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BY 4.0 license Open Access Published by De Gruyter Open Access January 26, 2023

Ab initio study of fundamental properties of XInO3 (X = K, Rb, Cs) perovskites

  • Ülkü Bayhan ORCID logo EMAIL logo
From the journal Open Chemistry


The structural, elastic, anisotropic, and lattice dynamical properties of cubic perovskite compounds XInO3 (X = K, Rb, and Cs) are investigated using first-principles calculations. Electronic band structures and state densities revealed that the electronic nature of the studied materials exhibited half-metallicity properties. The existence of O p–d states close to the Fermi level contributes to the half-metallic properties. Moreover, polycrystalline properties, such as bulk, Young, and shear moduli and Pugh and Poisson ratios, have been determined. As a result of these characteristics, the compounds under consideration exhibited ductility behavior. As far as is known, since this is the first study of XInO3 (X = K, Rb, and Cs) compounds, this work sheds light on future works.

1 Introduction

Researchers’ favorites and prominent in all areas of material sciences are perovskites, which are found in the world’s natural formations and whose effective and rare physical features have lately been recognized. Although it is referred to as perovskite, the calcium–titanium–oxygen complex CaTiO3 is also used to characterize it. The first man who finds this mineral was the Russian mineralogist Gustav Rose. In 1839, researchers recognized other minerals with a comparable crystalline structure called perovskites. These new compounds, which have a general structure of type ABC3, were discovered by Russian mineralogists and named Perovskite in honor of Lev Perovski (1792–1856). Perovskite materials’ interesting and surprising properties are newly recognized, and they are being pursued by researchers with rising momentum [1,2,3].

The challenge of being able to store energy generated and utilize it later is a matter of importance when resolving energy problems persists. New materials, particularly perovskite oxides as electrochemical energy materials, offer a great advantage to be utilized as a possible host or carrier for applications. This theoretical study covers the latest progress of one group example of ABO3 perovskite oxides, with no more information in the literature. In this study, the structural, elastic, anisotropic elastic, electronic, and lattice dynamical properties of XInO3 (X = K, Rb, and Cs) were examined using density functional theory (DFT) implemented by the Vienna ab initio simulation package (VASP). The lattice constant, bulk, Young’s, and shear moduli, and Poisson’s ratio have been investigated. Current compounds are stable, both mechanically and dynamically. The calculations revealed that these compounds retain some brittleness while also exhibiting ductility. The material may show bending behavior. With this feature, it can be said that it has the potential to be a new material that can be used in eco-friendly wearable technologies [3,4,5,6].

2 Calculation methods

DFT calculations on XInO3 (X = K, Rb, and Cs) perovskites were performed using the VASP [7,8]. Electron–ion interaction was handled by the projector-augmented wave method with a 500 eV cutoff energy [9,10]. The Perdew–Burke–Ernzerhof functional with generalized gradient approximation has been used for exchange-correlation in electron–electron interactions [11]. For the compounds investigated, gamma-centered 16 × 16 × 16 with an automatic k-mesh has been performed. Methfessel–Paxton smearing has been addressed to oneself as 0.025 eV [12]. The convergence criteria were taken up as 10−6 eV Å−1 and 10−8 eV, respectively.

3 Results and discussions

The XInO3 (X = K, Rb, and Cs) perovskites crystallize/take shape in space group Pm 3 ̅ m. The Wyckoff locations 1a (0.0, 0.0, 0.0) for the X atoms, 1b (0.5, 0.5, 0.5) for the In, and 3c (0.0, 0.5, 0.5), (0.5, 0.0, 0.5), and (0.5, 0.5, 0.0) for the three O atoms, respectively, are where the atoms in compounds under investigation are located. Figure 1 details the structure of the current compounds.

Figure 1 
               The structure of XInO3 (X = K, Rb, and Cs) compounds.
Figure 1

The structure of XInO3 (X = K, Rb, and Cs) compounds.

Table 1 accounts for the calculated lattice constants (a in Å), volume (V in Å3), density (ρ in g cm−3), and formation energy (ΔH f in eV atom−1).

Table 1

Calculated structural properties for XInO3 (X = K, Rb, and Cs)

Compounds a (Å) V3) ρ (g cm−3) ΔH f (eV atom−1)
KInO3 4.293 79.101 4.239 −1.473
RbInO3 4.336 81.512 5.058 −1.358
CsInO3 4.395 84.915 5.783 −1.271

It can be concluded that the lattice constants, volume, and density have increased for the investigated compounds, as categorized in Table 1. Furthermore, the results of the formation energy, calculated by using equation (1), have demonstrated that those compounds can be both synthesizable and thermodynamically stable:

(1) Δ H f = E XIn O 3 Total ( E X Total + E In Total + ( 3 × E O Total ) ) .

3.1 Mechanical properties

Either conceptual or portable applications require mechanical characteristics, which are both beneficial and essential. As a result, it is necessary to compute the mechanical properties of the compounds considered. Therefore, current compounds must adhere to the Born stability conditions [13], which are as follows: C 11C 12 > 0; C 11 + 2C 12 > 0; C 44 > 0. Table 2 depicts the calculated elastic constants (C ij in GPa), bulk, shear, and Young’s moduli (B, G, and E in GPa), B/G, G/B, Poisson’s ratio, and Vicker’s hardness (H f in GPa).

Table 2

Calculated elastic constants (C ij in GPa), bulk, shear, and Young’s moduli (B, G, and E in GPa), B/G, G/B, Poisson’s ratio (ν), and Vicker’s hardness (H f in GPa)

Compounds KInO3 RbInO3 CsInO3
C 11 157.406 144.325 117.118
C 12 40.359 46.484 48.490
C 44 1.424 10.191 16.180
B 79.375 79.097 71.366
G 37.788 56.096 59.789
E 13.300 20.298 21.975
B/G 5.968 3.897 3.248
G/B 0.168 0.257 0.308
ν 0.421 0.382 0.360
H f 0.754 1.651 2.149

It is possible to see that the compounds meet Born stability criteria, and those compounds are mechanically stable. Thus, they are suitable for conceptual or portable applications. The elastic constants can be used to express the polycrystalline properties such as bulk (B), shear (G), Young’s moduli (E), B/G, G/B, Poisson’s ratio (ν), and Vicker’s hardness (H f ), and they are calculated by using equations (2)–(6), respectively. In equations (2) and (3), the Voigt [14] and Reuß [15] approximations are symbolized as subscripts V and R, respectively. The protection of the compound to volume modification under applied hydrostatic pressure could be referred to as the bulk modulus, as it is commonly known in [16]. As already concluded from Table 2, KInO3 has the highest bulk modulus, while CsInO3 has the lowest of the investigated compounds. The relationship between shear stress and shear strain can be used to discover the shear modulus, also known as elastic shear stiffness [17]. As can be seen in Table 2, CsInO3 has the highest shear modulus, whereas KInO3 has the lowest one. As an indicator of elasticity, Young’s modulus is determined by stress-to-strain ratios caused by uniaxial deformation [18]. Among the investigated compounds, KInO3 has the lowest Young’s modulus, while CsInO3 has the highest. The B/G ratio, an essential parameter for determining the consistency of the compound, indicates brittleness if it is less than 1.75; otherwise, it indicates ductility. As can be noted in Table 2, the computed results of the B/G are larger than the vital value (1.75); therefore, it is possible to say that current compounds have shown ductility characteristics within observations [19]. The ratio G/B, another serious criterion, helps predict the bonding peculiarities of compounds and is directly related to the bonding nature of compounds. The ratio G/B, which is another decisive criterion owing to helping predict the bonding peculiarity of compounds, identifies that if it is around 0.6, the compound has a predominantly ionic bonding nature. In contrast, if this ratio is about 1.1, the compound has demonstrated covalent bonding predominantly. Since the G/B ratios of these compounds are less than 0.6, the investigated compounds have exhibited dominantly ionic bonding characteristics, as is seen in Table 2 [20]. Analogous to G/B, the Poisson’s ratio is useful for describing bonding properties. Ionic and covalent bonding compounds have Poisson’s ratios of about 0.25 and 0.1, respectively [21]. As can be seen in Table 2, Poisson’s ratios for the studied compounds are larger than 0.25; hence, the present compounds have indicated ionic bonding in harmony with G/B results. Vicker’s hardness, the last specification in Table 2, was computed utilizing the semiempirical equation proposed by Tian et al. [22] standing on G/B known as Pugh’s modulus, as follows:

(2) B = B V + B R 2 ,

(3) G = G V + G R 2 ,

(4) E = 9 BG G + 3 B ,

(5) ν = 1 2 B 2 G 3 B + G 3 ,

(6) H ν = 0 . 92 k 1 . 137 G 0 . 708 k = G / B .

In all aspects, as concluded from Vicker’s hardness results, these compounds are not so hard materials. This behavior makes the compounds ductile.

3.2 Anisotropic properties

Anisotropic behaviors are beneficial for determining microcracks in the compounds. In crystals with cubic symmetry, the Zener anisotropy (A), given in equation (7), and maximum–minimum polycrystalline properties are enough to explain this nature. Table 3 depicts these quantities.

(7) A = 2 C 44 C 11 C 12 .

Table 3

The calculated Zener ratio (A) and max–min points of Young’s modulus (E in GPa), linear compressibility (β in TPa−1), shear modulus (G in GPa), and Poisson’s ratio (ν)

KInO3 RbInO3 CsInO3
A 0.024 0.208 0.472
Young’s modulus E min 4.247 29.314 45.129
E max 140.930 121.680 88.722
Linear compressibility β min = β max 4.200 4.214 4.671
Shear modulus G min 1.424 10.191 16.180
G max 58.523 48.920 34.314
Poisson’s ratio ν min 0.008 0.072 0.170
ν max 0.968 0.775 0.590

The considered compounds have exhibited anisotropic properties due to the A being far from 1. The A measures that the compounds are far from isotropic, as is known. As can be seen in Table 3, KInO3 has largest anisotropy, whereas CsInO3 has the smallest. Furthermore, with the exception of linear compressibility, analyzed polycrystalline properties have inferred an anisotropic nature. The observed isotropic characteristics of linear compressibility are caused by cubic symmetry. The calculated Poisson ratios of these compounds show that they exceed the theoretical upper bound [23,24]. As a result, these compounds are likely to exhibit significant elastic deformation under minimally applied strain. In addition, the current results are visible in Figure 2. The parameters for different materials for different purposes have also been investigated, and interesting results have been found [2536].

Figure 2 
                  The graphical notation of polycrystalline properties for XInO3 (X = K, Rb, and Cs) compounds. (a) KInO3, (b) RbInO3, and (c) CsInO3.
Figure 2

The graphical notation of polycrystalline properties for XInO3 (X = K, Rb, and Cs) compounds. (a) KInO3, (b) RbInO3, and (c) CsInO3.

The thermal characteristics of a compound, such as melting point and thermal conductivity, can be determined using the Debye temperature (θ D), which is denoted by equation (11), where the Planck constant is h, the Boltzmann constant is k B, the Avogadro number is N A, the density is ρ, the number of atoms in the unit cell is n, and the molecular mass of the compound is M. The compound has a high melting point and thermal conductivity when the θ D is high. Among handled compounds, RbInO3 has the highest melting point and thermal conductivity due to large θ D, as considered in Table 4.

(8) V l = 3 B + 4 G 4 ρ 0 . 5 ,

(9) V t = G ρ 1 2 ,

(10) V m = 1 3 2 V t 3 + 1 V l 3 1 3 ,

(11) θ D = h k B 3 n 4 π N A ρ M 1 3 × V m .

Table 4

The longitudinal (V l), transverse (V t), and average (V m) wave velocities and Debye temperature (θ D) for XInO3 (X = K, Rb, and Cs) compounds

Compounds V l (m s−1) V t (m s−1) V m (m s−1) θ D (K)
KInO3 4786.415 1771.347 2010.841 238.479
RbInO3 4581.397 2003.284 2262.097 265.604
CsInO3 4172.218 1949.357 2194.765 254.210

3.3 Electronic properties

The electronic behavior of handled compounds could be revealed by calculating their electronic properties. Figure 3 presents the band structures and, relatedly, the density of states (DOSs) for XInO3 (X = K, Rb, and Cs) compounds along with respective symmetry lines.

Figure 3 
                  The band structures and related DOSs for XInO3 (X = K (a), Rb (b), and Cs (c)) compounds.
Figure 3

The band structures and related DOSs for XInO3 (X = K (a), Rb (b), and Cs (c)) compounds.

The investigated compounds have exhibited half-metallic properties. Current computations show that the spin-up status’ semiconductor behavior, whereas the spin-down state has a metallic nature owing to some bands originating from O p–d occurrences, as seen in Figure 4, reaching the Fermi level and giving the compound a half-metallic character by reducing the gap.

Figure 4 
                  The partial DOSs (PDOSs) for XInO3 (X = K (a), Rb (b), and Cs (c)) compounds.
Figure 4

The partial DOSs (PDOSs) for XInO3 (X = K (a), Rb (b), and Cs (c)) compounds.

It is possible to observe that the X-atom contributions are about −10 eV for K, −8 eV for Rb, and −5 eV for Cs, respectively, according to Figure 4. In addition to the contribution of roughly −15 eV, the O makes a contribution that lends half-metallicity nature, while the In makes no significant contribution. Moreover, as a result of spin-polarized calculations, each compound investigated has a magnetic moment of about 2μ B .

3.4 Lattice dynamical and thermodynamical properties

Figure 5 depicts the phonon curves and, relatedly, the PDOS for the respective compound under investigation. Owing to the five atoms that make up their unit cell, there are likely 15 phonon branches, as is consistent with observations. Twelve of these branches are optical modes, whereas the remaining branches are acoustic modes. The considered compounds are also dynamically stable since no soft mode has been observed.

Figure 5 
                  The calculated phonon dispersion curves and, relatedly, PDOS for XInO3 (X = K (a), Rb (b), and Cs (c)) compounds.
Figure 5

The calculated phonon dispersion curves and, relatedly, PDOS for XInO3 (X = K (a), Rb (b), and Cs (c)) compounds.

Figure 6 demonstrates the thermal properties of considered compounds. These representations deal with the relationship between temperature and free energy, entropy, and heat capacity. In addition, it is evident that as temperature rises, free energy falls dramatically. Entropy, on the other hand, increases when the temperature rises. The heat capacity grows dramatically at low temperatures and reaches the Dulong–Petit limit, which is constant at high temperatures.

Figure 6 
                  The calculated thermal properties for XInO3 (X = K (a), Rb (b), and Cs (c)) compounds.
Figure 6

The calculated thermal properties for XInO3 (X = K (a), Rb (b), and Cs (c)) compounds.

4 Conclusion

The objective of this examination was to reveal the structural, elastic, anisotropic, electronic, lattice dynamical, and thermal properties of XInO3 (X = K, Rb, and Cs) compounds using DFT implemented in VASP 544. Moreover, the investigated compounds are both thermodynamically stable and experimentally synthesizable due to having negative formation energy. In addition, these compounds have demonstrated stable lattice dynamical properties. Since the calculated ν max of these compounds is larger than the upper limit of Poisson’s ratio, it is estimated that current compounds will show persistent plastic deformation under applied strain. These compounds have exhibited half-metallic behavior. Besides, they have dominant ionic characteristics. Based on our knowledge, this theoretical study, which is the first examination of investigated compounds, may provide insight into future research.

  1. Funding information There is no funding for this article.

  2. Conflict of interest: The author states no conflict of interest.

  3. Ethical approval: The conducted research is not related to either human or animal use.

  4. Data availability statement: Derived data supporting the findings of this study are available from the corresponding author on request.


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Received: 2022-11-24
Revised: 2022-12-13
Accepted: 2022-12-15
Published Online: 2023-01-26

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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