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

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