The crystal structure of α-K3AIF6: Elpasolites and double perovskites with broken corner-sharing connectivity of the octahedral framework

Article abstract of DOI:10.1021/ic9013043

The crystal structure of α-K₃AIF₆ was solved and refined from a combination of powder X-ray and neutron diffraction data (a = 18.8385(3)A, c = 33.9644(6)A, S.G. /4₁ Z= 80, R _P(X-ray) = 0.037, R_p(neutr

Full text of DOI:10.1021/ic9013043

9336 Inorg. Chem. 2009, 48, 9336–9344
DOI: 10.1021/ic9013043
The Crystal Structure of r-K3AlF6: Elpasolites and Double Perovskites with Broken
Corner-Sharing Connectivity of the Octahedral Framework
Artem M. Abakumov,*,†,§ Graham King,‡ Veronika K. Laurinavichute,§ Marina G. Rozova,§ Patrick M. Woodward,‡
and Evgeny V. Antipov§
†EMAT, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium, ‡Department of Chemistry,
§
The Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210-1185, and Department of Chemistry,
Moscow State University, Moscow 119992, Russia
Received July 6, 2009
The crystal structure of R-K3AlF6 was solved and refined from a combination of powder X-ray and neutron diffraction
˚
˚
data (a = 18.8385(3)A, c = 33.9644(6)A, S.G. I41/a, Z = 80, RP(X-ray) = 0.037, RP(neutron) = 0.053). The crystal
√
structure is of the A2BB0X6 elpasolite type with the a = b ≈ ae 5, c = 4ae superstructure (ae, parameter of the
elpasolite subcell) and rock-salt-type ordering of the K and Al cations over the B and B0 positions, respectively. The
remarkable feature of R-K3AlF6 is a rotation of 2/5 of the AlF6 octahedra by ∼π/4 around one of the crystal axes of the
elpasolite subcell, coinciding with the 4-fold symmetry axes of the AlF6 octahedra. The rotation of the AlF6 octahedra
replaces the corner-sharing between the K and Al polyhedra by edge-sharing, resulting in an increase of coordination
numbers of the K cations at the B positions up to 7 and 8. Due to significant deformations of the K polyhedra, the
corner-sharing connectivity of the octahedral elpasolite framework is broken and the rotations of the AlF6 octahedra do
not have a cooperative character. Elpasolites and double perovskites with similar structural organization are
discussed. The difference in ionic radii of the B and B0 cations as well as the tolerance factor are proposed to be
the parameters governing the formation of elpasolites and double perovskites with broken corner-sharing connectivity
of the octahedral framework.
1. Introduction
tilting distortions are restricted by the fact that the octahedral
units behave as rigid bodies and the corner sharing of
the octahedra is maintained at reasonably small tilt angles
(< 20o). That is, the octahedral tilting occurs in a cooperative
manner. The corner-linked tilting distortions for the B-site
ordered A2BB0X6 compounds are enumerated using a group
theory analysis, including derivations of superstructure unit
cells, space symmetry, and phase transition paths between
different tilting modes.2-5
However, some of the elpasolite-type compounds, such as
R-K3AlF6 and K3MoO3F3, demonstrate superstructures
which cannot be attributed to any of the cooperative tilt
systems. Electron diffraction investigation revealed that both
compounds at room temperature have a tetragonal (or
monoclinically distorted pseudotetragonal) supercell with
The crystal structures of elpasolites (complex fluorides
A2BB0F6, named after the K2NaAlF6 elpasolite) and double
perovskites (complex oxides A2BB0O6, named after the
CaTiO3 perovskite) are based on the perovskite structure,
where the B and B0 cations are ordered in a chess-board (rock
salt) manner, resulting in a Fm3m cubic structure with ae =
2ap (where ap is the length of the ABX3 perovskite subcell
edge) (Figure 1). This B-site ordering is driven by size and
charge difference between the B and B0 cations.1 The BX6 and
B0X6 (X = O, F) octahedra are linked by common corners
into a network, where the A cations occupy 12-coordinated
cavities. A mismatch between the A-X and B(B0)-X intera-
tomic distances results in structural distortions in elpasolites
and double perovskites. If the A cation is too small for the 12-
coordinated cavity formed by corner-sharing BX6 and B0X6
octahedra, the octahedral framework undergoes a tilting
distortion with bending B-X-B0 bonds and a reduced
volume of the coordination polyhedron of the A cation and
its coordination number. Possible patterns of corner-linked
(2) Howard, C. J.; Kennedy, B. J.; Woodward, P. M. Acta Crystallogr.
2003, B59, 463–471.
(3) Flerov, I. N.; Gorev, M. V.; Aleksandrov, K. S.; Tressaud, A.;
Grannec, J.; Couzi, M. Mater. Sci. Eng. 1998, R24, 81–151.
(4) Aleksandrov, K. S.; Misyul, S. V. Sov. Phys. Crystallogr. 1981, 26,
612–618.
(5) Stokes, H. T.; Kisi, E. H.; Hatch, D. M.; Howard, C. J. Acta
Crystallogr. 2002, B58, 934–938.
(6) Abakumov, A. M.; Rossell, M. D.; Alekseeva, A. M.; Vassiliev, S.
Yu.; Mudrezova, S. N.; Van Tendeloo, G.; Antipov, E. V. J. Solid State
Chem. 2006, 179, 421–428.
*To whom correspondence should be addressed. Tel.: þ32(3) 2653259.
Fax: þ32(3) 2653257. E-mail: artem.abakumov@ua.ac.be.
(1) Anderson, M. T.; Greenwood, K. B.; Taylor, G. A.; Poeppelmeier,
K. R. Prog. Solid State Chem. 1993, 22, 197–233.
r
pubs.acs.org/IC
Published on Web 09/03/2009
2009 American Chemical Society

Article
Inorganic Chemistry, Vol. 48, No. 19, 2009 9337
confirmed using X-ray powder diffraction. A sample with an
overall mass of 12 g and a KF/AlF3=3.1:1 ratio was prepared,
placed in a glassy carbon crucible, melted at 1000 oC for 1.5 h,
and cooled down to room temperature with a 100 oC/h cooling
rate. The crystallized melt was crushed, and the excess of KF
was removed by washing with distilled water.
The X-ray powder diffraction (XRPD) data for structure
analysis were collected with a STADI-P diffractometer (Cu
KR1 radiation, curved Ge monochromator, transmission
mode, linear PSD). Time-of-flight neutron powder diffrac-
tion (NPD) data were collected at the HRPD beamline at the
ISIS facility of the Rutherford Appleton Laboratory in the
United Kingdom. Because of significant peak overlap arising
from the very large unit cell volume, only the high-resolution
168° databank was used in the refinement. The JANA2006
program package was used for the structure determination
and joint Rietveld refinement from XRPD and NPD data.10
3. Results
Figure 1. The crystal structure of the cubic A2BB0X6 elpasolites and
double perovskites. Larger B cations are situated at the centers of the gray
BX6 octahedra; the smaller B0X6 octahedra are darker shaded. The A
cations are shown as spheres.
According to the results of a previous electron diffraction
(ED) investigation,6 the unit cell vectors of R-K3AlF6 are
related to the unit cell vectors of the cubic elpasolite structure
with ae ≈ 8.5 A by a transformation matrix:
˚
√
0
1
a=b ≈ ae 5 and c=4ae, but the origin of this superstructure
1
-2
0
2
1
0
0
0
4
is still unclear.6,7 Taking into account the large difference in
the size of the B= K and B0 = Al and Mo cations, it was
suggested that only the B0X6 octahedra behave as rigid units,
whereas the coordination polyhedron around the B cation
can be subjected to significant deformations, thus breaking
B
B
C
C
@
A
√
This results in a tetragonal unit cell with a=b ≈ ae 5 and c=
4ae. The reflection conditions hkl, h þ k þ l=2n; hk0, h,k =
2n, observed with ED, leave the space group I41/a as the only
possibility. The reflection positions and intensity distribution
on the ED patterns match well with the 4/m point group, but
a slight monoclinic distortion with very close a and b para-
meters and the γ angle slightly deviating from 90° could
not be excluded (we will keep the monoclinic first setting
(γ setting) for easy transition between the tetragonal and
monoclinic unit cells). A small monoclinic distortion was also
found for K3MoO3F3; this room-temperature polymorph
demonstrates the same superstructure as R-K3AlF6.7 Thus,
I112/b and I11b (nonstandard settings of the space groups
C2/c (no. 15) and Cc (no. 9), respectively) monoclinic sub-
groups of I41/a, matching the experimentally observed reflec-
tion conditions, should also be taken into account for
constructing initial structure models. It should be noted that
the I41/a space group does not have subgroups within the
orthorhombic crystal system.
The starting models used for the Rietveld refinement were
constructed by considering different possibile arrangements
of the symmetry elements in the supercell with respect to the
atomic positions in the basic cubic Fm3m elpasolite A2BB0X6
structure. The elpasolite structure has three positions of
inversion centers: at 0,0,0, which is the 4a position of the B
cation; at 1/2,1/2,1/2, which is the 4b position of the B0 cation;
and at 0,1/4,1/4, the 24d position, which is not associated with
atomic entities. These positions can be chosen as an origin for
the tetragonal I41/a supercell. Fixing the origin to the 0,1/4,1/
4 position of the cubic subcell results in the structure shown in
Figure 2a along with the positions of inversion centers and
four-fold axes of the I41/a space group. The second setting of
the I41/a space group was chosen because the structure can be
the corner connectivity of the octahedral framework.6-8
A
clue to a possible mechanism of this distortion was given by
the structural analysis of the elpasolite-type Rb2KCrF6 and
Rb2KGaF6 complex fluorides.9 It suggests that a fraction of
the B0F6 (B0 = Cr, Ga) octahedra rotateasrigid bodies by π/4
(the limiting tilt angle for an octahedron) around the four-
fold octahedral symmetry axis, changing the coordination
environment of part of the B=K cations from octahedral to
pentagonal bipyramidal.9 In this contribution, we demon-
strate that a very similar structural mechanism is realized in
the R-K3AlF6 structure. Extensive microtwinning, arising
from phase transitions that occur upon cooling from
the high-temperature polymorph, has hampered efforts
to use single crystals for structure solution. In this manu-
script, we report the use of rigid body constraints to solve the
structure of R-K3AlF6 from X-ray and neutron powder
diffraction data. We also discuss rotation modes of the
octahedral units and the structural parameters governing
the formation of elpasolites and double perovskites with
broken corner-sharing connectivity of the octahedral frame-
work.
2. Experimental Section
The K3AlF6 sample was prepared from anhydrous AlF3
(“Reakhim”, “pure”puritygrade)andKF. TherawAlF3 was
annealed at 300 C for 12 h to remove possible traces of
o
absorbed water. Anhydrous KF was prepared by a dehydra-
tion of KF 2H2O (“Reakhim”, “pure for analysis” purity
3
grade) at 500 oC. The purity of the initial materials was
(7) Brink, F. J.; Withers, R. L.; Friese, K.; Madariaga, G.; Noren, L.
J. Solid State Chem. 2002, 163, 267–274.
(8) Withers, R. L.; Welberry, T. R.; Brink, F. J.; Noren, L. J. Solid State
Chem. 2003, 170, 211–220.
(9) Zuniga, F. J.; Tressaud, A.; Darriet, J. J. Solid State Chem. 2006, 179,
3607–3614.
(10) Petricek, V.; Dusek, M. JANA2000; Institute of Physics: Praha, Czech
Republic, 2000.

9338 Inorganic Chemistry, Vol. 48, No. 19, 2009
Abakumov et al.
location of the origin at the 0,1/4,1/4 or symmetrically
equivalent subcell position is the unique choice, and the other
possibilities can be discarded. In the resulting structure, the 41
screw axes pass through the columns of the alternating
corner-sharing BX6 and B0X6 octahedra, whereas the
4 inversion axes pass through the columns of the A cations.
Reducing the symmetry from I41/a to I112/b is then straight-
forward and requires a replacement of the 41 screw axes with
the 21 screw axes and the 4 inversion axes with 2-fold rotation
axes (Figure 2b). By an origin shift over the [1/4,1/4,1/4]
vector of the supercell, a second possible structure can be
obtained with the I112/a space group, where the 21 screw
axes are located at the A-cation columns and 2-fold rota-
tion axes - at the octahedral columns (Figure 2c). Although
both monoclinic structures have the same unit cell and
space group, they are different because the site symmetry
of the B and B0 cations at the 1/4,0,z position of the super-
cell is 1 in the I2/b structure and 2 in the I2/a structure. It
should be noted that fixing the origin to either the 0,0,0 or
1/2,1/2,1/2 subcell position is also not allowed in both I2/b
and I2/a structures. In the acentric space group Ib, the origin
position is not fixed in the ab plane and can be chosen
arbitrarily.
The symmetry analysis resulted in four models (I41/a, I2/b,
I2/a, and Ib), which should be verified with Rietveld refine-
ment. However, even the most symmetric I41/a model con-
tains 53 symmetrically independent atoms with 147 refined
atomic coordinates. Taking into account additional difficul-
ties arising from extensive peak overlap due to the very large
3
˚
unit cell volume (>12 000 A ), some approximations must be
made to reduce the number of refined parameters, at least at
the first stage of the refinement. As suggested earlier,6-8 in
the K3MoO3F3 and R-K3AlF6 structures, the B0X6 (B0=Mo,
Al; X = O, F) octahedra behave likerigidunits, whereas rigid
unit behavior does not necessarily occur for the KX6 octahe-
dra with significantly larger K-X separation. The rigid
body approximation then looks plausible to describe dis-
placements and rotations of the AlF6 octahedral units in
R-K3AlF6.
In the I41/a model, there are five symmetrically indepen-
dent Al atoms located at general 16f positions. Thus, 105
variable atomic coordinates are required to describe the
positions and orientation of the AlF6 octahedra. Each
octahedron can be described by a position of its center
(the Al atom) and three rotation angles defining the orienta-
tion of the local coordinate system of the octahedron with
respect to the crystal axes (see Petricek and Dusek11 for more
details). This reduces the amount of refined parameters to
30 for the AlF6 octahedra. Additionally, 42 refined atomic
coordinates are necessary to describe the positions of the K
atoms.
Figure 2. The projection of the parent elpasolite structure within the
√
a=b ≈ ae 5, c=4ae supercell with overlaid positions of symmetry axes
and inversion centers of the I41/a (a), I112/b (b), and I112/a (c) space
groups. The B0X6 octahedra are shown; the A and B cations are shown as
empty and gray circles, respectively. The notations for symmetry elements
correspond to those in the International Tables for Crystallography.
The positions and rotation angles of the AlF6 units
reproducing the octahedral arrangement in the cubic elpaso-
lite structure were chosen for the starting I41/a model. The
˚
Al-F distance was set to be equal to 1.80 A. The refinement
was performed first from XRPD data only. The positions of
the K atoms at the A sites, the positions of the K atoms at the
B sites, the positions of the centers of the AlF6 octahedra,
and their rotation angles were subsequently included into
the refinement. After the achievement of convergence, the
transformed to the I2/b subgroup without shifting the origin.
It is also obvious from Figure 2 that fixing the origin to either
0,0,0 or to 1/2,1/2,1/2 subcell positions would result in the
four-fold axes of the I41/a space group passing through the 1/
4,0,0 and 0,1/4,0 24e positions of the cubic subcell with the
point symmetries 4mm and m4m, respectively, which does not
match the four-fold axes parallel to the c axis. Thus, the
(11) Petricek, V.; Dusek, M. JANA98: The Crystallographic Computing
System, Manual; Institute of Physics: Praha, Czech Republic, 1998.

Article
Inorganic Chemistry, Vol. 48, No. 19, 2009 9339
high-resolution NPD data bank was added, and the refine-
ment was performed from joint XRPD and NPD data sets.
At the final stage, the Al-F distances were included in the
refinement. The residual reliability factors revealed an accep-
table agreement between the experimental and calculated
diffraction profiles (RF=0.060 and RP=0.038 for the XRPD
data and RF=0.055 and RP=0.058 for the NPD data). In
order to ensure that the obtained structure is unique, the
structure solution using a Monte Carlo based global opti-
mization was undertaken using the FOX program.12 The
rotation angles of the AlF6 octahedra were selected as
variable parameters. The optimization revealed the same
structure as the one obtained from the Rietveld refinement.
Decreasing the symmetry down to the I2/b subgroup
decreases the reliability factors (RF = 0.053 and RP=0.036
for the XRPD data and RF= 0.039 and RP = 0.052 for the
NPD data). However, the resulting atomic arrangement
reproduces the I41/a model. Moreover, the a and b lattice
parameters stay equal in the range of standard deviation, and
the monoclinic angle γ was found to be equal to 90° (a =
Table 1. Selected Parameters from the Rietveld Refinement of R-K3AlF6
formula
space group
K3AlF6
I41/a
18.8385(3)
33.9644(6)
80
12053.6(3)
2.845
0.0085(2)
˚
a, A
˚
c, A
Z
cell volume, A
3
˚
calcd density, g/cm3
2
˚
overall U, A
XRPD data set:
radiation
˚
CuKR1, λ = 1.5406 A
10 e 2θ e 100; 0.01
0.058, 0.037, 0.049
2θ range; step, deg
RF, RP, RwP
NPD data set:
˚
d range, A
0.725-2.61
0.046, 0.053, 0.057
148
RF, RP, RwP
params refined
GOF
1.63
˚
interatomic distance of 1.81 A. The BVS values for the Al
cations, calculated with the parameters given by Brown and
Altermatt,13 vary in the range of 2.74-3.11 with an average
value of 2.92, which is in good agreement with the nominal
valence. The remarkable difference between the cubic elpa-
solite structure and R-K3AlF6 is a rotation of 2/5 of the AlF6
octahedra by an angle of π/4 around one of the crystal axes of
the elpasolite subcell (coinciding with the 4-fold symmetry
axesof the AlF6 octahedra). This results ina drastic change of
the coordination polyhedra of the KB cations. The rotation of
the AlF6 octahedra replaces the corner-sharing between
the KB and Al polyhedra by edge-sharing that increases the
coordination number of the KB cations. If one out of six AlF6
octahedra surrounding the KB atom rotates over π/4, the
fluorine octahedron around the KB atom is transformed into
a distorted pentagonal bipyramid with CN = 7 (Figure 5a).
This coordination is realized for two KB atoms, K(17) and
K(18). The average K-F interatomic distance for these
˚
˚
˚
18.8396(5)A, b = 18.8388(5)A, c = 33.9657(6)A, and γ =
90.000(2)°). The standard deviations of the atomic coordi-
nates of the K atoms, symmetrically equivalent in the I41/a
model, become twice as large on going to the I2/b subgroup,
indicating the absence of a noticeable deviation from the I41/
a symmetry. For the refinement of the I2/a model, the AlF6
octahedra were split into two groups: with centers positioned
at the general 8f position and with centers at the 4e position.
The site symmetry of the 4e position is 2, and this two-fold
axis can pass either through two trans vertices or through the
midpoints of the opposite edges of the AlF6 octahedra.
Monte Carlo based global optimization was also performed,
and different combinations of octahedral tilts were tried that
finally resulted in the reliability factors RF = 0.068 and RP =
0.045 for the XRPD data and RF= 0.056 and RP = 0.072 for
the NPD data, significantly higher than those for the I2/b and
I41/a models. Thus, the I2/a model was discarded. The
refinement in the acentric Ib space group does not converge.
Even if some structure distortion is present, eliminating the
inversion center, in this particular case, the detection of this
distortion is beyond the capabilities of powder diffraction.
The I41/a structure was chosen for final refinement. For
the final refinement, the rigid body coordinates were trans-
formed into conventional atomic coordinates, which were
refined without any other constrains. An overall atomic
˚
positions is 2.65 A. For these atoms, the BVS values,
calculated with the parameters given by Adams,14 are larger
than the nominal valence (1.26 for K(17) and 1.09 for K(18)),
indicating that they remain slightly overbonded. For the KB
atoms K(14)-K(16), two AlF6 octahedra in cis positions are
rotated over π/4 around mutually perpendicular axes, which
results in an 8-fold polyhedron (a capped pentagonal
bipyramid). The average K-F interatomic distance of
˚
2.77 A for these positions is larger than that for the 7-fold
coordinated KB positions. However, for the K(14)-K(16)
atoms, one K-F interatomic distance (3.08-3.20 A) is
˚
2
noticeably larger than the average distance, so that the co-
ordination number of these cations is better described as 7 þ 1.
For the K14-K16 atoms, the BVS values are in the range of
0.97-1.01, in perfect agreement with the nominal value.
In order to represent the ordering pattern of the rotated
AlF6 octahedra, it is more convenient to consider the struc-
ture as consisting of octahedral layers, alternating along the c
axis and positioned at z ≈ (2n þ 1)/16 (n=0-7). In every
layer, there are 10 AlF6 octahedra, six of which nearly retain
their orientation with respect to the elpasolite crystal axes
(marked as 0 in Figure 6), two are rotated by ∼π/4 around the
ce axis (marked as c in Figure 6), and two are rotated by ∼π/4
around either the ae or be axis (marked as a or b in Figure 6,
respectively). The layers are symmetry related by operations
of the I41/a space group.
˚
displacement parameter was refined (U=0.0085(2)A ). The
crystallographic data of R-K3AlF6 are summarized in
Table 1. The relevant interatomic distances are listed in
Table 2. Experimental, calculated, and difference XRPD
and NPD profiles are shown in Figure 3a and b, respectively.
The positional parameters for the R-K3AlF6 structure are
listed in Table 1 of the Supporting Information.
An overview of the R-K3AlF6 crystal structure is shown in
Figure 4. The cation positions in this structure roughly
correspond to the cation positions in the cubic elpasolite
structure: the A positions are occupied by the K cations
(K(1)-K(13), denoted further as KA), and the B and B0
positions are occupied in a chess-board ordered manner by
the K cations (K(14)-K(18), denoted further as KB) and Al
cations, respectively. The Al cations are situated in an
octahedral fluorine environment with an average Al-F
(13) Brown, I. D.; Altermatt, D. Acta Crystallogr. 1985, B41, 244–247.
(14) Adams, S. Acta Crystallogr. 2001, B57, 278–287.
ꢀ
(12) Favre-Nicolin, V.; Cerny, R. J. Appl. Crystallogr. 2002, 35, 734–743.

9340 Inorganic Chemistry, Vol. 48, No. 19, 2009
Abakumov et al.
˚
Table 2. Selected Interatomic Distances for R-K3AlF6 (A)
KA cations
K(1)-F(14)
K(1) - F(15)
K(1)-F(22)
K(1)-F(23)
K(1)-F(24)
2.61(1)ꢀ2
3.10(1)ꢀ2
2.65(2)ꢀ2
3.04(1)ꢀ2
2.85(1)ꢀ2
K(2)-F(11)
K(2)-F(12)
K(2)-F(13)
K(2)-F(31)
K(2)-F(33)
K(2)-F(35)
K(2)-F(45)
K(2)-F(46)
2.50(1)ꢀ1
2.72(1)ꢀ1
2.64(1)ꢀ1
2.58(2)ꢀ1
2.84(1)ꢀ1
2.74(1)ꢀ1
2.58(1)ꢀ1
2.87(1)ꢀ1
K(3)-F(11)
K(3)-F(15)
K(3)-F(32)
K(3)-F(33)
K(3)-F(34)
K(3)-F(41)
K(3)-F(51)
K(3)-F(52)
K(3)-F(53)
K(6)-F(13)
K(6)-F(33)
K(6)-F(34)
K(6)-F(35)
2.50(1)ꢀ1
2.97(1)ꢀ1
2.90(1)ꢀ1
2.64(2)ꢀ1
3.00(1)ꢀ1
2.83(1)ꢀ1
2.85(1)ꢀ1
2.73(1)ꢀ1
2.74(1)ꢀ1
2.57(1)ꢀ2
3.03(1)ꢀ2
2.70(1)ꢀ2
2.92(1)ꢀ2
K(4)-F(12)
K(4)-F(16)
K(4)-F(31)
K(4)-F(32)
K(4)-F(34)
K(4)-F(35)
K(4)-F(36)
K(4)-F(36)
K(4)-F(41)
K(7)-F(14)
K(7)-F(23)
K(7)-F(24)
K(7)-F(31)
K(7)-F(32)
K(7)-F(36)
K(7)-F(43)
K(7)-F(45)
2.87(1)ꢀ1
2.81(1)ꢀ1
2.98(1)ꢀ1
2.80(1)ꢀ1
2.86(1)ꢀ1
2.68(1)ꢀ1
2.78(1)ꢀ1
2.73(1)ꢀ1
2.55(1)ꢀ1
2.49(1)ꢀ1
3.00(1)ꢀ1
2.92(1)ꢀ1
2.78(1)ꢀ1
2.74(1)ꢀ1
2.99(1)ꢀ1
2.75(1)ꢀ1
2.78(1)ꢀ1
K(5)-F(15)
K(5)-F(16)
K(5)-F(21)
K(5)-F(22)
K(5)-F(23)
K(5)-F(42)
K(5)-F(51)
K(5)-F(52)
K(5)-F(56)
K(8)-F(34)
K(8)-F(35)
K(8)-F(36)
2.72(1)ꢀ1
2.60(1)ꢀ1
2.85(1)ꢀ1
3.09(1)ꢀ1
2.69(1)ꢀ1
2.78(1)ꢀ1
2.91(1)ꢀ1
2.73(1)ꢀ1
2.93(1)ꢀ1
2.946(9)ꢀ4
3.00(1)ꢀ4
2.879(9)ꢀ4
K(9)-F(21)
K(9)-F(21)
K(9)-F(22)
K(9)-F(25)
K(9)-F(26)
K(9)-F(26)
K(9)-F(42)
K(9)-F(53)
K(9)-F(55)
K(12)-F(21)
K(12)-F(23)
K(12)-F(25)
K(12)-F(43)
K(12)-F(44)
K(12)-F(52)
K(12)-F(55)
K(12)-F(56)
3.00(1)ꢀ1
2.75(1)ꢀ1
3.04(1)ꢀ1
3.05(1)ꢀ1
2.82(1)ꢀ1
2.95(1)ꢀ1
2.69(1)ꢀ1
2.91(1)ꢀ1
2.76(1)ꢀ1
2.74(1)ꢀ1
2.89(1)ꢀ1
2.87(1)ꢀ1
3.00(1)ꢀ1
2.44(1)ꢀ1
3.08(1)ꢀ1
2.77(1)ꢀ1
2.73(1)ꢀ1
K(10)-F(24)
K(10)-F(25)
K(10)-F(26)
K(10)-F(31)
K(10)-F(32)
K(10)-F(33)
K(10)-F(34)
K(10)-F(36)
K(10)-F(52)
K(10)-F(54)
K(13)-F(55)
K(13)-F(56)
2.91(1)ꢀ1
2.86(1)ꢀ1
2.85(1)ꢀ1
2.99(1)ꢀ1
3.07(1)ꢀ1
2.92(1)ꢀ1
2.66(1)ꢀ1
2.72(1)ꢀ1
3.04(1)ꢀ1
3.03(1)ꢀ1
3.01(1)ꢀ4
2.874(9)ꢀ4
K(11)-F(22)
K(11)-F(24)
K(11)-F(26)
K(11)-F(54)
2.83(1)ꢀ2
2.88(1)ꢀ2
3.09(1)ꢀ2
2.79(1)ꢀ2
KB cations
K(14)-F(14)
K(14)-F(16)
K(14)-F(22)
K(14)-F(24)
K(14)-F(32)
K(14)-F(41)
K(14)-F(42)
K(14)-F(53)
K(17)-F(11)
K(17)-F(16)
K(17)-F(25)
K(17)-F(31)
K(17)-F(43)
K(17)-F(46)
K(17)-F(51)
3.08(1)ꢀ1
2.80(1)ꢀ1
2.54(1)ꢀ1
2.81(1)ꢀ1
2.54(1)ꢀ1
2.82(1)ꢀ1
2.78(1)ꢀ1
2.74(1)ꢀ1
2.94(1)ꢀ1
2.82(1)ꢀ1
2.76(1)ꢀ1
2.75(1)ꢀ1
2.54(1)ꢀ1
2.50(1)ꢀ1
2.18(1)ꢀ1
K(15)-F(13)
K(15)-F(14)
K(15)-F(15)
K(15)-F(23)
K(15)-F(33)
K(15)-F(43)
K(15)-F(45)
K(15)-F(52)
K(18)-F(21)
K(18)-F(26)
K(18)-F(42)
K(18)-F(44)
K(18)-F(54)
K(18)-F(55)
K(18)-F(56)
2.89(1)ꢀ1
2.80(1)ꢀ1
2.74(1)ꢀ1
2.37(1)ꢀ1
2.64(1)ꢀ1
3.10(1)ꢀ1
2.78(1)ꢀ1
2.86(1)ꢀ1
2.56(1)ꢀ1
2.48(1)ꢀ1
2.88(1)ꢀ1
2.84(1)ꢀ1
2.45(1)ꢀ1
2.85(1)ꢀ1
2.57(1)ꢀ1
K(16)-F(11)
K(16)-F(12)
K(16)-F(13)
K(16)-F(34)
K(16)-F(35)
K(16)-F(36)
K(16)-F(41)
K(16)-F(45)
2.80(1)ꢀ1
2.42(1)ꢀ1
3.20(1)ꢀ1
2.59(1)ꢀ1
2.77(1)ꢀ1
2.71(1)ꢀ1
2.89(1)ꢀ1
2.75(1)ꢀ1
Al cations
Al(1)-F(11)
Al(1)-F(12)
Al(1)-F(13)
Al(1)-F(14)
Al(1)-F(15)
Al(1)-F(16)
Al(4)-F(41)
Al(4)-F(42)
Al(4)-F(43)
Al(4)-F(44)
Al(4)-F(45)
Al(4)-F(46)
1.81(2)ꢀ1
1.82(2)ꢀ1
1.82(2)ꢀ1
1.86(2)ꢀ1
1.76(2)ꢀ1
1.80(2)ꢀ1
1.83(2)ꢀ1
1.79(2)ꢀ1
1.86(2)ꢀ1
1.84(2)ꢀ1
1.87(2)ꢀ1
1.83(2)ꢀ1
Al(2)-F(21)
Al(2)-F(22)
Al(2)-F(23)
Al(2)-F(24)
Al(2)-F(25)
Al(2)-F(26)
Al(5)-F(51)
Al(5)-F(52)
Al(5)-F(53)
Al(5)-F(54)
Al(5)-F(55)
Al(5)-F(56)
1.81(2)ꢀ1
1.76(2)ꢀ1
1.79(2)ꢀ1
1.88(2)ꢀ1
1.81(2)ꢀ1
1.84(2)ꢀ1
1.75(2)ꢀ1
1.85(2)ꢀ1
1.88(2)ꢀ1
1.79(2)ꢀ1
1.76(2)ꢀ1
1.74(2)ꢀ1
Al(3)-F(31)
Al(3)-F(32)
Al(3)-F(33)
Al(3)-F(34)
Al(3)-F(35)
Al(3)-F(36)
1.80(2)ꢀ1
1.79(2)ꢀ1
1.76(2)ꢀ1
1.82(2)ꢀ1
1.87(2)ꢀ1
1.86(2)ꢀ1

Article
Inorganic Chemistry, Vol. 48, No. 19, 2009 9341
Figure 5. A formation of the KBF7 (a) and KAF8 (b) polyhedra as a
result of rotation of the AlF6 octahedra (green) over ∼π/4.
Figure 3. Experimental, calculated, and difference XRPD (a) and NPD
(b) profiles.
Due to rotations of the AlF6 octahedra, the coordination
number of the KA cations is reduced from 12 to 8-10 for all
atoms except K(8), which formally retains 12-fold coordina-
tion. The BVS values for the KA atoms do not depart
significantly from the nominal value varying in the range of
0.80-1.17 with an average of 0.97.
4. Discussion
The structure analysis of R-K3AlF6 confirms the earlier
√
suggestion that the a=b ≈ ae 5, c=4ae superstructure in the
seemingly isostructural room-temperature forms of K3AlF6
and K3MoO3F3 arises from large amplitude rotations of the
B0X6 (B0=Mo, Al; X=O, F) octahedra.6-8 In R-K3AlF6, the
AlF6 octahedra are only slightly deformed, whereas the
coordination environment of the KB atoms is subjected to
significant changes. In this sense, the crystal structure of
R-K3AlF6 is similar to the Rb2KB0F6 structures, where part
of the B0F6 (B0 = Cr, Ga) octahedra rotate as rigid units by π/
4 around the ce axis of the elpasolite cubic subcell, resulting in
√
the a = b ≈ ae 5, c = ae supercell.8 However, instead of
rotation around a single subcellaxis, inR-K3AlF6, octahedral
rotations occur around all three elpasolite subcell axes. The
R-K3AlF6 structure can be considered to be composed of
symmetrically equivalent layers of the AlF6 octahedra, con-
taining the octahedra rotated by π/4 around the ce and ae or
be axes. A close comparison revealed that, in both R-K3AlF6
and Rb2KB0F6 structures, the octahedra rotated by π/4
around the ce are placed according to the F-centered tetra-
√
Figure 4. The crystal structure of R-K3AlF6. The AlF6 octahedra are
green; the KBF7 and KAF8 polyhedra are yellow and blue, respectively.
The KA cations are shown as brown spheres.
gonal a=b ≈ ae 5, c=ae unit cell (Figure 7). The c=4ae
superstructure in R-K3AlF6 arises due to ordered pattern of

9342 Inorganic Chemistry, Vol. 48, No. 19, 2009
Abakumov et al.
Figure 7. A comparison of the Rb2KB0F6 (B0=Cr, Ga) and R-K3AlF6
structures. Both structures are drawn in the F-centered tetragonal a=
√
b ≈ ae 5, c=ae unit cell. The A and B cations arenot shown. The B0F6 and
AlF6 octahedra rotated over π/4 around the c axis are shaded a darker
gray.
as rigid units. However, indirect interaction between the
rotation modes of the octahedral units can be discussed.
Assuming only rotations over a fixed π/4 angle around one of
the ae, be, or ce axes, several variants can be constructed
(Figure 8), representing all possible cases of coordination
environments of the B cations with CN=6, 7, and 8. The B
cation can be surrounded by six B0X6 octahedra, keeping
their orientations as in the parent elpasolite structure, that is,
with four-fold octahedral symmetry axes parallel to the ae, be,
or ce axes (Figure 8a, two B0X6 octahedra above and below
the drawing plane are not shown for clarity). The B cation has
an octahedral environment with d(B-X) > d(B0-X). Rota-
tion of a single B0X6 octahedron over π/4 transforms the BX6
octahedron into the BX7 distorted pentagonal bipyramid
(Figure 8b). Increasing the coordination number up to CN=
8 can occur by the rotation of two B0X6 octahedra in cis
positions with respect to the B cation over π/4 around two
perpendicular axes, which can be either noncoplanar
(Figure 8c) or coplanar (Figure 8d). In all three cases of
CN=7 and 8, a displacement of the B cations from their ideal
positions is possible, resulting in optimization of the intera-
tomic distances between the B cations and X anions, belong-
ing to the B0X6 octahedra not subjected to rotations. The
cases shown in Figure 8a-c were experimentally observed in
the structures of Rb2KB0F6 (B0 =Cr, Ga;9 Figure 8a,b) and
R-K3AlF6 (Figure 8b,c) elpasolite-type fluorides and
A11B4O24 (A=Ca, Sr, B = Re, Os, part of the A positions
is vacant) perovskite-type oxides (Figure 8b),15-17 whereas
the rotation of two cis-positioned octahedra around the
coplanar axes has not been experimentally found yet. Two
more cases should also be considered, which seem to be
energetically less favorable (Figure 8e,f). Rotation of two cis-
positioned octahedra around the same axis would result in an
abnormally short X-X separation and strong electrostatic
repulsion. Assuming the elpasolite subcell parameter ae ≈
Figure 6. Sequence of the octahedral layers in the R-K3AlF6 structure.
The 0, a, b, and c notations stand to mark an absence of rotation of the
AlF6 octahedra over π/4 or rotation around ae, be, or ce axes, respectively.
The tetragonal (a, b) and cubic elpasolite (ae, be) lattice vectors are shown.
the octahedra rotated around the ae or be axes. The fraction of
rotated octahedra in R-K3AlF6 is twice as large as that in the
Rb2KB0F6 (B0 = Cr, Ga) structures. As a result, all KB cations
in R-K3AlF6 change their octahedral coordination to either a
pentagonal bipyramid (CN=7) or capped pentagonal bipyr-
amid (CN=7 þ 1), whereas in Rb2KB0F6 (B0=Cr, Ga), 20%
of the K atoms retain their octahedral coordination.
Due to obvious similarity between the ED patterns of R-
K3AlF6 and K3MoO3F3, it would be logical to assume that
both compounds have the same ordering pattern of rotated
B0X6 octahedra. However, in the case of K3MoO3F3, well
pronounced structured diffuse intensity was also observed,
originating fromlocal ordering of theO and F atoms.7 Due to
the presence of only fluorine anions, such diffuse scattering
was never observed for R-K3AlF6. A small monoclinic
distortion was proposed for both compounds, but the present
structural investigation demonstrates that R-K3AlF6 most
probably retains tetragonal symmetry. However, it is not
necessarily true for K3MoO3F3, where the monoclinic dis-
tortion can be caused by a loss of inversion centers due to off-
center displacement of the Mo6þ cations in the MoO3F3
octahedra, which can be facilitated by trans positions of the F
and O atoms in the octahedra.
˚
˚
8.5 A and an average Al-F interatomic distance of 1.81 A,
˚
the F-F distance would be as short as 2.38 A, much shorter
˚
than the F-F distance in the AlF6 octahedra (2.57 A).
Rotation of two octahedra in trans positions (Figure 8d) is
The crystal structure of R-K3AlF6 is beyond the commonly
known superstructures arising in B-site ordered A2BB0X6
(X = F, O) elpasolites and double perovskites that undergo
octahedral tilting but maintain the cooperative corner-linked
topology. In R-K3AlF6, there is no direct link between the
rotation directions of the AlF6 octahedra because the
coordination polyhedra around the KB cations do not behave
::
(15) Jeitschko, W.; Moens, H. A.; Rodewald, U. C.; Moller, M. H. Z.
Naturforsch. 1998, 53, 31–36.
(16) Bramnik, K. G.; Miehe, G.; Ehrenberg, H.; Fuess, H.; Abakumov,
A. M.; Shpanchenko, R. V.; Pomjakushin, V. Yu.; Balagurov, A. M. J. Solid
State Chem. 2000, 149, 49–55.
::
(17) Tomaszewska, A.; Muller-Buschbaum, H. Z. Anorg. Allg. Chem.
1993, 619, 1738–1742.

Article
Inorganic Chemistry, Vol. 48, No. 19, 2009 9343
Figure 8. Different modes of the B0X6 octahedra rotations resulting in
CN = 6 (a), 7 (b), and 8 (c-f) for the B cations. The octahedra above and
below the drawing plane are not shown for clarity. Arrows mark direc-
tions of displacements of the B cations. The double-headed arrow
indicates short X-X separation.
Figure 9. Coordination environment of the
A cation in the
cubic elpasolite structure (a) and its modification by a rotation of
one B0X6 octahedron over π/4 (b). 1/8 of the cubic elpasolite unit cell is
shown.
not compatible with the displacements of the B cations due to
the formation of centrosymmetric coordination. Shifting the
B cation towards the edge of the rotated octahedron intro-
duces very long distances to the X atoms of a second rotated
octahedron at the trans position and does not significantly
increase short distances to the X atoms of non-rotated
B0X6 octahedra. The same conclusion is applicable to the
rotation of octahedra in trans positions around two different
axes. Thus, the rotation modes of the octahedral units are
mediated by a possibility of relaxation of the B-X bonds due
to off-center displacement of the B cations and the an-
ion-anion repulsion between the neighboring B0X6 octahe-
dra. It should be noted that BX9 polyhedra can be also
constructed, for example, by rotation of three cis-B0X6
octahedra around different axes, but CN=9 has not been
observed yet in such structures.
Prediction of the K3AlF6 structure using SPuDS software18
revealed reasonably low global instability indexes, GII,19
for at least three tilt systems, a-bþa- (S.G. P21/n, GII =
0.0103), a0b-b- (S.G. I2/m, GII=0.0016), and a-a-a- (S.G.
R3, GII = 0.0002), although the low GII seen for the latter
system does not take into account unfavorably short F-F
distances that occur. Thus, the mismatch between the A-X
and (B,B0)-X interatomic distances cannot be the main
driving force for large octahedral rotations.
We suggest that a difference in ionic radii of the B and B0
cations ΔIR can be used as an indicator of the ability of the B
cations to increase their coordination number due to large
amplitude rotations of the relatively small B0X6 octahedra.
For K3AlF6, K3MoO3F3, and Rb2KB0F6 (B0 = Cr, Ga), this
The existence of the A11B4O24 (A=Ca, Sr; B=Re, Os)
perovskite-type oxides with broken corner-sharing connec-
tivity allows us to assume that other perovskite-like oxides
with similar structures would also exist. Although the num-
ber of known perovskites and elpasolites with broken corner-
sharing connectivity is limited, the analysis of their structures
˚
difference is remarkably large (ΔIR = 0.76 - 0.85 A) and
becomes only a little smaller for the A11B4O24 (A = Ca, Sr;
˚
B=Re, Os) compounds (ΔIR = 0.50-0.66 A). On going
from K3MoO3F3 to A2KMoF6 (A=K, Rb, Cs, Tl),20,21 the
˚
ΔIR value decreases to 0.71 A due to the increasing size of the
Mo cations upon reduction from Mo6þ to Mo3þ that stabi-
lizes the undistorted cubic elpasolite structure. The corner
sharing of the octahedral framework is restored in double
can suggest the key factors defining the stability of such
√
compounds. The tolerance factor t = (RA þ RX)/[ 2((RB þ
0
RB )/2 þ RX)], expressing a mismatch between the A-X and
˚
(B,B0)-X interatomic distances, is in the range of t =
0.89-0.93 for such compounds. This tolerance factor falls
in the range where octahedral tilting would be expected.
perovskites when the ΔIR value is near or below ∼0.5 A, as it
(19) Salinas-Sanchez, A.; Garcia-Munoz, J. L.; Rodriguez-Carvajal, J.;
Saez-Puche, R.; Martinez, J. L. J. Solid State Chem. 1992, 100, 201–211.
(20) Toth, L. M.; Brunton, G. D.; Smith, G. P. Inorg. Chem. 1969, 8,
2694–2697.
(18) Lufaso, M. W.; Woodward, P. M. Acta Crystallogr. 2001, B57, 725–
738.
(21) Hoppe, R.; Lehr, K. Z. Anorg. Allg. Chem. 1975, 416, 240–250.

9344 Inorganic Chemistry, Vol. 48, No. 19, 2009
Abakumov et al.
22,23
˚
occurs in Ca3ReO6, Ba2CaReO6 (ΔIR = 0.48 A),
Ba2-
re-investigated because the superlattice reflections arising
from ordered rotations of the B0X6 octahedra can be easily
overlooked due to complex multiple twinning associated with
such superstructures. Such twinning was observed for
R-K3AlF6, Rb2KB0F6 (B0 = Cr, Ga), and K3MoO3F3.
24
24
˚
˚
LaRuO6 (ΔIR = 0.50 A), Ca2LaRuO6 (ΔIR = 0.44 A),
and Ba2CaOsO6 (ΔIR=0.45 A). Thus, the limiting ΔIR
values can be evaluated as ΔIR ≈ 0.75 A for elpasolites and
23
˚
˚
˚
ΔIR ≈ 0.5 A for double perovskites.
The size of the A cation can be considered a secondary
factor. A rotation of one of the B0X6 octahedra decreases the
coordination number of the A cation by 1 and shortens one of
the remaining 11 A-X distances (Figure 9). Reasonably
small A cations (t=0.89 - 0.93) would favor such transfor-
mation. Increasing t to 0.94-0.98 again stabilizes the cubic
elpasolite structure in Cs2TlMoF6 and Cs2KCrF6 in spite of
Acknowledgment. This work was supported by the
Russian Foundation of Basic Research (RFBR Grants
07-03-00664-a, 06-03-90168-a). Financial support from
the NSF through a Materials World Network grant
(MWN-0603128) is gratefully acknowledged. We would
like to thank Aziz Daoud-Aladine and Kevin Knight for
assistance in collecting the NPD data. A.M.A. is grateful
to Ray Withers and Gustaaf Van Tendeloo for fruitful
discussion.
large ΔIRs of 0.83 and 0.76 A, respectively.21,25 However, it
should be noted that such structures should be thoroughly
˚
(22) Abakumov, A. M.; Shpanchenko, R. V.; Antipov, E. V.; Lebedev,
O. I.; Van Tendeloo, G. J. Solid State Chem. 1997, 131, 305–309.
(23) Yamamura, Y.; Wakeshima, M.; Hinatsu, Y. J. Solid State Chem.
2006, 179, 605–612.
Supporting Information Available: A table with positional
parameters for the R-K3AlF6 structure and a crystallographic
information (CIF) file. This material is available free of charge
via the Internet at http://pubs.acs.org.
(24) Battle, P.D. Mater. Res. Bull. 1981, 16, 397–405.
(25) Siebert, G.; Hoppe, R. Z. Anorg. Allg. Chem. 1972, 391, 117–125.