Anomalous lattice parameter increase in alkali earth aluminium substituted tungsten defect pyrochlores

Article abstract of DOI:10.1016/j.jssc.2008.11.014

The structures of the defect pyrochlores AAl_0.33W_1.67O₆ where A=K, Rb or Cs have been investigated using X-ray and neutron powder diffraction methods as well as the ab initio modelling program VASP. The three cubic pyrochl

Full text of DOI:10.1016/j.jssc.2008.11.014

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Journal of Solid State Chemistry 182 (2009) 457–464
Contents lists available at ScienceDirect
Journal of Solid State Chemistry
journal homepage: www.elsevier.com/locate/jssc
Anomalous lattice parameter increase in alkali earth aluminium substituted
tungsten defect pyrochlores
Ã
Gordon J. Thorogood a,b, , Brendan J. Kennedy b, Vanessa K. Peterson c, Margaret M. Elcombe c,
Gordon J. Kearleyc, John V. Hanna a, Vittorio Luca a
a Institute of Materials Engineering, Australian Nuclear Science and Technology Organisation (ANSTO), Lucas Heights, NSW 2234, Australia
b School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia
c Bragg Institute, Australian Nuclear Science and Technology Organisation (ANSTO), Lucas Heights, NSW 2234, Australia
a r t i c l e i n f o
a b s t r a c t
Article history:
The structures of the defect pyrochlores AAl0.33W1.67O6 where A ¼ K, Rb or Cs have been investigated
using X-ray and neutron powder diffraction methods as well as the ab initio modelling program VASP.
The three cubic pyrochlores exhibit a non-linear increase in lattice parameter with respect to ionic
radius of the A cation as a consequence of displacive disorder of the A-type cations. Solid state 27Al MAS
Received 15 August 2008
Received in revised form
23 October 2008
Accepted 2 November 2008
Available online 20 November 2008
NMR studies of this pyrochlore system reveal shifts in the
dꢀ21–22 ppm range that are indicative of
pseudo-5 coordinate Al environments and emanate from distorted Al octahedral with one abnormally
long Al–O bond. Solid state 39K, 85Rb, 87Rb and 133Cs MAS and static NMR studies reflect the local cation
disorder demonstrated in the structural studies.
Keywords:
Oxides
Neutron scattering
X-ray diffraction
Modelling
& 2008 Elsevier Inc. All rights reserved.
VASP
Solid state NMR
1. Introduction
of formula A2O0. These two networks only interact weakly and
vacancies in the A2O0 network are common place and defect
pyrochlores such as Pb2Ru2O6.5 [9] KOs2O6 [5], and (NH4)NbWO6
[10] are regularly encountered. In these defect pyrochlores the
A-type cations bond to six-oxygen atoms from the puckered
hexagonal rings formed by the B2O6 network. Charge balance of
the pyrochlore can be achieved either by combinations of different
valences for the A and B cations, or by vacancies in the A2O0
network. It is this compositional flexibility of the pyrochlore
structure that makes these oxides potentially attractive for many
applications in materials chemistry.
Oxides exhibiting the pyrochlore structure display a large
variety of physical properties including catalytic activity, piezo-
electric behaviour, ferro- and ferrimagnetism, and giant magne-
toresistance [1,2]. Other pyrochlores exhibit a range of electrical
and ionic conductivities [3], that include metallic, semiconducting
and superconductivity [4,5]. Because pyrochlores possess such a
wide range of properties they have been utilised in many
applications including the immobilisation and treatment of
nuclear waste [6,7]. Pyrochlores have also been reported to
undergo order/disorder transformations upon heating [8]; this
property is potentially important as the amount of disorder of the
A cation may have an influence on the ion exchange properties of
the material.
The ideal A2B2O6O0 pyrochlore structure has cubic Fd3m
symmetry with each of the four atoms occupying special
1
positions, the A-type cations on 16c at ð2; 12; 21Þ, the B cations on
3
16d at (0,0,0), the O on 48f at ðx; 18; 81Þ and O0 on 8b at ð8; 38; 38Þ. In a
number of recent studies, including that of Whittle et al. [7] of the
defect pyrochlores CsB0.5W1.5O6 (BQTi, Zr, Hf), displacive dis-
order of the A-cations in the /111S planes has been observed
[11–18].
The general formula of pyrochlore oxides is A2B2O7, although
this can also be written as A2B2O6O0 or B2O6 A2O0 to highlight the
two interpenetrating networks [1]. The corner-shared BO6
octahedra form a B2O6 network that intersects with A–O0 chains
The importance of such disorder is now being realised.
For example displacive disorder is believed to contribute to the
high relative permittivities displayed by (Bi,Zn)2(Zn,Nb)2O7 that
makes these materials attractive for use as capacitors [11,12].
Neutron and X-ray diffraction studies suggest that the disorder
involves displacement of the A-cation along the six /112S or
Ã
Corresponding author at: Institute of Materials Engineering, Australian Nuclear
Science and Technology Organisation (ANSTO), Lucas Heights, PMB 1, Menai, NSW
2234, Australia. Fax: +612 95437179.
E-mail address: gordon.thorogood@ansto.gov.au (G.J. Thorogood).
0022-4596/$ - see front matter & 2008 Elsevier Inc. All rights reserved.
doi:10.1016/j.jssc.2008.11.014

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133
5
7
/110S directions [14–16]. Previously we have described diffuse
scattering in electron diffraction patterns of CsTi0.5W1.5O6 pyro-
chlores [19] that suggests there are strong local correlations
among the disordered ions. Withers has suggested that the O0A4
tetrahedra within the pyrochlore average structure type rotate as
essentially rigid bodies with the O0 anions remaining in the centre
of the tetrahedra [14].
quadrupolar nature of these nuclei (27Al ðI ¼ 2Þ,
Cs ðI ¼ 2Þ, 87Rb
85
ðI ¼ 2Þ, Rb ðI ¼ 2Þ) necessitated that flip angles be close to the
3
5
condition [22,23]
1
ðI þ 2Þorf tpp
p=6
For the 27Al MAS NMR measurements, a non-selective
time of 5.0 s was measured on a 1.0 M Al(NO3)3 solution from
which a selective pulse time of 0.6 s was selected for data
p/2 pulse
3
Movement of the 48f O anion away from x ¼ reduces the
m
8
interaction between the two networks and so may influence
the magnitude of the displacive disorder of the A-cation. The
synthesis of AAl0.33W1.67O6 was first reported by Le Flem et al. [20]
and KAl0.33W1.67O6 ꢁ nH2O was included in the study of KBxW2ꢂxO6
(B ¼ Al, Ti and Ta) oxides by Subramanian et al. [21]. The aim of
our work was to examine the nature of the A cation disorder with
respect to ionic radius in the series AAl0.33W1.67O6 (where A ¼ K,
Rb, Cs) and to establish if this is correlated with the movement or
displacement of the O0 at the 8b position, and to probe the
m
acquisition on all solid samples. Relaxation delays of 3 s were
typically used; the quantification and speciation of these data
were verified with experiments that had delays extending to 30 s.
All 27Al chemical shifts were referenced to 1.0 M Al(NO3)3 that was
set to
calibrated on 1.0 M CsCl solution from which a non-selective
pulse time of 6 s was measured, with a subsequent selective
pulse time of 0.6 s employed for data acquisition. Typical
d
0.0 ppm. The 133Cs MAS NMR pulse conditions were
/2
p
m
m
possibility of local (short-range) ordering between the Al and W
relaxation delays were 3 s, however checks for abnormally long
T1s were undertaken with recycle delays of up to 60 s being
implemented. All 133Cs chemical shifts were referenced to 1 M
+
˚
˚
cations. The ionic radius, r, of K with 8-fold coordination is 1.51 A
+
and this increases, essentially linearly down group 1, Rb is 1.61 A
and Cs , 1.74 A. The X-ray diffraction patterns reveal a non-linear
+
˚
CsCl that was set to
d
0.0 ppm. Similar 87Rb and 85Rb MAS NMR
increase in the a lattice parameter as the A-cation size was
increased in the pyrochlore AAl0.33W1.67O6. We have used a
combination of neutron and X-ray diffraction data in a joint
Rietveld refinement to locate the positions of the A cations and 48f
oxygen and the site occupancies of the aluminium atoms.
experiments were performed, with pulse conditions for these
nuclei being calibrated on solid RbCl. For the 87Rb measurements,
a non-selective
pulse time of 0.6
calibrated with a non-selective
which a selective pulse time of 0.6
p
/2 pulse time of 3.5
s was used, while the 85Rb measurements were
/2 pulse time of 6.0 s from
s was chosen. Relaxation
ms from which a selective
m
p
m
m
delays of 3 s were employed for these nuclei, with both 87Rb and
85Rb chemical shifts being referenced to 0.01 M RbCl via the
2. Experimental
secondary solid RbCl standard (d 126.8 ppm).
Static (broadline) 39K NMR data were acquired at a 39K
frequency of 18.67 MHz. Data was acquired in a standard dual-
2.1. Synthesis
The appropriate stoichiometric amounts of KNO3, RbNO3,
CsNO3, Al(OH)3 and WO3 were mixed, calcined in air at 500 1C,
ball milled in cyclohexane for 12 h and then sintered in air or
vacuum at 750 1C for 12 h. The intended stoichiometries of the
samples were KAl0.33W1.67O6, RbAl0.33W1.67O6 and CsAl0.33W1.67O6.
Attempts were made to synthesise Na0.5K0.5Al0.33W1.67O6 to access
a smaller effective A cation radii; this material however yielded a
single phase hexagonal structure and was not examined further.
channel 7.5 mm solenoid coil probe with the
solid echo sequence with an extended phase cycle to minimise
echo distortion [24]. A non-selective /2 pulse time of 12.0 s was
calibrated on solid KCl, from which selective echo pulse times of
2.0 s were used. Relaxation delays of 5 s were implemented,
with 39K chemical shifts being referenced to 0.1 M KCl via the
secondary solid KCl standard ( 48.0 ppm).
Due to the disordered nature of the materials studied, all 27Al,
133Cs, 87Rb, 85Rb and 39K apparent shifts
are reported as
y–t1–y–t2-acquire
p
m
y
m
d
d
centre-of-gravity measurements and remain uncorrected for
second order quadrupolar effects unless specifically reported as
isotropic chemical shift values diso obtained from simulation or
graphical methods.
2.2. TGA/DTA
Simultaneous thermogravimetric analysis (TGA) and differen-
tial thermal analysis (DTA) were performed on a Setaram TAG 24
(Setaram, France). Approximately 10 mg of each powder was
placed on a platinum crucible and heated to 800 1C at a rate of
5 1C minꢂ1 in flowing air.
2.5. X-ray diffraction
Powder X-ray diffraction measurements were made using a
Panalytical X’Pert Pro X-ray diffractometer equipped with a Real
Time Multiple Strip (RTMS) X’celerator detector covering a solid
2.3. Electron microscopy
angular range of 21 at 25 1C using CuK
sample holder and an Anton Paar TTK 450 sample cell. Data of
sufficient quality for structural refinement were collected over
a radiation, a flat-plate
A JEOL JSM6400 scanning electron microscope (SEM) equipped
with a Noran Voyager energy-dispersive X-ray spectroscopy system
(EDS) was operated at 15 keV for microstructural analysis work.
101o2yo801, in 0.0171 steps, with an equivalent acquisition time
of 1000 s per step. Structures were refined by the Rietveld method
using the program RIETICA [25].
2.4. Solid state NMR
High resolution 27Al, 133Cs, 87Rb and 85Rb magic-angle-
spinning (MAS) NMR data were acquired at ambient temperatures
on a Bruker MSL-400 spectrometer (B0 ¼ 9.4 T) operating at the
27Al, 133Cs, 87Rb and 85Rb frequencies of 104.23, 52.46, 130.90 and
38.60 MHz, respectively. All one-dimensional data were acquired
with single pulses (Bloch decay) using a Bruker 4 mm double-air-
bearing probe using typical MAS rates of 15 kHz. For quantitative
estimates of the central transition intensities to be made, the
2.6. Neutron diffraction
Neutron powder diffraction data were collected, during
commissioning, on Wombat, the high intensity powder diffract-
ometer at the Open Pool Australian Light water reactor (OPAL)
facility at the Australian Nuclear Science and Technology
Organisation (ANSTO) [26]. Room temperature data was acquired

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459
over 3 min using an area detector from 22.751o2
y
o142.551, pixel
[21] although in that study KAl0.33W1.67O6 was reported to contain
2
˚
spacing 0.1251. The incident wavelength was 1.2212(1) A deter-
mined using the NIST Al2O3 standard, which refined with well
acceptable crystallographic parameters. The data had the back-
ground from an empty can subtracted before correction for
only 0.9% H2O, ꢀ3 of the value seen in the current study. The
percentage weight loss of 1.4% is equivalent to an n value of ꢀ0.35
if the formula is written as KAl0.33W1.67O6 ꢁ nH2O.
The change in slope of the KAl0.33W1.67O6 data at ꢀ150 1C is
thought to be related to the kinetics of dehydration, most of the
water has been removed from the structure at this point.
Subramanian et al. [21] reported that KAl0.33W1.67O6 could be
fully dehydrated by heating to 125 1C. No phase change was
observed over the temperature range investigated.
detector efficiency determined from a vanadium pattern.
A
curvature correction algorithm was then applied to the data, and
the data were reduced to 1 dimension by vertically summing over
the central third of the area detector.
2.7. Modelling
3.2. Diffraction
Modelling of the system was performed by ab initio quan-
tum–mechanical density functional theory (DFT) via the Vienna
Ab initio Simulation Package (VASP). For our purposes we used
VASP 4.6 planewave DFT code running on ACAPAC SGI Altix
3700B ꢃ 2 cluster. This configuration used 32 nodes and took
between 1 and 5 h real time per energy minimisation. Minimisa-
tion was achieved using a quasi-Newton algorithm with all atoms
free to relax, but the unit-cell parameters constrained to the
experimental values. Characteristics of the simulation were as
follows: Two k-points (000,111) in reciprocal space. Energy
cutoff ¼ 600 eV; Convergence for the self-consistent field (SCF)
was 1.0 ꢃ10ꢂ6 eV; Convergence limit for energy minimisation was
1.0 ꢃ10ꢂ7 eV; The Perdew–Burke–Ernzerhof (PBE) exchange cor-
relation functional was used along with projector augmented
wave (PAW) pseudopotentials.
Analysis of the X-ray diffraction patterns from the three
samples shows that they do not display a linear increase in the
a lattice parameter, with respect to A cation size (Fig. 2). This is
contrary to the results reported by Le Flem et al. [20] although Le
Flem did not account for the adsorption of H2O in the sample
containing K. This trend in lattice parameter is counter intuitive as
the ionic radii increases, essentially linearly, down group 1 from
+
+
+
˚
˚
˚
1.51 A in K to 1.61 A for Rb and 1.74 A in Cs . The possibility that
the increased lattice parameter in KAl0.33W1.67O6.0.35H2O is solely
a
consequence of the absorbed water was discounted by
measurements after dehydrating the sample at 200 1C for
30 min. It can be clearly seen in Fig. 2 that the lattice parameters
still do not vary linearly with ionic radii.
Phase analysis of the X-ray diffraction patterns from each of
the compounds indicate slight contaminant phases in some of the
materials, the results of which are summarised in Table 1. It is
evident from this table that only for RbAl0.33W1.67O6 was it not
possible to prepare single phase samples. Analytical microscopy
results of the RbAl0.33W1.67O6 sample yielded a stoichiometry of
the major pyrochlore phase in agreement with the desired
composition.
3. Results
3.1. Characterisation
TGA shows a ꢀ1.4% weight loss for the KAl0.33W1.67O6 sample
and ꢀ0.4% weight loss for RbAl0.33W1.67O6 and CsAl0.33W1.67O6,
indicating that there is a small amount of water associated with
the structure of KAl0.33W1.67O6, Fig. 1. The uptake of H2O by
KAl0.33W1.67O6 has been previously reported by Subramanian et al.
The structures of the three samples were refined in space
group Fd3m using a combination of powder X-ray and neutron
Fig. 2. Plot of a lattice parameter versus ionic radius for AAl0.33W1.67O6 ꢁ nH2O. The
circles are from the as-prepared samples and the squares after drying at 200 1C for
30 min. The diamonds are the results from La Flem [20]. The larger difference
between the as-prepared and dried samples reflects the greater water content in
this sample. Note error bars are smaller in dimension than data point markers.
Fig. 1. Plot of weight loss versus temperature for KAl0.33W1.67O6 (K), RbAl0.33W1.67O6
(Rb), and CsAl0.33W1.67O6 (Cs). The small anomalies in the RbAl0.33W1.67O6 and
CsAl0.33W1.67O6 data at ꢀ100 and ꢀ150 1C are an instrumental artefact.

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Table 1
Stoichiometry attempted at various environments and resultant phases, estimated using powder X-ray diffraction.
Stoichiometry
Air sinter, phases present
Vacuum sinter in quartz, phases present
Na0.5K0.5Al0.33W1.67O6
Hexagonal Na0.5K0.5Al0.33W1.67O6
Unknown Na3AlW3O12 ꢀ50%
Hexagonal Na0.5K0.5Al0.33W1.67O6 ꢀ50%
KAl0.33W1.67O6
RbAl0.33W1.67O6
CsAl0.33W1.67O6
Pyrochlore KAl0.33W1.67O6
Hexagonal KAl0.33W2.67O9 ꢀ10%
Unknown K2W4O13 ꢀ90%
Pyrochlore RbAl0.33W1.67O6 ꢀ95%
Orthorhombic Rb15W45.5O144 ꢀ5%
Pyrochlore RbAl0.33W1.67O6 ꢀ75%
Orthorhombic Rb15W45.5O144 ꢀ25%
Pyrochlore CsAl0.33W1.67O6 ꢀ98%
Cubic Cs2O ꢀ2%
Pyrochlore CsAl0.33W1.67O6
Fig. 3. Top: Observed (crosses), calculated and difference (lower solid line) X-ray diffraction patterns of KAl0.33W1.67O6 sintered in air. The vertical black markers show the
positions of the Bragg reflections. Below: Neutron Diffraction data of KAl0.33W1.67O6 sintered in air. The higher than expected background is due to the presence of water in
the sample.
diffraction data (Fig. 3). In these refinements the W and Al were
assumed to statistically occupy the 16c site.
TGA studies and the contraction in the lattice upon heating. The
neutron diffraction data were not of sufficient quality to establish
the precise position of these small amounts of water.
Selected atomic parameters and inter-atomic distances from
the refinements are given in Table 2 and 3. It is possible that short
range order of the Al/W cations is responsible for the larger than
typical displacement parameters for the 16c cations.
In the refined model the A-cation was initially located at the 8b
site at 38; 38; 38. This is positioned in the centre of the channels
running along the [111] direction and places the A-type cation
mid-way between two puckered O6 hexagons. Invariably this
model resulted in unacceptably high displacement parameters,
2
˚
Biso45 A . Equally important the Bond Valence Sums of the
The refined value of x for the O(1) site indicates compression of
the octahedra in the [111] direction. The displacements of the
A-cation was unacceptably low (approximately less than 0.77)
although that of the W and Al appeared reasonable. Recall that
there are two common reasons for the observation of large atomic
displacement parameters, namely the presence of vacancies or the
displacement of the atom away from the designated site. A-cation
vacancies should not impact on the BVS of the A-type cations.
Further the analytical microscopy did not indicate the existence of
appreciably non-stoichiometry of the A-cation. Consequently the
occupancy of this was fixed at the nominal stoichiometry in the
refinements. A number of displacement models were investigated
including placing A at 0; x; x and the most stable results were
obtained if A was placed at x, x, x with xꢀ0.3445 for the K
compound, similar results were obtained for the other two oxides
studies. There is some water in the structures as evident from the
333
A-type cation from the 8b site at ð888Þ decreased as the size of the
A-cation increased KoRboCs, illustrating that the A cation radius
had a systematic impact.
3.3. Electron microscopy
The scanning electron micrographs showed the samples
contain well shaped single crystals, together with variable
amounts of less well structured material. These particles were
ꢀ10
mm in size and an example of which is given in Fig. 4.
Analytical microscopy suggested that the air sintered K sample
and the vacuum sintered Cs sample only contained the pyrochlore

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461
Table 2
Selected atomic parameters for the most phase pure samples.
2
˚
Atom/site
x
y
z
N
B(iso) A
˚
KAl0.33W1.67O6 a ¼ 10.1808(1) A
K 32e
Al 16c
W 16c
O 48f
0.3445(6)
0.000
0.3445(6)
0.000
0.3445(6)
0.000
0.038
0.007
0.069
0.2500
3.3(5)
3.45(4)
3.45(4)
1.12(4)
0.000
0.000
0.000
0.3121(2)
0.125
0.125
˚
RbAl0.33W1.67O6 a ¼ 10.1726(2) A
Rb 32e
Al 16c
W 16c
O 48f
0.3569(3)
0.000
0.3569(3)
0.000
0.3569(3)
0.000
0.038
0.007
0.069
0.2500
3.1(4)
3.90(5)
3.90(5)
1.13(3)
0.000
0.000
0.000
0.3120(2)
0.125
0.125
˚
CsAl0.33W1.67O6 a ¼ 10.207(1) A
Cs 32e
Al 16c
W 16c
O 48f
0.3618(7)
0.000
0.3618(7)
0.000
0.3618(7)
0.000
0.038
0.007
0.069
0.2500
1.8(8)
3.4(1)
3.4(1)
1.09(4)
0.000
0.000
0.000
0.3106(3)
0.125
0.125
K (XRD) Rwp ¼ 6.97%, and Rp ¼ 5.53% (ND) Rwp ¼ 8.92%, and Rp ¼ 7.06%; Rb (XRD)
Rwp ¼ 5.67%, and Rp ¼ 4.51%(ND) Rwp ¼ 10.93%, and Rp ¼ 8.47%; Cs (XRD)
Rwp ¼ 6.73%, and Rp ¼ 5.25% (ND) Rwp ¼ 14.47%, and Rp ¼ 10.76%.
Table 3
Fig. 4. SEM of KAl0.33W1.67O6.
Selected bond angles, distances and bond valence sums (BVS) for the most phase
pure samples.
remained very close to the centre of the octahedra. In all models
the tungsten is displaced from the centre of the octahedra giving a
slightly reduced bond valence sum (down by 0.2 in the Rb
compound), and the A cations show a small displacement from
Sample
Framework atoms
W–Oa
W–O–W
K–O
ꢃ 6
ꢃ 3
1.9076 (8) A
BVS W 6.29(1)
BVS Al 3.032(7)
BVS K 0.70(1)
˚
KAl0.33W1.67O6
150.231(8)
˚
2.908 (5) A
333
the ð888Þ position but about half that estimated from the structural
refinement and not in any specific direction. Bond valence sums
˚
RbAl0.33W1.67O6
W–O
ꢃ 6
ꢃ 3
1.9059 (7) A
BVS W 6.32(1)
BVS Al 3.049(6)
BVS Rb 0.85(1)
333
for the Rb at (x,x,x) are 0.85 where as at the ð888Þ position they
W–O–W
Rb–O
155.441(2)
drop by around 10% to 0.77. All the A-type cations are significantly
underbonded at the 8b site.
˚
3.011 (3) A
The atomic displacement parameters derived from the average
mean square shifts across all three models are substantially
˚
CsAl0.33W1.67O6
W–O
ꢃ 6
ꢃ 3
1.9071 (9) A
BVS W 6.29(2)
BVS Al 3.034(8)
BVS Cs 1.18(2)
W–O–W
Cs–O
155.58 1(5)
1
˚
smaller than the refined values ðꢀ3Þ.
3.081 (7) A
This discrepancy is believed to be sample dependent (some
samples had traces of water and the structure of the standard
Al2O3 reference refined to acceptable values). Better statistics
and/or resolution will be needed to determine if this discrepancy
is real.
˚
All BVS have been calculated to a maximum bond length of 4 A.
a
The Al distances and angles are identical to the tabulated W values.
whereas the Rb sample always contained an impurity in general
agreement with phase analysis by XRD. It is possible that loss of
the A-type cation from the nominal stoichiometric composition
during calcination, under the relatively modest calcinations and
sintering temperatures would promote disproportionation and
the formation of a low temperature/transitional alumina such as a
3.5. Multinuclear solid state MAS and static NMR
The 27Al MAS NMR data of the pyrochlore series AAl0.33W1.67O6
presented in Figs. 5(a)–(c) shows that the Al3+ octahedra in this
structural series is characterised by a dominant narrow resonance
with an apparent shift in the
dꢀ21–22 ppm range. This observed
defect spinel-like g-alumina. This may account for some of the
shift is assigned to the octahedrally coordinated Al site comprising
the alumino-tungstate framework. These resonances exhibit a
significant downfield shift in comparison to previously reported
27Al resonances assigned to six coordinate Al positions in various
condensed and intermediate aluminas and aluminium hydroxide
decorations observed on the surface of the crystallites in Fig. 4.
3.4. VASP modelling
The crystal structure was modelled by replacing three tungsten
atoms with aluminium atoms in the unit cell. This gives one
excess electron which was included in the calculations, as a
delocalised electron. Three distinct models were minimized—the
first had two of the aluminium atoms in neighbouring octahedra,
the second had a variety of Al–Al distances and the third had the
Al as far apart as possible. The first model gave substantial
displacement of the aluminiums towards the common oxygen
giving one long, one short and four intermediate length bonds
precipitates, which are conventionally observed in the dꢀ0–13
ppm range [23,27–31]. The VASP calculations described above
show that where two Al (0,0,0 and 0,0,z) positions share a
common corner they are displaced towards each other resulting in
one long Al–O bond. It is thought that such a distorted octahedral
configuration where the long Al–O bond is collinear with the
molecular c axis justifies a pseudo-5 coordinate description for
the Al coordination in these systems, and rationalises the large
downfield shift towards the five coordinate 27Al chemical shift
˚
(2.00, 1.78 and 4 ꢃ1.90 A). In the other two models the aluminium
region of dꢀ25–40 ppm [23,28,30].

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Fig. 5. 27Al MAS NMR spectra of (a) KAl0.33W1.67O6, (b) RbAl0.33W1.67O6, and
(c) CsAl0.33W1.67O6. The insert shows example of the spectra from gamma alumina,
a contaminant phase from a failed sample. The peaks identified with arrows can be
seen in the spectra from the RbAl0.33W1.67O6 sample.
Additional 27Al resonances typical of six and four coordinate
environments are observed at
respectively. These are indicative of a poorly formed/highly
disordered -alumina phase and also observed in the Rb and Cs
d 8.2 ppm and d 64.4 ppm,
g
variants. This phase was undetected in the diffraction studies,
suggesting it to be amorphous, although poorly formed features
were observed in the electron micrographs (see Fig. 5). An
example of an incompletely reacted CsAl0.33W1.67O6 sample is
shown as an inset in Fig. 5 that demonstrates a dominance of this
g
-alumina phase.
The results of the multinuclear MAS and static NMR studies of
the alkali A cation is shown in Fig. 6. The static broadline 39K
measurement in Fig. 6(a) exhibits one broad featureless resonance
at
a shift dꢀ–63 ppm. The broadening of this quadrupole
dominated resonance is indicative of some local disorder that
influences the K environment. Within the resolution limits of this
experiment only one K site can be identified, in agreement with
the X-ray and neutron structural results. This contrasts with the
87Rb and 85Rb MAS measurements shown in Figs. 6(b) and (c),
respectively. The high resolution 87Rb MAS data clearly resolves
three resonances at shifts
narrower resonance at
impurity phase Rb15W45.5O144 and corroborates what was de-
d ꢂ28.0, ꢂ73.0 and ꢂ91.4 ppm. The
d
ꢂ91.4 ppm is assigned to a Rb-bearing
tected by diffraction methods at the ꢀ5–10% level. The broader
d
ꢂ28 ppm and dꢂ73 ppm resonances are associated with the
RbAl0.33W1.67O6 phase and these demonstrate two different types
of cation disorder influencing the Rb speciation. The most
prominent structural disorder distributes the Rb speciation
between two positions or environments in an approximate ratio
Fig. 6. (a) 39K static NMR spectra of KAl0.33W1.67O6, (b) 87Rb MAS NMR spectra of
RbAl0.33W1.67O6, (c) 85Rb MAS NMR spectra of RbAl0.33W1.67O6, and (d) 133Cs MAS
NMR spectra of CsAl0.33W1.67O6.
of ꢀ2.5:1, as evidenced by the intensities of the dꢂ28 ppm and
d
ꢂ73 ppm resonances, while more subtle local disorder is
demonstrated by each resonance lineshape which exhibits some
extended upfield tailing [32–35]. This observation of this
phenomenon is greatly enhanced in the 85Rb data by virtue of

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463
4. Conclusions
The structures of the defect AAl0.33W1.67O6 pyrochlores (A ¼ K,
Rb and Cs) have been investigated using diffraction (powder X-ray
and neutron) spectroscopic (Solid State NMR) and modelling
(VASP) methods. All the data shows the presence of displacive
3 3 3
8 8 8
disorder of the A-type cations from the 8b sites at
to a 32e
sites at (x,x,x) where x ¼ K(0.3445), Rb(0.3569) and Cs(0.3618) as
illustrated in Fig. 7. Combined X-ray and neutron data sets were
required to obtain accurate structural refinements of the three
pyrochlores. The magnitude of the displacement of the A-type
cation was observed to decrease as the size of the cation
increased, although for all cations the magnitude of the displace-
ment estimated from the diffraction studies was greater than
that calculated.
The disorder of the A-type cations is correlated with the non-
linear expansion of the structures observed with increase ionic
radii. An important consequence of this is that the K cation
effectively occupies a much larger volume than it would if it was
located on the 8b site. This opens up the structure which in turn
allows a small amount of H2O to enter the structure. The effect of
this on the favourable ion-exchange properties of KAl0.33W1.67O6
is the subject of on-going studies.
Acknowledgment
BJK acknowledges the support from the Australian Research
Council for the work conducted at the University of Sydney.
Fig. 7. Structures based on combined results of refined parameters. The purple
spheres represent K (a), Rb (b) is represented by the green spheres and Cs (c) as
pink. In all cases the A-type cation occupies 25% of all possible 32e sites. The
magnitude of the displacement from the nearby 8b site can be easily seen in this
[111] projection and is greatest in the K compound.
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