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Z. Kristallogr. 220 (2005) 231–244 # by Oldenbourg Wissenschaftsverlag, Mu¨nchen
The real structure of Na3BiO4 by electron microscopy, HR-XRD and PDF analysis Sascha VenskyI, Lorenz KienleI, Robert E. DinnebierI, Ahmad S. MasadehII, Simon J. L. BillingeII and Martin Jansen*, I I II
Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
Dedicated to Professor Dr. Hans-Jo¨rg Deiseroth on the occasion of his 60th birthday Received July 9, 2004; accepted September 16, 2004
Electrocrystallization / High resolution transmission electron microscopy / Pair distribution function / Sodium bismuthate / Powder diffraction structure analysis / X-ray diffraction Abstract. The real structure of a new crystalline high temperature phase, metastable at room temperature, in the system sodium – bismuth – oxygen, b-Na3BiO4, was determinated using high resolution X-ray powder diffraction, pair distribution function analysis, and high resolution transmission electron microscopy. b-Na3BiO4 was synthesized by anodic oxidation of bismuth(III)-oxide in a sodium hydroxide – lithium hydroxide melt. The average crystal structure of b-Na3BiO4 at ambient conditions (R3m, a ¼ 3.32141(9) A, c ¼ 16.4852(5) A) is structurally related to a-NaFeO2 with metal layers almost statistically occupied in a Na : Bi ratio of 3 : 1. Analysis of the longrange order on the bulk material by Rietveld refinement led to approximately Na : Bi ratios of 2 : 1 and 4 : 1, in consecutive metal layers, while a detailed analysis of the local order by means of the pair distribution function revealed the existence of almost pure sodium layers and mixed 1 : 1 – sodium : bismuth layers. Complementary studies on single crystallites using high resolution transmission electron miscroscopy exhibited a complex domain structure with short-range ordered, partially ordered, and long-range ordered domains.
Introduction The rock salt arrangement is among the fundamental building principles in three-dimensional space. Besides the vast families of chemically different AB compounds, it is realized in salts containing complex anionic and/or cationic constituents, even including extended cluster ions. Examples are calcite CaCO3, [1] sodium nitrate NaNO3, [2] sodium ozonide NaO3, [3] calcium carbide CaC2, [4] sodium azide NaN3, [5] and fulleride compounds of the * Correspondence author (e-mail:
[email protected])
[M(NH3)6] C60 6 NH3 type, M ¼ (Cd, Co, Mn, Zn) [6, 7]. Substitution variants, with either the cationic or anionic sublattices occupied by different species in an ordered manner, represent another class of rock salt derivatives. Here various ternary alkali metal oxides of general formula types ABO2, A2BO3, A3BO4, A4BO5, . . . (A ¼ alkali metal, B ¼ metal or nonmetal) need to be included. Some of the latter show order-disorder transitions within their cationic sublattices, and are reluctant to fully order, during the synthesis along the solid state route. In the past, this phenomenon has caused some confusion with respect to the correct indexing of the powder patterns of e.g. Li2SnO3, [8, 9] Li2MnO3, [10–12] or Na2RuO3 [13, 14]. The room temperature modification of Na3BiO4, referred to as a-Na3BiO4, hereafter, is a fully ordered rock salt substitution variant with monoclinic symmetry [15]. Here we report on a heavily disordered high temperature modification of Na3BiO4, i.e. b-Na3BiO4, grown electrochemically from a NaOH/Bi2O3 melt. The oxidation state of +V for bismuth in oxides is generally rare. However, it has been realized in a number of alkali bismuthates: ABiO3 and A3BiO4 with A ¼ Li, Na, K, Li5BiO5, and Li7BiO6 [15 – 25]. Out of these, the only one accessible through electrocrystallization from a melt, besides solid state routes, was KBiO3 [20 – 22].
Experimental Syntheses and analyses Crystalline material of b-Na3BiO4 was obtained by electrocrystallization from alkali hydroxide melts containing bismuth(III) oxide Bi2O3. The components of the melt, 1 g Bi2O3 (Riedel-de Haen, 10305), 12 g NaOH (Merck, 106498), 3.4 g LiOH (Merck, 105691), and 0.4 g ZnO (Chempur, 008417), were used without pre-treatment. Figure 1 shows a schematic drawing of the electrolysis cell used. A nickel crucible containing the components of the melts was placed into a closed glass reaction vessel and heated during three hours starting from a temperature of T ¼ 200 C up to a temperature slightly above the electro-
232
Fig. 1. Cell used for the electrocrystallization of b-Na3BiO4. (1) wires leading to the potentiostat, (2) gas inlet, (3) connectors, (4) Pt electrodes, (5) furnace, (6) nickel crucible.
lysis temperature (330–350 C), allowing the melt to equilibrate. ZnO levels the amount of water in the melt. After one hour, the temperature was decreased to the electrolysis temperature, the platinum electrodes were inserted, and the reaction vessel was closed. A platinum wire (˘ ¼ 1 mm) was used as the cathode, and a second platinum wire (˘ ¼ 0.3 mm) as the anode. A constant current density of 1 mA/cm2 was applied for 18 – 42 h using a VMP multipotentiostat (Bio-Logic, France). b-Na3BiO4 crystallized as dark red, shiny crystals at the platinum anode. The material was washed with bidestilled water and acetone, and was stored under an argon atmosphere. Crystalline material of a-Na3BiO4 was obtained by solid state reaction [15]. A thoroughly ground mixture of Na2O2 (Aldrich, 223417) and Bi2O3 (Riedel-de Haen, 10305) in the ratio 3 : 1 was placed in a corundum boat and reacted for 12 h at T ¼ 600 C, in a flow of oxygen. a-Na3BiO4 was obtained as a bright yellow powder. Images of the crystals were taken by means of scanning electron microscopy (ESEM XL30 TMP, Philips). Investigations of the stoichiometry of b-Na3BiO4 by chemical analysis using ICP-OES technique were conducted with an optical emission spectrometer ARL 3580 B. Thermal analysis (DTA/TGA) of b-Na3BiO4 was performed using a Simultaneous Thermo-Analyzer STA 409 (Netzsch) with the sample in a corundum crucible, in a flow of oxygen (100 mL/min).
High resolution X-ray powder diffraction High resolution X-ray powder diffraction data of bNa3BiO4 were collected at ambient conditions in transmission geometry with the sample sealed in a 0.5 mm lithiumborate glass (Hilgenberg glass No. 50) capillary at beam-
S. Vensky, L. Kienle, R. E. Dinnebier et al.
line X17B1 of the National Synchrotron Light Source at Brookhaven National Laboratory. X-rays of an energy of 67 keV were selected by a silicon(220)-Laue-Bragg-monochromator and analyzed by a sagittally bent silicon crystal [26–29]. The exact wavelength was determined as l ¼ 0.18528(2) A using the NIST SRM 660 LaB6 standard. Data were taken in steps of 0.001 2q from 1.00– 15.00 2q for 16 h. The samples were spun during measurement for better particle statistics. The powder pattern exhibits several peaks of small amounts of sodium hydroxide and bismuth oxide. Data reduction was performed using the GUFI program [30]. Indexing with ITO [31] led to a hexagonal cell with lattice parameters given in Table 1. The number of formula units (Na0.75Bi0.25O) per unit cell was deduced to be Z ¼ 6, from volume increments. The extinctions found in the powder pattern indicated R3, R3, R32, R3m, and R3m as the most probable space group. The latter was confirmed by Rietveld refinements. The peak profiles and precise lattice parameters were determined by LeBail-type fits [32] using the program GSAS [33]. The background exhibited various humbs caused by strong diffuse scattering and was modeled manually using GUFI. The peak-profile was described by a pseudo-Voigt function in combination with a special function that accounts for the asymmetry due to axial divergence [34, 35]. Rietveld refinements [36] were performed using the program package GSAS. Starting parameters for the atomic positions of b-sodium bismuthate were taken from the structurally related a-sodium ferrate NaFeO2. Starting values for the peak profile, background, and lattice parameters were taken from the corresponding LeBail-fit. No additional phases were included in the refinement, but several excluded regions containing reflections of sodium hydroxide and bismuth oxide were defined. Structural variations causing diffuse scattering were not included in the refinement. The Rietveld refinement converged to agreement factors (R-values) listed in Table 1. The atomic coor-
Table 1. Crystallographic data for b-Na3BiO4 (average structure, from synchrotron powder data) in comparison with a-Na3BiO4 [30]. a-Na3BiO4
b-Na3BiO4
Formula
Na3BiO4
Na0.75Bi0.25O4
Temperature (in K)
295
Space group (No.) Z ) a (in A
P2/c(13) 2
295 R 3m(166)
5.87(1)
3.32141(9)
b (in A) c (in A)
6.69(6) 5.65(0)
¼a 16.4852(5)
a (in )
90
90
b (in ) g (in ) ) V (in A
109.8 90
90 120
208.8(19)
6
157.50(1)
Rp (in %) Rwp (in %)
12.7 14.4
RF (in %)
25.8
RF 2 (in %)
29.9
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Table 2. Combined results of the refined parameters (Rietveld and PDF). Positional parameters and temperature factors for b-Na3BiO4 at ambient conditions. Standard uncertainties are given in parentheses. Temperature factors of metal atoms on the same position were restrained. Atom
x
y
z
sof
Bi(1)
0
0
0
0.206(1)
0.0113(3)
Na(1) Bi(2)
0 0
0 0
0 1 =2
0.794(1) 0.294(1)
Na(2)
0
0
1
=2
O
0
0
0.2407(6)
UPDF (sof values fixed to Rietveld values)
sof
20 0.0112(4)
0.0113(3) 0.0113(3)
0.706(1) 1.0
Rietveld
URietveld
UPDF
UPDF
20
20
6
0.081(15)
0.0111(6)
0.01095(14)
0.0112(4) 0.0112(4)
0.919(16) 0.419(16)
0.0111(6) 0.0111(6)
0.01095(14) 0.01095(14)
0.0113(3)
0.0112(4)
0.581(16)
0.0111(6)
0.01095(14)
0.037(2)
0.0242(7)
1.0
0.0203(5)
0.0306(10)
Rmax ( A)
dinates, temperature factors, and fractional occupancies are given in Table 21 .
Pair distribution function analysis The diffraction experiment for the Pair Distribution Function (PDF) analysis was performed at the 6ID-D mCAT beamline at the Advance Photon Source (APS) at Argonne National Laboratory. Data acquisition at a temperature of T ¼ 300 K employed the recently developed rapid acquisition PDF (RA-PDF) technique [37] with the X-ray energy of 87.97 keV. Data were collected using an image plate
PDF
camera (Mar345), with a usable diameter of 345 mm, mounted orthogonal to the beam path with a sample to detector distance of 159.88 mm. Lead shielding before the goniometer with a small opening for the incident beam was used to reduce the background. All raw data were integrated using the software Fit2D [38, 39] and converted to intensity versus 2q. The integrated data were normalized with respect to the average monitor count, then transferred to the program PDFgetX2 [40] to carry out data reduction to obtain S(Q) and the PDF which are shown in Fig. 2a and 2b, respectively.
High resolution transmission electron microscopy
a
For HRTEM investigations microcrystalline samples of Na3BiO4 were crushed under dry argon atmosphere in a glove box. Perforated carbon/copper nets were covered with the powder, leaving the crystallites in random orientations. These sample carriers were fixed in a side-entry, double-tilt holder (maximum tilt: 25 in two directions). An argon bag was used to transfer the sample holder to the microscope. High Resolution Transmission Electron Microscopy (HRTEM) and Selected Area Electron Diffraction (SAED) were performed in a Philips CM30ST (300 kV) which is equipped with a LaB6 cathode. SAED patterns were obtained using a diaphragm which limited the diffraction to a selected area of 2500 A in diameter. The EMS program package [41] served for the simulation of HRTEM micrographs (spread of defocus: 70 A, illumination semiangle: 1.2 mrad) and SAED patterns (kinematical approximation). All images were registered with a Multiscan CCD Camera (Gatan). EDX (energy dispersive X-ray spectroscopy) was performed with a Si/Li-EDX detector (Noran, Vantage System). All Fouriertransforms (FFT) were calculated from square regions of the HRTEM micrographs (Software: Digital Micrograph 3.6.1, Gatan).
b
Results and discussion
Fig. 2. The experimental reduced structure function FðQÞ ¼ QðSðQÞ 1Þ of b-Na3BiO4 (a) at room temperature from the X-ray measurement and (b) the corresponding PDF.
X-ray analysis und structure solution
1 Further details of the crystal structure investigation of bNa3BiO4 can be obtained from the Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen, Germany, (fax: (+49)7247808-666; e-mail:
[email protected]) on quoting the depository numbers CSD-414158.
b-Na3BiO4 crystallized as dark red, shiny crystals, exhibiting an undulated surface (Fig. 3) which gives hint towards a distorted crystal structure. No thermal degradation of the substance is observed in the thermal analysis up to a temperature of T ¼ 700 C. X-ray powder diffraction data of the sample recorded after the DTA/TGA measurement ex-
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Fig. 5. Average crystal structure of b-Na3BiO4 at ambient conditions. Oxygen atoms are shown in white. The atom positions named “Na” represent a mixed occupancy of 80 at% sodium and 20 at% bismuth atoms, while the atom positions named “Bi” represent a mixed occupancy of 70 at% sodium and 30 at% bismuth atoms. Fig. 3. SEM images b-Na3BiO4 crystals.
hibits exclusively reflections of the ordered a-modification. A Na : Bi ratio of 3 : 1 is found by chemical analysis (Na: exp. 18.0% (calc. 20,1%), Bi: 60,0% (61,1%)). The crystal structure of b-Na3BiO4 was solved by Rietveld Refinement (Fig. 4). b-Na3BiO4 crystallizes in trigonal symmetry (Fig. 5), showing strong relationship to the a-NaFeO2-type structure [42, 43], which may be derived from the rock-salt aristotype (cubic closest-packed oxygen anion arrangement with all octahedral voids occupied by cations) with alternating cation layers along [111] ([001] in hexagonal metric). In contrast to the a-NaFeO2-type,
where pure sodium and iron cation layers alternate, in bNa3BiO4 all cation layers are occupied by mixtures of Na : Bi ratio of close to 3 : 1. Two types of cation layers exist, which are stacked alternatingly: one is enriched by sodium up to a Na : Bi ratio of 3.85 : 1 (see Table 2), while the other is enriched by bismuth to a Na : Bi ratio of 2.40 : 1. Both, the Na enriched cation position Na(1)/Bi(1) and the Bi enriched position Na(2)/Bi(2) are coordinated by oxygen anions in a trigonally distorted octahedral coordination with shorter distances (cation oxygen distances 2.273(0) A for Na(2)/Bi(2); 2.451(0) A for Na(1)/Bi(1)) for the position enriched by the smaller cation Bi5+. The
Fig. 4. Scattered X-ray intensity for b-Na3BiO4 at ambient conditions as a function of the diffraction angle 2q. Shown are the observed pattern (diamonds), the best Rietveld fit profile in space group R 3m (a), the difference curve between observed and calculated profile (b), and the reflection markers (vertical bars). The wavelength was l ¼ 0.18528(2) A. Several regions representing the decompositions products sodium hydroxide and bismuth oxide were excluded from the refinement.
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coordination sphere of the oxygen anion can best be described as a slightly distorted octahedron formed by sodium and bismuth. Due to the long coherence length of X-rays used, the average crystal structure of b-Na3BiO4 was analyzed, resulting in a model with sodium und bismuth cations occupying almost statistically the same atomic positions. Because of the apparent diffuse scattering, the local order at the atomic level was studied by means of pair distribution function analysis.
Pair distribution function analysis The real-space pair distribution function (PDF), G(r), gives the probability of finding pairs of atoms separated by distance r, and thereby comprises peaks corresponding to all discrete interatomic distances. The experimental PDF is a direct Fourier transform of the total scattering structure function S(Q), the corrected, normalized intensity, from powder scattering data given by 2 GðrÞ ¼ p
1 ð
Q½SðQÞ 1 sin Qr dQ ;
0
where 4p sin q l is the magnitude of the scattering vector. Unlike crystallographic techniques, the PDF incorporates both Bragg and diffuse scattering intensities resulting in local structural information [44, 45]. Its high real-space resolution is ensured by measurement of scattering intensities over an extended Q range using short wavelength X-rays or neutrons. For the room-temperature data considered here, transformation of the FðQÞ ¼ QðSðQÞ 1Þ; to a Qmax of 25.0 A1 was found to be optimal. There are basically two considerations. The first is to have sufficient Qmax to avoid large termination effects; the second is to reasonably minimize the noise level due to statistical fluctuations as the signal-to-noise ratio decreases with increasing Q. We found that Qmax of 25.0 A1 has significantly lower noise level without losing useful structural information, i.e. no significant change of PDF peaks. The experimental PDF with Qmax 25.0 A1 was refined within the crystallographic model of b-Na3BiO4 as described in the chapter above. The constraints of space group R 3m were maintained. Lattice parameters, thermal displacement parameters, and some experimental factors were refined. The occupancy of the atoms on each site was fixed according to the values (sof Rietveld) given in Table 2. We obtained lattice parameters of a ¼ b ¼ 3.34(8) A, and c ¼ 16.48(1) A. Figure 6a shows both the experimental and model PDFs. The UPDF obtained are summarized in Table 2 (column 7). It is clear from the figure, that the fit [46] is quite good (Rwp ¼ 0.21) in the high-r region above r ¼ 6 A indicating the model agrees with the PDF in this region. However significant deviations between the model and the data exist below r ¼ 6 A. In particular, the two model peaks at 2.45 A and 4.77 A Q¼
(Figs. 6a and 7a) are poorly fit. They are (Na/Bi)–O and (Na/Bi)–(Na/Bi) peaks, respectively, originating from the O(Na/Bi)6 octahedra. These peaks can be reduced in amplitude if these correlations have an excess of Na over Bi. We therefore tried relaxing the constraint of Bi occupancy on the 000 and 001=2 sites, while maintaining the sample stoichiometry. We obtained a better value of the weightedprofile R-value, (Rwp ¼ 0.18) with the Bi occupancy at 000 refining to 0.081 and the Bi occupancy at 001=2 to 0.419. Figure 6b shows the fits with the refinement results summarized in Table 2. In particular, the fit in the low-r region is improved, but still more intensity needs to be removed from the 2.45 A and 4.77 A peaks. Therefore, we manually set the Bi atoms to have an occupancy of 0.0 at 000 and an occupancy of 0.5 at 001=2 and fixed these values. The resulting model agrees extremely well in the low-r region below 5 A (Rwp ¼ 0.13, Fig. 7b). However, the high-r region above 10 A is fit rather poorly (Rwp ¼ 0.30). On the surface, these results are in contradiction. The average structure refined from both, the Rietveld refinement and the PDF fitting over a wider range of r, suggests that Bi is distributed approximately equally over the two crystallographic sites, 000 and 001=2. However, the local structure refinement indicates clearly that Bi atoms preferredly localized at 001=2. Disagreements between local and average structures are not uncommon [44, 45] and these differences are always reconcilable by some averaging of local structural motifs that yield a higher-symmetry average structure. The 000 and 001=2 sites form sheets of (Na/ Bi) sites perpendicular to the c-axis coming from the edge-shared O(Na/Bi)6 octahedra. Three 000-site atoms in a triangle form one face of the octahedra while the three 001=2-site atoms, with the triangle rotated 60 degrees, form the opposite face of the same octahedron. According to a
b
c
Fig. 6. The experimental GðrÞ (solid dots) and the calculated PDF (solid line) from the refined structural model of b-Na3BiO4. The difference curve shown offset below: (a) Without refining the occupancy, (b) with refining the occupancy, (c) for manually setting Bi occupancy 0.0 at 000 and 0.5 at 001=2.
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a
b
Fig. 7. The experimental GðrÞ (solid dots) and the calculated PDF (solid line) from the refined structural model of b-Na3BiO4. The difference curve shown offset below: (a) Without refining the occupancy, (b) manually setting Bi occupancy 0.0 at 000 and 0.5 at 001=2.
Na3BiO4 (see X-ray analysis). It is characterized by the partial order of Na and Bi atoms in exactly one of the {111}cub layers with a slight enrichment of Bi in every second (001)trig layer. Following the conventions of transformations [47], the indices of directions in direct space of structure I and II are connected by the matrix Q1: 0 10 1 0 1 0 1 4=3 2=3 2=3 u u u C @ v A ¼ Q1 @ v A ¼ B @ 2=3 2=3 4=3 A @ v A w cub w trig w cub 1=6 1=6 1=6 Structure III (indices hklmon, [uvw]mon) is the ordered monoclinic structure, a-Na3BiO4[15] (P2/c, a ¼ 5.87 A, b ¼ 6.69 A, c ¼ 5.65 A, b ¼ 109.8 ). The transformations of [uvw]mon and [uvw]trig follow the matrix Q2: 0 10 1 0 1 0 1 3 0 0 u u u C @ v A ¼ Q2 @ v A ¼ B @ 1=4 1=4 0 A @ v A w trig w mon w trig 1=2 1=2 1
Electron diffraction the average structure the Bi ions are distributed equally over both faces, whereas the local structure indicates that one face is preferred to be pure Na. In this, PDF could tell us something different. In the average structure the difference between the (000) and the (001=2) sites is that the atoms on the former site form a long (2.45 A) bond with the oxygen at the center, whereas in the latter site form a shorter (2.27 A) bond to the oxygen. What is clear from the PDF is that the Bi ion always forms a short 2.27 A bond to the oxygen. As well, (Bi–Bi) try to have short bond (3.32 and 3.35 A) rather than 4.74 A, so that we can see the 4.74 A peak weak in the data but strong in the model.
HRTEM investigation While by HR-XRD and PDF techniques bulk materials are analyzed, high resolution transmission electron microscopy (HRTEM) studies were performed on single crystallites. Samples of Na3BiO4 with both, disordered crystals (bphase) from electrocrystallization and ordered crystals (aphase) from solid state synthesis were examined by electron microscopy. According to EDX, the ratio Na : Bi (3 : 1) is equal in ordered and disordered crystals. The ordered crystals were strongly affected by a segregation of sodium and the formation of amorphous particles during exposure to the electron beam. SAED patterns recorded on the ordered crystals can be indexed assuming the monoclinic metrics of a-Na3BiO4 [15]. Three different structure models (I–III) with different arrangements of Na and Bi atoms were chosen for the indexing of reflections and zone axes. The first one (structure I, space group: Fm 3m, a ¼ 4.716 A) represents an average NaCl-type structure with a random distribution of the metal atoms. Indices [uvw]cub refer to the metrics of this structure which is also used for the indexing of the fundamental reflections. Structure II (indices hkltrig, [uvw]trig) corresponds to the average structure of b-
Three different types of SAED patterns were observed within defined regions of b-Na3BiO4 crystals corresponding to long-range order, short-range order, and partially ordered domains. All phenomena can be observed within the same microcrystal. Electron diffraction patterns of long-range ordered microdomains exhibit no diffuse scattering, but fundamental reflections and superstructure reflections. Short-range ordered domains are characterized by prominent diffuse scattering besides sharp fundamental reflections, while partially ordered microdomains exhibit concentrations of the diffuse scattering. The order within the long-range ordered microdomains was evidenced in different orientations by tilting separated microdomains systematically. All superstructure reflections can be indexed assuming the monoclinic metrics of structure III, i.e. a-Na3BiO4. The experimental intensities recorded on thin ordered microdomains agree convincingly with simulated ones based on structure III, cf. Fig. 8a. Therefore, the structure of the microdomains is closely related to structure III. Additionally, for neighboring ordered microdomains multiple twinning is observed which can be rationalized by group-subgroup relations. The space group P2/c (structure III) is a maximal k subgroup (index 2) of C2/m, which is a maximal t subgroup of R3m (index 3). Taking into account the symmetry relation (t4) between the space groups R3m and Fm3m (structure I), the maximum number of coexisting monoclinic domains with different orientations is twelve. The twinning can be described as twinning by reticular pseudomerohedry. In diffraction patterns of multiply twinned crystals one would expect fundamental reflections and a variable pattern of superstructure reflections depending on the orientations of the transmitted ordered domains. One proof of this expectation is depicted in Fig. 8 for zone axis h100icub. The patterns of the separated ordered domains were recorded sequentially as depicted in Fig. 8a for the comparison of simulated and experimental patterns with zone axes h101imon (left and center) and [111]mon (right). In Fig. 8b
Real structure of Na3BiO4
237
a
b
Fig. 8. SAED patterns of multiply twinned domains of the same crystal. (a) SAED patterns of separated domains. Left and center: h101imon, 101imon, (left) and of [ 101]mon with [111]mon (right). right: [111]mon. (b) Superpositions of two rotated h
two regions with different superpositions are shown (left: two rotated h 101imon, right: [ 101]mon and [111]mon). The twin boundaries in h100icub orientations are almost parallel to the incident electron beam. Therefore, double diffraction is not significant and all patterns can be approximated by superimposed simulated patterns based on the monoclinic structure III, cf. Fig. 8b. The multiple twinning can also be demonstrated by HRTEM. The FFTs of neighboring domains correlate with variable orientations of multiple twinned monoclinic domains (not shown). Short-range order in microdomains leads to curved diffuse streaks in the SAED patterns. These streaks are not passing through the almost sharp fundamental reflections hklcub. A splitting of the latter was observed in many zone axes orientations, indicating deviations from cubic average metrics. The profile of the diffuse scattering perpendicular to the streaks is almost sharp. The 3D shape of the diffuse
intensity in reciprocal space defines a surface which can be reconstructed by tilting the crystals systematically. This surface is quite similar to the P* surface applied for the description of crystal structures (see Fig. 9a) [48–50]. Sections of a surface with cos ph + cos pk + cos pl – 3(cos ph cos pk cos pl) ¼ 0 reproduce the diffuse streak’s geometry, see diffraction patterns and corresponding sections for the zone axes h100icub (b), h110icub (c), h111icub (d), h112icub (e) and h013icub (f) in Fig. 9. Similar surfaces had been previously observed for various short-range ordered NaCl-type compounds, e.g. non stoichiometric transition metal carbides, nitrides and oxides, as well as for chemically rather different compounds like the ternary oxide LiFeO2 [51, 52]. The similarity of these surfaces [53–60] and that of b-Na3BiO4 indicate some relations of the disorder phenomena. A first and qualitative interpretation of the diffuse scattering is based on a cluster model [55, 56].
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Applying this model to our problem, the structure of bNa3BiO4 would be considered to contain centered ONaxBi6x octahedra (i.e. clusters) which represent the smallest ordered building units of the structure. Following generalized electrostatic valence rules [61, 62], one would expect
that the compositions of the clusters and the stoichiometry of the sample are preferably identical. Hence, b-Na3BiO4 would require ONa5Bi- and ONa4Bi2-octahedra at a ratio of 1 : 1. A related ratio of clusters (VC5& and VC4&2) has been reported for short-range ordered V4C3 [63]. Assum-
b
c
a
d
e
f
Fig. 9. Surface of the diffuse intensity. (a) 3D model, (b)–(f) comparison of experimental SAED patterns and sections of the surface. (b) h100icub, (c) h110icub, (d) h111icub, (e) h012icub, (f) h013icub.
239
Real structure of Na3BiO4
ing these two types of clusters for b-Na3BiO4 seems reasonable since these are realized in the experimentally observed (ordered) structure III, i.e. a-Na3BiO4. This simple model of the real structure holds for constant diffuse intensity within the surface. However, characteristic deviations were observed by SAED recorded in selected regions of one crystal. The most common fluctuation of the diffuse intensity is connected with partial order of the real structure in one of the {111}cub layers, as described for the (001)trig layers of structure II. Consequently, the concentrations of the diffuse intensities are observed at the positions of superstructure reflections hkltrig (cf. structure II). These concentrations occur in different extent within one crystal, as depicted in Fig. 10a and c (left and center) for the zone axes h110icub and h013icub, respectively. For the h110icub pattern, the concen-
a
b
Fig. 10. SAED patterns of b-Na3BiO4. (a) SAED patterns recorded on shortrange ordered domains (left) and partially ordered domains (right) of the same crystal. (b) Twinning of partially ordered domains h100itrig. Left and right: h100itrig, center: superposition. (c) SAED patterns recorded on differently ordered domains of the same crystal. Left: short-range ordered domain h013icub, center: partially ordered domain [ 141]trig, right: ordered domain [212]mon. (d) SAED patterns of partially ordered ðh100itrigÞ and ordered domains ([ 101]mon).
c
d
trations (Fig. 10a, right) are exclusively observed on positions 1=2 hhhcub or 1=2 hhhcub. SAED patterns with simultaneous concentrations on both positions (Fig. 10b, center) were produced by twinning, as indicated by recording the diffraction patterns of the single domains sequentially, see Fig. 10b, left and right. The twinning can be rationalized by the symmetry relations between the aristotype of Na3BiO4 (i.e. structure I) and structure II. In a first step the symmetry of the aristotype is reduced to space group R3m which is a maximal t subgroup (index 4) of Fm3m (structure I). The c-axis of this trigonal unit cell is half of that assumed for structure II. Due to this symmetry reduction, a maximum number of four distinguishable orientations is expected for domains with average trigonal symmetry. In a second step (i2), the symmetry is reduced by doubling the c-axis. The coexistence of tilted domains
240 with h100itrig orientations is consistent with this scenario. Microdiffraction [60, 64] is a useful tool to analyze the number of concentrations on different 1=2 hhhcub-type positions by inspection of HOLZ (higher order Laue zone) patterns. These experiments support the SAED results, particularly, concentrations of the diffuse intensity in separated domains occur exactly on one 1=2 hhhcub-type position. The concentrations of the diffuse intensity in h013icub-patterns (Fig. 10c, center) are again observed on positions of superstructure reflections hkltrig. All concentrations can be interpreted according to the partial order as observed for Ca5Y4S11 (symmetry of the average structure: R 3m [60]). In that case, the 1=2 hhhcubtype concentrations originate from structural relaxation of the S atoms and partial order of cations and vacancies. That type of order is characterized by an alternation of the average metal atoms occupancy in consecutive (001)trig layers. In b-Na3BiO4 all metal positions are fully occupied, therefore, the alternation is due to the aggregation of Na and Bi atoms in every second (001)trig metal layer. As observed, this ordering involves concentrations of the diffuse intensities and significant splitting of the fundamental reflections. It should be noted, that besides the diffuse concentrations produced by a trigonal partial order, we also observed other types of diffuse intensity distributions in SAED patterns. Again, they break the uniform intensity distribution of a pure short-range ordered structure. Such deviations from the cubic intensity distribution can be examined by tilting experiments which demonstrate the differences in patterns which should be equivalent. A coexistence of short-range order, partial order and long-range order within microdomains can be verified by shifting the SAED aperture relative to the surface of one crystal. Following this strategy, the diffraction patterns of Fig. 10c were recorded on the same crystal. The different scattering phenomena in addition to the fundamental reflections (left: exclusively diffuse scattering, center: concentrations of the diffuse scattering, right: superstructure reflections) indicate the complex domain structure of Na3BiO4. Multiple twinning (cf. transformation matrices Q1,2) must be considered in order to rationalize possible orientations of coexisting domains. In Fig. 10d, the coexistence of partially ordered (left) and long-range ordered (right) domains in one crystal is presented for the zone axis h110icub. Due to the multiple twinning, the corresponding orientations of the domains are [100]trig and [101]mon. The different degree of order in neighboring domains can also be evidenced by Fourier transformation of HRTEM micrographs (not shown).
Structure models Several hypothetical structures were assumed in order to model different distributions of Bi and Na atoms. A first series of structures is based on a suitable supercell of structure II. The initial symmetry was chosen triclinic (space group: P1) which enables us to vary the metal atoms arrangement without symmetry restrictions. In a following step the real (higher) symmetry of the metal arrangements was determined. As a matter of principle, two
S. Vensky, L. Kienle, R. E. Dinnebier et al.
basic possibilities for the separation of the metal atoms in one of the {111}cub layers exist. The first one (space group: R3m, metrics of structure II) is designated structure IV. It is characterized by an alternation of pure Na and mixed Na/Bi (001)trig layers (ratio Na : Bi ¼ 1 : 1). This motif of alternating layers reminds of structure II and the a-NaFeO2-type structure [42, 43]. The second possibility (structure V, space group P3m1) is based on a complete separation of the metal atoms, i.e. the formation of pure Na and Bi layers in large supercells. A common feature of structures III and IV are ONa5Biand ONa4Bi2 octahedra, in cis and trans configurations of the Bi atoms. The cis arrangement produces a remarkably short interatomic distance dBi–Bi 3.36 A which is unfavorable with respect to the repulsion of Bi5þ. However, it is possible to generate structures (VI and VII) with optimized dBi–Bi by introducing trans configuration of the ONa4Bi2 octahedra [15]. These structures were described in space group P1, but they can be transformed to higher symmetry. Structure VI (Pm3m, a ¼ 4.716 A) reminds of the LiTiO2-type structure [65, 66], but the ratio of the metal atoms of 1 : 3 and 3 : 1 in alternating dense metal atom layers must be changed completely to 3 : 1, in the case of Na3BiO4. In contrast to structures III and IV, structure VI contains ONa6- and trans ONa4Bi2 octahedra at a ratio of 1 : 3. Structure VII (I4mm, a ¼ 4.715 A, c ¼ 9.434 A) contains ONa5Bi- and trans-ONa4Bi2 octahedra at a ratio of 1 : 1. As deduced from MAPLE calculations [15] (Madelung-part of the lattice energy) [67], a trans configuration of the ONa4Bi2 octahedra seems not to be the commanding criterion for the formation of ordered a-Na3BiO4. Nevertheless, it is possible that small domains with an optimized (i.e. trans) arrangement of the Bi atoms exist in the real structure. Therefore, structures VI and VII were included.
HRTEM The arrangement of Na and Bi atoms in the real structure was examined by means of HRTEM and image simulations based on the four structure models mentioned above. The thickness and defocus values of the simulations were chosen similar. Structure V requires large supercells with Bi atoms at least in every forth (001)trig layer. Such an ordering served for a first simulation of HRTEM micrographs. A close inspection of all experimental HRTEM micrographs gives evidence that neither this variant nor more complex ones of this type is present in Na3BiO4 – even not in nano-sized domains of the crystals. Hence, the real structure of Na3BiO4 does not consist of pure layers of Na and Bi atoms, but of mixed Na/Bi layers. Therefore, structure V can be ruled out. HRTEM micrographs recorded on areas with different orderings of the metal atoms are shown in Fig. 11. The simulated micrographs are based on structure IV (Fig. 11b) and structure III (Fig. 11c), respectively. Structural relaxation was neglected in all simulations. As a first approximation, the white dots in all simulated micrographs
241
Real structure of Na3BiO4
a
b
c
Fig. 11. HRTEM micrographs and FFTs of differently ordered domains. (a) Domain with shortrange order, (b) Partially ordered domain with simulation based on structure IV (h100itrig, Df ¼ 15 nm, thickness: 1.5 nm). (c) Ordered domain with simulation based on structure III ðh101imon, Df ¼ 15 nm, thickness: 2.0 nmÞ.
(Df ¼ 15 nm) correlate with high values of the projected potential, hence, mainly with positions strongly occupied by Bi atoms. A distinct interpretation of wide areas of HRTEM micrographs is not possible in the case of domain crystals. The reconstruction of the 3D real structure from the 2D information of HRTEM micrographs are not interpretable in terms of a defined real structure due to unsystematic superposition of differently ordered and orientated domains in the course of tilting experiments. However, a qualitative interpretation of the 2D metal atoms arrangement of separated and thin microdomains is possible. This had been checked for all four assumed structure models in the zone axis h110icub of the aristotype
(similar parameters for all simulations). For a distinct assignment of the projections (HRTEM micrographs) to a 3D metal atoms arrangements, twinning must be taken into account as one of the h110icub correspond to a defined set of zone axis in structures IV–VII. As the main result of the simulations, only two types of characteristic simulated patterns of white dots exist: 1) Zigzag patterns of white dots along h100icub. This pattern is characteristic for the projection of structure III along zone axis [101]mon, cf. Fig. 11c. 2) White contrasts in every second consecutive line which correlate with traces of {100}cub layers (not shown). This pattern is characteristic for all
242 orientations of structure VI and was not observed in the HRTEM micrographs. Therefore, structure VI has to be excluded and ordering of ONa6- and ONa4Bi2 octahedra with trans configuration of the Bi atoms (optimized dBiBi, see above) can be discarded by the HRTEM observations. Experimentally, only type 1 patterns were observed in separated microdomains (see Fig. 11c). A formation of consecutive lines with white contrast corresponding to traces of {111}cub layers – not {100}cub, cf. type 2 – is the most frequently observed pattern in h110icub images (cf. Fig. 11b). However, this pattern is not specific for one 3D arrangement of the metal atoms. The extent and separation of such {111}cub-ordering is quite different, as shown by Fig. 11a and b. In both images, the dominating motifs are white contrasts in every second trace of {111}cub layers. In Fig. 11a, partial order of the structure is not significant as both types of {111}cub traces form alternating lines with white spots. In the FFT, no concentrations of diffuse intensities occur. In Fig. 11b, one of the {111}cub layers is preferably occupied by Bi atoms. Hence, the local structure is characterized by partial order, as evidenced by the FFT (see concentrations of the diffuse scattering). In Fig. 11c, the zigzag patterns expected for the monoclinic order (structure III) are clearly visible. As images like Fig. 11a and 11b are representative for b-Na3BiO4, it seems at least probable that the motif of alternating {111}cub layers is a typical feature of the 3D real structure. The precise occupancies of the metal positions within the microdomains cannot be derived from HRTEM, however, a more pronounced ordering of the metal atoms than derived from Rietveld refinement has to be assumed. For the interpretation of HRTEM micrographs, image processing is a useful tool and gives additional evidence for the partial order. Information about the sizes of the domains and their relative orientations can be obtained by applying a Fourier filter which extracts the diffuse concentrations for the inverse Fourier transformation (see circles in the FFT of Fig. 12a). The resulting image may show artifacts due to the filtering. Yet, it verifies clearly the presence of microdomains (average diameter < 50 nm), cf. Fig. 12a. Additionally, a second feature of the real structure is clearly visualized, i.e. the formation of antiphase boundaries between the microdomains, see arrows in Fig. 12a highlighting a defined shift of t ¼ 1=2 ctrig between neighboring domains. The formation of antiphase boundaries is interconnected with the ordering of the metal atoms. Like the twinning, this feature of the real structure can be rationalized by the group-subgroup relations (see above, second step (i2)). The micrograph and the simulations in Fig. 12b demonstrate the amount of the ordering in two neighboring microdomains. Simulation 1 is characterized by a uniform distribution of the contrasts corresponding with the random distribution of Na and Bi atoms of structure I. Simulation 2 shows alternating lines of gray and white spots perpendicular to [001]trig correlating with the alternating Na and Na/Bi layers of structure IV. In the experimental micrograph both characteristics, alternation and uniform distribution is observed. The first within separated microdomains (cf. simulation 2), the second in the superpositioned area between antiphase domains. Hence, the uniform distribu-
S. Vensky, L. Kienle, R. E. Dinnebier et al.
a
b Fig. 12. HRTEM on domain crystals of b-Na3BiO4. (a) Processed image for partially ordered domains (see text) with FFT. (b) HRTEM micrograph (non processed image) of partially ordered domains with simulations (simulation 1: h110icub, Df ¼ 10 nm, thickness: 1.5 nm, simulation 2: h100itrig, Df ¼ 10 nm, thickness: 1.5 nm).
tion of the contrasts (simulation 1, structure I) is produced by averaging of partially ordered microdomains.
Conclusion We have investigated the average and the real structure of b-Na3BiO4 using high resolution X-ray powder diffraction, pair distribution function analysis, and high resolution transmission electron microscopy. The tools employed show specific weaknesses and strengths, each. Evaluation of Bragg powder reflexions, provides insights into the average structure only, while Fourier transformations of the total scattering, still integrating over the whole sample, provide the average local pair interactions. Finally, HRTEM images local defect structures, but does not give the statistical weights with which specific defect patterns occur. Thus, it is not coming as a surprise, that, at a first glance, the different techniques applied are producing different and even deviating structural information. However, HRTEM and PDF are in good agreement. Fitting the measured Bragg intensities of the powder pattern result in a rock salt structure with a slight trigonal distortion with respect to the cubic unit cell. This symme-
243
Real structure of Na3BiO4
try reduction is caused by a partial ordering of the cations. Along [001]trig, corresponding to [111]cub, layers containing random distribution of the Naþ and Bi5þ cations, however, with slightly varying Na : Bi ratios follow each other alternatingly. Thus, the average structure is coming very close to the a-NaFeO2 type of structure. Fitting the total scattered intensity, is basically confirming the results of the Rietveld refinement. However, there are discrepancies concerning the Na : Bi ratios for the two crystallographically different cationic positions. This can be traced back to a larger amount of local structure information revealed by the total scattering experiment. In addition, the HRTEM results document a complex domain structure within single cristallites. Three different local structures are found. One corresponds to the ideal rock salt structure with short-range order of the cations. The second is based on the ordered crystal structure of a-Na3BiO4 with defined atomic positions for the sodium and bismuth atoms. The third, which represents the majority of the investigated grains, matches what has been found as the average crystal structure of b-Na3BiO4 by PDF analysis with approximately pure sodium and mixed sodium-bismuth layers. Taking into account the many stacking faults of this highly distorted crystal structure, it is evident that superpositions of these local structures yield the average structure, as found by Rietveld analysis. No indication for fully ordered sections/regions which would comprise a cation sequence of Na/Na/Na/Bi were detected which is in full agreement with electrostatic reasoning. The results of the structural studies shed light on the way how b-Na3BiO4 forms. It can be assumed that at the conditions of electrocrystallization a rock salt structure forms with the cations randomly distributed. During cooling, the partially ordered structure of b-Na3BiO4 is obtained, while the totally ordered form of a-Na3BiO4 occures while annealing, or by solid state synthesis. It has been shown that even with the lack of crystals suitable for single crystal X-ray diffraction, a detailed analysis of the real structure of highly disordered materials is possible using a complementary methodical approach of electron microscopy and high resolution diffraction techniques. Acknowledgments. Special thanks go to Viola Duppel for her assistance of the TEM measurements as well as to Sanela Kevric´ for her assistance in sample preparation. Thanks also go to Dr. Alexander Hannemann and Zeljko Cˇancˇarevic´ for visualizing the P* surface, Dr. Christian P. M. Oberndorfer for conducting the thermal analysis, Eva-Maria Peters for the SEM images, and to Prof. Dr. Dr. h.c. mult. Arndt Simon for providing time at his TEM. SJLB and AM would like to thank Drs. Doug Robinson and Didier Wermeille for help in collecting the PDF data. Work in the Billinge group was supported by NSF through grant DMR-0304391. Research was carried out in part at beamline X17B1 of the National Synchrotron Light Source, Brookhaven National Laboratory, which is supported by the U.S. Department of Energy, Contract No. DE-AC02– 76CH00016. PDF experiments were carried out at sector 6 of the Advanced Photon Source (APS). Sector 6 is supported by the USDOE through the Ames Laboratory under Contract No. W-7405Eng-82. The APS is supported by DOE under contract W-31-109Eng-38. Financial support by the Deutsche Forschungsgemeinschaft (DFG), the Bundesministerium fu¨r Bildung und Forschung (BMBF), and the Fonds der Chemischen Industrie (FCI) is gratefully acknowledged.
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