Synthesis and structural characterization of new perovskite phases, Ba₂Bi_0.572TeO_6±δ and SrLa₂NiFeNbO₉

Abstract

Ba₂Bi_0.572TeO_6±δ and SrLa₂NiFeNbO₉ ceramics were prepared in polycrystalline form by conventional solid-state reaction techniques in air. The crystal structures of the title compounds were determined at room temperature from X-ray powder diffraction (XRPD) data using the Rietveld method. The Ba₂Bi_0.572TeO_6±δ structure crystallizes in a triclinic space group I–1 with unit-cell parameters a = 6.0272(2) Å, b = 6.0367(1) Å, c = 8.5273(3) Å, α = 90.007(7)°, β = 90.061(2)°, and γ = 90.015(4)°. The tilt system of the BiO₆ and TeO₆ octahedra corresponds to the notation a^–b^–c^–. The crystal structure of the SrLa₂NiFeNbO₉ compound adopts an orthorhombic Pbnm space group with lattice parameters a = 5.6038(5) Å, b = 5.5988(4) Å, and c = 7.9124(6) Å. The BO₆ octahedra (B = Ni/Fe/Nb) sharing the corners in 3D. Along the c-axis, the octahedra are connected by O(1) atoms of (x,y,1/4) positions; while in the ab-plane, they are linked by O(2) atoms of (x,y,z) positions. The bond angle of B–O1–B is 168.7° and that of B–O2–B is 156.3°. The octahedral lattice corresponds to the tilt pattern a^–a^–c⁺; it indicates that the octahedra tilt out-of-phase along the a,b-axes and in phase along the c-axis.

I. INTRODUCTION

Among inorganic materials, the ordered double perovskite of the A₂BB′O₆ family is one of the most studies by the scientific community due to its wide variety of interesting physical properties, including magnetic, magnetocaloric, ferroelectric, superconducting, photonic, catalytic, and microwave dielectric (Cava and Batlogg, 1989; Fukushima et al., 2011; El Hachmi et al., 2022, 2023; Guo et al., 2022; El Hachmi and Manoun, 2023; Algahtani et al., 2024).

The double perovskite structures Sr₂MMoO_6–δ (M = Fe, Ni, Mg, Mn, Co, Zn) have been reported using X-ray powder diffraction (XRPD) to adopt a lower symmetry of triclinic space group I–1 (Vasala et al., 2010). The calculated Goldschmidt tolerance factor (t) has been found between 0.952 (M = Mn) and 0.984 (M = Ni). The triclinic space group I–1 has also been described for the triple perovskite LaSr₂Cr₂SbO₉ at room temperature (Hunter et al., 2017); with unit-cell parameters a = 5.5344 Å, b = 5.5562 Å, c = 7.8292 Å, α = 89.986°, β = 90.350°, and γ = 89.926°. This material has been reported to exhibit a ferrimagnetic state below 150 K. It has been found that the B-site cations partially occupy the 2f (0,1/2,0) and 2g (1/2,0,0) Wyckoff sites.

The ordered double perovskite SrLaCuTaO₆ has been reported by West and Davies (2011), who used neutron powder diffraction (NPD) at 323 K as crystallizing in a triclinic space group P–1 (No. 2) with unit-cell parameters a = 7.801 Å, b = 7.813 Å, c = 8.399 Å, α = 89.67°, β = 90.32°, and γ = 90.09°. Moreover, the tilt system assignment has been given for the P–1 triclinic structure by the notation a ⁺b ⁻c ⁻. It has been noted that all atoms occupy 2i (x,y,z) Wyckoff sites.

Similar to our tellurium-based compound, it has been reported that the two materials Ba₂Bi_2/3TeO₆ and Ba₃Bi₂TeO₉ (with the same chemical elements and an order of 0.6667:1 and 2:1 on the B-site cations, respectively) have been prepared using the solid-state method at an annealing temperature of 950 °C and investigated by means of NPD at room temperature (Park and Woodward, 2000). The double perovskite Ba₂Bi_2/3TeO₆ has been described as crystallizing in cubic symmetry with a Fm–3m space group. It has also been described that the triple perovskite Ba₃Bi₂TeO₉ adopts a trigonal structure with a P–3c1 space group.

On the other hand, the simple perovskites LaNi_0.5Ti_0.5O₃ and LaNi_0.45Co_0.05Ti_0.5O₃ have been studied using the Rietveld method (Souza et al., 2021). These two compounds have been described in the orthorhombic structure, with space group Pbnm (No. 62) and Glazer notation a ⁻a ⁻c ⁺. The two monoclinic structures SrLa₂Ni₂TeO₉ and Sr₃NiNb₂O₉ have been characterized by NPD at room temperature and 20 K, respectively; the first compound crystallizes in the P2₁/n space group with lattice parameters a = 5.6008 Å, b = 5.5872 Å, c = 7.9018 Å, and β = 90.021° (Sena et al., 2016), and the second structure adopts a P12₁/c1 space group with lattice constants a = 9.7268 Å, b = 5.6175 Å, c = 16.8704 Å, and β = 125.024° (Lee et al., 2016). Furthermore, the Sr₃FeNb₂O₉ compound has been presented as crystallizing in the P4/mmm tetragonal space group (Cha et al., 2014).

In this work, we describe the synthesis procedure and crystal structure determination of the double perovskite oxides Ba₂Bi_0.572TeO_6±δ and SrLa₂NiFeNbO₉ from room temperature XRPD using the Rietveld method.

II. EXPERIMENTAL DETAILS

A. Synthesis

Polycrystalline powders of the Ba₂Bi_0.572TeO_6±δ and SrLa₂NiFeNbO₉ ceramics were prepared using solid-state reaction route in air, and the raw materials BaCO₃ (99.98%), Bi₂O₃ (99.9%), TeO₂ (≥99%), SrCO₃ (≥99.9%), La₂O₃ (99.999%), NiO (99%), Nb₂O₅ (99.99%), and Fe₂O₃ (≥96%) were used as starting reagents (all received from Sigma-Aldrich). The quantity of each reagent was weighed according to its stoichiometric coefficient to obtain the appropriate metal ratios of the final products, then mixed and ground in an agate mortar to form a homogeneous powder. The resulting mixtures were placed in alumina crucibles, and then increasingly heated in air at different temperature stages with intermittent grinding; these two samples were calcined at 950 °C for 12 h and 1200 °C for 24 h, respectively. During the heat treatment process, the samples were cooled to room temperature, reground and sintered several times to improve homogeneity. The chemical reactions are:

$$2\cdot {\rm BaC}{\rm O}_3{\rm} + 1{\rm /}3\cdot {\rm B}{\rm i}_2{\rm O}_ 3{\rm} + {\rm Te}{\rm O}_2{\rm} + 1{\rm /}2\cdot {\rm O}_2\displaystyle{{\Delta ( 950\,{\rm ^\circ C}) } \over {{\rm AIR}}}\to {\rm B}{\rm a}_2{\rm B}{\rm i}_{2/3}{\rm Te}{\rm O}_6{\rm} + 2\cdot {\rm C}{\rm O}_2$$

$${\rm SrC}{\rm O}_3{\rm} + {\rm L}{\rm a}_2{\rm O}_3{\rm} + {\rm NiO} + 1{\rm /}2\cdot {\rm F}{\rm e}_2{\rm O}_3{\rm} + 1{\rm /}2 \cdot {\rm N}{\rm b}_2{\rm O}_5\displaystyle{{\Delta ( {{\rm 1200 \,^\circ C}} ) } \over {{\rm AIR}}} \to {\rm SrL}{\rm a}_2{\rm NiFeNb}{\rm O}_9{\rm} + {\rm C}{\rm O}_2 $$

B. X-ray powder diffraction

Diffraction data of the Ba₂Bi_0.572TeO_6±δ and SrLa₂NiFeNbO₉ samples were collected at room temperature on a D2 PHASER diffractometer, with the Bragg-Brentano geometry, using a copper anti-cathode tube as the radiation source (K_{α 1}, K_{α 2}) of the wavelengths λ(K_{α 1}) = 1.54056 Å and λ(K_{α 2}) = 1.54439 Å with 30 kV and 10 mA, Soller slits of 0.02 rad on incident and diffracted beams; divergence slit of 0.5°; anti-scatter slit of 1°; receiving slit of 0.1 mm; with sample spinner, and a Lynxeye detector type with a maximum global count rate >1 000 000 000 cps. The Ba₂Bi_0.572TeO_6±δ pattern was scanned in steps of 0.010142° (2θ), between 15 and 105° (2θ) with a fixed-time counting of 2 s per step; while the SrLa₂NiFeNbO₉ pattern was scanned through steps of 0.020283° (2θ) between 10 and 70° (2θ). The WinPlotr software (Roisnel and Rodríguez-Carvajal, 2001) integrated in the FullProf program (Rodríguez-Carvajal, 1990) was used to determine the crystal structures by means of the Rietveld method (Rietveld, 1969). The peak-shape was described by a pseudo-Voigt function using linear interpolation between set background points with refinable heights.

The following structural and instrumental parameters: scale factor, unit-cell parameters, pseudo-Voigt corrected for asymmetry parameters, FWHM parameters (U, V, and W), preferred orientation, atomic positions, and isotropic thermal factors are included in the refinement of the investigated XRD patterns.

III. RESULTS AND DISCUSSION

A. Crystallite size and microstrain

The crystallite size of these two studied compounds was determined by means of X-ray line broadening using the Scherrer equation and the Williamson-Hall (W–H) method. X-ray peak broadening may be due to crystallite size, microstrain, instrumental profile, temperature factors, and solid solution inhomogeneity. The Scherrer equation can be described by the following expression (Scherrer, 1918):

(1)$$D = \displaystyle{{K\lambda } \over {\beta _{\rm Sch}\cos \theta }}$$

where D is the average crystallite size in (nm), K is the Scherrer constant equal to 0.9, λ is the X-ray wavelength (Cu K_α average = 1.54178 Å), θ is the Bragg angle of the most intense X-ray diffraction peak and β _Sch is the grain size broadening (i.e. full width at half maximum) of the highest peak. Herein, the crystallite size was deduced from the XRD pattern in the strongest peak at 2θ ≈ 29.60° for Ba₂Bi_0.572TeO_6±δ and 2θ ≈ 31.93° for SrLa₂NiFeNbO₉.

According to the Williamson-Hall technique, the strain-induced broadening that results from imperfections and distortions was described by the following equation (Williamson and Hall, 1953):

(2)$$\varepsilon {\rm} = \displaystyle{{\beta _{\rm s}} \over {4\tan \theta \;}}$$

where ε ≈ Δd/d is the upper limit on the lattice distortion, and β _s is the strain broadening in the material. Assuming that the contributions of particle size and strain to the diffraction line broadening are unrelated to each other and that they both have a Cauchy-type profile, the observed peak breath β_hkl can be considered as the sum of the β _s and β _Sch widths (El Hachmi and Manoun, 2023):

(3)$$\beta _{hkl}{\rm} = \beta _{\rm s} + \beta _{\rm Sch}$$

and from Eqs (1) and (2), we get

(4)$$\beta _{hkl}\cos \theta {\rm} = \varepsilon ( 4\sin \theta ) {\rm} + \displaystyle{{K\lambda } \over D}$$

By plotting the values of β_hkl cosθ on the y-axis against 4sinθ on the x-axis, we can determine crystallite size directly from the y-intercept (Kλ/D) and microstrain from the slope (ɛ) of the linear regression line. The values for the crystallite size and microstrain of these two compounds are summarized in Table I. It can be noted that the crystallite size derived by the Williamson-Hall method is larger than that obtained by the Scherrer formula.

TABLE I. Details of Rietveld refinement, crystallite size, and microstrain.

B. Crystal structure determination and structure description

At room temperature, the XRD patterns of the two compounds Ba₂Bi_0.572TeO_6±δ and SrLa₂NiFeNbO₉ are successfully identified by the PDF2 database (Gates-Rector and Blanton, 2019) integrated into the HighScore plus software (Degen et al., 2014) and analyzed using the DICVOL program (Louër and Boultif, 2014) to adopt a single phase related to perovskite structure. Previously, the Ba₂Bi_2/3TeO₆ structure was reported to crystallize in cubic symmetry with a Fm–3m space group (Park and Woodward, 2000). The crystal structures of the two studied compounds were determined using the Rietveld analysis method (Rietveld, 1969).

Table I gives the crystal data, data collection, and details of the Rietveld refinements, including lattice parameters, cell volumes, crystal system, space group, and various statistical agreement factors. The values of the reliability factors, R _B, R _F, R _p, R _wp, and R _exp, and the goodness-of-fit (χ ²), are small and indicate that we have obtained a good quality of the refinements. The quality of the fits is also confirmed by Figures 1 and 2, which provide excellent agreement between the experimental (dots) and theoretical (solid line) patterns. For the Ba₂Bi_0.572TeO_6±δ compound, the impurity Ba_0.89Bi_8.11O_13.05 (PDF# 00-045-0289) was included in the refinement as a second phase crystallizing in a rhombohedral symmetry R–3m (No. 166) with lattice constants a = 3.9942 and c = 28.4667 Å. Based on the most intense peaks of both phases, the impurity content is estimated at around 3.5%. The crystal structure presented in Figures 3 and 4 for these two studied compounds were drawn by means of the Vesta software (Momma and Izumi, 2011).

Figure 1. Final Rietveld plot of the triclinic compound Ba₂Bi_0.572TeO_6±δ. The experimental pattern is represented by dots (red) and the calculated pattern is represented by a solid line (black). The vertical (green) marks indicate the Bragg positions of the main phase and the impurity. The lower curve (blue) is the difference diagram.

Figure 2. Final Rietveld plot of the orthorhombic compound SrLa₂NiFeNbO₉. The experimental pattern is symbolized by dots (red) and the calculated pattern is represented by a solid line (black). The vertical (green) marks designate the Bragg positions. The lower curve (blue) is the difference diagram.

Figure 3. Structural views of the I–1 triclinic phase Ba₂Bi_0.572TeO_6±δ. It illustrates octahedra tilt effects in accordance with Glazer's notation a ^–b ^–c ^–.

Figure 4. Structural representation of the Pbnm orthorhombic phase SrLa₂NiFeNbO₉. It shows BO₆ octahedra sharing corners in 3D, as well as octahedral tilting effects in accordance with Glazer notation a ^–a ^–c ⁺. Ni²⁺/Fe³⁺/Nb⁵⁺ cations are located inside octahedra. Sr²⁺/La³⁺ cations are represented by green spheres.

1. Ba₂Bi_0.572TeO_6±δ

Rietveld refinement analysis reveals that this structure adopts the triclinic symmetry of space group I–1 (No. 2) with unit-cell parameters a = 6.0272(2) Å, b = 6.0367(1) Å, c = 8.5273(3) Å, α = 90.007(7)°, β = 90.061(2)°, and γ = 90.015(4)°. The cell volume is calculated to be 310.26(2) Å³. The number of unit formulas within a cell is Z = 2. Reflections from the triclinic structure with space group I–1 (No. 2) are correctly indexed on the studied XRD pattern; where the reflection conditions can be described as follows: hkl → h + k + l = 2n; 0kl → k + l = 2n; h0l → h + l = 2n; hk0 → h + k = 2n; h00 → h = 2n; 0k0 → k = 2n; 00l → l = 2n (Cockcroft, 1999). The double perovskite Ba₂LaRuO₆ (PDF# 01-085-1103) was used as a starting model for refinement (Battle et al., 1983). It is worth mentioning that the triclinic space group I–1 is a non-standard setting of the triclinic space group P–1 (No. 2). Fractional atomic coordinates and isotropic thermal parameters are provided in Table II. The structural information indicates that the formal oxidation state of bismuth was oxidized to +3.5 and that of tellurium was oxidized to +6, under synthesis conditions. The site occupancy fraction for bismuth has been refined alone to 0.572(8), and with the constrained occupancies (1 for each Ba, Te, and oxygen), the Ba₂Bi_0.572TeO_6±δ structure can be considered almost electroneutral. The isotropic displacement parameters B _iso (Ų) for Ba, Bi, and Te atoms were refined separately, while for oxygen atoms; they were considered equivalent. It can be seen that the isotropic displacement factor B _iso of the Bi atom (1.21(1) Ų) is greater than that of the Ba, Te, and oxygen atoms. These anomalous isotropic displacement factors can be explained by assuming the presence of a possible positional disorder (either static or dynamic) on the bismuth atoms. The two Bi and Te cations were found to occupy octahedral sites of C_i symmetry at 2f (0,1/2,0) and 2g (1/2,0,0) positions, respectively. The Ba²⁺ and O^2– ions were located at 4i (x,y,z) positions of C ₁ symmetry.

TABLE II. Atomic coordinates and isotropic temperature factors for triclinic Ba₂Bi_0.572TeO_6±δ and orthorhombic SrLa₂NiFeNbO₉ phases.

The selected interatomic distances (Å) and angles (deg.) are given in Table III. The average distances 〈Ba–O〉, 〈Bi–O〉, and 〈Te–O〉 obtained at room temperature after Rietveld refinement of the Ba₂Bi_0.572TeO_6±δ structure are about the same as those found in other perovskite compounds containing Ba²⁺, Bi³⁺, and Te⁶⁺ cations: Bi³⁺MTe⁶⁺O₆ (M = Cr³⁺, Mn³⁺, Fe³⁺) (Kim et al., 2016); Ba₂Bi³⁺MO₆ (M = Bi⁵⁺, Sb⁵⁺) (Kennedy et al., 2006); and are very close to those calculated from Shannon's effective ionic radii: Ba²⁺ (1.61 Å), Bi³⁺ (1.03 Å), Te⁶⁺ (0.56 Å), and O²⁻ (1.40 Å) for coordination number 12 and 6 (Shannon, 1976). The Bi and Te cations are surrounded by 6 oxygen ions, and the Ba²⁺ cations are surrounded by 12 oxygen anions.

TABLE III. Selected interatomic distances (Å) and angles (°).

The structural view of the triclinic compound Ba₂Bi_0.572TeO_6±δ with space group I–1 (No. 2) is made up of alternating octahedra sharing corner by means of oxygen atoms, as displayed in Figure 3. Along the c-axis, the BiO₆ and TeO₆ octahedra are linked by oxygen atoms O(3) of 4i (x,y,z) positions with x = 0.494(13), y = 0.018(18), and z = 0.225(11). Due to the positions occupied by the Bi and Te atoms in sites 2f (0,1/2,0) and 2g (1/2,0,0), respectively, and by the O(3) oxygen atoms, looking through the c-axis, the bond angle Bi–O3–Te is found to be 174°. In the ab-plane, the octahedra are connected by the oxygen atoms O(1) and O(2) at sites 4i (x,y,z), where the bond angles Bi–O1–Te and Bi–O2–Te are calculated to be 163° and 151°, respectively. The tilting system conforms to Glazer's notation (a ^–b ^–c ^–); it indicates that the octahedra tilting out-of-phase along the three pseudo-cubic directions [100]_p, [010]_p, and [001]_p with an unequal amplitude, as derived for the ordered double perovskites with an I–1 (No. 2) space group of triclinic crystal system (Battle et al., 1983). Each BiO₆ octahedron consists of six long distances between Bi and O with an average distance of 2.37 Å. While the TeO₆ octahedron consists of six short distances between Te and O, with an average distance of 1.96 Å. The volume of the BiO₆ octahedron is calculated to be 17.204 Å³; and is larger than that observed in the TeO₆ octahedron which is 9.673 Å³.

Since the cell angles determined in the triclinic symmetry are very close to 90°, we attempted to resolve this structure in the Pbnm orthorhombic space group, but found that the coordination of the cations on the A and B-sites increased to 16 instead of 12 for Ba and to 8 instead of 6 for the Bi/Te atoms. For this reason, we concluded that the orthorhombic symmetry is not appropriate for the Ba₂Bi_0.572TeO_6±δ structure.

2. SrLa₂NiFeNbO₉

This compound was analyzed using the Rietveld refinement method and revealed that its crystal structure adopts an orthorhombic system of the Pbnm (No. 62) space group with lattice parameters a = 5.6038(5) Å, b = 5.5988(4) Å, and c = 7.9124(6) Å. The cell volume was calculated to be 248.25(4) Å³. The number of unit formulas contained in a cell is Z = 4. It is important to note that the orthorhombic structure with the Pbnm (No. 62) space group is properly identified on the XRD pattern as the single perovskite Sr_0.2La_0.8Ni_0.8Te_0.2O₃ (PDF# 01-087-0276); where the reflection conditions can be expressed as follows: 0kl → k = 2n; h0l → h + l = 2n; h00 → h = 2n; 0k0 → k = 2n; 00l → l = 2n (Cockcroft, 1999). Impurity phases were not detected in XRD pattern of the as-synthesized sample.

To justify the orthorhombic Pbnm model, we also tried to refine the structure in the monoclinic space group P2₁/n as was proposed earlier; by introducing the parameters a = 5.6132 Å, b = 5.5973 Å, c = 7.9036 Å, and β = 90.01° (PDF# 01-088-0137), and the atomic coordinates of Sr/La at 4i (x,y,z) site, Ni/Fe/Nb(1) at 2c (0,1/2,0) site, Ni/Fe/Nb(2) at 2d (1/2,0,0) site, and oxygen atoms at 4i (x,y,z) site. This model did not refine well at all stages. For example, the full divergence occurs when refining the FWHM (U, V, and W) and isotropic displacement parameters. It seems that the P2₁/n structural model is not very satisfactory.

Atomic positions, isotropic displacement parameters, occupancy, and site symmetry are provided in Table II. The isotropic displacement parameters (B _iso) for the oxygen atoms were taken as equivalent, the same for the Ni/Fe/Nb atoms at 4b-sites, and Sr/La atoms at 4c-sites. It can be noted that the isotropic displacement factor (B _iso) of Ni/Fe/Nb atoms (0.18(7) Å²) is quite low compared to that of Sr/La atoms 1.05(9) Å², assuming that B-site cations are more ordered than A-site cations. The fraction of site occupancy for all elements was not refined. Despite some differences in ionic size and valence charge, the three elements Ni²⁺, Fe³⁺, and Nb⁵⁺ have only one crystallographic B-site. As well, the two elements Sr²⁺ and La³⁺ have only one crystallographic A-site in the AA′₂B₂B′O₉ triple perovskite structure. The Sr²⁺/La³⁺ cations and O^2–(1) anions were located at the 4c (x,y,1/4) positions of the C_s symmetry. The Ni²⁺, Fe³⁺, and Nb⁵⁺ cations were arranged at the 4b (1/2,0,0) positions with C_i symmetry, and the O^2–(2) anions were distributed at the 8d (x,y,z) sites with C ₁ symmetry. The Sr²⁺/La³⁺ cations are surrounded by 12 oxygen ions, and the Ni²⁺/Fe³⁺/Nb⁵⁺ cations are surrounded by 6 oxygen anions. The selected bond lengths (Å) and angles (deg.) obtained from the refined XRD data of the SrLa₂NiFeNbO₉ structure are listed in Table III.

The average distances 〈Sr/La–O〉 and 〈Ni/Fe/Nb–O〉 obtained at room temperature are comparatively very close to those found in other perovskite compounds containing Sr²⁺, La³⁺, Ni²⁺, Fe³⁺, and Nb⁵⁺ cations; such as SrLa₂Ni₂TeO₉ (Sena et al., 2016), Ba₃NiNb₂O₉ (Lufaso, 2004), and Sr₃Fe_2+xMo_1–xO_9–3x/2 (El Hachmi et al., 2021), and are roughly identical to the distances calculated from Shannon's effective ionic radii; where Sr²⁺ (1.44 Å), La³⁺ (1.36 Å), Ni²⁺ (0.69 Å), Fe³⁺ (0.55 Å), Nb⁵⁺ (0.64 Å), and O²⁻ (1.40 Å) those are for 12- and 6-fold coordination (Shannon, 1976). The structural lattice of the orthorhombic phase (space group Pbnm, Z = 4) of the triple perovskite SrLa₂NiFeNbO₉ is composed of octahedra with shared corners in three dimensions (3D), as depicted in Figure 4. Along the c-axis, the BO₆ octahedra (B = Ni/Fe/Nb) are linked by O(1) oxygen atoms of positions (x,y,1/4); where the bond angle B–O1–B is calculated to be 168.7°. However, in the ab-plane, the BO₆ octahedra are connected by O(2) atoms of positions (x,y,z) and the bond angle B–O2–B is found to be 156.3°.

The interatomic distances between Ni/Fe/Nb and O(1) were calculated to be 1.988(2) Å, and between Ni/Fe/Nb and O(2) were found to be 1.95(2) and 2.09(2) Å. The volume of the BO₆ octahedra was calculated to be 10.7127 Å³. The octahedral lattice corresponds to the Glazer tilting system (a ^–a ^–c ⁺); it indicates that the octahedra tilt out-of-phase along the two [100]_p and [010]_p pseudo-cubic axes with an equal amplitude and in phase along the [001]_p axis with a different amplitude, as determined for the “orthorhombic” ABO₃ simple perovskites with the Pbnm (No. 62) space group (Mitchell et al., 2017). The I/I _o intensities of the XRPD data presented in Tables IV and V are obtained from the calculated intensities of the Rietveld refinement and the observed intensities of all peaks. The values of the d-spacings d(Å) were calculated for Cu K_{α 1} radiation of wavelength 1.54056 Å.

TABLE IV. Powder diffraction data of Ba₂Bi_0.572TeO_6±δ (Cu K_{α 1}, λ = 1.54056 Å).

TABLE V. Powder diffraction data of SrLa₂NiFeNbO₉ (Cu K_{α 1}, λ = 1.54056 Å).

IV. CONCLUSION

The crystals of the Ba₂Bi_0.572TeO_6±δ and SrLa₂NiFeNbO₉ perovskites were obtained by conventional solid-state reaction techniques. Their structures were determined at room temperature from XRPD data using the Rietveld method. The crystal structure of the Ba₂Bi_0.572TeO_6±δ phase adopts an I–1 (No. 2) triclinic system with unit-cell parameters a = 6.0272(2) Å, b = 6.0367(1) Å, c = 8.5273(3) Å, α = 90.007(7)°, β = 90.061(2)°, and γ = 90.015(4)°. The Bi and Te cations fully occupy the octahedral sites at positions 2f (0,1/2,0) and 2g (1/2,0,0), respectively. Ba²⁺ cations and O^2– anions are located at 4i (x,y,z) sites. The average distance of 〈Bi–O〉 is 2.37 Å, and that of 〈Te–O〉 is 1.96 Å. The BiO₆ and TeO₆ octahedra share corners via oxygen atoms. The tilt system is given by the notation (a ^–b ^–c ^–); this means that the octahedra tilting out-of-phase along the three pseudo-cubic axes [100]_p, [010]_p, and [001]_p with an unequal amplitude. On the other hand, Rietveld analysis of the crystal SrLa₂NiFeNbO₉ reveals that its structure adopts an orthorhombic space group Pbnm (No. 62) with lattice constants a = 5.6038(5) Å, b = 5.5988(4) Å, and c = 7.9124(6) Å. The BO₆ octahedra (B = Ni/Fe/Nb) sharing the corners in 3D. Along the c-axis, the octahedra are connected by O(1) atoms of (x,y,1/4) positions; while in the ab-plane, they are linked by O(2) atoms of (x,y,z) positions. The bond angle of B–O1–B is 168.7° and that of B–O2–B is 156.3°. The octahedral lattice corresponds to the tilt pattern (a ^–a ^–c ⁺); it indicates that the octahedra tilt out-of-phase along the two [100] and [010] axes and in phase along the [001] axis. The three Ni, Fe, and Nb elements have only one crystallographic B-site; similarly, the Sr and La elements have only one crystallographic A-site in the structure of AA′₂B₂B′O₉ triple perovskite. The Sr²⁺/La³⁺ cations and O^2– (1) anions were located at the 4c (x,y,1/4) positions. The Ni²⁺, Fe³⁺, and Nb⁵⁺ cations were situated at the 4b (1/2,0,0) positions, and the O^2– (2) anions were distributed at the 8d (x,y,z) sites.

V. DEPOSITED DATA

Selected powder patterns from this XRD study have been submitted to ICDD for inclusion in the Powder Diffraction File. The Crystallographic Information Framework (CIF) files containing the results of the Rietveld refinement (including the raw data) were deposited with the ICDD. The data can be requested at [email protected].