Inverse-perovskite oxides Ca3EO with E=Si, Ge, Sn, Pb: Structural, elastic and thermal properties

doi:10.1016/j.ssc.2010.08.021

Solid State Communications

Volume 150, Issues 41–42, November 2010, Pages 1995-2000

https://doi.org/10.1016/j.ssc.2010.08.021 Get rights and content

Abstract

First-principles pseudo-potential plane-wave calculations have been performed for the first time in order to investigate the systematic trends for structural, elastic and thermal properties of the ideal cubic inverse-perovskite oxides Ca₃EO depending on the type of E atoms ( $E = Si$ , Ge, Sn, Pb). The computed equilibrium lattice constants are in excellent agreement with the experimental findings. Pressure dependence up to 40 GPa of the single-crystals and polycrystalline elastic parameters, namely, $C_{11}$ , $C_{12}$ , $C_{44}$ , bulk modulus $B$ , shear modulus $G$ , Young’s modulus $E$ , Poisson’s ratio $σ$ , and Lamé’s constants $λ$ and $μ$ , have been investigated in detail. The analysis of the $B / G$ ratios shows that all studied compounds can be classified as brittle materials. We have estimated the sound velocities in the principal directions: [100], [110] and [111]. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the temperature and pressure effects on the lattice constant, bulk modulus, heat capacity and Debye temperature are performed.

Introduction

Inverse-perovskites of the general formula ${(A, R)}_{3} E Z$ , where $A$ are alkaline-earth metals, $R$ are rare-earth metals, E are $p$ -group elements and $Z$ are C, N or O, were frequently reported [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]. These ternary compounds display a wide range of physical properties, from wide-gap insulators to ferroelectrics and superconductors, as well as wide range of structural instabilities. Physical properties of the inverse-perovskite nitrides and carbides have received much attention and have been the subject of many theoretical and experimental works in the last two decades. Particularly, the alkaline-earth metal nitrides of the group 15 elements (E = P, As, Sb, Bi), with the composition $A_{3} EN$ , show electrically insulating properties [15], [16], [17]. The crystalline structures cover the range of cubic inverse-perovskite-type at ambient conditions for $A_{3} EN (A = Ca, Sr and E = Sb, Bi)$ and orthorhombic distortion variants in space group Pnma for ${Ca}_{3} EN (E = P, As)$ [16], [17]. The compounds with the composition ${Ba}_{3} EN (E = Sb, Bi)$ crystallize in the inverse hexagonal (2H) perovskite-type (BaNiO3-type) [15]. Additionally Mg-containing compounds ${Mg}_{3} EN (E = Sb, Bi)$ were reported, which crystallize in the cubic inverse-perovskite-type structure [18].

Compared to the cubic inverse-perovskite nitrides and carbides, which have been intensively investigated, the inverse-perovskite oxides constitute a relatively unknown branch of the perovskite family. The family of inverse-perovskite oxides is still poorly studied and many of their properties are not explored. Remarkably, only few inverse-perovskite oxides of the rare-earth metals have been reported: La₃InO [8], La₃AlO,Ce₃AlO [3] and $R_{3} EO (R = Eu, Y b)$ [11], [12]. Alkaline-earth metal inverse-perovskite oxides are exclusively known containing group 14 elements and are semiconductors with the general formula $A_{3} EO$ [1], [2], [12], [13], [14]. The ideal cubic inverse-perovskite compounds $A_{3} EO (A = Ca, Sr, Ba and E = Sn, Pb, Ge)$ were reported by Widera and Schäfer [1], [2] and by Röhr [13].

In the present work, we investigate the structural, elastic and thermodynamic properties of the ideal cubic inverse-perovskites: Ca₃SiO,Ca₃GeO,Ca₃SnO and Ca₃PbO, using the state of the art pseudo-potential plane-wave method (PP-PW), in the framework of the density functional theory (DFT) within two different approximations for the exchange–correlation functional. The paper is organized as follows: In Section 2, we briefly describe the computational method used in this study. The most relevant results obtained for the structural, elastic and thermal properties of Ca₃EO compounds are presented and discussed in Section 3. Concluding remarks are given in Section 4.

Section snippets

Computational details

The calculations were carried out by means of the pseudo-potential plane-wave (PP-PW) method within the framework of the density functional theory (DFT), implemented in the CASTEP package [19]. Interactions of valence electrons with ion cores were treated using the Vanderbilt-type ultra-soft pseudo-potential [20]. The exchange–correlation energy was treated within both the generalized gradient approximation of Perdew, Burke and Ernzerhof (GGA–PBE) [21] and the local density approximation (LDA)

Structural properties

The calculated equilibrium lattice constants of Ca₃SiO, Ca₃GeO, Ca₃SnO and Ca₃PbO are presented in Table 1, along with the available experimental findings. Better theoretical results are obtained with the GGA. The computed lattice constants using the GGA deviate from the measured ones within 0.42%, 0.16%, 0.17% and 0.57% for Ca₃SiO,Ca₃GeO,Ca₃SnO and Ca₃PbO, respectively. The bulk modulus $B_{0}$ and its pressure derivative $B^{'}$ were calculated by fitting the pressure–volume data to a third-order

Conclusion

To summarize, for the first time, we have performed first-principles calculations on the Ca₃SiO,Ca₃GeO,Ca₃SnO and Ca₃PbO compounds in cubic inverse-perovskite-type phase. The structural and elastic properties have been calculated by using a pseudo-potential plane-wave approach based on the density functional theory, within the GGA and LDA. The optimized lattice parameters agree very well with the experimental findings; validating the used method. The mechanical behavior was investigated and

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Inverse-perovskite oxides Ca3EO with E=Si, Ge, Sn, Pb: Structural, elastic and thermal properties

Abstract

Introduction

Section snippets

Computational details

Structural properties

Conclusion

Mater. Res. Bull.

J. Less-Common Met.

Solid State Sci.

J. Less-Common Met.

J. Alloys Compd.

J. Solid State Chem.

J. Solid State Chem.

Phys. B: Condens. Matter

Comput. Mater. Sci.

J. Phys. Chem. Solids

J. Mech. Phys. Solids

J. Alloys Compd.

J. Phys. Chem. Solids

Z. Kristallogr.

Z. Naturforsch. B

Monatsh. Chem.

Z. Anorg. Allg. Chem.

Z. Anorg. Allg. Chem.

Z. Anorg. Allg. Chem.

Z. Kristallogr.

Z. Anorg. Allg. Chem.

Z. Anorg. Allg. Chem.

Solid State Commun.

J. Phys.: Condens. Matter

Phys. Rev. B

Phys. Rev. Lett.

Phys. Rev. Lett.

Inverse-perovskite oxides ${Ca}_{3} EO$ with $E = Si$ , Ge, Sn, Pb: Structural, elastic and thermal properties