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Ab initio study of structural, electronic and thermodynamic properties of tungstate double perovskites Ba2MWO6 (M = Mg, Ni, Zn)
O. Sahnoun a,c,⇑, H. Bouhani-Benziane a, M. Sahnoun a, M. Driz b, C. Daul c a Laboratoire de Physique Quantique de la Matière et Modélisation Mathématique (LPQ3M), University of Mascara, Algeria b Laboratoire de Sciences des Matériaux (LSM), University of Sidi Bel Abbes, Algeria cDepartment of Chemistry, University of Fribourg, Switzerland
The structural and electronic properties of the double perovskite Ba2MWO6 with M = Mg, Ni, Zn have been studied using the full-potential linearized augmented plane wave (FP-LAPW) method by employing both the local density approximation (LDA) and the generalized gradient approximation (GGA), which are based on exchange–correlation energy optimization to calculate the total energy. Also we have used the Engel–Vosko GGA formalism, which optimizes the corresponding potential for band structure calcula- tions. However, we have evaluated the ground state quantities such as lattice parameter, bulk modulus and its pressure derivative. Also, we have presented the results of the band structures and densities of states. These results were in favorable agreement with previous theoretical works and the existing exper- imental data. To complete the fundamental characteristics of these compounds we have analyzed the thermodynamic properties such as thermal expansion coefficient, heat capacities and other structural parameters in the whole pressure range from 0 to 20 GPa and temperature range from 0 to 1000 K.
Because of their variable structure and composition, perovskite materials have attracted intense research interest in many applied and fundamental areas of solid-state science and advanced materi- als research at least for half a century. The perovskite structure (with general formula ABO3) can be described as a framework of oxygen octahedral sharing corners [1,2]. The B-cations are located in the centers of octahedra and the interstitial sites are occupied by the A-cations. In complex perovskites two (or more) cations of dif- ferent valences are located in the equivalent crystallographic posi- tions . Among the A2B0B0 0O6 complex perovskite oxides, where B0
and B0 0 are the cations of different valences, the mixed alkaline earth tungstate double perovskites with the general formula A2BWO6 (A = Ba, Sr, Ca; B = Mg, Co, Zn, Ni) are of interest for their complete 1:1 ordered state due to their larger differences in charge and ionic radii on B-site . The barium containing tungstate dou- ble perovskites were determined to be cubic and in the space group Fm3m . Ba2MWO6 (where M = Ni, Mg) have shown great poten- tial as ceramic components for temperature sensors for example in petroleum wells . These ceramics were produced by solid-state reaction process and sintered at different sintering conditions . Understanding properties of these compounds and related materi-
als at the atomistic level may help to improve the performance of their applications. Despite the recent progress in understanding the physics of the double perovskites there is still an open debate on the adequate theoretical modeling. In particular, the details of the interplay between structural, electronic, and magnetic degrees of freedom in the double perovskites are not yet clearly under- stood. To our knowledge, there is less or none theoretical studies in the literature devoted to electronic and thermal properties of mixed alkaline earth tungstate double perovskites.
The aim of this work is to provide information of some ordered tungstate double perovskites, and describes results for three of these, namely Ba2MgWO6, Ba2NiWO6 and Ba2ZnWO6. These partic- ular compounds are reported to be cubic at room temperature , in contrast to many others which are somewhat distorted. The pa- per is organized as follows: in Section 2 we briefly describe the technical details of the employed methods for calculations. Sec- tion 3 presents and discusses the results of the electronic and ther- modynamic properties. A summary concludes the paper in Section 4.
2. Computational details
The calculations presented in this work were performed using the FP-LAPWmethod, as implemented in the Wien2k code . This method allows the inclusion of local orbital in the basis, improving upon linearization and making possible a consistent treatment of
⇑ Corresponding author at: Laboratoire de Physique Quantique de la matière et Modélisation Mathématique (LPQ3M). University of Mascara, Algeria.
E-mail address: firstname.lastname@example.org (O. Sahnoun).
Published in " which should be cited to refer to this work.
semicore and valance states in an energy window, hence ensuring proper orthogonality. It is well known in the self-consistent band structure calculation within DFT , both LDA  and general- ized gradient approximation (GGA)  usually underestimates the energy gap . This is mainly due to the fact that they have simple forms that are not sufficiently flexible to accurately repro- duce both the exchange–correlation energy and its charge deriva- tive. Engel and Vosko considered this shortcoming and constructed a new functional form of GGA  which is able to better repro- duce the exchange potential at the expense of less agreement in the exchange energy. This approach called EV-GGA yields better band splitting and some other properties which mainly depend on the accuracy of exchange–correlation potential.
All the calculations were converged with respect to Brillouin zone (BZ) sampling and the size of the basis set. Brillouin zone (BZ) integrations within the self-consistency cycles were per- formed via a tetrahedron method, using 8 � 8 � 8 special k-points mesh . The convergence parameter RmtKmax, which controls the size of the basis sets, was set to 8. The Gmax parameter was taken to be 12 Bohr�1. The muffin-tin radii were taken as (2.5, 1.8, 1.6, 2.0, 2.0, 1.98) a.u. for (Ba, W, O, Mg, Ni, Zn), respectively. Careful con- vergence tests show that with these parameters relative energy converged to better than 10�5 Ry per formula unit.
3. Results and discussion
3.1. Structural properties
We employed the experimentally observed cubic crystalline structures  for the three compounds in the calculation, which can be described by the space group Fm3m, with Ba ions in 8(c) positions at 1/4, 1/4, 1/4; M (M = Mg, Ni or Zn) in 4(a) at 0,0,0; W in 4(b) at 1/2, 1/2, 1/2; and O in 24(e) at x,0,O. In the ordered cubic double perovskites Ba2MWO6 (M = Mg, Ni or Zn), the M and W cations are octahedrally coordinated by oxygen anions (see Fig. 1). In this aristotype cubic structure, the highly electropos- itive Ba cation is coordinated to 12 oxygens, while each M cation has 6 W cations as nearest neighbors and vice versa. With this arrangement the intermediate oxygen anions can satisfy the differ- ent bond length requirements of the two cations by moving toward the smaller ion. This structure is often viewed in terms of an or- dered alternation of M and W cation layers perpendicular to the  direction. The lattice parameters, the bulk moduli and the oxygen parameter x which can deviate from the ideal value of 0.25 realized in the simple perovskite structure, are summarized
in Table 1, together with the available experimental [17–21] and other theoretical calculation data [22–26]. It can be seen that cal- culated lattice constants are overestimated with the experimental data not more than 1%, which indicates that the present calcula- tions are highly reliable. In the current work, the bulk modulus is in reasonable agreement with other theoretical calculations in the case of Ba2MgWO6.
3.2. Electronic properties
All electronic properties have been calculated for the equilib- rium geometry. We collected data on the optical gaps in Table 2. In Fig. 2 we presented the band structures for each crystal calcu- lated using the Engel–Vosko GGA formalism. It can be seen from Fig. 2 that the conduction band (CB) structure is nearly unaffected by the different B-cations in the lattice while the top of valence band (VB) increases inducing an obvious band gap narrowing. The bottom of the conduction band lies at the X-point in all three double-perovskite crystals. The electron energy in the lowest con- duction band at the X-point is just 0.7–1.3 eV higher than at the bottom of conduction bands. So, there is a little dispersion in the lowest conduction band between the W, L and X points in the Brill- ouin zone. The top of the valence band is displaced from the L point of the Brillouin zone in Ba2NiWO6 and Ba2ZnWO6 to the C-point in Ba2MgWO6. The highest valence electron states at the C-point ap- pear only about 0.05 eV below the highest states in X-point for both Ba2MgWO6 and Ba2ZnWO6 compounds. The dispersion of the top valence band is almost flat between C and X points for these two compounds. The additional d-orbitals on Zn ions in Ba2- ZnWO6 cause the appearance of an additional valence band below the other bands. They cause also the highest states at the C-point to rise above all other valence states and to make a new top of the valence band. The effect of the electronic structure perturbation caused by different B-cations located in the centers of octahedra is illustrated by a comparison of the total and projected densities of states (DOSs) for the three compounds Ba2MgWO6, Ba2NiWO6 and Ba2ZnWO6. From Fig. 3, we can find that the DOS can be mainly divided into four parts. The first part extending from �11 to �9.5 eV is characterized by a peak mainly due to the contribution of Ba ions. On the other hand