambda

Approximation method Voigt Reuss Hill 200.45(182.1) 200.45(182.0) 200.45(182.0) 115.57(111.6) 114.81(110.5) 115.19(111.1) 123.40(107.6) 123.91(108.3) 123.65(108.0)

Based on the single-crystal independent elastic constants, the related properties for polycrystal CaSnO3 can be determined in terms of the shear modulus 𝐺, bulk modulus 𝐵, Young’s modulus 𝐸, Poisson’s ratio, and Lame’s coefficients 𝜇 and 𝜆 using the Voigt–Reuss–Hill approximation.[25−27] The relations used are given by 𝐵H = (𝐵V + 𝐵R )/2, 𝐺H = (𝐺V + 𝐺R )/2, 𝐸 = 9𝐵H 𝐺H /(3𝐵H + 𝐺H ), 𝑣 = (3𝐵H − 2𝐺H )/(2(3𝐵H + 𝐺H )),

(2)

where the subscripts H, V, and R refer to Hill, Voigt and Reuss approximation, respectively, and 𝑣 is Poisson’s ratio. Using DFPT, we can calculate the dielectric permittivity and Born effective charge tensors of the ingredient atoms in orthorhombic CaSnO3 . The full tensors (PBE) of the Born effective charge in CaSnO3 are as follows: (︃ )︃ 2.499 −0.068 0 * 𝑍 (Ca) = −0.081 2.446 0 , 0 0 2.405 (︃ )︃ 3.846 −0.003 −0.034 * 𝑍 (Sn) = 0.067 3.849 −0.049 , 0.126 −0.032 3.850 (︃ )︃ −2.193 −0.324 −0.033 * 𝑍 (O1 ) = −0.308 −2.233 −0.042 , −0.043 −0.042 −1.869

(︃ *

𝑍 (O2 ) =

−1.957 0.069 0.000 0.099 −1.829 0.000 0.000 0.000 −2.517

)︃ .

The calculated electronic 𝜀∞ and static 𝜀0 dielectric tensors of CaSnO3 are shown in Table 3. Note the average dielectric tensor 𝜀¯ = 13 (𝜀𝑥𝑥 +𝜀𝑦𝑦 +𝜀𝑧𝑧 ), a measure of the 𝑥–𝑦 anisotropy ∆𝜀‖ = 𝜀𝑥𝑥 −𝜀𝑦𝑦 , and a 𝑧 measure of anisotropy ∆𝜀⊥ = 𝜀𝑧𝑧 − 12 (𝜀𝑥𝑥 + 𝜀𝑦𝑦 ), are listed in Table 3. It is worth noting that the calculated dielectric tensors of CaSnO3 are the first theoretical study reported. Hence, it is instructive to further investigate both the theoretical and experimental studies. Table 3. The calculated electronic 𝜀∞ and static 𝜀0 dielectric tensors of CaSnO3 . 𝜀∞ 𝜀0

𝑥𝑥 3.60 13.01

𝑦𝑦 3.58 13.56

𝑧𝑧 3.57 15.15

average 3.58 13.90

Δ𝜀‖

Δ𝜀⊥

−0.55

1.86

The LDA phonon dispersion curve along highsymmetry lines in the Brillouin zone of orthorhombic CaSnO3 is calculated from the optimized geometry, as shown in Fig. 3. Note a similar phonon band structure obtained from GGA calculation is not shown here. It is worth noting that our calculated phonon band structure is the first study reported. Since there is no experimental full phonon dispersion curve available, our calculation could be considered as a prediction study with the accuracy of LDA (GGA). Our calculations suggest the stability of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 , as it is obviously seen in Fig. 3 that the phonon modes have positive frequencies in the whole Brillouin zone.

077101-3


It is worth noting that CaSnO3 is one of the materials under intensive investigation based on Raman spectroscopy.[8,28,29] Surprisingly, there is no theoretical investigation on lattice dynamics at the Γ -point in the Brillouin zone of CaSnO3 available, which is crucial for the interpretation of the Raman spectroscopy. For example, phonon frequencies at the Γ -point at ambient conditions and at pressures up to 20 GPa, and Raman spectrum modes of CaSnO3 were investigated experimentally and reported recently.[8] The Ramanactive mode assignment in this study is mainly based on assignments of similar compounds, based on the group theory and considering the crystallographic positions of ions in CaSnO3 , in which the Ca4++ and Sn4++ ions are located in 4(c) and 4(b), respectively, while the O2− ions are in 4(c) and 8(d). The zone center lattice modes and optical activities for this structure are Γ = 7𝐴𝑔 + 5𝐵1𝑔 + 7𝐵2𝑔 + 5𝐵3𝑔 + 8𝐴𝑢 + 10𝐵1𝑢 + 8𝐵2𝑢 + 10𝐵3𝑢 ,

(3)

in which the following irreducible representation of the different sublattices in the unit cell can be expressed as Ca4++ -sublattice, 4(c) site = 2𝐴𝑔 + 𝐵1𝑔 + 2𝐵2𝑔 + 𝐵3𝑔 + 𝐴𝑢 + 2𝐵1𝑢 + 𝐵2𝑢 + 2𝐵3𝑢 , Sn4++ -sublattice, 4(b) site = 3𝐴𝑢 +3𝐵1𝑢 +3𝐵2𝑢 +3𝐵3𝑢 , O2− -sublattice, 4(c) site = 2𝐴𝑔 +𝐵1𝑔 +2𝐵2𝑔 +𝐵3𝑔 +𝐴𝑢 +2𝐵1𝑢 +𝐵2𝑢 +2𝐵3𝑢 , O2− -sublattice, 8(d) site = 3𝐴𝑔 + 3𝐵1𝑔 + 3𝐵2𝑔 + 3𝐵3𝑔 + 3𝐴𝑢 + 3𝐵1𝑢 + 3𝐵2𝑢 + 3𝐵3𝑢 . Note there are 24 Raman active optical phonon modes with Γ = 7𝐴𝑔 + 5𝐵1𝑔 + 7𝐵2𝑔 + 5𝐵3𝑔 and 25 IR active modes with Γ = 9𝐵1𝑢 + 7𝐵2𝑢 + 9𝐵3𝑢 and three translational modes: 𝐵1𝑢 + 𝐵2𝑢 + 𝐵3𝑢 , while the 8𝐴𝑢 modes are non-active. The calculated Raman-active frequencies at the zone center of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 in comparison with the available experimental data are listed in Table 4. Our study reported here is the first theoretical investigation of zone center phonons and non-resonant Raman-active modes of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 within the accuracy of the PBE (LDA) functional approximation. It can be seen that our calculated Raman-active frequencies (PBE) are in good agreement with the experiments, especially for the frequency range below 500 cm−1 .[8,28,29] It is worth noting that among the experimental Raman frequencies reported, the first peak at 145 cm−1 only reported in Ref. [29] can be well assigned to the 𝐴𝑔 mode with our calculated value of 149.6 cm−1 . In addition, the weak band 699 cm−1[29] or 700.9 cm−1[8] found experimentally may be assigned to the 𝐵1𝑔 mode with our calculated peak at 720.3 cm−1 . Considering the recent study reported in Ref. [8], there are 10 Raman modes under ambient conditions and the spectrum is dominated by three major peaks at 182.5, 278.2 and 357.5 cm−1 , six weak peaks at 163.4, 226.7, 245.3, 442.5, 501.9, and 700.9 cm−1 , and one shoulder at 264.3 cm−1 . All these Raman-active frequencies are consistent with the previous studies also shown in Table 4 for comparison. The three major peaks can be assigned to 182.6(𝐵2𝑔 ), 274.6(𝐴𝑔 ), and 354.8(𝐵1𝑔 ) cm−1 , while the six weak peaks can be assigned to 168.6(𝐵2𝑔 ), 228.1(𝐵2𝑔 ), 241.6(𝐵1𝑔 ),

449.5(𝐵2𝑔 ), 495.0(𝐵2𝑔 ), and 720.3(𝐵1𝑔 ) cm−1 . Note that the consideration above relies on the assumption that the shoulder at 264.3 cm−1 is considered to coincide with the peak 274.6(𝐴𝑔 ) in our calculation. Table 4. The calculated Raman active frequencies (cm−1 ) of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 in comparison with the available experimental data.[8,28,29] Symmetry 𝐴𝑔 𝐵2𝑔 𝐴𝑔 𝐵1𝑔 𝐵2𝑔 𝐵3𝑔 𝐵2𝑔 𝐴𝑔 𝐵1𝑔 𝐴𝑔 𝐴𝑔 𝐵3𝑔 𝐵1𝑔 𝐵2𝑔 𝐵2𝑔 𝐵3𝑔 𝐴𝑔 𝐵2𝑔 𝐵1𝑔 𝐵3𝑔 𝐴𝑔 𝐵1𝑔 𝐵2𝑔 𝐵3𝑔

Calc(PBE) 149.6 168.6 171.4 184.4 182.6 197.5 228.1 236.3 241.6 274.6 324.8 332.9 354.8 368.4 449.5 463.0 467.6 495.0 526.0 525.8 533 720.3 759.4 787.4

Expt[8]

Expt[28]

163.4

161

Expt[29] 145 165

182.5

181

183

226.7

226

230

245.3 264.3 278.2

246 263 277

247 265 278

357.5

355

354

442.5

442

442

501.9

500

700.9

620 699

Based on our phonon band structure and Raman frequency results, it is worth mentioning the structural stability of the orthorhombic CaSnO3 under pressure. Note that our calculations are performed at 𝑇 = 0 K and zero pressure, considering that our calculated phonon dispersion presented in Fig. 3 has positive frequencies at any wave vectors, including the zone centers in the Brillouin zone. This suggests that the orthorhombic CaSnO3 structure is dynamically stable. In Ref. [8], high-pressure (up to 20 GPa) Raman spectroscopy reveals that some Raman modes disappear on compression by merging into neighboring bands or vanishing. However, these Raman peaks were recovered during decompression and there is no extra Raman peak found upon compression. Correlating our calculated phonon results with experimental Raman active frequencies of orthorhombic CaSnO3 at ambient pressure and pressure up to 20 GPa, as reported in Ref. [8], suggests that there is no phase transition in CaSnO3 from a GdFeO3 -type perovskite (𝑃 𝑏𝑛𝑚) to GdIrO3 -type structure (𝐶𝑚𝑐𝑚) for pressures up to 20 GPa in contrast to that predicted in Ref. [7]. It is worth noting that the behavior of the lattice vibrations of materials under pressure provides information regarding structural instability, phase transitions and electron-phonon interactions. In addition, to estimate the zero-temperature transition pressure 𝑃 of CaSnO3 calculations with conditions of equal enthalpies of the enthalpy (𝐻 = 𝐸 + 𝑃 𝑉 ) of both phases, the same is required. Hence, it is instructive to further study the structural and lattice vibrational properties, including the behavior of Raman modes under pressure and the mechanisms underlying the phase transition

077101-4


of CaSnO3 . In fact, this detailed study is currently being investigated and will be reported elsewhere. 900

Frequency (cm

-1

)

800 700 600 500 400 300 200 100 0

Fig. 3. The calculated phonon dispersion curve of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 along the high symmetry lines of the Brillouin zone.

In conclusion, first principles density functional theory was performed to investigate the structural and electronic properties of 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 within the standard functional approximation. The calculated equilibrium lattice parameters were found to be in favorable agreement with other experimental and theoretical works. In addition, it was found that 𝑃 𝑏𝑛𝑚 orthorhombic CaSnO3 is an indirect gap material with gap values of 3.10 eV and 2.69 eV for the LDA and GGA calculations, respectively. Furthermore, the phonon frequencies at the zone center were calculated within the framework of density functional perturbation theory. The peak assignment of the CaSnO3 Raman spectrum, which has previously relied on using the peak assignment of similar compounds, was confirmed by first principles calculations for the first time. The calculated Raman-active frequencies of CaSnO3 are in good agreement with the prominent peaks of the corresponding experimental spectra. The author acknowledges the computer resources available at the Large Scale Simulation Research Laboratory (LSR) of NECTEC in Bangkok, Thailand.

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