The real structure of Na3BiO4 by electron ... - Columbia University

Z. Kristallogr. 220 (2005) 231–244 231
# by Oldenbourg Wissenschaftsverlag, München
The real structure of Na3BiO4 by electron microscopy,
HR-XRD and PDF analysis
Sascha Vensky I , Lorenz Kienle I , Robert E. Dinnebier I , Ahmad S. Masadeh II , Simon J. L. Billinge II and Martin Jansen*,I
I Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
II Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
Dedicated to Professor Dr. Hans-Jörg Deiseroth on the occasion of his 60 th 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: m.jansen@fkf.mpg.de)
[M(NH3)6] C60 6NH3 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 S. Vensky, L. Kienle, R. E. Dinnebier et al.
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/cm 2 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 b-
Na3BiO4 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-
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) 295 295
Space group (No.) P2/c(13) R3m(166)
Z 2 6
a (in A) 5.87(1) 3.32141(9)
b (in A) 6.69(6) ¼ a
c (in A) 5.65(0) 16.4852(5)
a (in ) 90 90
b (in ) 109.8 90
g (in ) 90 120
V (in A) 208.8(19) 157.50(1)
Rp (in %) 12.7
Rwp (in %) 14.4
RF (in %) 25.8
R F 2 (in %) 29.9

Real structure of Na3BiO4
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 Rietveld URietveld UPDF (sof values fixed to
Rietveld values)
dinates, temperature factors, and fractional occupancies are
given in Table 2 1 .
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
1 Further details of the crystal structure investigation of b-
Na3BiO4 can be obtained from the Fachinformationszentrum Karlsruhe,
D-76344 Eggenstein-Leopoldshafen, Germany, (fax: (+49)7247-
808-666; e-mail: crysdata@fiz.karlsruhe.de) on quoting the depository
numbers CSD-414158.
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
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).
Results and discussion
sof PDF UPDF UPDF
Rmax (A) 20 20 20 6
Bi(1) 0 0 0 0.206(1) 0.0113(3) 0.0112(4) 0.081(15) 0.0111(6) 0.01095(14)
Na(1) 0 0 0 0.794(1) 0.0113(3) 0.0112(4) 0.919(16) 0.0111(6) 0.01095(14)
Bi(2) 0 0 1
=2 0.294(1) 0.0113(3) 0.0112(4) 0.419(16) 0.0111(6) 0.01095(14)
Na(2) 0 0 1
=2 0.706(1) 0.0113(3) 0.0112(4) 0.581(16) 0.0111(6) 0.01095(14)
O 0 0 0.2407(6) 1.0 0.037(2) 0.0242(7) 1.0 0.0203(5) 0.0306(10)
a
b
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
233
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-

234 S. Vensky, L. Kienle, R. E. Dinnebier et al.
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,
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.
where pure sodium and iron cation layers alternate, in b-
Na3BiO4 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 Bi 5+ . 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 R3m (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.

Real structure of Na3BiO4
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
where
GðrÞ ¼ 2
p
ð1
0
Q½SðQÞ 1Š sin Qr dQ ;
Q ¼ 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 ¼QðSðQÞ 1Þ; to a Qmax of
25.0 A 1 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 A 1 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 A 1 was refined
within the crystallographic model of b-Na3BiO4 as described
in the chapter above. The constraints of space
group R3m 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
235
(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 00 1 =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 00 1 =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 00 1 =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 00 1 =2. However, the local
structure refinement indicates clearly that Bi atoms preferredly
localized at 00 1 =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 00 1 =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
00 1 =2-site atoms, with the triangle rotated 60 degrees, form
the opposite face of the same octahedron. According to
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 00 1 =2.
a
b
c

236 S. Vensky, L. Kienle, R. E. Dinnebier et al.
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 00 1 =2.
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 (00 1 =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: Fm3m, 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-
a
b
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 1
u
@ v A
w
trig
¼ Q1
0 1
u
@ v A
w
cub
0
4=3
B
¼ @ 2=3
2=3
2=3
1 0 1
2=3 u
C
4=3 A @ v A
1=6 1=6 1=6 w
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 1
u
@ v A
w
mon
¼ Q2
Electron diffraction
0 1
u
@ v A
w
trig
cub
0
0
B
¼ @ 1=4
0
1=4
1 0 1
3 u
C
0A@vA
1=2 1=2 1 w
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
trig

Real structure of Na3BiO4
a
b
Fig. 8. SAED patterns of multiply twinned domains of the same crystal. (a) SAED patterns of separated domains. Left and center: h101imon,
right: [111]mon. (b) Superpositions of two rotated h101imon, (left) and of [101]mon with [111]mon (right).
two regions with different superpositions are shown (left:
two rotated h101imon, 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
237
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].

238 S. Vensky, L. Kienle, R. E. Dinnebier et al.
Applying this model to our problem, the structure of b-
Na3BiO4 would be considered to contain centered ONaxBi6 x
octahedra (i.e. clusters) which represent the smallest ordered
building units of the structure. Following generalized
electrostatic valence rules [61, 62], one would expect
a
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
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.

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-
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).
a
b
c
d
239
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 S. Vensky, L. Kienle, R. E. Dinnebier et al.
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: R3m [60]). In that case, the 1 =2hhhcubtype
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
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 unfa-
vorable with respect to the repulsion of Bi 5þ .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

Real structure of Na3BiO4
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
a
b
c
241
(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 S. Vensky, L. Kienle, R. E. Dinnebier et al.
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 dBi Bi, 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-
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-

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 Na þ and Bi 5þ 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 Kevrić for her
assistance in sample preparation. Thanks also go to Dr. Alexander
Hannemann and Zeljko Čančarević 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 US-
DOE through the Ames Laboratory under Contract No. W-7405-
Eng-82. The APS is supported by DOE under contract W-31-109-
Eng-38. Financial support by the Deutsche Forschungsgemeinschaft
(DFG), the Bundesministerium für Bildung und Forschung (BMBF),
and the Fonds der Chemischen Industrie (FCI) is gratefully acknowledged.
References
243
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