The high-temperature polymorphs of K3AlF6.

Abstract

The crystal structures of the three high-temperature polymorphs of K(3)AlF(6) have been solved from neutron powder diffraction, synchrotron X-ray powder diffraction, and electron diffraction data. The β-phase (stable between 132 and 153 °C) and γ-phase (stable between 153 to 306 °C) can be described as unusually complex superstructures of the double-perovskite structure (K(2)KAlF(6)) which result from noncooperative tilting of the AlF(6) octahedra. The β-phase is tetragonal, space group I4/m, with lattice parameters of a = 13.3862(5) Å and c = 8.5617(3) Å (at 143 °C) and Z = 10. In this phase, one-fifth of the AlF(6) octahedra are rotated about the c-axis by ∼45° while the other four-fifths remain untilted. The large ∼45° rotations result in edge sharing between these AlF(6) octahedra and the neighboring K-centered polyhedra, resulting in pentagonal bipyramidal coordination for four-fifths of the K(+) ions that reside on the B-sites of the perovskite structure. The remaining one-fifth of the K(+) ions on the B-sites retain octahedral coordination. The γ-phase is orthorhombic, space group Fddd, with lattice parameters of a = 36.1276(4) Å, b = 17.1133(2) Å, and c = 12.0562(1) Å (at 225 °C) and Z = 48. In the γ-phase, one-sixth of the AlF(6) octahedra are randomly rotated about one of two directions by ∼45° while the other five-sixths remain essentially untilted. These rotations result in two-thirds of the K(+) ions on the B-site obtaining 7-fold coordination while the other one-third remain in octahedral coordination. The δ-phase adopts the ideal cubic double-perovskite structure, space group Fm ̅3m, with a = 8.5943(1) Å at 400 °C. However, pair distribution function analysis shows that locally the δ-phase is quite different from its long-range average crystal structure. The AlF(6) octahedra undergo large-amplitude rotations which are accompanied by off-center displacements of the K(+) ions that occupy the 12-coordinate A-sites.

Full text

Page 1

Published:July 11, 2011
r2011 American Chemical Society
7792
dx.doi.org/10.1021/ic200956a|Inorg. Chem. 2011, 50, 7792–7801
ARTICLE
pubs.acs.org/IC
The High-Temperature Polymorphs of K3AlF6
Graham King,*,†,‡Artem M. Abakumov,§Patrick M. Woodward,‡Anna Llobet,†Alexander A. Tsirlin,
Dmitry Batuk,§and Evgeny V. Antipov^
||
†Lujan Neutron Scattering Center, Los Alamos National Laboratory, MS H805, Los Alamos, New Mexico 87545, United States
‡Department of Chemistry, The Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210-1185, United States
§Electron Microscopy for Materials Research (EMAT), University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
)
Max Planck Institute for Chemical Physics of Solids, N€ othnitzer Strasse 40, 01187 Dresden, Germany
^Department of Chemistry, Moscow State University, Moscow 119991, Russia
b
S Supporting Information
1. INTRODUCTION
Despite its relatively simple chemical formula, the room-
temperature crystal structure of K3AlF6 is exceptionally
complex.1It is a member of a rare group of double-perovskite-
related compounds which display patterns of noncooperative
octahedraltilting.Thebasicperovskitestructure(ABX3)isbased
on a three-dimensional network of corner-sharing BX6octahe-
dra, with the A-site cations residing in the large cubooctahedral
spaces that exist between any eight such BX6units. The closely
related double-perovskite structure (A2BB0X6) can be derived
from the basic perovskitestructure byhaving two different B-site
cations which are ordered in a rock salt pattern, such that each
BX6unit shares corners with six B0X6units and vice versa.
Octahedral tilting is quite common in perovskites and occurs
when the A-site cation is too small to fill the cubooctahedral
cavity. When this is the case, the BX6octahedra will rotate as
nearly rigid units to make shorter A?X bonds while maintaining
the ideal B?X bond length. The possible patterns of octahedral
tilting are generally assumed to be limited by the corner-sharing
connectivityoftheoctahedralframework,whichrequiresthetilts
to act cooperatively.2In a few rare cases, such as that of K3AlF6,
the connectivity of the octahedral framework is broken and the
tilting is no longer cooperative. When this occurs, entirely new
crystal structures emerge. Such structures tend to be much more
complex than those normally adopted by perovskites. Noncoo-
perative octahedral tilting tends to occur in double perovskites
whichhaveaverylargedifferenceinionicradiibetweentheBand
B0cationsandarelativelysmalltolerancefactor(t=0.89?0.93).1
When these criteria are met, some of the smaller B0X6octahedra
undergo ∼45? rotations, which result in these octahedra sharing
edges (instead of corners) with the coordination polyhedra of
some of the surrounding B cations. This serves to increase the
coordination environment of the larger B cations to values
greater than 6. Other compounds which are known to display
such patterns of noncooperative octahedral tilting include
Received:May 6, 2011
ABSTRACT: The crystal structures of the three high-temperature polymorphs of
K3AlF6have been solved from neutron powder diffraction, synchrotron X-ray powder
diffraction,andelectrondiffractiondata.Theβ-phase(stablebetween132and153?C)
and γ-phase (stable between 153 to 306 ?C) can be described as unusually complex
superstructures of the double-perovskite structure (K2KAlF6) which result from
noncooperative tilting of the AlF6octahedra. The β-phase is tetragonal, space group
I4/m, with lattice parameters of a = 13.3862(5) Åand c = 8.5617(3) Å (at 143 ?C) and
Z=10.Inthisphase,one-fifthoftheAlF6octahedraarerotatedaboutthec-axisby∼45?
while the other four-fifths remain untilted. The large ∼45? rotations result in edge
sharing between these AlF6octahedra and the neighboring K-centered polyhedra,
resulting in pentagonal bipyramidal coordination for four-fifths of the K+ions that
reside on the B-sites of the perovskite structure. The remaining one-fifth of the K+ions
on the B-sites retain octahedral coordination. The γ-phase is orthorhombic, space
group Fddd, with lattice parameters of a = 36.1276(4) Å, b = 17.1133(2) Å, and c = 12.0562(1) Å (at 225 ?C) and Z = 48. In the
γ-phase, one-sixth of the AlF6octahedra are randomly rotated about one of two directions by ∼45? while the other five-sixths
remain essentially untilted. These rotations result in two-thirds of the K+ions on the B-site obtaining 7-fold coordination while the
other one-third remain in octahedral coordination. The δ-phase adopts the ideal cubic double-perovskite structure, space group
Fm3m,witha=8.5943(1)Åat 400 ?C. However, pairdistribution functionanalysisshowsthatlocallytheδ-phase isquite different
from its long-range average crystal structure. The AlF6octahedra undergo large-amplitude rotations which are accompanied by off-
center displacements of the K+ions that occupy the 12-coordinate A-sites.

Page 2

7793
dx.doi.org/10.1021/ic200956a |Inorg. Chem. 2011, 50, 7792–7801
Inorganic Chemistry
ARTICLE
Rb2KCrF6, Rb2KGaF6, K3MoO3F3, Sr3WO6, Sr3TeO6, Ba3-
TeO6, and A11B4O24(A = Ca, Sr; B = Re, Os; some of the
A-sites are vacant).3?9
The room-temperature crystal structure of R-K3AlF6is based
on the double-perovskite structure (K2KAlF6) with K+occupy-
ingtheA-siteandK+andAl3+rocksaltorderedovertheBandB0
positions.1In this structure all Al3+cations retain a nearly
undistorted octahedral coordination by fluorine. Four out of
ten of the AlF6octahedra undergo large (∼45?) rotations rela-
tive to their positions in the ideal double-perovskite structure.
One-fifth of the AlF6octahedra are rotated about the c cubic
perovskite subcell axis, while 1/10 are rotated about the a cubic
perovskite subcell axis and 1/10 are rotated about the b cubic
perovskitesubcellaxis.Theserotationsincreasethecoordination
numbers of the K+ions on the B-sites (hereafter denoted KB)
such that now two-fifths are 7-coordinate and three-fifths are
8-coordinate. This pattern of octahedral tilting results in a
structure with Z = 80 and a unit cell with a volume of over
12000 Å3.
A previous study has shown that four polymorphs of K3AlF6
exist within the temperature range of 20?800 ?C.10Upon being
heating fromroomtemperature,theR-phase transforms intothe
β-phase.Differentialscanningcalorimetry(DSC)measurements
have shown that the β-phase exists within the narrow tempera-
ture range of 132?153 ?C. It is only observed upon heating,
whereas upon cooling the sample appears to undergo a direct
γ f R phase transition at 129 ?C. Previous attempts to observe
the β-phase using X-ray and electron diffraction were not
successful, and therefore, no structural information is available
on this phase. The previous DSC results have shown that the
γ-phaseexistsinthetemperaturerangeof153?306?C.Electron
diffraction experiments have indicated space group Fddd and
have provided the unit cell dimensions, but the crystal structure
has remained unsolved. The X-ray diffraction (XRD) and DSC
resultsindicated thatabove300?310?CK3AlF6transforms into
theδ-phase.10?12Theδ-phaseisreportedtohavetheidealcubic
double-perovskite structure with space group Fm3m, although
atomic coordinates have not yet been reported.10,12
The crystal structure of the room-temperature R-phase has
already been solved and is described above.1In this study, we
reportthecrystal structures ofthe β-,γ-,andδ-phasesof K3AlF6
as determined from neutron powder diffraction (NPD), syn-
chrotron X-ray powder diffraction (SXPD), and electron diffrac-
tion (ED) measurements. We also show using the pair distri-
bution function (PDF) method that the local structure of the
δ-phase differs greatly from its cubic long-range average.
2. EXPERIMENTAL SECTION
The synthesis of the K3AlF6sample has been reported elsewhere.1
The time-of-flight neutron powder diffraction data used for the Rietveld
refinements were collected on the high-resolution powder diffract-
ometer (HRPD) of the ISIS facility of the Rutherford Appleton Labo-
ratory. Data sets with long collection times were taken at 143, 225, and
400 ?C. In addition, a number of data sets with shorter collection times
were taken at 125, 130, 135, 140, 145, 150, 155, 160, and 177 ?C.
Rietveld refinements were performed using the Topas Academic and
JANA2006 software packages.13,14
The neutron total scattering data used for the PDF analysis were
collected at 400 ?C on the neutron powder diffractometer (NPDF) of
the Lujan Neutron Scattering Center at Los Alamos National Labora-
tory. Data reduction to obtain the G(r) function was done using the
program PDFgetN.15Large box reverse Monte Carlo simulations were
done using the program RMCProfile.16
Synchrotron X-ray powder diffraction data were collected on the
ID31 beamline of the European Synchrotron Radiation Facility (ESRF)
(λ = 0.3962 Å). The data were collected by eight scintillation detectors,
each preceded by a Si(111) analyzer crystal, in the angular range 2θ =
1?40?. The powder sample was placed into a quartz capillary with an
internaldiameterof0.5mm.Toachieveproperstatisticsandtoavoidthe
preferred orientation,thecapillarywasspunduringtheexperiment.The
sample was heated above room temperature (RT) with a flow of
nitrogen or hot air. Data sets with long collection times were taken at
142, 227, and400 ?C.Datasets with shortercollection timeswere taken
as a series of continuous scans in the temperature range from 25 to
375 ?C, with the averaged temperatures provided in Table S2 of the
Supporting Information. The samples for the ED investigation were
preparedbycrushingthepowdersampleinethanolanddepositingitona
holey carbon grid. Selected area ED patterns were recorded using Philips
CM20 and Tecnai G2 microscopes equipped with heating holders.
3. RESULTS AND DISCUSSION
3.1. Electron Diffraction: Unit Cells and Space Groups of
the β- and γ-Polymorphs. ED patterns at different tempera-
tures demonstrate a sequence of transformations on going
through the R f β and β f γ phase transitions (Figure 1).
The RT ED patterns of the R-phase are indexed according to an
I41/a tetragonal unit cell, with the lattice vectors related to the
basic double-perovskite lattice vectors as aR= 2adp? bdp, bR=
adp+2bdp,andcR=4cdp(adp,bdp,andcdparethebasisvectorsof
the parent double-perovskite cubic unit cell with a ≈ 8.6 Å).10
Heating to 150 ?C completely suppresses the 4cdpsuperstruc-
ture, but the structure remains tetragonal and the superlattice
reflectionsinthea*?b*planestayintact.ThissetofEDpatterns
belongs to the β-phase and can be indexed with an I-centered
tetragonal unit cell with aβ=1/2adp?3/2bdp, bβ=3/2adp+
conditions were observed except those imposed by the I-center-
ing.Thegeometryofthe[001]EDpatternreflectstheabsenceof
2-fold axes perpendicular to the 4-fold axis and mirror planes
parallel to the 4-fold axis. The presence of a 41screw axis is
incompatible with cβ= cdp. This restricts the space groups to
I4/m, I4, and I4. The ED patterns of the γ-phase were registered
at 190 ?C. They are indexed in an orthorhombic unit cell with
latticevectorsaγ=3adp?3bdp,bγ=adp+bdp,andcγ=2cdpand
space group Fddd, in agreement with the earlier report.10
3.2. High-Temperature NPD and SXPD: Monitoring the
Phase Transitions. An overview of the changes in the SXPD
patterns of K3AlF6is shown in Figure 2. The SXPD patterns
collectedbetweenRTand132?CcanbeindexedastheR-phase.
The SXPD pattern collected at 137 ?C contains peaks corre-
sponding to both the R- and β-phases. The SXPD patterns in
the 142?152 ?C temperature range belong exclusively to the
β-phase. The β f γ transition occurs over a broad temperature
range: SXPD patterns collected between 157 and 172 ?C show a
mixture of the β- and γ-phases, while SXPD patterns taken
between 177 and 275 ?C correspond to the γ-phase only. The
γ-phase transforms to the δ-phase at 300 ?C. The NPD patterns
are in good agreement with the SXPD data (Figure 3). The tem-
peratures of the R f β and β f γ phase transitions were
estimated from NPD data as ∼135 and ∼145?160 ?C. The
transitiontemperaturesestimatedfromtheSXPDandNPDdata
areconsistentwiththepreviousDSCmeasurementswhichshow
1/2bdp,andcβ=cdp(aβ=aR/√2;cβ=1/4cR).Nootherreflection

Page 3

7794
dx.doi.org/10.1021/ic200956a |Inorg. Chem. 2011, 50, 7792–7801
Inorganic Chemistry
ARTICLE
the critical temperatures of the R f β, β f γ, and γ f δ phase
transitions to be 132, 153, and 306 ?C, respectively.10Lattice
parameters obtained by fitting the NPD and SXPD patterns are
given in Tables S1 and S2 of the Supporting Information,
respectively.Variationoftheparametersofthedouble-perovskite
subcell and the subcell volume with temperature for the R-, β-,
γ-, and δ-phases are shown in Figure 4. The unit cell parameters
and volume demonstrate clear discontinuities at the phase
transitions.This,togetherwiththeobservationofthecoexistence
ofthelow-andhigh-temperaturephasesattheRfβandβfγ
phase transitions, indicates that all transitions are of first order.
3.3. Crystal Structure of the β-Phase. The unit cell of the
β-phase is the same as the unit cells of the related compounds
Rb2KCrF6and Rb2KGaF6(after transformation from the non-
standard F-centered unit cell to the standard I-centered cell).3
Thecrystalstructuresofthesecompoundswerethereforeusedas
a starting point for the refinement of the β-phase crystal struc-
ture. Rietveld refinements were done in space groups I4/m,
Figure 2. Part of the SXPD patterns showing thermal evolution of the
222 and 004 reflections of the cubic face-centered δ-phase. The stability
regions of the four polymorphs are marked. The intensity of the
reflections is given in a color code (lowest, blue; highest, yellow). The
temperature scale is not linear.
Figure 3. Selected regions of the NPD patterns of K3AlF6at various
temperatures showing the R f β and β f γ phase transitions. The 222
and 004 subcell peak groups have been labeled.
Figure 1. Electron diffraction patterns at RT (R-phase, left column), 150 ?C (β-phase, central column), and 190 ?C (γ-phase, right column).

Page 4

7795
dx.doi.org/10.1021/ic200956a |Inorg. Chem. 2011, 50, 7792–7801
Inorganic Chemistry
ARTICLE
I4, and I4. A satisfactory fit to the peak intensities could be
obtainedusingspacegroupI4/m.RefinementsusinganI4model
gave a distinctly worse fit and negative atomic displacement
parameters (ADPs) for the Al atoms, so this model was dis-
carded.RefinementsinspacegroupI4providedasmallimprove-
ment to the fit and allowed for a small amount of additional
octahedraltilting.Whileitisnotpossibletoconclusivelydifferen-
tiatebetweenI4/mandI4,itisapparentthatanydeviationsfrom
I4/m symmetry, if they exist, are subtle. Therefore, the results of
the I4/m refinement are given. The refinement was done jointly
against both the NPD pattern taken at 143 ?C and the SXPD
pattern taken at 142 ?C, with both patterns weighted equally.
TherwpofthefittotheSXPDdatawas10.7,andtherwpofthefit
to the NPD data was 8.0. The ADPs of all atoms corresponding
tothesametypeofposition(KA,KB,Al,andF)wereconstrained
to be the same. Experimental, calculated, and difference SXPD
and NPD profiles after the Rietveld refinement are shown in
Figure 5. Crystallographic data are given in Table 1. The atomic
coordinates are given in Table 2, and selected bond distances are
given in Table 3.
The crystal structure of β-K3AlF6 can be described as a
derivative of the double-perovskite structure. The key difference
is large (∼45?) rotations about the c-axis of one-fifth of the AlF6
octahedra. The other octahedra have the positions they would
have in the ideal double-perovskite structure. The ∼45? rota-
tions result in four-fifths of the KBatoms obtaining a 7-coordi-
nate pentagonal-bipyramidal geometry while the remaining one-
fifth retain octahedral coordination (Figure 6). The F atoms of
the common edge of the heavily rotated AlF6octahedron and
KBF7polyhedron form particularly long bonds to the KBatoms.
In response, these KBatoms undergo large displacements of
∼0.48 Å from their ideal positions toward the edge shared with
the AlF6octahedra.
Bond valence sums (BVSs) were calculated for all of the
cations. According to Brown et al., the R0constant in the
BVS equation as estimated from the room-temperature bond
lengths cannot be directly used for calculating BVSs at higher
temperatures.17,18The R0value as a function of temperature
can be calculated as R0(T) = R0+ (dR/dT)ΔT, where dR/dT
is a function of the bond valence s and ΔT is the temperature
increase with respect to room temperature.18For the Al?F
bond with a length of 1.81 Å, dR/dT ≈ 2 ? 10?5Å3K?1(see
Figure 5 in ref 18). For the maximal temperature of 400 ?C
used in this investigation, this gives only a ∼0.5% increase
of R0 and a ∼2% increase in the bond valence. These
changes are comparable with those caused by experimental
Figure 4. Temperature variation of the double-perovskite subcell
parameters and subcell volume for the four polymorphs. For the R- and
β-phases the subcell is tetragonally distorted. The subcell of the γ-phase
has adp= bdpand is slightly monoclinically distorted with the monoclinic
angle γ ≈ 90.07?.
Figure5. ResultsofthejointRietveldrefinementoftheXRDandNPD
patternsofβ-K3AlF6.Thegraycirclesarethedatapoints,thesolidlineis
the fit, the difference curve is shown beneath, and the tick marks show
the positions of allowed hkl reflections.
Table 1. Crystallographic Data for the Four Polymorphs of
K3AlF6a
R-phase
β-phase
γ-phase
δ-phase
temp (?C)
space group
a (Å)
b (Å)
c (Å)
V (Å3)
Z
density (g/cm3)
aThe data for the R-phase were taken from ref 1.
25
I41/a
18.8385(3)
143
I4/m
13.3862(5)
225
Fddd
36.1276(4)
12.0562(1)
17.1133(2)
7,453.9(3)
48
2.761
400
Fm3m
8.5943(1)
33.9644(6)
12,053.6(3)
80
2.845
8.5617(3)
1,534.2(2)
10
2.801
634.79(1)
4
2.702

Page 5

7796
dx.doi.org/10.1021/ic200956a |Inorg. Chem. 2011, 50, 7792–7801
Inorganic Chemistry
ARTICLE
uncertainties in the bond lengths and will be ignored in
further BVS calculations.
TheAl(1) andAl(2) atomshaveBVSsof2.91 and3.17,which
are in good agreement with their expected valence of 3. The
KB(1) atom, which is in octahedral coordination, has a BVS of
1.78, showing it to be strongly overbonded. The KB(2) atom,
which is in pentagonal-bipyramidal geometry, has a BVS of 1.22,
whichismuchcloser toits idealvalenceof 1.However,thisatom
isstilldistinctlyoverbonded.Thelargedegreeofoverbondingfor
the KBatoms may be responsible for the apparent instability of
the β-phase. The K atoms that reside on the A-site (KA) have
BVSs that are fairly close to their ideal values, although there is a
small degree of underbonding. The BVSs for the KA(1) and
KA(2) atoms are 0.80 and 0.86, respectively.
The crystal structureof β-K3AlF6isisostructural withthe low-
temperature crystal structures of Rb2KCrF6and Rb2KGaF6.3
The β-phase of K3AlF6is also closely related to the R-phase of
K3AlF6. In both crystal structures one-fifth of the AlF6octahedra
arerotatedby∼45?aboutthec-axis.TheRfβphasetransition
can bethought toprimarily involvetheAlF6octahedra whichare
rotated by ∼45? about the a and b subcell axes in the R-phase.
During the transition, these octahedra rotate back to their original
positionsintheidealdouble-perovskitestructure.Thechangesin
the orientations of these octahedra appear to expand the
structure along the c-axis. As can be seen in Figure 4, there is a
discontinuous increasein the cdpsubcell parameter upon passing
through the phase transition. Meanwhile, the adpsubcell para-
meter increases smoothly, seemingly unaffected by the phase
transition.
3.4. Crystal Structure of the γ-Phase. In constructing a
starting model for the refinement of the γ-phase, several simpli-
fying assumptions were made. First, it was assumed that the
cation sublattice remains essentially the same as in the double-
perovskite structure. It was also assumed that the Al cations
retain octahedral coordination by fluorine but the KBcations do
not necessarily have octahedral coordination. The initial posi-
tionsforallatomswerethepositionstheywouldhaveintheideal
double-perovskite structure. When the cubic structure is trans-
formed into the Fddd supercell, there are two possible choices of
origin which place the B and B0cations on sites with different
symmetries. One possibility is to have four B cations: two
residing on the 8a and 8b Wyckoff sites and two others residing
on 16e sites. In this setting, there are two B0cations which sit on
Table 3. Selected Interatomic Distances for β-K3AlF6(Å)
Al(1)?F(1)
Al(1)?F(2)
Al(2)?F(3)
Al(2)?F(4)
Al(2)?F(5)
Al(2)?F(6)
Al(2)?F(7)
KB(1)?F(2)
KB(1)?F(3)
KB(2)?F(1)
KB(2)?F(1)
KB(2)?F(4)
KB(2)?F(5)
KB(2)?F(6)
KB(2)?F(7)
1.816(7)?4
1.806(9) ?2
1.823(8)
1.967(8)
1.712(8)
1.728(8)
1.757(3)?2
2.475(9)?2
2.426(7)?4
2.763(9)
2.811(8)
2.756(8)
2.487(8)
2.638(7)
2.563(3)?2
KA(1)?F(4)
KA(1)?F(5)
KA(1)?F(7)
KA(2)?F(1)
KA(2)?F(2)
KA(2)?F(3)
KA(2)?F(3)
KA(2)?F(4)
KA(2)?F(5)
KA(2)?F(6)
KA(2)?F(6)
KA(2)?F(7)
KA(2)?F(7)
KA(2)?F(7)
3.005(7)? 4
2.972(6)?4
3.001(4)?4
2.669(4)
3.191(2)
3.036(7)
2.927(7)
2.848(7)
3.144(7)
3.093(7)
2.804(8)
2.989(4)
3.007(4)
2.928(4)
Table 2. Atomic Coordinates and Displacement Parameters
for β-K3AlF6at ∼143 ?C from the Joint Rietveld Refinement
of the NPD Pattern and SXPD Patterns
atomWyckoff sitex/ay/bz/cUiso(Å2)
KA(1)
KA(2)
KB(1)
KB(2)
Al(1)
Al(2)
F(1)
F(2)
F(3)
F(4)
F(5)
F(6)
F(7)
4d
16i
2b
8h
2a
8h
8h
4e
8h
8h
8h
8h
16i
0
0.1069(1)
0
0.2316(2)
0
0.1995(2)
0.0653(6)
0
0.3260(5)
0.1529(7)
0.0759(5)
0.2446(8)
0.2021(3)
1/2
0.2097(1)
0
0.4178(2)
0
0.3989(3)
0.1189(5)
0
0.4493(7)
0.5382(5)
0.3660(7)
0.2779(5)
0.4074(3)
1/4
0.2698(2)
1/2
1/2
0
0
0
0.2110(9)
0
0
0
0
0.2047(4)
0.0440(4)
0.0440(4)
0.0625(7)
0.0625(7)
0.0179(5)
0.0179(5)
0.0633(5)
0.0633(5)
0.0633(5)
0.0633(5)
0.0633(5)
0.0633(5)
0.0633(5)
Figure 6. Two views of the crystal structure of β-K3AlF6. (a) shows a
singleunitcell.ThesmallgreenatomsareAl,thelargeblueatomsareKB,
the large gray atoms are KA, and the small red atoms are F. The lines
show the unit cell boundaries. (b) shows a single layer of Al and KB
coordination polyhedra viewed down the c-axis.

Page 6

7797
dx.doi.org/10.1021/ic200956a |Inorg. Chem. 2011, 50, 7792–7801
Inorganic Chemistry
ARTICLE
16g and 32h sites. The other origin choice has the B and B0
cations reversed.
Refinements were done jointly against the NPD and SXPD
datasetsusingbothoriginchoiceswithrigid-bodyconstraintsfor
the AlF6octahedra to reduce the number of variables during the
early stages of refinement. During the final stages of the refine-
ment,allconstraintswereremovedanddisplacementparameters
were allowed to refine. Despite the large number of structural
variables (41 degrees of freedom for the atomic positions), good
fits to the data could not be obtained using either model. After
having exhaustively searched for a solution in space group Fddd,
symmetry lowering was considered. Two models were found in
space groupsFdd2and F2ddwhichfitthe dataequallywell. Both
modelsarestructurallyverysimilar,andeachhasone-sixthofthe
AlF6octahedra undergoing large rotations while the remaining
five-sixths remain essentially untilted and undistorted. This
suggested that having one-sixth of the octahedra heavily rotated
couldbeakeystructuralfeatureofthisphase.Inbothmodels,the
rotated octahedron was strongly distorted, resulting in unrea-
sonably short F?F distances. The fact that equivalent good fits
with nearly the same structure could be obtained with d-glide
planes perpendicular to either the a- or c-axis suggests that both
glide planes are present and the true symmetry is indeed Fddd.
The large distortion of the rotated octahedra can be taken as a
sign that there is positional disorder of the F atoms that are part
of these octahedra. On the basis of this knowledge, a new model
was constructed with Fddd symmetry. The origin choice which
has the Al cations on the 8a, 8b, and two 16e sites was chosen,
since this permits one-sixth of the octahedra to be unique. The F
atomssurroundingtheAlonsite8bweresplitintotwopositions.
The F3 atom (on site 16g) was moved onto a general position
with 32-fold multiplicity. The F4 atom, which was already on a
generalposition,wassplitintotwoatoms(F4aandF4b).TheF3,
F4a, and F4b atoms were all given site occupancies equal to one-
half. This increased the total number of atomic degrees of
freedom to 46. It should be noted that without split positions
it is not possible to have one-sixth of the AlF6octahedra with a
uniquerotationangle inspace groupFdddsincethesymmetryof
the 8-fold sites prohibits these octahedra from rotating. This
model provided an excellent fit to both the SXPD and NPD
diffraction patterns(Figure7).TherwpofthefittotheXRDdata
was 10.0, and the rwpof the fit to the NPD data was 2.86.
Crystallographic data for γ-K3AlF6are given it Table 1. The
atomic coordinates are given in Table 4, and selected bond
distances are given in Table 5.
The crystal structure of γ-K3AlF6is shown in Figures 8 and 9.
It can be described as a superstructure of the double-perovskite
structure where one-sixth of the AlF6octahedra are rotated by
∼45? while the other five-sixths of the AlF6octahedra remain
nearly untilted and undistorted. These large rotations are dis-
ordered and randomly occur about either the [110] or [110]
direction (corresponding to the adpor bdpsubcell axes). The
disorder could be related to the weak interaction between the
rotated octahedra due to the large separation between them. A
largerotationinoneofthesetwodirectionsisprobablyneededto
stabilize the structure, but since the rotated octahedra are far
apart, it makes little energy difference in which direction this
rotation occurs relative to the other rotated octahedra. Disor-
dered anion positions in double-perovskite-related compounds
Figure7. ResultsofthejointRietveldrefinementoftheXRDandNPD
patternsofγ-K3AlF6.Thegraycirclesarethedatapoints,thesolidlineis
the fit, the difference curve is shown beneath, and the tick marks show
the positions of allowed hkl reflections.
Table 4. Atomic Coordinates, Site Occupancies (Occ), and
Displacement Parameters for γ-K3AlF6at ∼225 ?C from the
Joint Rietveld Refinement of the NPD and SXPD Patterns
atom
Wyckoff
sitex/ay/bz/cOccUiso(Å2)
Al(1)
Al(2)
Al(3)
Al(4)
KB(1)
KB(2)
KA(1)
KA(2)
KA(3)
F(1)
F(2)
F(3)
F(4a)
F(4b)
F(5)
F(6)
F(7)
F(8)
F(9)
F(10)
8a
8b
16e
16e
32h
16g
32h
32h
32h
32h
16g
32h
32h
32h
32h
32h
32h
32h
32h
32h
1/8
1/8
0.2892(2)
0.4581(2)
0.1979(1)
1/8
0.1247(1)
0.2102(1)
0.2159(1)
0.1575(1)
1/8
0.1545(3)
0.0815(3)
0.1311(3)
0.2901(2)
0.2544(2)
0.3240(2)
0.4594(2)
0.4925(2)
0.4242(2)
1/8
5/8
1/8
1/8
0.3965(3)
1/8
0.3442(3)
0.1210(4)
0.1283(4)
0.0175(5)
1/8
0.5679(9)
0.5614(8)
0.7401(8)
0.1203(6)
0.2311(4)
0.0162(5)
0.1382(5)
0.2361(5)
0.0178(5)
1/8
1/8
1/8
1/8
0.1258(2)
0.4127(3)
0.2642(2)
0.2504(2)
0.7619(2)
0.1199(4)
0.2314(4)
0.1934(6)
0.1559(6)
0.1939(5)
0.0206(3)
0.1253(5)
0.1249(5)
0.0217(3)
0.1270(5)
0.1230(5)
1
1
1
1
1
1
1
1
1
1
1
0.5
0.5
0.5
1
1
1
1
1
1
0.0102(5)
0.0102(5)
0.0102(5)
0.0102(5)
0.0389(5)
0.0389(5)
0.0389(5)
0.0389(5)
0.0389(5)
0.0428(5)
0.0428(5)
0.0428(5)
0.0428(5)
0.0428(5)
0.0428(5)
0.0428(5)
0.0428(5)
0.0428(5)
0.0428(5)
0.0428(5)

Page 7

7798
dx.doi.org/10.1021/ic200956a |Inorg. Chem. 2011, 50, 7792–7801
Inorganic Chemistry
ARTICLE
withalargeB/B0sizedifferencehavebeenobservedbefore,suchas
inthecaseofBa11W4O23.19BondvalencesumsfortheAl(1),Al(2),
Al(3), and Al(4) cations were calculated to be 3.24, 3.08, 3.02, and
3.07, respectively, in good agreement with their expected values.
The large ∼45? rotations of the AlF6octahedra serve to
increase the coordination numbers of some of the B-site cations.
A large ∼45? rotation of an AlF6octahedron will result in edge
sharing between the AlF6 octahedron and the coordination
polyhedra of four out of six neighboring B-site cations. In
γ-K3AlF6, every KBatom is surrounded by one heavily tilted
AlF6octahedron andfivenearlyuntiltedoctahedra. Edgesharing
will occur if the rotation axis is perpendicular to the vector
connecting the Al and KBatoms. If this vector coincides with the
rotation axis, corner sharing persists. There are two crystal-
lographically unique KBatoms in γ-K3AlF6, the KB(1) atom on
Wyckoff position 32h and the KB(2) atom on Wyckoff position
16g. Due tothe disorderin the direction of the octahedraltilting,
half of the KB(1) atoms become 7-coordinated while the other
halfretaina6-coordinatedoctahedral environment.TheBVSfor
KB(1)is1.31,indicatingthatthisatomissomewhatoverbonded.
It could be expected that the KB(1) atoms which are 7-coordi-
natedareabletoobtainaBVSwhichisclosetheidealvaluewhile
the overbonding is more severe for those that are 6-coordinated.
The KB(2) atoms are always 7-coordinated and have a BVS of
1.12, which is much closer to the ideal valence. There is still
disorderinthewaytheKB(2)atomiscoordinatedbytheFatoms
on the heavily rotated octahedron, but whichever way this
octahedron is rotated, edge sharing results. Depending on the
direction the AlF6octahedron is rotated, the shared edge runs
along one of two perpendicular directions.
As discussed earlier, edge sharing results in two long bonds
between F atoms belonging to the heavily rotated AlF6octahe-
dron and the KBatoms. This causes the KBatoms to shift toward
the edge shared with the rotated AlF6octahedron. The KB(1)
atom is found to shift about 0.42 Å, while the KB(2) atom shifts
about 0.64 Å. The smaller apparent shift of the KB(1) atom is
probablyrelatedtothefactthat,duetothedisorderoftheFatom
positions, only half of these atoms share an edge of their
coordination polyhedron with an AlF6octahedron. When the
edge sharing occurs, those KB(1) atoms may be shifted by a
distancewhichisverysimilartowhattheKB(2)atomsareshifted
by, whereas those KB(1) atoms that do not share an edge with a
neighboring AlF6octahedron undergo only small displacements.
The shift observed in the crystal structure would be an average of
these two situations. The large ADPs obtained for the K atoms
suggestthatasmalldegreeofpositionaldisordermayexistfortheK
atoms,whichismostlikelycausedbythedisorderintheFpositions.
The large rotation of one-sixth of the AlF6octahedra also
changes the coordination environments of some of the KAatoms.
Inthedouble-perovskitestructure,eachA-sitecationisneighbored
by four B and four B0cations. There are three crystallographically
unique KAatoms in γ-K3AlF6. The KA(1) and KA(3) atoms are
each surrounded by three nearly untilted AlF6octahedra and one
heavily tilted AlF6octahedron. This tilting reduces their coordina-
tionnumberbelow12andallowsfortheformationofsomeshorter
K?F bonds. The BVSs for the KA(1) and KA(3) atoms are 0.94
and 0.93, respectively, showing that they have a nearly ideal
coordination environment. The KA(2) atom is surrounded by
nearly untilted AlF6octahedra only and therefore retains a nearly
undistorted cubooctahedral coordination environment. The BVS
of the KA(2) atom is calculated to be 0.76, which shows that the
lack of octahedral tilting around it leaves this atom underbonded.
Table 5. Selected Interatomic Distances for γ-K3AlF6(Å)
Al(1)?F(1)
Al(1)?F(2)
Al(2)?F(3)
Al(2)?F(4a)
Al(2)?F(4b)
Al(3)?F(5)
Al(3)?F(6)
Al(3)?F(7)
Al(4)?F(8)
Al(4)?F(9)
Al(4)?F(10)
KB(1)?F(4a)
KB(1)?F(1)
KB(1)?F(5)
KB(1)?F(8)
KB(1)?F(9)
KB(1)?F(3)
KB(1)?F(6)
KB(1)?F(4b)
KB(2)?F(10)
KB(2)?F(7)
KB(2)?F(3)
KB(2)?F(4b)
KB(2)?F(2)
KA(1)?F(4b)
KA(1)?F(2)
KA(1)?F(10)
KA(1)?F(7)
KA(1)?F(1)
1.751(6)?4
1.821(7)?2
1.73(1)?4
1.83(1)? 4
1.83(1)? 4
1.788(5)? 2
1.795(7)? 2
1.816(7)? 2
1.776(5)? 2
1.827(7)? 2
1.779(7)? 2
2.32(1)
2.460(7)
2.550(6)
2.565(6)
2.577(6)
2.84(1)
2.853(6)
3.02(1)
2.550(6)? 2
2.590(6) ?2
2.77(1)?2
2.83(1)?2
3.102(8)?2
2.34(1)
2.702(4)
2.790(8)
2.800(8)
2.914(7)
KA(1)?F(1)
KA(1)?F(8)
KA(1)?F(10)
KA(1)?F(5)
KA(1)?F(7)
KA(1)?F(3)
KA(2)?F(5)
KA(2)?F(8)
KA(2)?F(6)
KA(2)?F(7)
KA(2)?F(6)
KA(2)?F(9)
KA(2)?F(6)
KA(2)?F(5)
KA(2)?F(10)
KA(2)?F(2)
KA(2)?F(1)
KA(2)?F(1)
KA(3)?F(4a)
KA(3)?F(3)
KA(3)?F(9)
KA(3)?F(8)
KA(3)?F(6)
KA(3)?F(5)
KA(3)?F(7)
KA(3)?F(10)
KA(3)?F(9)
KA(3)?F(9)
KA(3)?F(8)
3.044(7)
3.069(8)
3.072(8)
3.088(8)
3.126(8)
3.15(1)
2.911(7)
2.926(8)
2.949(8)
2.969(9)
2.983(8)
3.004(9)
3.009(8)
3.042(9)
3.084(9)
3.094(4)
3.109(7)
3.188(7)
2.60(1)
2.61(1)
2.734(8)
2.763(7)
2.785(8)
2.929(9)
2.930(8)
2.998(8)
3.081(8)
3.098(9)
3.226(8)
Figure8. Oneunitcellofγ-K3AlF6.Thecolorschemeisthesameasfor
Figure 4.
Figure 9. A single layer of AlF6octahedra and KBatoms in γ-K3AlF6
viewed down the c-axis. The color scheme is the same as for Figure 4.

Page 8

7799
dx.doi.org/10.1021/ic200956a |Inorg. Chem. 2011, 50, 7792–7801
Inorganic Chemistry
ARTICLE
3.5. Crystal Structure and Local Structure of the δ-Phase.
A previous study has reported that above 306 ?C the crystal
structureofK3AlF6transformsintothatoftheidealcubicdouble
perovskite with space group Fm3m.10Our SXPD data show that
the γ f δ transition occurs between 275 and 300 ?C. The NPD
and SXPD patterns collected at 400 ?C can be indexed using
space group Fm3m. A Rietveld refinement using the NPD data
was carried out in this space group to determine the structural
parameters. The only structural variables to refine in Fm3m are
the x position of the F site and the four atomic displacement
parameters. Refinement of these variables was not able to
produce a satisfactory fit to all peak intensities. Refinement of
anisotropic ADPs for the F atom improved the fit significantly
and resulted in all peak intensities being reasonably well fit
(Figure 10). The refinement had an rwpof 2.49. The resulting
structure is shown in Figure 11. Crystallographic data are
given in Table 1, and the atomic coordinates are given in
Table 6. A Rietveld refinement of the 400 ?C SXPD data
(Figure S1, Supporting Information) produced nearly iden-
tical results.
The anisotropy of the ADPs for the F atom is quite large. The
fluorine mean square displacements perpendicular to the Al?F
andKB?Fbondswererefinedtobeabout4timeslargerthanthe
displacements parallel to these bonds. This suggested the possi-
bility that large-amplitude dynamic rotations of the AlF6octahe-
dra are occurring in this phase. Additional Rietveld refinements
werecarriedoutwheretheAlF6octahedronwasdefinedasarigid
body and the TLS definition was used for the displacement
parameters. The TLS method defines the displacements of the
atoms in terms of translations, librations, and screw motions
of the entire rigid body. The advantage of using the TLS defi-
nition in this particular case is that the average rotation of the
AlF6octahedron is given in units of degrees. These refinements
showed that the average rotational displacement of the AlF6
octahedron is 9.7(1)?.
The bond distances in the crystal structure of δ-K3AlF6as
obtained from the Rietveld refinements were also unusual. The
Al?F distance of 1.798(1) Å is slightly shorter than expected
considering the average Al?F distance at room temperature is
1.81 Å.1 The KB?F bond length was refined to be 2.500(1) Å,
which is much shorter than expected and gives a bond valence
sumfortheKBatomof1.52.TheKA?Fbondlengthwasrefined
to be 3.0588(1) Å, which leaves this atom severely underbonded
with a BVS of only 0.67. The large deviation of the BVS
parameters of all the K atoms from their ideal valence of 1 would
seem to suggest that the δ-phase should be unstable. One
possible explanation for these observations is that there are large
local deviations from the average structure which relieve these
bonding instabilities. Disorder of the F atoms has been reported
in the related compound Na3AlF6.20To test this hypothesis and
gain further information about the local structure of this phase, a
pairdistributionfunctionanalysiswascarriedoutontheδ-phase.
To see if the local structure differs significantly from the long-
rangeaveragestructure,thelowrregionoftheexperimentalG(r)
functionwasfitusingtheaveragecubicstructureasamodel. The
resulting fit is extremely poor (Figure S2, Supporting In-
formation), showing that large local distortions do exist. To
model G(r), large box reverse Monte Carlo (RMC) simulations
were performed using the RMCProfile program. A 7 ? 7 ? 7
supercell of the crystallographic unit cell was constructed which
contained 13720 atoms. The initial positions for the atoms were
theirpositionsintheaveragestructure.Therefinementwasdone
jointly against both the G(r) and S(Q) functions. The final fit is
shown in the Supporting Information as Figure S3.
One way to visualize the results of the RMC refinement is to
fold the supercell back into a single unit cell so that “clouds” of
atom spatial distributions can be seen. The folded supercell of
δ-K3AlF6is shown in Figure 12. The Al distribution is small and
sphericalandcanbefullyaccountedforbythethermalvibrations
of the Al atoms around their average position, indicating that
Figure 10. Results of the Rietveld refinement of the NPD pattern of
δ-K3AlF6.Thegraycircles arethe datapoints,thesolid lineisthefit,the
differencecurveisshownbeneath,andthetickmarksshowthepositions
of allowed hkl reflections.
Figure 11. Crystalstructureofδ-K3AlF6.Thecolorscheme isthesame
as for Figure 4.
Table 6. Atomic Coordinates and ADPs for δ-K3AlF6from
Rietveld Refinement of the 400 ?C NPD Pattern
atom
Wyckoff
sitex/ay/bz/c
ADP,
Å2
KA
KB
Al
F
8c
4a
4b
24e
1/4
0
1/2
0.29085(1)
1/4
0
1/2
0
1/4
0
1/2
0
Uiso= 0.0654(1)
Uiso= 0.0505(1)
Uiso= 0.0243(1)
U11= 0.0292(1)
U22= U33= 0.1126(2)

Page 9

7800
dx.doi.org/10.1021/ic200956a |Inorg. Chem. 2011, 50, 7792–7801
Inorganic Chemistry
ARTICLE
there is no local disorder of these atoms. The spatial distribution
of the KBatoms is also spherical but slightly broader than the
distribution of the Al atoms, showing a small degree of disorder.
The KAatoms show a very broad spatial distribution that is also
spherical. This very broad distribution is consistent with the
largerthannormalADPobtainedforthisatomfromtheRietveld
refinement. Close inspection of the KAdistribution reveals that
these atoms do not tend to lie exactly on the A-site, but rather
undergo off-center displacements.
The RMC results also show that the spatial distribution of F
atoms is highly anisotropic. The distribution is quite narrow in
the direction parallel to the Al?F and KB?F bonds but very
broadperpendiculartothesebonds.Thiswouldseemtoindicate
that the AlF6octahedra undergo significant rotations. To more
quantitatively understand the nature of these rotations, the
distribution of Al?F?KBangles was extracted from the RMC
configuration (Figure 13). The average Al?F?KBangle in the
configuration is 162.5?. This corresponds to a rotation of the
AlF6octahedral unit by 10.2?, which is in good agreement with
the result obtained from the TLS Rietveld refinement. One
important observation is that there are essentially no Al?F?KB
bond angles at or near 180?, meaning that the F atoms almost
never lie on their average position. The most likely explanation
for these observations is that the AlF6octahedra in the δ-phase
are undergoing dynamic rotations within a bimodal potential
energy well. The potential energy minimum occurs when the
octahedral rotation angleis∼10?,andthelinear180?Al?F?KB
configuration (0? tilt) represents a local maximum.
The RMC results give more reasonable average bond lengths
than were obtained from the Rietveld refinements. The large
rotations of the AlF6ocahedra allow for longer Al?F and KB?F
bond lengths. The average Al?F bond length in the RMC
configuration is 1.826 Å, which is 0.028 Å longer than that
obtained from the Rietveld refinement and represents a slight
elongation relative to that of the room-temperature structure.
TheaverageKB?Fbondlengthof2.532Åis0.032Ålongerthan
in the average structure and results in the overbonding of the KB
atom being less severe than it appears to be from the average
structure. The octahedral rotations and off-center displace-
ments of the KAatoms result in a broad distribution of KA?F
bond lengths and serve to relieve the underbonding of this
atom. It could be expected that the direction of the KA
displacements is dictated by the local instantaneous arrange-
ment of octahedral tilts.
Theobservationofdynamicrotations oftheAlF6octahedra in
δ-K3AlF6raises the possibility that such rotations could be
occurring in some of the lower temperature phases as well. The
R f β phase transition involves some heavily tilted octahedra
transforming to an untilted configuration. If these octahedra are
not simply changing orientation but are also beginning to
undergo dynamic rotations, it could mean that some of the
apparent overbonding and underbonding of the K atoms in this
phase is not as severe as it appears to be. The β f γ phase
transition involves a more significant rearrangement of the
structure where the distribution of the heavily tilted octahedra
changes. It is likely that in this phase some or all of the untilted
octahedra undergo large-amplitude dynamic rotations as well.
Theexistenceoflarge-amplitudedynamicrotationsintheβ-and
γ-phases is supported by the large values of the F atom ADPs
obtained from the Rietveld refinements.
There are a few other double perovskites which display
noncooperativeoctahedraltiltingatlowertemperaturebuttrans-
formintoacubicphaseathighertemperature,suchasRb2KCrF6,
Rb2KGaF6, and Sr3WO6.3,5These results raise the question of
whetherlargeoctahedralrotationsarepresentinthecubicphases
of these other compounds as well.
’CONCLUSIONS
This investigation demonstrates for the first time a complete
structural characterization of a series of polymorphs which result
from a sequence of phase transitions in double-perovskite-based
structures with noncooperative octahedral tilting. The remark-
ablefeatureofthesephase transitionsisasteplike decreaseinthe
fraction of the AlF6octahedral units which are rotated over a
large angle of ∼45? on going from the low-temperature to high-
temperature polymorphs. The fraction of rotated octahedra
decreases from two-fifths in R-K3AlF6to one-fifth in β-K3AlF6,
one-sixth in γ-K3AlF6, and zero in δ-K3AlF6. Other octahedra in
thesestructuresundergoonlyrelativelysmalltilts.Thereduction
in the number of AlF6octahedra which undergo large tilts also
results in a systematic decrease in the coordination numbers of
theKionsontheB-sites.InR-K3AlF6,three-fifthsoftheseatoms
are 8-coordinate and two-fifths are 7-coordinate. In β-K3AlF6,
there are no longer any 8-coordinate B-site K atoms, but instead
Figure 13. Distribution of Al?F?KB bond angles in δ-K3AlF6
extracted from the RMC configuration.
Figure12. FinalconfigurationoftheRMCsupercellofδ-K3AlF6folded
backintoasingleunitcell.ThegreendotsareAlatoms,thebluedotsare
KBatoms, the gray dots are KAatoms, and the red dots are F atoms.

Page 10

7801
dx.doi.org/10.1021/ic200956a |Inorg. Chem. 2011, 50, 7792–7801
Inorganic Chemistry
ARTICLE
four-fiths are 7-coordinate and one-fifth are 6-coordinate. Upon
going toγ-K3AlF6,thecoordination oftheK atoms onthe B-site
is further reduced so that two-thirds are 7-coordinate and one-
third are 6-fold coordinate. In the highest temperature δ-phase,
all B-site cations have a coordination number of 6. This behavior
results in a discontinuous nature of the phase transitions and is
drastically different from octahedral tilting distortions in con-
ventional perovskites, where the corner-sharing links between
the octahedral units force them to behave cooperatively.
This study also shows an increase in the amount of structural
disorder as the temperature is increased. The R-phaseappears to
be very crystalline, with all atoms having well-defined positions.
Intheβ-andγ-phasesitissuspectedthatmanyoftheapparently
untilted AlF6octahedra begin to undergo large-amplitude dy-
namic rotations. The highly tilted AlF6octahedra in the γ-phase
alsoshowdisorderinthedirectionoftheirrotations.Theaverage
crystal structure of δ-K3AlF6 is cubic, but pair distribution
function analysis shows that all AlF6octahedra undergo large
uncorrelated rotations which are accompanied by off-center
displacementsoftheK+ionsontheA-sites.Theaveragerotation
of the AlF6octahedra in the δ-phase is about 10? at 400 ?C.
’ASSOCIATED CONTENT
b
S
Supporting Information.
turedependence ofthelattice parameters andunitcellvolumein
the temperature range of 125?145 ?C as obtained from Pawley
fits of the NPD patterns and lattice parameters of K3AlF6at
various temperatures as determined by Pawley fitting of the
synchrotron X-ray powder diffraction data and figures showing
the results of the Rietveld refinement of the XRD pattern of
δ-K3AlF6, experimental PDF of δ-K3AlF6and fit using the
average long-range structure as a model, and fit of the PDF of
δ-K3AlF6from the RMC refinement. This material is available
free of charge via the Internet at http://pubs.acs.org.
Tables showing the tempera-
’AUTHOR INFORMATION
Corresponding Author
*E-mail: gking@lanl.gov.
’ACKNOWLEDGMENT
This work has benefited from the use of the NPDF at the
Lujan Center at Los Alamos Neutron Science Center, funded by
the Department of Energy (DOE) Office of Basic Energy
Sciences. Los Alamos National Laboratory is operated by Los
Alamos National Security LLC under DOE Contract DE-AC52
06NA25396. P.M.W. acknowledges financial support from the
National Science Foundation (Award Number DMR-0907356).
We thank Joan Siewenie and Thomas Proffen for assistance in
collectionofthetotalscatteringdata.WearegratefultotheESRF
for providing the beamtime at ID31 and acknowledge Caroline
Curfs for her kind help during the experiment. We thank Aziz
Daoud-Aladine and Kevin Knight for assistance in collecting the
NPD data on the HRPD. A.T. was funded by the Alexander von
Humboldt Foundation.
’REFERENCES
(1) Abakumov, A. M.; King, G.; Laurinavichute, V. K.; Rozova,
M. G.; Woodward, P. M.; Antipov, E. V. Inorg. Chem. 2009, 48, 9336.
(2) Howard,C.J.;Kennedy,B.J.;Woodward,P.M.ActaCrystallogr.
2003, B59, 463.
(3) Zuniga, F. J.; Tressaud, A.; Darriet, J. J. Solid State Chem. 2006,
179, 3607.
(4) Withers, R. L.; Welberry, T. R.; Brink, F. J.; Noren, L. J. Solid
State Chem. 2003, 170, 211.
(5) King, G.; Abakumov, A. M.; Hadermann, J.; Alekseeva, A. M.;
Rozova, M. G.; Perkisas, T.; Woodward, P. M.; Van Tendeloo, G.;
Antipov, E. V. Inorg. Chem. 2010, 49, 6058.
(6) Stoger, B.; Weil, M.; Zobetz, E. Z. Kristallogr. 2010, 225, 125.
(7) Jeitschko, W.; Mons, H. A.; Rodewald, U. C.; M€ oller, M. H. Z.
Naturforsch. 1998, 53, 31–36.
(8) 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.
(9) Tomaszewska, A.; M€ uller-Buschbaum, H. Z. Anorg. Allg. Chem.
1993, 619, 1738–1742.
(10) Abakumov, A. M.; Rossell, M. D.; Alekseeva, A. M.; Vassiliev,
S. Y.; Mudrezova, S. N.; Van Tendeloo, G.; Antipov, E. V. J. Solid State
Chem. 2006, 176, 421.
(11) Grjotheim, K.; Holm, J. L.; Mikhael, S. A. Acta Chem. Scand.
1973, 27, 1299.
(12) Steward, E. G.; Rooksby, H. P. Acta Crystallogr. 1953, 6, 49.
(13) Topas Academic, General Profile and Structure Analysis Software
for Powder Diffraction Data; Bruker AXS: Karlsruhe, Germany, 2004.
(14) Petricek, V.; Dusek, M. The Crystallographic Computing System
JANA2000; Institute of Physics: Praha, Czech Republic, 2000.
(15) Peterson, P. F.; Gutmann, M.; Proffen, Th.; Billinge, S. J. L.
J. Appl. Crystallogr. 2000, 33, 1192.
(16) Tucker, M. G.; Keen, D. A.; Dove, M. T.; Goodwin, A. L.; Hui,
Q. J. Phys.: Condens. Matter 2007, 19, 335218.
(17) Brown, I. D.; Altermatt, D. Acta Crystallogr. 1985, B41, 244.
(18) Brown, I. D.; Dabkowski, A.; McCleary, A. Acta Crystallogr.
1997, B53, 750.
(19) Hong, S.-T. J. Solid State Chem. 2007, 180, 3039.
(20) Zhou, Q.; Kennedy, B. J. J. Solid State Chem. 2004, 177, 654.