Rational Design of a Commensurate (3 + 3)-D Modulated Structure

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Rational design of a commensurate (3+3)-D modulated structure within the fast-ion conducting stabilized #-Bi2O3 series Julia Wind, Julia Polt, Zhaoming Zhang, Douglas A Blom, Thomas Vogt, Ray L Withers, and Chris D. Ling Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b03012 • Publication Date (Web): 04 Oct 2017 Downloaded from http://pubs.acs.org on October 8, 2017

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Chemistry of Materials

Rational design of a commensurate (3+3)-D modulated structure within the fast-ion conducting stabilized δ-Bi2O3 series Julia Wind1, Julia Polt1, Zhaoming Zhang2, Douglas A. Blom3, Thomas Vogt4, Ray L. Withers5 and Chris D. Ling1,* 1

School of Chemistry, the University of Sydney, Sydney 2006, Australia

2

Australian Nuclear Science and Technology Organisation, New Illawarra Road, Lucas Heights 2234,

Australia 3

NanoCenter & Electron Microscopy Center, University of South Carolina, Columbia, SC 29208, USA

4

NanoCenter & Department of Chemistry and Biochemistry, University of South Carolina, Columbia,

SC 29208, USA 5

Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia

Abstract We report the systematic design, preparation and characterization of the first commensurate member of the oxide-ionic conducting, (3+3)-D modulated, Type II phases of doped δ-Bi2O3. The incommensurate Type II modulation vector ε was previously described as continuously variable, but high-resolution synchrotron X-ray powder diffraction data show that close to the composition Bi23CrNb3O45, it “locks in” to ε = 1/3. The space group of the resulting 3x3x3 fluorite-type supercell was found to be F4ത3m by selected-area electron diffraction, and the structure solved and Rietveld-refined against neutron powder diffraction data in conjunction with local structural information from X-ray absorption spectroscopy, high-resolution transmission electron microscopy, and ab initio geometry optimization calculations. The result unambiguously validates the crystal-chemical model of the Type II phases as being based on the local ordering of oxygen around transition metals M into tetrahedral clusters of MO6 octahedra and isolated MO4 tetrahedra, separating relatively disordered fluorite-type regions that facilitate the highest oxide-ionic conduction among transition metal-doped δ-Bi2O3 phases.

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1. Introduction The cubic high-temperature polymorph of bismuth oxide, δ-Bi2O3, is the best oxide-ionic conductor known. It shows conductivities of 1-2 S cm-1 between 729 and 817°C,1-2 almost two orders of magnitude higher than yttria-stabilized zirconia (YSZ) at comparable temperatures.3 The exceptionally high conductivity of δ-Bi2O3 is attributed to the very high concentration (25%) of intrinsic vacancies on the oxygen sites of its disordered cubic fluorite-type (CaF2, space group Fm3തm) lattice,4-6 combined with the presence of stereochemically active 6s2 electron lone-pairs on Bi3+ that help to stabilize those vacancies, reducing the energy barriers for oxygen diffusion.7 However, its narrow stability range between 729°C and its melting point at 817°C prevents its practical use. In the lower temperature polymorphs (β and γ phases1, 8) these vacancies are eliminated, leading to an immense drop in conductivity of about three orders of magnitude. The average fluorite-type structure of δ-Bi2O3 can be preserved down to room temperature by doping with rare earth (RE) or transition metals (TM), while retaining conductivity comparable to that of pure δ-Bi2O3 at high temperatures. Most research has focused on the REdoped phases, which have disordered structures and are better conductors.9-10 Work on the TM-doped phases has concentrated on their crystallography, as they are a rich source of fascinating modulated structures based on the fluorite type cell. The most interesting amongst these from a crystallographic point of view are the (3+3)-dimensional incommensurately modulated ‘Type II’11 solid-solution phases Bi1-xNbx5+O1.5+x (0.06 < x < 0.23),12-14 Bi15+ xTax O1.5+x

(0.20 < x < 0.25),11-12,

6+ xMox O1.5+1.5x

15-17

Bi1-xCrx6+O1.5+1.5x (0.05 < x < 0.15),18-19 Bi1-

(0.05 < x < 0.16)19-20 and Bi1-xWx6+O1.5+1.5x (0.15 < x < 0.19).21,22

The crystal structures of these (3+3)-dimensional incommensurately modulated materials have to be described in six dimensions using a superspace-symmetry formalism. They are characterized by a series of three coupled modulations of the fluorite-type sub-cell with lattice parameter a and a modulation parameter ε: 1 (ℎ + ߝ݉)ଶ + (݇ + ߝ݊)ଶ + (݈ + ߝ‫)݌‬ଶ = . ݀ଶ ܽଶ The most heavily studied Type II phase lies at the Bi-rich end of the Bi2O3-Nb2O5 phase diagram. This is also the only one that has been fully refined14 in superspace group ‫݉ܨ‬3ത݉(ߙ, ߙ, ߙ)‫ݍ‬00(ߙ, ߙത, ߙത)‫ݍ‬00(ߙത, ߙ, ߙത)000 23 (# 225.3.215.8; P:Fm3തm:Fd3തm in the notation 2/27


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of Yamamoto24-25). Its highly complex structure features corner-connected NbO6 chains along all the directions, surrounded by three-dimensional δ-Bi2O3-like channels. The modulation vector was reported to vary over its solid-solution range, from ε = 0.354 (x = 0.1) to ε = 0.377 (x = 0.21).12, 14 For other TM-doped Type II phases, detailed diffraction (neutron and X-ray), high resolution transmission electron microscopy (HRTEM) as well as X-ray absorption spectroscopy (XAS) studies have been used to determine space group, lattice and modulation parameters as well as basic structural features. Type II Bi1-xTax5+O1.5+x was shown to crystallize in space group ‫݉ܨ‬3ത݉(ߙ, ߙ, ߙ )‫ݍ‬00(ߙ, ߙത, ߙത)‫ݍ‬00(ߙത, ߙ, ߙത)000 with reported incommensurate modulation parameters in a similar range as observed in the niobium system (ε = 0.388 for x = 0.25;16 ε = 0.385 for x = 0.20

17

). XAS measurements confirmed exclusively octahedral coordination

environments around the Ta dopants except at very low Ta concentrations.26 At these lower Ta concentrations, a larger pseudo-cubic Type I phase was reported between 0.05 < x < 0.07 (a ~ 5.52 Å), and a mixture of Type I and Type II phases found at intermediate compositions (0.07 < x < 0.20). The M6+-doped systems, on the other hand, all crystallize in superspace group ‫݉ܨ‬3ത݉(ߙ, ߙ, ߙ)000(ߙ, ߙത, ߙത)000(ߙത, ߙ, ߙത)000 (# 225.3.215.7; P:Fm3തm:Fm3തm 25); i.e., they do not have the d-glide plane for the modulations. This symmetry suggests tetrahedral coordination around the dopant atoms, and the incommensurate modulation vectors are generally shorter (Cr6+: 0.285 < ε< 0.307;18-19 Mo6+: ε = 0.295 for x = 0.16,19-20 W6+: 0.317 < ε < 0.321 21). With the modulation vector in the Bi1-xWx6+O1.5+1.5x system being very close to the commensurate value of 1/3, the crystal structure could be solved and refined within a 3x3x3 supercell in space group F4ത3m.27 However, there are still some crystal-chemical shortcomings to this solution, reflecting the fact that the real structure is actually slightly incommensurate over its entire solid solution range (0.317 < ε < 0.321 21). Although the superspace description of the Type II phase is crystallographically correct and complete, in practice it is difficult to visualize and interpret the interplay among occupational, positional and displacive atomic modulation functions (AMFs: linear combinations of sine and cosine functions that are related to each other by point-group symmetry). The most intuitive way to rationalize and verify the incommensurate model would be to find a truly 3/27



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commensurate version. This was the goal of the work reported here. Our approach was based on the fact that M5+-doped systems exhibit a modulation parameter slightly larger than 1/3, while modulation parameters in M6+-doped systems are lower than 1/3 (see Figure 1); and that mixed doping has been shown to yield Type II phases in the W6+/Nb5+ system.28-30 We therefore hypothesized that mixed-valence transition metal doping could lead to a truly commensurate Type II phase.

Figure 1: Modulation parameter range for different dopants within the Type II solid solution ranges.

Because the modulation vector ε varies with both the type of M and the Bi:M ratio, we have two independent variables to chemically tune the composition in search for a commensurate ε = 1/3 structure. However, the proposed combination of M5+ and M6+ limits the accessible range of doping parameter space before the oxygen stoichiometry exceeds the crystal-chemical requirements of the Type II structure. For simplicity, in this study we have chosen to work with a fixed Bi:M ratio of 23:4, for two reasons. Firstly, it lies comfortably within the Type II solid-solution field for M5+ and M6+ single dopants. Secondly, the integer stoichiometry 23 + 4 = 27 matches the number of fluorite-type subcells in a 3x3x3 supercell, maximizing the likelihood of the structure “locking in” to the desired commensurate value ε =1/3.

2. Experimental and computational details 2.1. Synthesis Stoichiometric mixtures of MoO3 (99.96 %), WO3 (99.999 %), Cr2O3 (99.999 %), Ta2O5 (99.99 %), Nb2O5 (99.998 %) and Bi2O3 (99.999%, preheated to 600°C for 5 h) were thoroughly ground with acetone in an agate mortar and pestle and preheated to 850°C (Mocontaining samples) or 850°C (all other samples) for 5 h. The reground mixtures were then heated to 950°C (Mo-containing samples) or 1000°C (all other samples) for another 5 h and slowly cooled down to room temperature. When necessary, another heating step was performed after which samples were quenched to room temperature onto a steel plate. Larger sample quantities (>5 g) were ground together with ethanol in a planetary ball-mill with thorough regrinding in an agate mortar and pestle after the second heating step. 4/27


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2.2. Data collection and analysis To follow reaction progress and check for sample purity, room-temperature powder X-ray diffraction data were collected on a Panalytical X’pert Pro diffractometer in Bragg-Brentano geometry using non-monochromated Cu Kα radiation. Synchrotron X-ray powder diffraction (SXRD) data were collected at the Powder Diffraction (PD) beamline of the Australian Synchrotron in a Debye-Scherrer geometry using a Mythen microstrip detector.31 Finely ground samples were packed into 0.1 mm boron glass capillaries for room temperature measurements. Depending on sample composition, data were recorded at 13 keV (λ = 0.952652(2) Å) or 21 keV (λ = 0.589263(3) Å, calibrated against a NIST LaB6 standard) over the range 2° ≤ 2θ ≤ 82°. Neutron powder diffraction (NPD) experiments were carried out at the high-resolution diffractometer Echidna at the OPAL research reactor at ANSTO.32 For room temperature measurements, 5-10 g samples were packed into 9 mm vanadium cans. Structure refinements against these data were carried out using the Rietveld method as implemented in GSAS with the EXPGUI graphical interface.33 Le Bail profile fits were performed using Jana 2006.34 Low-energy XANES spectra at the O K-edge were collected at the soft-X-ray (SXR) beamline at the Australian Synchrotron.35 Finely ground powder samples were thinly dusted onto double-sided carbon tape and transferred into the high-vacuum analysis chamber (pressure less than 10-9 torr). Spectra were collected in X-ray fluorescence yield (FY) mode. For energy calibration purpose, all spectra were taken simultaneously with a total electron yield (TEY) signal measured from an oxidized Cr reference foil positioned upstream in the beamline. The reference foil removed approximately 10% of the beam intensity. This allowed for a precise energy alignment of the spectra obtained from different samples, with the maximum in the first derivative of the O K-edge from the oxidized foil set at 531.0 eV (i.e., the absolute energy scale was not calibrated). Intermediate-energy XANES spectra at the Nb and Mo L3-edges were collected at the Tender beamline 16A1 at the National Synchrotron Radiation Research Center (NSRRC) in Hsinchu, Taiwan.36 Finely ground powder samples were dispersed onto Kapton tape and placed in front of the X-ray beam at a 45° angle. Spectra were collected in fluorescence yield mode using a

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Lytle detector. The energy scale for both the Nb and Mo L3-edge spectra was calibrated using the L3-edge of a pure Mo foil (with the maximum in the first derivative set to 2520.2 eV). XANES spectra at the W L3-edge and Nb K-edge for selected samples were collected at the XAS beamline at the Australian Synchrotron.37 Powder samples were diluted with cellulose powder (concentrations ~5000 ppm), sandwiched between Kapton tape and positioned in front of the X-ray beam. Measurements were performed at room temperature in fluorescence mode using a multi-element solid state Ge fluorescence detector. The energy scale was calibrated using the L3-edge of a pure Pt foil (with the maximum in the first derivative set to 11562.8 eV) at the W L3-edge, and the K-edge of a pure Nb foil (with the first derivative maximum set to 18986.0 eV) at the Nb K-edge. All XANES spectra were analyzed using the Athena software package.38 Selected area electron diffraction (SAED) patterns were collected using a JEOL 2100F transmission electron microscope (TEM) on crushed grains of the powder sample dispersed onto holey carbon-coated copper grids. Aberration-corrected scanning TEM (AC-STEM) data in the Z-contrast high angle annular dark-field (HAADF) imaging modes were collected from the powdered samples. The dry powder was lightly ground in an agate mortar and pestle before loading onto holey carbon-coated copper grids. A JEOL JEM2100F with a CEOS aberration corrector for the electron probe was used at 200 kV to image the sample with a 24 mrad convergence angle. The images were acquired using a Fischione Model 3000 detector with a camera length such the detector spanned between 75 and 178 mrad. The scanning acquisition was synchronized to the 60 Hz AC electrical power to minimize 60 Hz noise in the images, and a pixel dwell time of 15.8 µs was used.

2.3. Computational details Structure solution for commensurate Bi23CrNb3O45 was assisted by density functional theory (DFT) based methods as implemented in the Vienna ab initio simulation package (VASP). Calculations used projector-augmented wave (PAW)39 pseudopotentials within the generalised gradient approximation (GGA) and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional.40 A cut-off energy of 400 eV (determined by oxygen) was used for the plane-wave basis set. The Brillouin zone was sampled using a Monkhorst-Pack k-point grid centered at the Γ-point, with one single k-point. Initially refined experimental structures were used as starting configurations and were optimized by allowing ions to relax to their minimum energy position using the conjugate gradient algorithm. The cell dimensions were fixed to the experimentally 6/27


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determined values. At each step, all forces were relaxed below 0.01 eV Å-1. Total energies were converged to within 10-5 eV.

3. Results and discussion 3.1. Doping M6+ for Nb5+ in Type II Bi2O3:Nb2O5 For each dopant (M = Cr, Mo, W), we synthesized a range of samples of Bi23(M,Nb)4Oy with different M6+:Nb5+ ratios. Cubic fluorite-related structures were obtained over most of this parameter space. Figure 2 shows NPD patterns across the Bi23(Cr,Nb)4Oy series. Table 1 summarizes sample compositions, lattice and modulation parameters as extracted from combined Le Bail profile fits against SXRD and NPD data. All fits are based on a simple cubic δ-Bi2O3 model with lattice parameter aF in space group Fm3തm with three coupled modulation vectors F. Lattice and modulation parameters follow Vegard’s law (Figure 3).

Intensity (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Bi23Cr3NbO46 Bi23Cr2Nb2O45.5 Bi23CrNb3O45

20

40

60

80

100

120

140

160

2Θ (°) Figure 2: Neutron powder diffraction patterns (λ = 2.4395 Å) across the Bi23(Cr,Nb)4Oy series. Bi23Cr3NbO46 is purple, Bi23Cr2Nb2O45.5 is green, and Bi23CrNb3O45 is blue. The patterns are staggered on the y-axis for clarity.

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Table 1: Summary of lattice parameters and modulation parameters for doped Type II Bi2O3:Nb2O5 samples. (Notes: a no superstructure reflections in SXRD patterns; b no NPD data collected – modulation parameter extracted from SXRD data only; c manual fit, ε not refined).

Composition Bi23W4O46.5 Bi23Nb4O44.5 Bi23Mo4O46.5 Bi23W3NbO46 Bi23W2Nb2O45.5 Bi22W2.5Nb2.5O46.75 Bi23WNb3O45 Bi23Cr3NbO46

a/Å 5.56888(2) 5.510201(5) 5.65400(2) 5.5530(1) 5.54018(2) 5.52221(2) 5.521381(8) 5.57876(2)

ε 0.3208(2)a 0.3632(1)b 0.2930(1)b 0.3288(1)a 0.3497(4)a 0.3563(1) 0.2964(2)

Bi23Cr2Nb2O45.5

5.55755(2)

0.3130(2)

Bi23CrNb3O45 Bi23Mo3NbO46 Bi23Mo2Nb2O45.5

5.530375(5) 5.620840(8) 5.57947(4)

⅓ 0.3054(1) 0.3211(1)

Bi23MoNb3O45

5.54269(6)

0.3456(2)a

Bi23Cr4-xNbxOy

Å

Very broad peaks; not Type II

Commensurate

Very weak superstructure reflections even in NPD data

b Bi23Cr4-xNbxOy

Bi23Mo4-xNbxOy

5.61

Comment

0.36

Bi23Mo4-xNbxOy

Bi23W4-xNbxOy

Bi23W4-xNbxOy

Bi23Nb4O44.5

Bi23Nb4O44.5

0.34

ε = 1/3

5.58

0.32

5.55 0.30

modulation parameter

a 5.64

lattice parameter ( )

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5.52 0.28

0

1

2 Nb content x

3

4 0

1

2 Nb content x

3

4

Figure 3: Lattice (top) and modulation (bottom) parameters vs. dopant concentrations, based on a Type II cubic fluorite-related based unit cell with three coupled modulation vectors F.

Figure 4 shows the partial phase diagram for the Bi2O3-Nb2O5-W2O6 system, summarizing sample compositions and structure types. The cubic fluorite type structure was easily obtained for Bi23WNb3O45 and Bi23W2Nb2O45.5 by slow-cooling in the furnace (< 2.5°C/min). On the W-rich end, slow cooling of Bi23W3NbO46 gave a tetragonal phase (related to the Type Ib phase reported in the Bi2O3:W2O6 system41); quenching from 1000°C gave an apparently cubic structure with rather broad peaks, but close inspection of the SXRD pattern revealed shoulders suggestive of tetragonal peak-splitting. This is consistent with the limited solubility of WO3 in the bismuth niobate system reported by Borowska et al.,30 which they attributed to crowding in the oxygen sub-lattice after 8/27


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introduction of W6+. The structural features of well-defined clusters of W4O18 tetrahedra of octahedra and the limited solid solution range of Type II Bi1-xWx6+O1.5+1.5x (0.15 < x < 0.19) based on substitution of W onto the fcc site (i.e., positions at corners and face centers, cf. Wind et al.

21

), as well as the limited stability of Bi-rich Type II Bi-W-O (the Type II phase

can only be obtained by quenching from temperatures > 900°C), further supports this explanation. The Type II Bi-Nb-O phase, on the other hand, incorporates a larger variety of NbO6 clusters (including corner connected NbO6 chains), resulting in samples with a higher Nb:W ratio being more stable.

Figure 4: Partial phase diagram for the Bi2O3-Nb2O5-W2O6 system. Crosses indicate samples reported in literature,29-30 dots samples of this work. Red indicates samples with cubic fluorite-related structure.

All Bi23(Mo,Nb)4Oy samples have Type II structures. The intensity of the superstructure reflections in SXRD data increases with increasing Mo content. No quenching was necessary to stabilize the cubic structure in samples that are richer in Nb, i.e., Bi23Cr2Nb2O45.5, Bi23CrNb3O45, Bi24Cr1.5Nb1.5O42.25 and Bi22Cr2.5Nb2.5O46.75. As for the bismuth-tungsten niobates, slow-cooling of the Cr-rich sample Bi23Cr3NbO46 led to splitting of the (200), (220) and (311) reflections, i.e., tetragonal phases, while quenching retained cubic symmetry. All samples showed very weak superstructure reflections in SXRD patterns, which were much more intense in NPD data. The relationships between modulation parameter and dopant concentration (Figure 3b) show that our approach was successful. In particular, Bi23CrNb3O45 appears to be truly commensurate at ε = 1/3. This sample will be discussed further in Section 3.4. Interpolation 9/27



suggests two further possible commensurate compositions, Bi23W1.75Nb2.25O45.375 and Bi23Mo1.5Nb2.5O45.25, which will be investigated in future studies.

3.2. Doping M6+ for Ta5+ in Type II Bi2O3:Ta2O5 For each dopant (M = Cr, Mo, W), we synthesized a range of samples of Bi23(M,Ta)4Oy with different M6+:Ta5+ ratios. The end-member sample Bi23Ta4O44.5 contained two cubic phases, in agreement with Struzik et al.:17 one with a = 5.5302(3) Å, referred to as Type I by Zhou11); and a smaller Type II phase with cell dimensions (a = 5.4802(3) Å). Mixed doping also yielded two cubic phases (except for Bi23W3TaO46). As the superstructure peaks could not be unambiguously assigned to either of the two phases present in the samples, modulation parameters could not be determined. Extracted lattice parameters are summarized in Figure 5 and Table 2. On increasing the M6+ concentration (or decreasing the Ta content), the lattice parameter of the Type I phase, as well as its weight fraction, generally increased (Figure 5). The Type II phase does not show any significant compositional dependency (empty symbols in Figure 5a). This suggests a constant Ta concentration in the Type II phase, with doping only occurring within the Type I phase.

Å

1.0

b

5.72

Bi23Cr4-xTaxOy

Bi23Cr4-xTaxOy

5.68

Bi23Mo4-xTaxOy

Bi23Mo4-xTaxOy

Bi23W4-xTaxOy

Bi23W4-xTaxOy

Bi23Ta4O44.5

Bi23Ta4O44.5

5.64

0.9

0.8

5.60 5.56

0.7 5.52 5.48

weight fraction type I

a

lattice parameter ( )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.6

5.44

0

1

2 Ta content x

3

4

0

1

2 Ta content x

3

4

Figure 5: (a) Lattice parameters vs. dopant concentrations for doped Bi2O3:Ta2O5 samples, based on the presence of two cubic phases: Type I (filled markers) and Type II (hollow markers). (b) Weight fraction of Type I vs. dopant concentrations.

Figure 6 shows SXRD patterns across the Ta-W mixed doping range. Ta-rich samples contain two phases. Increasing W content reduces the amount of Type I phase. For the W-rich sample Bi23W3TaO46, all peaks could be indexed using one simple cubic model. In the (Ta,Mo) and (Ta,Cr) systems, all samples exhibit two phases and SXRD data could be fitted using two cubic fluorite-based models. 10/27


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Intensity (arb. units)

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Bi23WTa3O45 Bi23W 2Ta2O45.5 Bi23W 3TaO46

28

30

32

34

2Θ (°) Figure 6: Excerpts of SXRD patterns for different compositions in the Bi-Ta-W-O system. Ta-rich samples contain two phases, while Bi23W3TaO46 only contains one fluorite-related phase. Bi23WTa3NbO45 is purple, Bi23W2Ta2O45.5 is green, and Bi23W3TaO45 is blue. The patterns are staggered on the y-axis for clarity. Table 2: Summary of samples based on Ta6+-doping and Rietveld refinements based on cubic δ-Bi2O3 models.

Composition

a1/Å

a2/Å

Weight % (phase 1)

5.56888(2)

100

Bi23W4O46.5 Bi23Mo4O46 Bi23W3TaO46

5.65400(2) 5.55888(9)

-

Bi23W2Ta2O45.5 Bi23WTa3O45

5.54264(8) 5.53847(4)

5.47449(8) 5.47081(4)

74 60

Bi23Cr3TaO46 Bi23Cr2Ta2O45.5

5.5894(7) 5.5863(7)

5.4683(7) 5.4728(7)

96 81

Bi23CrTa3O45

5.5708(5) 5.65400(2)

5.4753(5) -

64 100

5.62714(5) 5.61804(8)

5.45848(6) 5.46456(8)

94 76

5.5928(1) 5.5302(3)

5.46845(9) 5.4802(3)

62 66

Bi23Mo4O46.5 Bi23Mo3TaO46 Bi23Mo2Ta2O45.5 Bi23MoTa3O45 Bi23Ta4O44.5

100 100

3.3. X-ray absorption near-edge structure (XANES) X-ray absorption near-edge structure (XANES) spectroscopy was used to probe the shortrange local chemical environments of the dopant species, including valence state, coordination and site geometry.

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Nb coordination environments Figure 7a shows selected Nb K-edge XANES spectra for mixed doped samples, Bi23Cr2Nb2O45.5, Bi23Mo2Nb2O45.5, Bi23W2Nb2O45.5, along with two standards of Bi3Nb5+O7 (Nb in purely octahedral coordination environment) and LaNb5+O4 (Nb in purely tetrahedral coordination environment). The pre-edge feature of the Nb K-edge corresponds to a dipoleforbidden 1s to 4d transition42 and is very sensitive to local distortions and coordination number.43 The spectra of all mixed doped samples look essentially identical to the spectrum for the Bi3Nb5+O7 standard. This indicates that Nb atoms adopt oxidation state 5+ and occupy octahedral sites in all samples.

1.4

b

e

t2

1.2

LaNbO4 (tet)

Normalized µ(E)

1.0

1.5 0.8

LaNbO4 (tet)

0.6

Bi23Cr2Nb2O45.5 1.0

Bi23Cr2Nb2O45.5

0.4

2.0

0.5

Bi3NbO7 (oct)

Bi23W2Nb2O45.5

0.0 18990

19020

19050

19080

2360

2370

Energy (eV)

c

Bi23Cr3NbO46

t2g e g

Bi23Mo2Nb2O45.5

0.2 0.0 18960

Bi23CrNb3O45

Bi3NbO7 (oct)

Normalized µ(E)

2.0

2380

2390

Energy (eV)

Bi23MoNb3O45

Bi23Mo3NbO46

Bi23Mo2Nb2O45.5

Bi14MoO24 (tet)

d

3.0

Bi14CrO24

Cr 3d-e

2.5

Bi23Cr3NbO46 2.0

1.5

Bi23Cr2Nb2O45.5 Bi23CrNb3O45

1.0

t2

1.5 1.0

Bi14MoO24

e

Normalized µ(E)

a

Normalized µ(E)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.5

0.5 0.0 2520

2522

2524

2526

2528

2530

2532

525

530

Energy (eV)

535

540

545

Energy (eV)

Figure 7: Normalized XANES spectra: (a) at the Nb K-edge for Bi23Cr2Nb2O45.5, Bi23Mo2Nb2O45.5, Bi23W2Nb2O45.5 and (b) at the Nb L3-edge for Bi23CrNb3O45, Bi23Cr3NbO46; both including Bi3Nb5+O7 (Nb5+: octahedral) and LaNb5+O4 (Nb5+: tetrahedral) standards. (c) At the Mo L3-edge for Bi23MoNb3O45, Bi23Mo2Nb2O45.5, Bi23Mo3NbO46, and Bi14Mo6+24 (tetrahedral) standard. (d) At the O K-edge for selected Crcontaining samples, Bi14Cr6+24 (Cr6+: tetrahedral) and Cr-free Bi14Mo6+24 standards (Mo6+: also tetrahedral).

Figure 7b shows the Nb L3-edge XANES spectra, resulting primarily from the Nb 2p3/2 → 4d dipole transitions, for selected samples, i.e., Bi23CrNb3O45, Bi23Cr2Nb2O45.5 and Bi23Cr3NbO46 as well as standards (Bi3Nb5+O7 and LaNb5+O4). These spectra provide direct information on 12/27


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the occupancy and energy distribution of the final Nb(4d) states, which is determined mainly by the local crystal field exerted by the surrounding oxygen ligands. As shown in Figure 7b, the L3-edge spectrum displays a bimodal feature due to crystal field splitting of the unoccupied Nb(4d) orbitals. The energy gap between the two peaks is directly related to the crystal field splitting (CFS). For an octahedral MO6 unit (where M is at the origin and O ligands are positioned on the Cartesian axes), the triply degenerate t2g orbitals are located at lower energy than the doubly degenerate eg orbitals, as the latter point towards the ligand orbitals and hence are subject to a stronger electrostatic repulsion from the ligands.44 The intensity of the t2g peak is higher than that of the eg peak due to higher degeneracy of the t2 orbitals (3) than that of the eg orbitals (2). In contrast, the three d-t2 orbitals lie higher in energy with respect to the two d-e orbitals for a tetrahedral MO4 unit (where M is at the center of a cube and O ligands are situated at the four alternate corners of the cube), as the t2 orbitals are now oriented with their lobes much closer to the ligands than the e orbitals. The peak intensity ratio is reversed from t2g/eg > 1 for an octahedral site to e/t2 < 1 for a tetrahedral site. In summary, the results shown in Figure 7b confirm that the Nb oxidation state is 5+ in all the samples and all Nb atoms are coordinated to 6 oxygen atoms. In addition, the CFS in all the samples is very similar to that in Bi3Nb5+O7, suggesting similar Nb-O bond distances.

W coordination environments W L3-edge XANES spectra originate predominantly from the dipole transition of the W 2p3/2 core electrons into the empty 5d states in the conduction band. This edge is sensitive to both the W oxidation state and its local coordination environment.45-46 Standards used were Aurivillius type Bi2W6+O6, in which W6+ is found to adopt purely octahedral coordination environments,47-48 and Bi14W6+O24, which has exclusively tetrahedral W environments.49-50 Figure 8 shows W L3-edge spectra for selected (W,Nb) co-doped samples, i.e., Bi23W3NbO46, Bi23W2Nb2O45.5 and Bi23WNb3O45. The W L3-edge position of all samples is essentially the same as that for the two standards, confirming the oxidation state of W6+ in all samples.

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Bi2WO6 (oct)

3

0.0

Bi14WO24 (tet)

2 10200

10210

10220

First derivative

0.6

Normalized µ(E)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-0.6 10230

Energy (eV)

1

Bi23W 3NbO46 Bi23W 2Nb2O45.5 Bi23WNb3O45

0

10200

10210

Bi2WO6 (oct) Bi14WO24 (tet)

10220

10230

Energy (eV) Figure 8: Normalized W L3-edge XANES spectra obtained from Bi23W3NbO46, Bi23W2Nb2O45.5, Bi23WNb3O45 along with Bi14W6+O24 (tetrahedral) and Bi2W6+O6 (octahedral) standards.

The shape of the absorption peaks gives insights into the local coordination environments. Bi14WO24 looks like a single peak while Bi2WO6 exhibits two overlapping peaks (this difference is more apparent in the first derivative plots in the inset of Figure 8). This results from a smaller ligand field splitting of the W 5d orbitals in the tetrahedral environment than the octahedral environment.46 The XANES spectra shown in Figure 8 illustrate that W6+ is found predominantly in octahedral coordination environment in all the co-doped samples, with small tetrahedral contributions in Bi23W3NbO46 > Bi23W2Nb2O45.5 > Bi23WNb3O45. These tetrahedral contributions appear to be closely related to the stability of the cubic Type II phase vs. the tetragonal Type Ib phase. Similar results were observed for other dopant combinations.

Mo coordination environments The Mo L3-edge XANES spectra arise from the transition from Mo 2p3/2 core level electrons to the unoccupied 4d states.51-52 Two peaks, representing crystal field splitting (CFS), are observed in all spectra (Figure 7c). Bi14Mo6+O24, which has an exclusively tetrahedral Mo coordination environment,49-50 was included as a standard. As shown, the Mo L3-edge spectra for (Mo,Nb) co-doped samples, Bi23MoNb3O45, Bi23Mo2Nb2O45.5, and Bi23Mo3NbO46, are essentially identical to that of the tetrahedral standard of Bi14Mo6+O24. The two peaks correspond to the Mo 4d-e and 4d-tg components respectively. The intensity of the e peak has a lower intensity than that of the tg 14/27


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peak as explained above. The edge position of all samples is the same as that of the Bi14Mo6+O24 standard, confirming the presence of Mo6+ in all Mo-doped samples. In addition, the same CFS and peak intensity ratio between the two peaks confirms that the Mo coordination environment is tetrahedral in all the compounds.

Cr coordination environments The Cr coordination environment was deduced from the O K-edge XANES spectra, as shown in Figure 7d for (Cr,Nb) co-doped samples of Bi23CrNb3O45, Bi23Cr2Nb2O45.5, Bi23Cr3NbO46, along with tetrahedral standards of Bi14Mo6+O24

50

and Bi14Cr6+O24.50 These spectra

correspond to transitions from the O(1s) core level to the unoccupied O(2p) states in the conduction band. If these compounds are purely ionic, no absorption peak would be observed as the O(2p) orbitals would be fully occupied. The large intensity seen at the O K-edge clearly demonstrates the covalent nature of M-O bonding in these materials, reflecting unoccupied density of states of the various cation orbitals hybridized with the O(2p) states. Hence the O Kedge line shape is also quite sensitive to the local structure.53 As shown in Figure 7d, the intensity of the lowest energy peak (~529.4 eV) increases with increasing Cr content in the doped samples, showing a positive Cr concentration dependence. Furthermore, based on the similarity between the spectra from the (Cr,Nb) co-doped samples and that of the Bi14Cr6+O24 tetrahedral standard, the presence of Cr6+ in tetrahedral coordination environment is indicated in all the (Cr,Nb) co-doped samples, i.e., the peak at ~529.4 eV is attributed to Cr 3d-e states

alone.

3.4. Bi23CrNb3O45 – a truly commensurate (3+3)-D phase For Bi23CrNb3O45, Le Bail fits against SXRD and NPD data yield a commensurate modulation parameter of ε = 1/3. The commensurate modulation was confirmed by selected area electron diffraction (SAED) patterns shown in Figure 9, in which all Bragg reflections can be indexed to both the (3+3)-D modulated and the 3x3x3 supercell of fluorite-type δ-Bi2O3, with perfect overlap. SAED patterns were collected from multiple crystallites, with no changes observed between them, demonstrating that the modulation parameter is genuinely “locked in” to this commensurate value.

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Figure 9: (a) (100), (b) (112) and (c) (110) zone axis SAEDs of commensurate Type II Bi23CrNb3O45. The intense bright spots correspond to the simple fluorite-related unit cell, and less intense spots to the commensurate 3x3x3 superstructure. Bragg reflections are indexed to both the (3+3)-D modulated (yellow) and the 3x3x3 supercell (blue) of fluorite-type δ-Bi2O3.

We carried out Rietveld refinements using a 3x3x3 supercell in space group F4ത3m against the NPD data, using the commensurate approximation for Bi22W5O4827 as a starting model. Careful initial refinement against NPD data pointed towards mixed Nb-Bi occupancy on the Bi1 site (within the tetrahedra of octahedra) and Cr on the fcc site, but at lower occupancy than the expected 100%. This suggests some underlying disorder in the structure, especially around the Cr site. To allow for local structural relaxation, we subsequently performed ab initio DFT simulations on a (in terms of composition) hypothetical perfectly ordered system with composition Bi22CrNb4O45 (100% Nb on the Bi1 site, 100% Cr on the fcc site). Geometry optimization relaxed the distorted average coordination environments obtained from the refinement to tetrahedra of highly symmetric NbO6 octahedra and CrO4 tetrahedra on the corner and face centered positions of the unit cell. This is in perfect agreement with XANES results for local coordination environments around Nb5+ (Figures 7a and 7b) and Cr6+ (Figure 7d). The local structural ordering suggested by these simulations was incorporated into our refinement model. Cr was found to be located on the tetrahedral site, and 75%Nb (+ 25% Bi) on the octahedral/cluster site. The O sites around the transition metals have large atomic displacement parameters (ADPs) and refine towards the fluorite-type positions. For our final refinement, these positions were constrained to their DFT-optimized ones. Furthermore, to stabilize the Rietveld refinement with such a limited q-range, we assigned the same isotropic displacement parameter to all cation sites. This average disorder is unsurprising because the 25% Bi on the octahedral/cluster sites should have very different O coordination. On a local 16/27


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scale we suspect that either all four sites within a cluster are occupied by Nb atoms, or none. This in turn would affect the stability of the O sites around the Cr. The final fit is shown in Figure 10, with results summarized in Table 3. Refined experimental and optimized experimental structures are shown in Figure 11.

Figure 10: Rietveld refinement against NPD data collected on ECHIDNA (λ = 2.4395 Å) of a single phase Bi23CrNb3O45 sample. The blue line represents the difference between observed (black crosses) and calculated (red line) profile, the green line is background. The blue markers indicate peak positions for the 3x3x3 supercell in space group F4ത3m.

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Table 3: Refined structural parameters against NPD data (ECHIDNA, λ = 2.4395 Å) for Bi23CrNb3O45 in space group F4ത3m, a = 16.5897(2) Å. Overall powder R-factors: Rp = 0.0438, wRp = 0.0621, R(F2) = 0.0551.

0.0867(7) 0.0867(7)

frac. occ. 0.25 1

site multiplicity 16 48

0 0.3279(5)

0.0867(7) 0.0867(7)

1 1

24 16

0.6647(7) 0

0.6647(7) 0

0.0867(7) 0.0867(7)

0.75 1

16 4

0.9392 0.0608

0.9392 0.0608

0.9392 0.0608

0.34(7) 0.34(7)

0.33(6) 0.67(6)

16 16

O2 O3

0.0802(8) 0.25

0.0802(8) 0.25

0.2397(14) 0.25

0.1435(31) 0.1435(31)

1 1

48 4

O4 O5

0.6274 0.0919

0.25 0.0919

0.25 0.7166

0.383(22) 0.383(22)

1 1

24 48

O6 O7

0.0736(17) 0.4269(13)

0.25 0.4269(13)

0.25 0.4269(13)

0.1435(31) 0.1435(31)

1 1

24 16

Atom

x

y

z

Uiso

Bi1 Bi2

0.6647(7) 0.3363(4)

0.6647(7) 0.3363(4)

0.6647(7) 0.0019(4)

Bi3 Bi4

0.3272(10) 0.3279(5)

0 0.3279(5)

Nb1 Cr1

0.6647(7) 0

O1 O1 (bis)

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Figure 11: (a,b) Experimental (refined) and (c,d) computational (geometry optimized) structures for Bi23CrNb3O45. Bi atoms are purple, CrO4 tetrahedra are blue, NbO6 octahedra are green and O atoms are red.

3.5. HAADF-STEM Imaging Figure 12 shows the experimental HAADF micrograph in the [110]F zone axis of the fluorite lattices. The cation sites are all evident in the image, while the oxygen sites are not apparent. In this projection of the structure, each column of cations consists of two different atomic sites overlapped (cf. Figure 11d). Also shown in Figure 12 is a fast Fourier transform (FFT) of the real space image. Note that this FFT of the HAADF-STEM image is the same as found in the SAED shown in Figure 9c. In order to obtain reliable dark-field intensities we needed to subtract a background that varied significantly due to sample thickness variations. After establishing regions of interest for the various atom columns shown in this projection we carefully chose regions where the electron probe did not interact with the projected location of atoms in the structure and subtracted these from the HAADF signal. In Figure 13 this procedure is shown for the Bi2Cr1 columns. Using this procedure, we obtained integrated HAADF signals for the six cation column projections shown in Figure 14. We analyzed a total 19/27



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of 781 atomic columns (85 Bi3BiNb1. 89 Bi2Cr1, 171 BiNb1Bi2, 85 Bi3Bi4, 180 Bi2/Bi3 and 171 Bi2Bi4 columns) to obtain good counting statistics for the HAADF-STEM intensities. Integrating the HAADF-STEM signal over many projected atom columns has shown to be insensitive to minute focus changes and drifts due to small environmental changes (temperature, vibration, electromagnetic interferences).54,55

Figure 12: Experimental HAADF micrograph in the [110]F zone axis of the fluorite lattices and fast Fourier transform (FFT) of the real space image. The area shown in the blue box was used for data analysis. Below the HAADF-STEM signal of the 6 different columns and their atomic content is shown.

Figure 13: The HAADF-STEM signal is measured on a varying background shown on the left. To subtract this background we defined regions of interest (ROI). The ROIs for all Bi2Cr1 columns are shown (middle). The background was determined in the green rectangles to the left of the ROIs where no atoms are present in this projection as shown in Figure 11d. 20/27


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Figure 14: The mean integrated HAADF-STEM signal of the 6 atomic columns shown in Figure 12. The error bars are the 95% confidence limit on the mean using Student’s t distribution.

As expected from the Z-contrast approximation, the column containing 50% Nb is the dimmest, followed by the Bi2Cr1 column containing 33.3% Cr. An initial model based on combined SXRD and NPD data had both Cr and Nb co-located on an octahedral site. As the XANES data suggested and the observed HAADF-STEM contrast variation proved unequivocally, Cr has a tetrahedral coordination and is located on (0,0,0). We note that the BiNb1Bi2 column is slightly brighter than expected from the model structure based on Z-contrast. Furthermore, the two columns Bi3Bi4 and Bi2Bi3 reveal less HAADF intensity when compared to the Bi2Bi4 column, even though they all contain only Bi. Our careful background evaluation and experience in comparing HAADF images with model structures55 suggests that ADPs of the cations, which were constrained to be the same in the Rietveld refinement of the NPD data, might vary due to the high degree of disorder in the oxygen sublattice. The HAADF signal is dominated by thermal diffuse scattering and highly sensitive to the ADPs. The data suggest that the channeling of electrons in the Bi3Bi and Bi2Bi3 atomic columns are different to those in the Bi2Bi4 columns. To further investigate such a hypothesis one would require high-q NPD data permitting an atomic pair-distribution function analysis, which would then become the basis of extensive dark- and bright-field frozen phonon image calculations as outlined in Tate et al.56 21/27



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4. Conclusions We have shown for the first time that (3+3)-D modulated “Type II” transition metal-stabilized δ-Bi2O3 phases can be rationally prepared in a truly commensurate form, with a 3x3x3 supercell at Bi23CrNb3O45, by appropriately varying the co-dopant concentration. The modulation vector does not smoothly cross over the commensurate value but “locks in” to ε = 1/3, as shown by the lack of any peak splitting in high-resolution synchrotron X-ray powder diffraction and the consistency of selected-area electron diffraction patterns obtained from multiple crystallites. Although analogous commensurate phases were not found for Bi23WNb3O45 or Bi23MoNb3O45, in the course of this work we mapped out the Type II phase space for Bi23(M,Nb)4Oy where M = Cr, Mo, and W. The reason for why ε locks in to 1/3 can be understood firstly in terms of the metal atom stoichiometry, whereby an integer number (4 x 4 = 16) of the 4 x 27 = 108 Bi sites in the targeted 3x3x3 supercell are replaced by a transition metal; and secondly in terms of the local ordering of oxygen coordination environments around those transition metals, based on tetrahedral clusters of MO6 octahedra and isolated MO4 tetrahedra. Our ability to rationally design the commensurate phase is thus an intuitive “real space” validation of the crystalchemistry of the Type II phases, developed by ourselves and others using the superspace formalism in reciprocal space. Nevertheless, there is still some residual disorder in the structure of Bi23CrNb3O45. This can be seen in the refined long-range average structure, which has mixed crystallographic site occupancies compared to an ideal model optimized in ab initio simulations; in the average local structure, where X-ray absorption spectroscopy shows a mixture of coordination environments for Nb5+ and Cr6+; and directly by high-resolution scanning transmission electron microscopy, which reveals differences between projected atomic columns nominally containing only Bi. This should not be seen as a shortcoming, given that the underlying motivation for studying these stabilized δ-Bi2O3 phases is oxide ionic conduction, which requires local coordinative flexibility. Indeed, our failure to obtain single-phase Type II phases for (Ta,M) co-doped phases may be a consequence of the lower coordinative flexibility of Ta compared to Nb. The promise of the transition metal-doped phases is that they provide better long-term stability than the (more conductive) rare earth-doped phases. If their conductivities could be tuned to the comparable levels, they would therefore be more attractive options. The

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improved crystal chemical understanding of the Type II phases delivered by the work presented here is an important step in that direction.

Acknowledgments The authors thank Dr Peter Kappen (XAS beamline), Dr Lars Thomsen (Soft X-ray beamline) and Dr Justin Kimpton (Powder Diffraction beamline) at the Australian Synchrotron, and Dr Maxim Avdeev (Echidna beamline) of the Australian Centre for Neutron Science, ANSTO, for their assistance with data collection. Computational resources were provided by National Computational Infrastructure Australia. JW received funding for this project from the Australian Institute for Nuclear Science and Engineering (Postgraduate Research Award) and CDL from the Australian Research Council (DP150102863).

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Graphical Abstract

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Rational Design of a Commensurate (3 + 3)-D Modulated Structure

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