Comparison of the crystal chemistry of tellurium (VI), molybdenum (VI), and tungsten (VI) in double perovskite oxides and related materials

Comparison of the crystal chemistry of tellurium (VI), molybdenum (VI), and tungsten (VI) in double perovskite oxides and related materials

Progress in Solid State Chemistry xxx (xxxx) xxxx Contents lists available at ScienceDirect Progress in Solid State Chemistry journal homepage: www...

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Progress in Solid State Chemistry xxx (xxxx) xxxx

Contents lists available at ScienceDirect

Progress in Solid State Chemistry journal homepage: www.elsevier.com/locate/pssc

Comparison of the crystal chemistry of tellurium (VI), molybdenum (VI), and tungsten (VI) in double perovskite oxides and related materials Ashley V. Floresa, Austyn E. Kruegera, Amanda J. Stinera, Hailey M. Alberta, Travis Mansura, Victoria Willisa, Chanel C. Leeb, Luis J. Garayb, Loi T. Nguyenb, Matthew A. Franka, Paris W. Barnesa,∗∗, Allyson M. Fry-Petitb,∗ a b

Department of Chemistry, Millikin University, 1184 West Main Street, Decatur, IL, 62522, United States Department of Chemistry and Biochemistry, California State University, Fullerton, 800 N. State College Blvd., Fullerton, CA, 92831, United States

ARTICLE INFO

ABSTRACT

Keywords: Crystal structure and symmetry Double perovskite oxides Synchrotron powder diffraction Neutron powder diffraction Infrared spectroscopy Cooperative octahedral tilting Non-cooperative octahedral tilting

A comprehensive structural comparison of 56 Te6+-, Mo6+-, and W6+-containing oxides with the double perovskite stoichiometry (A2BB′O6) is presented. This work shows that much like d0 Mo6+- and W6+-containing perovskites, p0 Te6+-containing compositions are strongly affected by the tolerance factor and identities of the Aand B-cations. To make this comparison more complete, the ambient temperature crystal structures of five A2BTeO6 (A = Ca2+, Sr2+, or Ba2+; B = Zn2+ or Cd2+) perovskites were determined via powder diffraction and their vibronic and electronic structures were probed via infrared and diffuse reflectance spectroscopy. The new structural information reported here coupled with a thorough review of relevant literature demonstrates that Te6+, with its sigma bonding preference and lack of allowed orbital mixing gives rise to additional structure types that are not commonly observed in the Mo6+ or W6+ analogues. Analysis of double perovskites containing the hexavalent cations comparing the tolerance factor to the difference in ionic radii of the cations with octahedral coordination is presented. Additionally, examination of the Coulombic repulsions between the B and Te6+ cations plotted as a function of difference in the twelve- and seven-coordinate ionic radii for the A- and Bcations respectively provides new insight on why A2BTeO6 and A2BWO6 (A = B = Sr2+ or Ba2+) adopt perovskite structures with non-cooperative octahedral tilting distortions, while cooperative octahedral distortions are observed when the A and B sites are occupied by smaller cations like Ca2+ and Cd2+.

1. Introduction Materials adopting the perovskite structure have diverse compositions that lead to a variety of interesting and technologically useful physical properties. Simple perovskites have the general formula ABX3 and the aristotype structure has Pm3 m space group symmetry (Z = 1; ap ~ 4 Å). The small, highly charged B cations are octahedrally coordinated by X anions. The BX6 octahedra share corners, forming twelve-coordinate cuboctahedral holes where the relatively larger A cations reside. The most frequently observed perovskite derivative is obtained by substituting two different B cations in a 1:1 ratio on the octahedral sites. The double perovskite structure has a stoichiometry of A2BBʹX6 and typically adopts rock-salt ordering of the two different octahedral cations (B and Bʹ) [1,2]. Consequently, the unit cell dimensions double in all three directions relative to the aristotype perovskite and the space group symmetry is lowered from Pm3 m to Fm3 m. ∗

While rock-salt ordering is not the only type of ordering double perovskites can adopt, it is energetically favored by differences in the ionic radii, bonding preferences, and/or oxidation states of the B and Bʹ cations. Thus, rock-salt ordering is more commonly observed than column or layered ordering [1,2]. Vasala and Karppinen published a comprehensive review on 1111 unique A2BBʹO6 compositions, and approximately 84% of compounds examined were reported with double perovskite structures with at least partial rock-salt B-cation ordering [3]. Symmetry of the perovskite structure is typically lowered by cooperative rotations of the octahedra along the crystallographic axes. The (B,Bʹ)X6 octahedra rotate to accommodate the size mismatch of the cuboctahedral hole to the A-cation [4,5]. One metric that is particularly useful for predicting octahedral tilting distortions in double perovskites is the tolerance factor [6]. The tolerance factor (τ) is a ratio that measures how well the A-cations fit the cuboctahedral holes within the octahedral framework. Glazer first described tilting patterns and

Corresponding author. Corresponding author. E-mail addresses: [email protected] (P.W. Barnes), [email protected] (A.M. Fry-Petit).

∗∗

https://doi.org/10.1016/j.progsolidstchem.2019.100251

0079-6786/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Ashley V. Flores, et al., Progress in Solid State Chemistry, https://doi.org/10.1016/j.progsolidstchem.2019.100251

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developed a system for describing cooperative rotations of octahedra while maintaining their corner-sharing connectivity [7]. Glazer notation will be used through this paper to describe the observed cooperative octahedral tilting distortions. Empirical evidence showed that octahedral tilting patterns in double perovskites oxides containing Nb5+, Ta5+, Mo6+, and W6+ depend largely upon the tolerance factor and the difference in the ionic radii of the six-coordinated cations [8]. If the A cations fit the cuboctahedral holes perfectly, τ is 1 and there is an absence of octahedral tilting (space group symmetry – Fm3 m; Glazer tilt notation – a0a0a0). Structures without octahedral tilting distortions are strongly preferred when A is Ba2+ due to its relatively large size. When τ is greater than 1, the double perovskite typically displays a0a0a0 or a–a–a– (R3 ) tilting and can form hexagonal perovskites. A variety of tilt systems (a0a0a0, a0a0c–, a0b–b– and a–a–c+) and space group symmetries (Fm3 m, I4/m, I2/m, and P21/n respectively) are observed when 0.96 ≤ τ ≤ 1. When the tolerance factor falls below 0.96, the a–a–c+ tilt system (P21/n) is seen almost exclusively. Relatively recently, a new family of perovskites has emerged in which the tolerance factor suggest that they should possess cooperative octahedral tilting (COT) as described above, but they actually show large degree rotations of some of the octahedra such that corner sharing is broken. The resulting octahedral units change coordination and share edges. These materials are termed non-cooperative octahedral tilted (NCOT) perovskites. The overarching purpose of this work is to probe the effect of p0 versus d0 Bʹ-site cations on the crystal structures of double perovskites. We previously reported the complete crystal structures of d0 molybdenum- or tungsten-containing double perovskites and showed that while the tolerance factor plays a role in the tilting pattern observed, the identity of the A cation acts as a secondary structure-directing factor [8]. To understand the role that a p0 cation plays in the octahedral tilting patterns of perovskites, we studied a series of compositions where Te6+ occupies the Bʹ-site. We describe the synthesis and structural analysis of five A2BTeO6 (A = Ca2+, Sr2+, or Ba2+; B = Zn2+ or Cd2+) compositions using powder diffraction and spectroscopic data. Although the oxidation state differences between the B and Bʹ cations are identical in all systems investigated and the six-coordinate ionic radii of the hexavalent cations are similar (Mo6+ = 0.59 Å; W6+ = 0.60 Å; Te6+ = 0.56 Å) [9], Te6+ clearly exhibits different bonding preferences. The unique behavior of Te6+ affects the tilt systems and structure types adopted by compositions crystallizing with double perovskite structures. Layered hexagonal perovskite structures are observed in Ba2BTeO6 (B = Mn, Co, Ni, or Zn) compositions, but are not found in Mo/W-containing equivalent compositions with nearly identical tolerance factors. Finally, we will describe the relation of these materials to NCOT perovskites found in A2BTeO6 and A2BWO6 (A = B = Sr2+ or Ba2+) with the goal of better understanding of this new member of the perovskite family.

earth carbonates and dehydrate the telluric acid. The preheated reaction mixtures were ground and heated to higher temperatures multiple times until the powders appeared homogenous by laboratory X-ray powder diffraction (XRPD). The final heating temperatures for the six compositions ranged between 1273 and 1623 K. 2.2. Powder diffraction data collection and analysis Ambient temperature high-resolution synchrotron X-ray diffraction data were collected on A2CdTeO6 materials using beamline 11-BM at the Advanced Photon Source at Argonne National Laboratory. Samples sealed in 0.8 mm diameter polyimide tubes were rotated during data collection to improve powder averaging. The diffraction patterns were measured at room temperature using monochromatic X-rays (λ = 0.4137280 Å). 11-BM is equipped with a Si (111) crystal analyzer detection system to achieve unmatched resolution and sensitivity. Instrumental resolution at high Q is better than ΔQ/Q ≈ 2 × 10−4, with a typical 2θ resolution of less than 0.01° at 30 keV [10]. Neutron powder diffraction (NPD) were collected on Ba2ZnTeO6 and Sr2ZnTeO6 using the medium resolution Nanoscale-Ordered Materials Diffractometer (NOMAD; BL-1B) [11] at the Spallation Neutron Source at Oak Ridge National Laboratory via the mail-in program. Space group symmetries were determined by indexing the diffraction data, paying close attention to peak splitting, and identifying weak reflections resulting from octahedral tilting and A-cation shifts [12]. Initial structural models were generated for all materials except Ba2ZnTeO6 using the perovskite structure prediction software SPuDS [4,13]. Complete refinements of diffraction data were completed via the Rietveld method using either EXPGUI/GSAS or TOPAS Academic Version 6 [14–16]. The refined range for all data collected using 11-BM was 4–30° 2θ. The d-spacing range refined for data collected with NOMAD was 0.5–5.5 Å. The shift (or zero), scale factor, 10–18 background terms modeled by a Chebyschev polynomial, lattice parameters, atomic positions, and atomic displacement parameters were refined as part of the structural analysis. Up to six anisotropic displacement parameters were refined to model the displacements for individual oxygen atoms more appropriately, leading to improved Rietveld fits. 2.3. Spectroscopic measurements Infrared spectroscopic data were collected using a Thermo Nicolet 380 Fourier transform infrared spectrometer equipped with a Thermo Smart Performer attenuated total reflectance (ATR) attachment. A ZnSe crystal used in the ATR and care was taken to ensure that the applied pressure was consistent between all measurements. Diffuse reflectance data were collected using an Ocean Optics Flame spectrometer over the range of 300–800 nm using a PX-2 pulsed Xenon light source with a strobe period set to 20,000 μs and an integration time of 20 ms. The data was smoothed using a local regression that applies a lower weight to outliers due to inconsistencies in the light source and uses a first-degree polynomial model. To transform the reflectance data (R) into absorption (K) with scattering (S) contributions, the Kubelka-Munk function was used [17,18]:

2. Materials and methods 2.1. Synthesis Polycrystalline A2BTeO6 (A = Ca2+, Sr2+, or Ba2+; B = Zn2+ or Cd ) samples were prepared by mixing stoichiometric amounts of ZnO (Alfa Aesar, 99.99%) or CdO (Alfa Aesar, 99.99%), H2TeO4·2H2O (Alfa Aesar, 99+%), and an appropriate alkaline earth carbonate (CaCO3, SrCO3, or BaCO3; Alfa Aesar, 99.99%). The starting materials were mixed intimately using an agate mortar and pestle. Acetone was added to the combined powders to aid in the mixing process. The dried reaction mixtures were transferred to high form alumina crucibles and heated overnight between 973 and 1173 K to decompose the alkaline 2+

F (R ) =

(1

R )2 K = 2R S

The band gaps were estimated from the K/S vs. energy plots by extrapolating the region of the curves with the highest slopes back to the x-axis.

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Fig. 2. (a) 12-R structure of Ba2ZnTeO6. (b) The 12-R structure shown along the [001] direction. Legend: Ba – yellow spheres; O – red spheres; [ZnO6] – blue octahedra; [TeO6] – green octahedra. All structural figures were generated with the VESTA software, version 3.2.1 [25,26]. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) Fig. 1. Neutron powder diffraction data for Ba2ZnTeO6 as fit by the Rietveld method. The calculated curve is shown in red, observed data are shown as black circles, and the difference curve is shown in blue. Vertical bars below the fitted data indicate the d-spacing of the observed reflections. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

atomic positions for Ba2ZnTeO6 are given in Table 1. The structure of Ba2ZnTeO6 is shown in Fig. 2. 3.1.2. Ba2CdTeO6 Politova and Venevtsev first reported the synthesis and lattice parameters for Ba2CdTeO6 (τ = 0.987) [27]. The lattice parameter reported for this material suggests it is an ordered double perovskite, but no additional structural information was provided. Recently, Ward et al. reported that Ba2CdTeO6 crystalized with the cubic (Fm3 m) double perovskite structure, but they did not report the complete crystal structure [28]. Indexing of the synchrotron X-ray diffraction data for Ba2CdTeO6 reveals only sublattice (all even hkl values) and Rpoint superlattice (all odd hkl values) peaks and shows no evidence of reflection splitting. Compounds with diffraction data displaying only sublattice and R-point reflections have rock salt ordering of the B-cations with either no octahedral tilting (a0a0a0) or only out-of-phase tilting (a0a0c–, a0b–b–, or a–a–a–) distortions. If the large difference in the ionic radii of the B cations (ΔIR = 0.39 Å), the identity of the A cation (Ba2+), and the tolerance factor are considered [8], the best space group assignment for this is Fm3 m. The Rietveld fit of the synchrotron diffraction pattern for Ba2CdTeO6 is shown in Fig. 3. The crystal structure of Ba2CdTeO6 is reported in Table 2 and the cubic double perovskite structure is illustrated in Fig. 4.

3. Results 3.1. Crystal structures 3.1.1. Ba2ZnTeO6 Ba2ZnTeO6 (τ = 1.035) was first reported by Gerhard Bayer in 1967 [19]. He stated that no deviation for cubic symmetry was observed in the X-ray diffraction data and reported a lattice parameter equal to 8.27 Å. In 1974, Köhl and Reinen reported that Ba2ZnTeO6 was isostructural with Ba2NiTeO6, forming the 12-R structure type [20]. Although additional spectroscopic reports were found in the literature [21–23], a complete description of the crystal structure has not been reported to our knowledge. Peak splitting in the XRPD data for Ba2ZnTeO6 is very different than the patterns commonly observed in double perovskites. Indexing of the diffraction data revealed that Ba2ZnTeO6 has trigonal symmetry. The observed reflections are nearly identical to those reported for Ba2NiTeO6 (τ = 1.048; space group R [fx]m) [24]. Powder diffraction data were refined using the R3 m space group. The Rietveld fit to the NPD data is shown in Fig. 1. The unit cell dimensions and refined

3.1.3. Sr2ZnTeO6 Sr2ZnTeO6 (τ = 0.977) was previously described as an “orthorhombic (possibly monoclinic)” material but only lattice parameters were given [29]. Later, the crystal system of Sr2ZnTeO6 was reported as monoclinic and unit cell parameters were reported based upon the assumption that a ≈ c [30]. More recently, Dias et al. suggested that the structure of this material was tetragonal based upon the number and types of first-order modes present in both Raman and IR spectra. They reasonably concluded that the space group symmetry of Sr2ZnTeO6 was I4/m, but did not perform structural refinement on their X-ray diffraction data [31]. Manoun contradicted this, reporting that the space group of this material is the monoclinic I2/m based upon refinement of X-ray diffraction data [32]. The space group assignments proposed by Dias and Manoun suggest the presence of sublattice reflections indicative of the fundamental perovskite structure and R-type superlattice peaks associated with Bcation ordering and possibly out-of-phase tilting distortions. The report

Table 1 Room temperature structure of Ba2ZnTeO6 as determined from neutron powder diffraction data. The space group symmetry is R3 m. The unit cell dimensions are a = 5.8453(3) Å and c = 28.769(4) Å. Goodness-of-fit parameters for this refinement are Rp = 7.69%, Rwp = 7.54%, and χ2 = 1.139. Atom

Site

x

y

z

Uiso (Å2; × 100)

Ba1 Ba2 Zn Te1 Te2 O1 O2

6c 6c 6c 3a 3b 18h 18h

0 0 0 0 0 0.1505(3) 0.1776(3)

0 0 0 0 0 0.8495(3) 0.8224(3)

0.1273(3) 0.2815(3) 0.4035(2) 0 0.5 0.4597(1) 0.6281(1)

0.06(8) 0.06(8) 0.2(2) 0.7(3) 1.3(1) 0.80(9) 1.8(1)

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Fig. 3. Synchrotron X-ray powder diffraction data for Ba2CdTeO6 as fit by the Rietveld method. The calculated curve is shown in red, observed data are shown as black circles, and the difference curve is shown in blue. Vertical bars below the fitted data indicate the d-spacing of the observed reflections. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5. Neutron powder diffraction data for Sr2ZnTeO6 as fit by the Rietveld method. The calculated curve is shown in red, observed data are shown as black circles, and the difference curve is shown in blue. Vertical bars below the fitted data indicate the d-spacing of the observed reflections. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Table 2 Room temperature structure of Ba2CdTeO6 as determined from synchrotron Xray powder diffraction data. The space group symmetry is Fm3 m. The unit cell dimensions are a = 8.353930(3) Å. Goodness-of-fit parameters for this refinement are Rp = 3.61%, Rwp = 4.89%, and χ2 = 1.836.

published by Dias includes a figure showing an indexed X-ray diffraction data, presumably with a primitive cubic cell with a length of ~8 Å. We confirmed this using laboratory XRPD data collected on the Sr2ZnTeO6 sample prepared for this study. Reflection splitting observed in the XRPD data and the lack of reflections associated with in-phase tilting allowed us to narrow the possible space groups to I4/m, I2/m, and R3 . Rietveld refinement to the neutron diffraction data using an I2/ m model (Fig. 5) resulted in the best fit to the data when compared to the other possible models. The refined crystallographic data and the structure are presented in Table 3 and Fig. 6, respectively.

Atom

Site

x

y

z

U (Å2; × 100)

Ba Cd Te O

8c 4a 4b 24e

¼ 0 ½ 0.2705(1)

¼ 0 0 0

¼ 0 0 0

0.593(5) 0.38(1) 0.54(1) U11 = −1.46(7), U22 = 1.35(4), U33 = 1.35(4)

3.1.4. Sr2CdTeO6 and Ca2CdTeO6 Sr2CdTeO6 (τ = 0.930) and Ca2CdTeO6 (τ = 0.880) were reported to crystallize with monoclinic symmetry [30]. However, no structural information has been reported on these materials. The diffraction data suggests the correct space group assignment for Sr2CdTeO6 and Ca2CdTeO6 is P21/n (a–a–c+; Figs. 8 and 10). Reflection splitting in the X-ray diffraction data collected on the Cd analogues can be indexed using a 2 ap × 2 ap × 2ap orthorhombic unit cell. Additionally, sublattice reflections indicative of cation ordering (R-point), out-of-phase tilting (R- and X-point), and in-phase tilting (M- and X-point) are present in the diffraction data. The refined crystal structure of Sr2CdTeO6 is reported in Table 4. The Rietveld refinement for Sr2CdTeO6 is shown in Fig. 7, the corresponding crystallographic parameters are presented in Table 4, and the structure is shown in Fig. 8. In refining the P21/n model to the synchrotron data for Ca2CdTeO6, we recognized that reflections like (020) and (200), which should have the nearly the same shape and intensity, were different. Two possible explanations exist for this type of asymmetry: (1) preferred orientation or (2) multi-phase co-existence [33]. Given that there is no indication of A-site ordering, there is also no precedence for preferred orientation in this system [1]. However, as shown in Fig. 9, both (020) and (200) peaks can be fit simultaneously if several phases are added that differ in their Ca2+ and Cd2+ ratio and thus b-axis, indicating that this system is

Fig. 4. Structure of Ba2CdTeO6 (space group: Fm3 m; tilt system a0a0a0). Legend: Ba – yellow spheres; O – red spheres; [CdO6] – blue octahedra; [TeO6] – green octahedra. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

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Table 3 Room temperature structure of Sr2ZnTeO6 as determined from neutron powder diffraction data. The space group symmetry is I2/m. The unit cell dimensions are a = 5.6619(18) Å, b = 5.6118 (13) Å, c = 7.9154(20) Å, and β = 90.24(6)°. Goodness-of-fit parameters for this refinement are Rp = 5.71%, Rwp = 5.07%, and χ2 = 1.396. Atom

Site

x

y

z

U (Å2; × 100)

Sr Zn Te O1

4i 2a 2d 4i

0.4983(22) 0 ½ −0.0432(17)

0 0 ½ 0

0.2538(25) 0 0 0.2598(6)

O2

8j

0.2704(15)

0.2508(20)

0.0254(6)

0.81(7) 0.5(2) 0.0(1) U11 = 1.0(3); U22 = 1.2(5); U33 = −1.4(2); U13 = −0.2(3) U11 = 2.7(4); U22 = 1.5(4); U33 = 0.9(2); U12 = −0.5(2); U13 = −0.2(3); U23 = 0.1(5)

best modeled as multi-phase co-existence. Incorporating multiple phases allows for the broadening of the (020) relative to the (200) peak. This result is not unexpected given that both Ca2CaTeO6 and Cd2CdTeO6 exist and adopt the same P21/n structure. The data was fit with four phases, but as shown by the distinct peaks still present in the difference curve for both (020) and (200), it is likely that more phases are needed to fully describe the complex phase mixture. This indicates that a full solid solution should exist between Ca2CaTeO6 and Cd2CdTeO6, but the isolation of a single phase at any point in the binary phase diagram is not expected [34].

3.4. Diffuse reflectance spectroscopy The Kubelka-Munk transformation of the diffuse reflectance data (Fig. 11) and extrapolation of the steepest part of the slope to the energy axis of these white powders gives the semi-conductor to insulating band gaps ranging from approximately 3.2 eV to greater than 5 eV Ba2CdTeO6 has the lowest band gap at ~3.2 eV followed by Sr2CdTeO6 at ~4.0 eV. The other three materials show an upturn in the absorbance between 4 and 5 eV that is similar to the upturn in Ba2CdTeO6, but the steep slope associated with the band gap is greater than 5 eV and thus outside of the reliable range of the instrument. Optical data does not show a clear trend related to crystal structure, A-site cation, or B-site cation. To fully understand these results, density functional theory calculations to obtain the electronic density of states would need to be carried out.

3.3. Infrared spectroscopy Many studies have shown that at ~600 cm−1, perovskite structures display a B/B′–O stretching vibration, which all five compounds that were measured show in Fig. 10 [35–39]. If the octahedra are regular, they will possess Oh symmetry and present a symmetric peak that is assigned to degenerate T1u modes. These modes are also very sensitive to deviations from local octahedral symmetry, as shown in Ba2CdTeO6. From the cubic symmetry of Ba2CdTeO6, determined from high resolution synchrotron XRPD, a single symmetric peak is expected. However, the IR peak for Ba2CdTeO6 has a shoulder around 700 cm−1, indicating that while the long-range average structure is cubic, locally there is some deviation from this highly symmetric structure. This spectral shoulder is observed in all of the other compounds, which crystallographically have a lowering of the symmetry of the octahedra but maintain the same overall B2+–O–Te6+ connectivity of the cubic double perovskite. The symmetry lowering distortions of the octahedra is consistent with the variations in the bond lengths as shown in Table 5. It should be noted that the resolution of the Ca2CdTeO6 shoulder is weaker than the others; this is due to the different local structures that are present in the variety of solid solution phases. The largest difference in the IR spectra is observed in the hexagonal perovskite Ba2ZnTeO6, which does not maintain connectivity through oxygen vertices as in cubic and COT perovskites, but shares faces between the octahedra. In Ba2ZnTeO6, the main peak is clearly resolved into two peaks, indicative of the change in the octahedral connectivity.

4. Discussion Selected bond lengths, bond valence sums (Σvij) [40], octahedral distortion indices (Δd), and bond angles for all compounds analyzed by synchrotron XRPD or NPD are reported in Table 5. Discussion of the crystal chemistry of the four homogeneous materials include a description of the regularity of the octahedra as described by the octahedral distortion index. This distortion index compares the individual B/B′–O bond lengths (dn) to the average length (< d >): d

=

1 6

dn n = 1,6

< d> < d>

2

Octahedra with significant distortions have distortion index values greater than 10−3 [41]. The regularity of the octahedra was also probed via the change in the T1u vibrationally active infrared mode as shown in Fig. 10. Ba2ZnTeO6 crystallizes with the 12-R hexagonal perovskite structure. Köhl et al. [20,24] described this structure type as a close-packed arrangement of BaO3 layers separated by face-sharing octahedral chains containing alternating Te6+ and Zn2+ cations. The Zn2TeO12 trimers Fig. 6. Structure of Sr2ZnTeO6 (space group: I2/m; tilt system a0b–b–) projected along the (a) [110] direction showing out-of-phase tilting and the (b) [001] direction showing no octahedral tilting. Legend: Sr – yellow spheres; O – red spheres; [ZnO6] – blue octahedra; [TeO6] – green octahedra. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

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Table 4 Room temperature structure of Sr2CdTeO6 as determined from synchrotron X-ray powder diffraction data. The space group symmetry is P21/n. The unit cell dimensions are a = 5.78749(4) Å, b = 5.83076(4) Å, c = 8.19455(5) Å, and β = 90.129(1)°. Goodness-of-fit parameters for this refinement are Rp = 7.49%, Rwp = 9.38%, and χ2 = 2.438. Atom

Site

x

y

z

U (Å2; × 100)

Sr Cd Te O1

4e 2c 2d 4e

0.5081(2) 0 ½ 0.228(1)

0.53213(8) ½ 0 0.183(1)

0.2488(3) 0 0 −0.051(1)

O2

4e

0.297(1)

0.742(1)

−0.045(1)

O3

4e

0.429(1)

−0.0239(7)

0.2257(9)

1.31(5) 1.54(6) 1.30(6) U11 = −1.0(4); U22 = −1.0(3); U33 = 5.5(8); U12 = −0.5(3); U13 = −0.3(4); U23 = 2.9(4) U11 = 2.6(7); U22 = 2.6(5); U33 = 4.1(7); U12 = −4.6(4); U13 = 1.5(4); U23 = −5.6(4) U11 = 2.4(5); U22 = 2.4(3); U33 = 4.0(6); U12 = 1.1(3); U13 = −1.7(5); U23 = −3.0(5)

are connected to one another by sharing corners with TeO6 octahedra. Aoba et al. stated that when τ is greater than 1 for Ba2BBʹO6 compositions where Bʹ is Sb5+ or Te6+, they tend to form “hexagonal nonperovskite structures” to relieve the strain caused by the oversized Ba2+ cation [42]. Tolerance factor comparisons of Ba2BTeO6 compositions to analogous Mo6+ or W6+-containing perovskites strongly suggests that nature of the B′cation also plays an integral role in the structure type adopted. Ba2BTeO6 compositions where B = Co2+ (τ = 1.038), Mn2+ (1.014) [43], Ni2+ (1.048), Cu2+ (1.045) [20,24], or Zn2+ (1.035) all crystallize with some variation of the hexagonal layered perovskite structure. This structure type is not observed in similar compositions in which Te6+ is replaced by Mo6+ or W6+. Ba2CoMoO6 (1.041), Ba2CoWO6 (1.038), Ba2MnMoO6 (1.016), Ba2MnWO6 (1.014), Ba2NiMoO6 (1.051), Ba2NiWO6 (1.048), Ba2ZnMoO6 (1.038), and Ba2ZnWO6 (1.035) all crystallize with Fm3 m symmetry. Furthermore, this observation is consistent with other double perovskites where A = Ba2+ and Bʹ is a transition metal cation resulting in tolerance factors greater than 1 [8,12]. Ba2CuWO6 (τ = 1.045) also adopts the perovskite structure and contains the Jahn-Teller active Cu2+ cation, reducing its symmetry to I4/m [44]. To our knowledge, Ba2CuMoO6 (τ = 1.048) has not been reported in the chemical literature. In comparison, Ba2CdTeO6 has a tolerance factor less than 1 and crystallizes with the cubic double perovskite structure. Day et al. outlined two different ways the cubic perovskite structure (tilt system – a0a0a0) could accommodate the bond strains resulting from the A cation being too small for its crystallographic site: (1) the A–O bonds are longer than their normal lengths, causing the A cation to be underbonded; or (2) the B–O and/or Bʹ–O bond lengths contract, leading to one or both of the cations being overbonded [8]. Inspection of the bond lengths and bond valence sums support that Ba2CdTeO6 adopts a cubic

Fig. 7. Synchrotron X-ray powder diffraction data for Sr2CdTeO6 as fit by the Rietveld method. The calculated curve is shown in red, observed data are shown as black circles, and the difference curve is shown in blue. Vertical bars below the fitted data indicate the d-spacing of the observed reflections. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 8. Structure of Sr2CdTeO6 (space group: P21/n; tilt system a–a–c+) projected along the (a) [001] direction showing in-phase tilting and the (b) [110] direction showing out-of-phase octahedral tilting. Legend: Sr – yellow spheres; O – red spheres; [CdO6] – blue octahedra; [TeO6] – green octahedra. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

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Fig. 9. Synchrotron X-ray powder diffraction data for Ca2CdTeO6 as fit by the Rietveld method. Vertical bars below the fitted data indicate the d-spacing of the observed reflections for four different phases modeled with different ratios of Ca and Cd. The two panels on the right show the fit of the (200) and (020) peaks with four different phases (top) and one phase (bottom).

the identity of the A cation, the identity of the Bʹ cation, and the difference in ionic radii for B and Bʹ′ (ΔIR). Similar to analogous double perovskite compositions containing Mo6+ or W6+, Sr2ZnTeO6 (ΔIR = 0.18 Å) was reasonably predicted to crystallize with a0a0c– tilting based upon the τ vs. ΔIR plot included in Day et al. [8]. The difference in the crystal chemistry of Sr2ZnTeO6 when compared to the Sr2ZnMoO6 and Sr2ZnWO6 is once again associated with the nature of the Bʹ-cation. I2/m symmetry is also reported in Sr2MgTeO6 (ΔIR = 0.16 Å; τ = 0.979) [45] and Sr2NiTeO6 (ΔIR = 0.13 Å; τ = 0.989) [46]. Even though Sr2CoTeO6 has an ionic radius difference (0.19 Å) and tolerance factor (0.979) similar to the three aforementioned compositions, it crystallizes with P21/n symmetry (tilt system – a–a–c+). This suggests that Sr2BTeO6 compositions with tolerance factors that fall in the very narrow range between 0.989 ≤ τ ≤ 0.977 and ΔIR ≤ 0.19 Å can adopt the intermediate a0b–b– tilt system. The observed differences in crystal structures between d0 and p0 containing perovskites indicate that covalent bonding and molecular orbitals of the octahedra must be considered when comparing the crystal chemistry of Mo6+, Wo6+, and Te6+. The Te–O bonds inherently have a greater degree of covalent character than Mo–O and W–O bonds as demonstrated by the Pauling electronegativity differences. The electronegativity difference for a Te–O bond is approximately 1.4, much smaller than the differences for Mo–O (1.9) and W–O (2.0) bonds. The smaller difference in electronegativity supports that the Te–O bonds would be more covalent in nature, resulting in regular octahedra. Table 5 highlights the regularity of the TeO6 octahedra observed in this study. The Te–O bond lengths fall between 1.92 and 1.95 Å with the exception of the Te–O(3) bonds in Sr2CdTeO6. The bond valence sums reported for Te6+ are continually within 6% of their ideal value, unlike Zn2+ and Cd2+ which deviate from +2 by up to 15%. Octahedral distortion index values for TeO6 are smaller when compared to the more distorted BO6 octahedra. This supports the argument that, much like the conclusions drawn by Day et al. on materials containing Mo6+ and W6+ [8], all A2BTeO6 compounds should be viewed as ionic salts

Fig. 10. ATR infrared spectroscopy in the range from 550 cm−1 and 850 cm−1 which highlights the T1u mode of a symmetric perovskite octahedra.

structure at room temperature primarily due to overbonding of Cd2+, with a bond valence sum equal to 2.292. Both Sr2ZnTeO6 (τ = 0.977) and Sr2CdTeO6 (τ = 0.930) adopt monoclinic symmetry but have different octahedral tilting patterns. Sr2ZnTeO6 exhibits out-of-phase rotations along the [010] and [001] axes, consistent with the a0b–b– tilt system. Secondary factors that influence the tilt system energetically preferred by perovskites include

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Table 5 Selected bond distances, bond angles, bond valence sums (Σvij), and octahedral distortion indices (Δd) as determined from the crystallographic data reported in Tables 1–4. Sr2ZnTeO6 Bond A

B

Te

O(1) O(2) O(3) B-O(1)-Te B-O(2)-Te B-O(3)-Te

Sr1-O1 Sr1-O1 Sr1-O1 Sr1-O1 Sr1-O2 Sr1-O2 Sr1-O2 Sr1-O2 Sr1-O3 Sr1-O3 Sr1-O3 Sr1-O3

Zn1-O1 Zn1-O2 Zn1-O3

Te1-O1 Te1-O2 Te1-O3

Sr2CdTeO6

Mult.

Length (Å)

×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1

2.50(3) 2.84(3) 2.86(3) 3.07(3) 2.64(3) 2.70(3) 2.96(3) 2.96(3) 2.60(2) 2.73(2) 2.90(2) 3.06(2)

0.359 0.143 0.133 0.076 0.245 0.210 0.102 0.104 0.268 0.189 0.119 0.079

Σvij

2.028

2.10(1) 2.07(1) 2.04(1)

0.347 0.374 0.401

Σvij Δd

2.242 0.009

1.93(1) 1.94(1) 1.95(1)

0.956 0.948 0.925

Σvij Δd Σvij Σvij Σvij

×2 ×2 ×2

×2 ×2 ×2

Angle (°) 165.9(5) 167.6(3) –

v

Mult.

Length (Å)

×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1 ×1

2.777(7) 2.424(8) 2.968(8) 3.576(8) 2.72(1) 2.575(7) 2.96(1) 3.447(7) 3.280(5) 2.639(5) 3.292(6) 2.548(8)

0.168 0.437 0.101 0.019 0.197 0.291 0.103 0.028 0.043 0.245 0.042 0.313

Σvij

1.987

2.311(5) 2.254(5) 2.292(6)

0.320 0.361 0.338

Σvij Δd

2.037 0.007

1.946(5) 1.944(5) 1.902(6)

0.985 1.007 1.072

5.657 0.002

Σvij Δd

2.014 1.983 1.981

Σvij Σvij Σvij

ij

Bond

Ba2ZnTeO6

Sr1-O1 Sr1-O1 Sr1-O1 Sr1-O1 Sr1-O2 Sr1-O2 Sr1-O2 Sr1-O2 Sr1-O3 Sr1-O3 Sr1-O3 Sr1-O3

Cd1-O1 Cd1-O2 Cd1-O3

Te-O1 Te-O2 Te-O3

×2 ×2 ×2

×2 ×2 ×2

v

Bond

Ba2CdTeO6

Mult.

Length (Å)

Ba1-O1 Ba1-O1 Ba1-O2

×6 ×3 ×3

2.927(2) 2.955(8) 2.973(8) Σvij

0.177 0.164 0.156 2.018

Ba2-O1 Ba2-O2 Ba2-O2

×3 ×6 ×3

2.847(8) 2.947(2) 3.147(9) Σvij

0.219 0.167 0.097 1.954

avg Σvij

2.018

2.236(6) 2.008(5)

0.237 0.440

Σvij Δd

2.032 0.054

1.920(4) Σvij Δd 1.936(4) Σvij Δd

0.993 5.959 0.000 0.949 5.693 0.000

6.130 0.006

avg Σvij avg Δd

2.030 1.987 2.053

Σvij Σvij

ij

Angle (°) 149.5(4) 156.1(4) 155.3(3)

Zn1-O1 Zn1-O2

×3 ×3

Te1-O1

×6

Te2-O2

×6

Angle (°) 83.4(1) 171.6(3) –

containing polyatomic TeO66− ions. However, the nature of the bonding that is present is significantly different between the d0 cations and p0 cation due to the molecular orbitals of the isolated octahedra (Fig. 12). For the d0 cations, it is well established that the valence band is comprised of bonding orbitals that are primarily oxygen 2p in nature which have the same t2g symmetry as the lowest lying π* orbitals that are primarily d in character. The fact that the edge of the valence and conduction bands is comprised of orbitals of the same symmetry (t2g) and similar in energy allows for their mixing resulting in second-order Jahn Teller distortions, which is ubiquitous in d0 containing perovskites [47,48]. However, those same distortions are not observed in TeO6 octahedra as σ-interactions between the p-orbitals of the metal and oxygen dominate. This results in a valence band edge comprised of non-bonding oxygen orbitals with eg symmetry while the conduction band is comprised of tellurium orbitals possessing t1u* symmetry; thus, the valence and conduction bands cannot mix based on symmetry. Moreover, the large band gap between the non-bonding eg and the t1u* orbitals is observed as absorption into the UV in these systems. The strong σ-interactions results in directional bonding and ridged octahedra that can be incorporated into a large

v

Bond

Mult.

Length (Å)

Ba1O1

× 12

2.95853(6)

0.162

Σvij

1.947

2.260(1)

0.382

Σvij Δd

2.292 0.000

1.917(1)

1.000

5.826 0.000

Σvij Δd

6.000 0.000

1.915 3.694

Σvij

2.031

ij

Cd1-O1

Te1-O1

×6

×6

v

ij

Angle (°) 180 – –

variety of structure types. Generalizations about the structure types adopted can be made by examining the tolerance factors and differences in ionic radii for 56 unique hexavalent Mo, Te, and W-containing oxides with the double perovskite formula as presented in Table 6 and Fig. 13. The cubic Fm3 m double perovskite structure is observed in Mo/W compounds with 1.051 ≤ τ ≤ 0.972. Similar compositions with nearly identical tolerance factors containing tellurium frequently crystallize with a layered hexagonal perovskite structure. We can reasonably rationalize that Ba2BTeO6 form layered structures when ΔIR is less than 0.27 Å and B has higher electronegativity values. The three tellurium (VI) double perovskite oxides reported here or found in the chemical literature contain less electronegative B-cations such as Mg (χ = 1.3) and Ca (χ = 1.0) and/or have ionic radii differences greater than 0.40 Å. Layered materials are not observed in Ba2BMoO6 or Ba2BWO6 compositions. Ba2SrTeO6, which is not included in Table 6 or Fig. 13, has the lowest tolerance factor (0.939) and largest ΔIR (0.62 Å) value of any barium-containing composition adopting the COT perovskite structure. Ba2SrTeO6 crystallizes with the R3 structure, indicative of a–a–a– tilting [49].

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Fig. 13. A review of the structures of 56 different A2BB′O6 or AAʹ′BB′O6 perovskites, where A = Ca2+, Sr2+, or Ba2+, AA′= BaSr or SrCa, and B′= Mo6+ (blue), Te6+ (green), or W6+ (orange). Cubic double perovskites are represented by circles, tetragonal double perovskites are represented by squares, monoclinic I2/m double perovskites are represented by triangles, and monoclinic P21/n double perovskites are represented by diamonds. Compositions represented by green stars represent layered hexagonal perovskite Te-containing materials [8,43,46,49,50,52–80]. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 11. Kubelka-Munk transformation of diffuse reflectance spectra for all five compounds.

Fig. 12. Qualitative molecular orbital diagrams highlighting the role of π-bonding (left) in d0 MoO66− octahedron versus the σ-bonding (right) that predominates in p0 TeO66− octahedron Electrons are added to highlight the difference between the symmetries of the conduction and valence band as related to the isolated octahedra. Table 6 Structure type adopted for A2BBʹO6 compositions based upon observed tolerance factors, identity of the A cation, and identity of the Bʹ cation. A



a0a0a0 (Fm3 m)

a0a0c– (I4/m)

a0b–b– (I2/m)

a+a+c– (P21/n)

Layered

NCOT

Ba Sr Ca Ba Sr Ca

Mo/W Mo/W Mo/W Te Te Te

1.051 ≤ τ ≤ 0.972 – – 1.038 ≤ τ ≤ 0.972 – –

– 0.991 ≤ τ ≤ 0.972 – – – –

– – – – 0.989 ≤ τ ≤ 0.977 –

– 0.977 ≤ τ ≤ 0.917 0.935 ≤ τ ≤ 0.867 – 0.979 ≤ τ ≤ 0.917 0.935 ≤ τ ≤ 0.867

– – – 1.048 ≤ τ ≤ 1.014 –

– τ = 0.886 – τ = 0.905 τ = 0.886 –

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symmetry, Sr2ZnTeO6 has I2/m symmetry, and Sr2ZnWO6 has P21/n symmetry. Since changing the temperature is equivalent to changing the tolerance factor, phase transitions in all three materials should occur near room temperature. Gateshki et al. demonstrated this with Sr2ZnWO6, reporting a phase transition from P21/n to I4/m at 343 K [50]. Raman studies performed by Manoun et al. supported this phase transition [51]. According to the authors, the X-ray and spectroscopic data suggest that Sr2ZnWO6 did not adopt the intermediate space group I2/m at any temperature. Sr2ZnTeO6 was recently reported to go through an I2/m to I4/m phase transition near 393 K, then further transform to Fm3 m symmetry above 543 K [32]. This allows us to conclude that the absence of I2/m in the series of phase transitions observed for Sr2ZnWO6, but its inclusion for Sr2ZnTeO6 should be attributed to the different bonding preferences of Te6+ when compared to W6+. It would be beneficial to study Sr2ZnMoO6 to learn which tilt systems are observed at lower temperatures. Double perovskite oxides with cooperative octahedral tilting where τ is less than 0.97 generally adopt the P21/n structure regardless of the identity of the A, B, or Bʹ cations. For double perovskites, this boundary means that octahedral tilting occurs to reduce the volume where the Acation resides, generating a range of bond distances that ultimately satisfy its bond valence. P21/n symmetry is the most frequently observed space group for Ca2BB′O6 materials with at least partial cation ordering. A new subgroup of perovskite materials with tolerance factors below 0.91 and ΔIR ≥ 0.58 Å have complicated structures that can be better understood by the information presented in this review. Thinking of B′O66− polytatomic ions (B′= Mo6+, W6+ or Te6+) as discrete units supports the observations of pronounced superstructures due to tilting distortions where corner-sharing connectivity between the octahedra is broken. NCOT compounds have only been observed in compounds with cations on the A- and B-sites that have similar ionic radii. Some examples are Sr3WO6 [81], Sr3TeO6, Ba3TeO6 [82], αK3MoO3F3, α-Rb3MoO3F3 [83], and K3AlF6 [84]. NCOT materials are marked by their loss of corner sharing due to a ~45° degree rotation of some of the rigid B′ octahedra, like TeO66−, around some or all of the crystallographic axis. This loss of corner sharing results in an increase in the coordination number of the B-site cations around the rotated octahedra (shown in Fig. 14a) and a decrease in the coordination number of the A-site cation [83]. Due to coordination environments that tend toward more similar coordination numbers, the similarities in the ionic radii for the cations that occupy the A and B sites thus make sense. Of the systems presented in this work, Ca2CdTeO6 has the smallest difference between the ionic radii of the twelve-coordinate A-sites and seven-coordinate B-sites with a value of 0.262 Å, which is similar to the

Fig. 14. (a) Portion of the Sr3TeO6 NCOT structure depicting the increase in coordination of the SrO6 octahedra (yellow) around the large degree rotation of the TeO6 octahedra in the center (green). (b) A schematic representation of the local coordination of the B and Bʹ octahedra to highlight the cation-cation Coulombic repulsion that occurs due to the edge sharing octahedra and pentagonal bipyramid. Each side of the blue triangle is a cation-cation interaction that is not present in a COT or cubic perovskite. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Differences in the crystal chemistry of Te6+ versus Mo6+ and W6+ are also observed when A = Sr2+. Over a narrow range of tolerance factors (0.969–0.991) and B-cation ionic radii differences (0.10–0.19 Å), compositions with I4/m, I2/m, and P21/n space group symmetries are reported. All six Sr2BMoO6 compositions found in this small region on Fig. 13 crystallize with I4/m symmetry and exhibit outof-phase tilting along the [001] direction only (tilt system – a0a0c–). Analogous tungsten-containing compounds also possess I4/m symmetry when ΔIR is less than 0.15 Å. Once ΔIR ≥ 0.15 Å, Sr2BWO6 compositions have P21/n symmetry indicative of octahedral tilting along all three crystallographic directions (tilt system – a+a+c–). There are no Sr2BMoO6 or Sr2BWO6 compounds reported with a0b–b– tilting, yet there are three tellurium-containing equivalent materials that exhibit this intermediate tilt system. Inspection of Fig. 13 shows that the points representing Sr2MgTeO6, Sr2NiTeO6, and Sr2ZnTeO6 are closely positioned to the equivalent W-containing materials. This observation further supports that the nature of the Bʹ cation plays a critical role in the structure of these materials. The structurally most interesting compounds found in this small region of Fig. 13 are the Sr2ZnBʹO6 materials. Although all three materials have nearly identical tolerance factors (0.977–0.979) and B-cation ionic radii differences (0.14–0.18 Å), Sr2ZnMoO6 has I4/m

Fig. 15. Coulombic repulsion (Vc) plotted as a function of the difference of the ionic radii of twelve-coordinate A-site and seven-coordinate B-site (RA(12) – RB(7)) showing a separation of structure types for B′ = Te6+ (circles) on the left and Bʹ = Mo6+ (triangles) or W6+ (squares) on the right for A2BB′O6 compositions [8,43,46,49,50,52–59,61–80,85–87]. In the COT region different tilt systems are denoted by different colors, a0b-b- is dark blue, aa-c+ is green, and a0a0c− is light blue. Coulombic repulsion was calculated based on the assumption that the TeO66− octahedra are regular and the B cations form regular pentagonal bipyramids. These assumptions were in good agreement with refined structures. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

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value of 0.199 Å for all of the previously listed NCOT materials.1 However, like Ca3TeO6 and Cd3TeO6, Ca2CdTeO6 displays COT with a distribution of Ca2+ and Cd2+ ratios across the A and B sites instead of the NCOT structure [34]. Mixing between the A and B sites is promoted by the same driving force that allows for NCOT compounds to form – a similarity in the size of ions on the cation sites. However, the small size of Ca2+ and Cd2+ restrict the formation of NCOT compounds due to the increase in cation-cation Coulombic repulsion that would be present if a NCOT structure formed. As highlighted in Fig. 14b, when the B′O6 octahedra rotate in the NCOT structure, the B-containing octahedra become pentagonal bipyramids (in the simple case where there is only one rotation), thus allowing for Coulombic repulsions between B- and B′-cation nearest neighbors as well as between B and B second nearest neighbors (marked by a blue triangle). This same repulsion is not present in COT or cubic perovskites due to the attraction to and the shielding by the anions on the corners of the octahedra. This important interaction must be taken into account when attempting to intelligently design new NCOT materials. The effects of Coulombic repulsions can be explored as a function of counterions. Fig. 15 shows the Coulombic repulsion that would be present between B and Bʹ cations if NCOT structures formed plotted as a function of the difference in the ionic radii of the twelve-coordinate Aand seven-coordinate B-site cations. For this calculation, the ideal ionic radii as tabulated from ideal bond valence sums calculations are used due to the availability of twelve- and seven-coordinate ionic radii. The Coulombic repulsion (Vc) is calculated by

Vc =

tolerance factors, but very different Coulombic repulsions. This understanding allows us to further predict which compounds would form NCOT structures, getting us closer to rationally designing these materials. It is also interesting to note that, to our knowledge, crystal structures have not been reported for Ba3WO6, Ba3MoO6, or Sr3MoO6. 5. Conclusions Space group assignments, unit cell dimensions, and atomic positions for four A2BTeO6 compositions were determined from Rietveld refinement of synchrotron X-ray powder diffraction or neutron powder diffraction. These results, when combined with previous studies on A2BMoO6 and A2BWO6, revealed striking differences in crystal chemistry stemming from the differences in bonding abilities of the hexavalent transition metal cations when compared to Te6+, a main-group semimetal cation. The most noticeable differences were observed in the Ba2BBʹO6 materials because cubic symmetry is almost always observed when B′= Mo or W (τ ≥ 0.972). However, Ba2BTeO6 materials with hexagonal layered structures preferentially formed, and fewer cubic Fm3 m structures were observed. Additional differences were observed in Sr2BB′O6 perovskites with the tolerance factor range between 0.972 and 0.991. The Sr2BMoO6 double perovskites included in our survey had I4/ m symmetry exclusively, whereas Sr2BWO6 materials crystallized with I4/m until the tolerance factor was less than 0.979. Sr2BTeO6 compositions in the aforementioned range had I2/m symmetry. All double perovskites with tolerance factors less than 0.977 adopted P21/n space group symmetry. The space groups adopted by Te6+-containing materials with tolerance factors greater than 0.977 demonstrate this cation's uniqueness when compared to Mo6+ and W6+. We also reported multiple phase coexistence for the nominal Ca2CdTeO6 composition. Finally, the observation that A2BB′O6 compositions should be viewed as ionic salts of B′O66− anions where Coulombic repulsions, combined with previously known geometric constraints must be considered in understanding why Sr3WO6, Ba3TeO6, and Sr3TeO6 exhibit non-cooperative octahedral tilting distortions while Ca3WO6, Ca2CdTeO6, and Ca3TeO6 possess cooperative octahedral tilting. This work demonstrates that like d0 Mo- and W-containing perovskites, the crystal structure of p0 Te-containing perovskites are strongly affected by tolerance factor, and identity of the counterions. Additionally, this work shows that the rigidity of the TeO66− octahedra, which is attributed to the strong σ-bonding and the lack of mixing between orbitals, allows for a wider variety of structure types than observed by distorted d0-containing double perovskites.

kZ1 Z2 e 2 d

where k is the proportionality constant (9 × 109 N m2/C2), Z1 and Z2 are the cation charges, e is the charge of an electron, and d is the distance between the two cations. This simple calculation allows for the separation of compounds based on observed structure type and indicates that the ionic radii of the B cations play a significant role in the interactions of the polyhedra in the Te, W, and Mo-based perovskites. If the Coulombic repulsion is too large, the COT structure will predominate over the NCOT structure. The COT structure type exists across all ionic radii differences. Maintaining a small ionic radius difference and increasing the Coulombic repulsion results in the formation of the corundum structure for three tellurium-containing compounds (Co3TeO6, Ni3TeO6, and Zn3TeO6) [85–87], resulting in a loss octahedral coordination of one of the A-site cations. Increasing both the ionic radius difference and the Coulombic repulsion results in the formation of the cubic perovskite structure. The largest ionic radii differences and greatest Coulombic repulsions are seen in the hexagonal layered structures in the tellurium compounds. The valence p-orbitals result in directional bonding in Te6+, allowing for the stabilization of face sharing octahedra in hexagonal compounds despite the large predicted Coulombic repulsion. Mo6+ and W6+-containing compounds, however, have a more spherical distribution of electron density resulting in a greater repulsion along the shared faces that are required in the hexagonal perovskite structure. As a result, in the region with the greatest Coulombic repulsions and largest differences in ionic radii shown in Fig. 15, Te6+-containing compounds predominantly crystallize with the hexagonal structure while Mo6+ and W6+ compounds exhibit the cubic structure exclusively. It should be noted that this important relation in understanding the driving forces for NCOT formation is not captured by the tolerance factor because the average A–O and B/B′–O bond distances are divided by one another. Having all small or all large cations can result in similar

Acknowledgements Dr. Allyson Fry-Petit would like to acknowledge start-up funds from California State University, Fullerton and a Research, Scholarship and Creative Activity Incentive Grant from the California State University Chancellor's Office. Dr. Paris Barnes, Austyn Krueger, and Amanda Stiner would like to acknowledge Millikin University for funding from its Leighty Science Scholarship and Summer Undergraduate Research Fellowship programs. Paris Barnes would like to thank Dr. Ed Acheson (deceased) and Dr. Clarence Josefson for their encouragement and support. Ashley Flores thanks the Sigma Zeta National Science & Mathematics Honor Society for financially supporting this project through their Research Award. Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This research also used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. The authors thank Patrick Woodward (Department of Chemistry and Biochemistry at The Ohio State University) and Keenan Dungey (Department of Chemistry at the University of Illinois at Springfield) for use of their X-ray powder diffractometers.

1 The differences in ionic radii discussed from this point forward compare seven- and twelve-coordinate environments and should not be confused with ΔIR. The seven-coordinate ionic radii are assumed as the B cation must adopt a pentagonal bipyramidal coordination at minimum in the NCOT structure.

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