Hypothetical AlF3 crystal structures

Article abstract of DOI:10.1016/j.jssc.2006.06.010

Applying a structure prediction computer programme (GRINSP=Geometrically Restrained INorganic Structure Prediction), the occurrence of 6-connected 3D networks was investigated, through AlF₆ octahedra exclusive corner sharing. The five known AlF₃ varieties were reproduced (α-, β-, η-, κ- and τ-AlF₃) and seven hypothetical models were predicted. Among these still to be synthesized AlF₃ phases, one can recognize two known structure types (TlCa₂Ta₅O₁₅, Ba₄CoTa₁₀O₃₀) and some easy to imagine intergrowths; however, a few others are completely unexpected, though simple. A comparison of the ab initio total energies of all the structures is provided, leading to the conclusion that the virtual models could well be viable.

Full text of DOI:10.1016/j.jssc.2006.06.010

ARTICLE IN PRESS
Journal of Solid State Chemistry 179 (2006) 3159–3166
www.elsevier.com/locate/jssc
Hypothetical AlF3 crystal structures
Ã
Armel Le Baila, , Florent Calvayracb
a
´
Universite du Maine, Laboratoire des Oxydes et Fluorures, CNRS UMR 6010, Avenue O. Messiaen, 72085 Le Mans, Cedex 9, France
´
Universite du Maine, Laboratoire des Physique de l’Etat Condense, CNRS UMR 6087, Avenue O. Messiaen, 72085 Le Mans, Cedex 9, France
b
Received 11 April 2006; received in revised form 23 May 2006; accepted 11 June 2006
Available online 15 June 2006
Abstract
Applying a structure prediction computer programme (GRINSP ¼ Geometrically Restrained INorganic Structure Prediction), the
occurrence of 6-connected 3D networks was investigated, through AlF6 octahedra exclusive corner sharing. The five known AlF3
varieties were reproduced (a-, b-, Z-, k- and t-AlF3) and seven hypothetical models were predicted. Among these still to be synthesized
AlF3 phases, one can recognize two known structure types (TlCa2Ta5O15, Ba4CoTa10O30) and some easy to imagine intergrowths;
however, a few others are completely unexpected, though simple. A comparison of the ab initio total energies of all the structures is
provided, leading to the conclusion that the virtual models could well be viable.
r 2006 Elsevier Inc. All rights reserved.
Keywords: Crystal structure prediction; Inorganic; AB3 compounds; Corner-sharing octahedra; aluminium fluorides; Monte Carlo simulation; Computer
modelling; Ab initio energy calculations
1. Introduction
reduce the number of false structure candidates, and to
establish serious databases which would include both
known and virtual crystal structures, the latter being
eventually confirmed. Using such databases would allow to
reduce the structure determination steps to a simple
identification (possibly by search-match techniques using
the powder pattern) followed by a refinement. Unfortu-
nately, a completely efficient theory is still lacking, so that
we are condemned to overload databases of virtual
structures with huge quantities of models that will never
be confirmed. Science must go on, even with imperfect
theories, so that a second database of hypothetical
compounds was built in 2003 [6], including zeolites as well
as other predicted oxides (phosphates, borosilicates,
titanosilicates, etc.) and fluorides. This database is essen-
tially filled in structure candidates by the Geometrically
Restrained Inorganic Structure Prediction (GRINSP) soft-
ware [7].
Contrarily to AB2 compounds with corner-sharing
tetrahedra (especially zeolites), it has been a long time
since the last AB3 structure built up from corner-sharing
octahedra was disclosed. An answer to the following
question may be of interest to solid state chemists: is it still
possible to find new AB3 structures of that kind? The
prediction of the stoichiometry and of the bond topology
(i.e., the approximate atomic arrangement) of the stable
compounds was long considered as being more difficult
than to calculate accurate static and dynamic properties of
a crystal, once accurate atomic coordinates and cell
dimensions were known [1]. However, generators of so-
called structure candidates [2] are developing and improv-
ing. A fabulous inorganic example consists in the more
than 1,000,000 zeolite models gathered into the hypothe-
tical zeolites database [3–4]. Concerning organic molecules,
the progress has been established by several recent blind
tests [5]. An efficient theory of materials should help us to
The aim of this work is to provide models with the AlF3
composition, built up from AlF6 octahedra sharing
exclusively their corners, by using GRINSP. Three-dimen-
sional AB3 compounds based on corner-sharing octahedra
were examined by the Automated Assembly of Secondary
Building Units approach, developed by Mellot-Draznieks
Ã
Corresponding author. Fax: +33 2 43 83 35 06.
E-mail addresses: alb@cristal.org (A. Le Bail),
Florent.Calvayrac@univ-lemans.fr (F. Calvayrac).
0022-4596/$ - see front matter r 2006 Elsevier Inc. All rights reserved.
doi:10.1016/j.jssc.2006.06.010

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3160
et al. [8–9], using Cerius2 [10] and GULP [11] in a sequence
of simulated annealing plus minimization steps for the
aggregation of large structural motifs, but no completely
new structure type was predicted, apparently, and not all
known structures were listed (t-AlF3 was lacking). From
the present study, 12 different AlF3 structure types will be
described, the conditions of the simulations are discussed
below.
In a second step the F atoms were added at the
midpoints of the Al–Al first neighbours and it was verified
by distance and cell improvements (by the MC method as
well) that regular AlF6 polyhedra could really be built, i.e.,
that there was a deep local minima existing close to this
previously selected rough arrangement of Al atoms. The
cost function allowing to establish a minimum is based on
the verification of the provided ideal distances Al–F
˚
˚
˚
(1.81 A), F–F (2.56 A) and Al–Al (3.5 A) first neighbours.
The total R factor is defined by the equation:
2. Prediction conditions
p
R ¼ ½ðR1 þ R2 þ R3Þ=ðR01 þ R02 þ R03Þꢀ,
The knowledge assumed in this study is limited to the
Al–F, F–F and Al–Al ideal first neighbour distances, and
the exclusive corner-sharing connection mode. More
generally, GRINSP makes use of the common geometrical
characteristics of a well-defined group of crystal structures
(N-connected 3D nets with N ¼ 3; 4; 5; 6 and possible
combinations of two N values), allowing to explore the
possible models, retrieving those already known (a proof of
efficiency), and listing those yet to be synthesized, in a
selected range of cell parameters.
Exploring AB3 models needed 230 days of calculation on
a single 2.4 GHz processor PC, 1 day per space group (SG).
GRINSP is a Monte Carlo (MC) software, applying a
pseudo-random number sequence to the heuristic solution
of the structural problem. Once a SG is selected, a first Al
atom is placed in a box (with cell parameters relations in
agreement with the SG) whose dimensions are selected at
random, at a Wyckoff position selected at random. One
then checks if the model is not already fulfilling all
requirements: one Al atom should have six Al first
where Rn and R0n for n ¼ 1; 2; 3 are defined by the
expressions:
2
Rn ¼ S½wnðd0n ꢁ dnÞꢀ ,
2
R0n ¼ S½wnd0nꢀ ,
where the d0n values for n ¼ 123 are the ideal first
interatomic distances Al–F ðn ¼ 1Þ, F–F ðn ¼ 2Þ and Al–Al
ðn ¼ 3Þ, whereas the dn values are the corresponding
observed distances in the structural model for these atom
pairs. The selected wn being w1 ¼ 2:0, w2 ¼ 0:61 and
w3 ¼ 0:23, attributing more weight to the respect of the
Al–F first distances. Models were retained if Ro0:03, they
may need further optimizations by using bond valence
rules, or energy calculation (as shown below), however, in
many cases the predicted cell parameters differ by less than
3% from the real ones when the real compounds are built
up from ideal polyhedra, which was the case with dense
SiO2 polymorphs or zeolites previously studied by
GRINSP [7] and AlF3 phases. During this second step,
the atoms are moving, but no jump is allowed because a
jump would break the coordinations established at the first
step. This is a simple routine for local optimization. The
change in the cell parameters from the rough structure
candidate to the final model may be quite considerable (up
to 30%). During the optimization, the original SG may not
be conserved, so that the final structure is always proposed
in the P1 SG, presented in a CIF file. The final choice of the
real symmetry has to be done by using a programme able
to detect missing symmetries, like PLATON [12].
One given model can be identified in different SGs with
slightly different or equal R values. For the automatic
recognition that a model is known or was already obtained
in previous predictions, tools are needed. An algorithm for
the efficient comparison of periodic structure (CMPZ) was
recently presented [13]. The way GRINSP recognizes a
structure type is by comparing the coordination sequence
(CS) [14] of any model with a list of previously established
ones (as well as with the other CS already stored during the
current run). CS originally developed for zeolites was
extended to the N-connected frameworks inside of the
GRINSP algorithm. Only one model was retained corre-
sponding to one structure type, selecting the model with
best R value and higher symmetry.
˚
neighbours in the approximated range 3.570.6 A, them-
˚
selves not distant outside of the range 4.2–6.7 A, as second
neighbours. The fact that distances are given a large
tolerance range allows many solutions to be captured
which may not correspond to regular polyhedra at this
stage. In other words, the model may stay far above the
local minima of interest. If the model is not already
completed, a second Al atom is inserted randomly at a new
(or identical) Wyckoff position, at random in the free space
(delimited by the distance ranges above) in the neighbour-
hood of the first atom and of its equivalents, if any. Then
this new model is checked again, etc., until a full agreement
with the geometrical specifications is reached. If after some
trials, no satisfying model is found, a new first Al will be
placed, and so on. For a given set of cell parameters,
300,000 MC events were performed, and at least 20,000 sets
of random cell parameters were explored for each SG. In
this first step, atoms do not move (this is not a simulated
annealing approach), their possible positions are tested and
checked, then they are retained or not. The cell is
progressively filled up to completely respect the geometrical
restraints, if possible. The total number of Al atoms placed
is not predetermined. For that search, the cell parameters
˚
were not larger than 16 A (known phases have cell
˚
parameters all smaller than 13 A).

ARTICLE IN PRESS
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3161
GRINSP is available via http://www.cristal.org/grinsp/.
The software is free of charge for non-profit organizations
and is delivered with the Fortran source code under the
GNU Public Licence. Parallelization of the code is in
project.
perovskite polymorph. A third framework is observed
crystallizing in the cubic pyrochlore structure for which
two aluminium fluoride equivalents have been reported,
Al(OH,F)3 [17] and Z-AlF3 [18]. The fourth framework is
the tetragonal tungsten bronze (TTB) for which a k-AlF3
phase was described [18]. The fifth one was described
only as an aluminium fluoride and named t-AlF3 [19]
(it was later given another designation: y-AlF3 [18]), which
is maybe the more complex structure with intrications of
tetrahedra of octahedra (as in the pyrochlore structure)
and infinite chains. Two other 6-connected frameworks
not known with AlF3 formula are typified by the structures
of Ca2TlTa5O15 [20] and Ba4CoTa10O30 [21]. It was
shown that these structures can be derived from the
ReO3 type by fourling and twinning operations [22], as
well as HTB and intergrowth tungsten bronze (ITB).
Many intergrowths could be imagined by increasing the
number of perovskite planes which is equal to two, between
two hexagonal ring regions in TlCa2Ta5O15. Finally,
two frameworks built up from octahedra of different
sizes may be listed: Na4Ca4Al7F33 [23] with an M11F33
corner-sharing net of CaF6 and AlF6 octahedra, and
Rb2NaAl6F21 [24] with an M7F21 net of NaF6 and AlF6
octahedra.
3. Known 6-connected 3D nets, AlF3 examples
When restricting considerations to the AB3 stoichiome-
try, among the various families of structures, there is one
where each A atom is connected to six others (through B
atoms) so that the A atoms lie at the points of a 3D 6-
connected net. Examining the existing 6-connected 3D nets,
one can distinguish nine different frameworks. The first
framework, and simplest of such structures corresponds, in
its most symmetrical configuration, to A atoms placed at
the vertex of a primitive cubic lattice, the B atoms being at
the middle of the edges, and represents the structure of
crystalline ReO3, more generally named as the perovskite
structure type (though perovskite is a mineral formulated
CaTiO3). Many of the main structure types belonging to
that family characterized by 6-connected 3D nets can be
found in the crystal chemistry of aluminium fluorides. The
stable perovskite-like form of AlF3 crystallizes with a
rhombohedral structure, SG R3c, and transforms rever-
sibly to the cubic ReO3-type polymorph at 725 K [15]. The
rhombohedral form is referred usually as a-AlF3. A
metastable form, called b-AlF3 is closely related to that
of hexagonal tungsten bronze (HTB), a second framework
In a strict classification of AB3 nets built from corner-
connected ideal octahedra, Herzig and Zemann [25]
retained only the perovskite, HTB and pyrochlore struc-
ture types because the representatives of TTB, and the
other structures, were containing some extra-framework
ions. Their comparative study in 1993 was incomplete,
since t-AlF3 [19] published in 1992 escaped to their
attention; moreover, the TTB AlF3 free of extra-frame-
work ion was obtained in 1995.
in this family. The distortion leads to an orthorhombic cell
with b/a ratio quite close to
pffiffi
3, pseudo-hexagonal,
generating systematic twinning, in SG Cmcm [16]. This b-
form transforms slowly and irreversibly to the cubic
Table 1
Comparison of AlF3 predicted cell parameters with observed ones
Predicted/observed
R
FD
Z
N
SG
Ref
PCOD entry No.
˚
a (A)
˚
b (A)
˚
c (A)
D(%)
a-AlF3 (perov)
b-AlF3 (HTB)
Z-AlF3 (pyr)
5.111
4.931
12.504
12.446
2.59
0.0062
0.0035
0.0046
0.0098
0.0159
21.21
19.67
17.71
20.78
21.17
6
1
1
1
2
3
1000048
1000049
1000017
1000050
1000014
¯
R3c
[15]
[16]
[17]
[18]
[19]
6.984
6.931
12.107
12.002
7.213
7.134
0.91
0.84
1.46
0.48
12
16
10
16
Cmcm
9.667
9.749
¯
Fd3m
k-AlF3 (TTB)
t-AlF3 (or y-)
11.539
11.403
3.615
3.544
P4/mbm
P4/nmm
10.210
10.184
7.241
7.174
D ð%Þ ¼ average discrepancy on the cell parameters.
3
˚
FD ¼ framework density (number of Al atoms reported to a volume of 1000 A ).
SG ¼ Space group of the real structure.
Z ¼ number of AlF3 formula per cell.
N ¼ number of Al atoms with different coordination sequences.
R ¼ quality factor regarding the ideal Al–F, F–F and Al–Al first neighbour interatomic distances.
Perov, perovskite; HTB, hexagonal tungsten bronze; pyr, pyrochlore; TTB, tetragonal tungsten bronze.

ARTICLE IN PRESS
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3162
Table 2
AlF3 virtual polymorphs proposed by GRINSP corresponding to known structure types
˚
a (A)
˚
b (A)
˚
c (A)
Structure type
FD
SG
Z
N
R
Ref
PCOD entry
Starting
Final
TlCa2Ta5O15
Ba4CoTa10O30
20.67
21.15
6.992
9.504
3.607
13.780
9.539
3.615
Pmmm
Iba2
Pmmm
Cm2m
5
10
2
2
0.0035
0.0093
[20]
[21]
1300007
1300008
Results from GRINSP for known Al/F-based 6-con-
nected 3D nets are reported in Table 1. The atomic
coordinates for these models were deposited at the
Predicted Crystallography Open Database (PCOD:
http://www.crystallography.net/pcod) [6] in CIF format
as well as three-dimensional drawings in VRML language.
The models can be obtained by using the PCOD entry
number as keyword, or the formulation, cell parameters,
volume, etc.
4. AlF3 polymorphs ‘‘yet to be synthesized’’, predicted by
GRINSP
One should treat apart structures which are not yet
existing with AlF3 formulation but are known for other
compositions. Table 2 gives the cell parameters predicted
by GRINSP for possible AlF3 polymorphs adopting the
structures of Ca2TlTa5O15 [20] and Ba4CoTa10O30 [21].
Up to Ro0:02, five unknown structure types are
disclosed by GRINSP which could well constitute ‘‘yet to
be synthesized’’ AlF3 compounds. Two of them (noted V-1,
V-2) have even R values smaller than for the known
metastable compound t-AlF3 ðR ¼ 0:0159Þ, and the three
others (noted V-3, V-4 and V-5) present R values only
slightly higher. V-1 is a simple HTB-perovskite intergrowth
(Fig. 1) with one more perovskite layer than into the
TlCa2Ta5O15 structure type. Tetrahedra of octahedra, like
in the pyrochlore or the t-AlF3 structure types are
recognized into the V-2 model (Fig. 2), they are separated
by perovskite planes, so that the structure looks like an
intergrowth between pyrochlore and perovskite. The
projection of the V-3 structure suggests octahedra face
sharing, but it is an illusion (Fig. 3). In spite of tunnels
delimited by rings of six octahedral sharing corners, this
model shows the highest density of the series with Ro0:02.
The V-4 model is exclusively built up from tetrahedra of
octahedra (Fig. 4), just as the pyrochlore structure type,
but with a denser packing (framework densities are
Fig. 1. Virtual AlF3 model V-1, intergrowth HTB–perovskite (three
layers).
3
˚
respectively 21.7 and 17.7 Al atoms per 1000 A ), so that
no ring larger that four octahedra exists in V-4, nor any
remarkable cavity as can be found in the pyrochlore
structure. One of the reviewers identified V-4 as corre-
sponding to the Fischer’s sphere packing 6/4/t41 and
having the RCSR symbol why (See http://okeeffe-ws1.la.
asu.edu/RCSR/home.htm). The V-5 model presents HTB
channels intercrossed at 901 in subsequent layers in the ab
plane, indeed the framework density is equal to that of the
Fig. 2. Virtual AlF3 model V-2, intergrowth pyrochlore–perovskite.
b-AlF3 HTB-like model (FDꢂ19.7). The shortest F–F
˚
distances in these models are larger than 2.42 A. For R
values larger than 0.02, problems arise generally, like too

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3163
Fig. 3. Virtual AlF3 model V-3.
Fig. 5. Virtual AlF3 model V-5, HTB tunnels intercrossed at 901 in the ab
plane.
Fig. 4. Virtual AlF3 model V-4, dense packing of tetrahedra of octahedra,
exclusively.
short interatomic distances for a small part of them, and
some octahedra may become distorted. For instance, in
spite of an interesting channel with rings of eight
octahedra, the V-6 model has the largest framework
density of the whole series ðFD ¼ 23:6Þ because of the
excessive proximity of the octahedra along the c-axis
Fig. 6. Virtual AlF3 model V-6, not viable due to a high level of octahedra
distortion and too short F–F distances.
˚
(leading to irrealistic interlayer distances Al–Al ¼ 3.195 A,
[23], replacing the Ca atoms by Al ones (PCOD1300011,
with R ¼ 0:0283). Indeed, the GRINSP software can
produce trigonal prisms instead of octahedra for R40:02
(Table 3).
˚
and to F–F distances as short as 1.8 A) (see Figs. 5 and 6).
However, the occurrence of structures built up from such
layers cannot be excluded if they were isolated, and if the
AB6 octahedra would accept some distortion. Five addi-
tional models with 0:02oRo0:03 appeared not viable
either and are not listed here; however, they can be found
into the PCOD with entry numbers 1300009–1300013.
Only one of them (PCOD1300011) was found to have an
FD equal to that of the pyrochlore, but some F–F
5. Ab initio calculations
Ab initio comparison of the total energies of the
predicted structures with the real ones was performed
using the WIEN2K code [26] which is a full potential
(Linearized) Augmented Plane Wave code for periodic
systems, renown for its accuracy. Computations were
˚
distances would be too short, close to 2.2 A. Finally, one
of these rejected models is isostructural to Na4Ca4Al7F33

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3164
Table 3
AlF3 virtual polymorphs proposed by GRINSP (unknown structure types)
˚
a (A)
˚
b (A)
˚
c (A)
Virtual AlF3
FD
b (1)
SG
Z
N
R
PCOD entry
Starting
P21/m
Final
V-1
V-2
V-3
V-4
V-5
V-6
21.27
20.43
22.37
21.71
19.74
23.65
6.992
6.889
7.218
6.889
13.513
8.252
7.402
6.678
11.977
6.391
105.22
90.00
90.00
90.00
90.00
90.00
P21/m
Pmm2
Pmna
14
8
3
2
2
1
2
2
0.0042
0.0054
0.0160
0.0181
0.0191
0.0233
1300001
1300002
1300003
1300004
1300005
1300006
¯
P4m2
5.207
6.960
Pnc2
I41/a
6
10.505
7.125
12.601
10.505
7.125
12.601
I41/a
16
12
12
P42/mmc
P4/nmm
P42/mmc
P4/nmm
3
˚
FD ¼ framework density (number of Al atoms in 1000 A ).
SG ¼ starting higher symmetry space group in which the initial model of Al-only atoms were obtained, and final space group deduced by PLATON after
including the F atoms and optimizing.
Z ¼ number of AlF3 formula per cell.
N ¼ number of Al atoms with different coordination sequences.
R ¼ quality factor regarding the ideal Al–F, F–F and Al–Al first neighbour interatomic distances.
performed on the Beowulf-type parallel computer in Le
Mans (cluster of five AMD64 dual-core nodes with 16 Go
of RAM each). Sphere sizes (Rmt) of 1.60 a.u. for F and Al
were used. The basis set was determined by a large cutoff
corresponding to RmtKmax ¼ 7. The full Brillouin Zone was
sampled with 100 k-points and we used the Generalized
Gradient Approximation of Perdew et al. [27] for the
description of exchange and correlation effects within
density functional theory. It was checked on the three
lowest energy structures that an increase of the number of
k-points up to 10000, of RmtKmax up to 10.5 or a decrease
of Rmt down to 1.5 a.u. would not change the ordering of
the total energies, although evidently changing by a few
digits their absolute values.
In principle, no adjustment of cell parameters is
necessary when dealing with the existing AlF3 phases,
contrary to the hypothetical models being somewhat
uncertain. However, in order to maintain some coherency
in the study, all structures (real or virtual) were volume-
optimized. The procedure did not yield changes greater
than 1% versus the original values. For instance, the cell
volume for a-AlF3 was decreased by 0.29% by this process.
Volume optimization should be considered as insufficient
for predicted structure candidates which would deserve the
individual optimization of the independent cell parameters
as well as atomic positions. However, this is not totally
automated in the current version of WIEN2K and judged
too time-consuming. For the so-called pyrochlore structure
we simply replaced the OH in the naturally occurring
structure by F atoms.
Table 4
Total energies obtained with the WIEN2 K ab initio code for natural and
predicted structures for AlF3
Phase or structure type
Total energy
per electron
in Ry
DE
R
a-AlF3 (perovskite)
V-1
ꢁ36.1856793
ꢁ36.1851923
ꢁ36.1844875
ꢁ36.1844544
ꢁ36.1844253
ꢁ36.1843461
ꢁ36.1842524
ꢁ36.1839795
ꢁ36.1839778
ꢁ36.1839340
ꢁ36.1835532
ꢁ36.1815946
0.
0.0062
0.0042
0.0035
0.0035
0.0093
0.0098
0.0046
0.0160
0.0181
0.0054
0.0191
0.0159
0.0004870
0.0011918
0.0012249
0.0012540
0.0013332
0.0014269
0.0016998
0.0017015
0.0017453
0.0021261
0.0040847
TlCa2Ta5O15-like
b-AlF3 (HTB)
Ba4CoTa10O30-like
k-AlF3 (TTB)
Z-AlF3 (pyrochlore-like)
V-3
V-4
V-2
V-5
t-AlF3 (or y-)
The energies (in Ry) are divided by the number of electrons in the cell for
comparison purposes. For the sake of clarity, DE is calculated by
difference with the total energy of a-AlF3.
6. Extending to more hypothetical MF3 ðM ¼ Fe; CrÞ
compounds
Even more difficult is the prediction of the synthesis
conditions for making these predicted crystal structures to
appear. We can already be sure that most predictions inside
of the PCOD will be vain, never confirmed, because the
synthesis route may depend on a precursor (organometal-
lic, hydrate, amorphous compound) which itself is yet
unknown, or because the prediction is simply false. The
latest discovered AlF3 phase, t-AlF3 [19], was obtained
from the thermolysis of either [(CH3)4N]AlF4 ꢃ H2O or
amorphous AlF3 ꢃ xH2O ðxo0:5Þ. Its structure determina-
tion was only possible from powder diffraction data, after
the preparation of a pure-enough sample obtained from the
Results are presented in Table 4. One sees that the
predicted structures are interclassed with the known ones,
with of course the ideal a-AlF3 structure having the lowest
energy although not by a very large amount. This leads to
the conclusion that these predicted structures might be
synthesized in the future. The classification does not follow
exactly the one deduced from R values; however, plotting
DE against R shows a small correlation.

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3165
Table 5
Estimated cell parameters for virtual FeF3 and CrF3 compounds
larger values. In the current conditions, no viable frame-
work with larger porosity than the pyrochlore structure
was found.
˚
a (A)
˚
b (A)
˚
c (A)
Model
b (1)
R
PCOD entry
Accurate prediction of both structures and properties
appears to be one of the main scientific challenge of the
XXIth century, probably finding some equilibrium between
these 1,000,000 models for SiO2 and 12 models for AlF3, or
the more than 1000 titanosilicates recently added into the
PCOD. The usefulness of databases of predicted structures
will be increased when powder patterns are calculated and
used by search-match software for identification purposes.
This is in project, as soon as enough structures are
incorporated into the PCOD, containing less than 3000
models up to now. Finally, investigations of the possible
physical properties of the FeF3 and CrF3 hypothetical
models (or with other compositions) could be worth trying,
especially for the magnetic aspects, just to see if efforts in
order to realize the predictions may have some interest.
V-1-Fe
V-1-Cr
V-2-Fe
V-2-Cr
V-3-Fe
V-3-Cr
V-4-Fe
V-4-Cr
V-5-Fe
V-5-Cr
t-Fe
7.357
7.298
7.324
7.204
7.441
7.327
11.211
11.042
7.544
7.439
10.875
10.726
7.543
7.415
7.324
7.204
7.864
7.736
11.211
11.042
7.544
7.439
10.875
10.726
14.362
14.027
8.812
8.677
5.552
5.466
7.117
6.991
12.784
12.585
7.720
7.603
105.82
105.08
90.
0.0026
0.0026
0.0056
0.0056
0.0156
0.0156
0.0176
0.0176
0.0186
0.0189
0.0158
0.0158
1300021
1300031
1300022
1300032
1300023
1300033
1300024
1300034
1300025
1300035
1300026
1300036
90.
90.
90.
90.
90.
90.
90.
90.
t-Cr
90.
above organometallic phase. The route from the amor-
phous phase always led to a mixture with dominant b-
AlF3. There is no doubt that if the predictions presented
here had been available by the end of the 1980s, the
structure would have been solved earlier. These considera-
tions suggest that a list of cell parameters for possible MF3
isostructural compounds (including those corresponding to
t-AlF3) would be of interest (Table 5). The models were
Appendix A. Supplementary materials
Supplementary data associated with this article can be
found in the online version at doi:10.1016/j.jssc.2006.
06.010.
˚
built by using the ideal M–F distances 1.930 and 1.900 A,
respectively, for the virtual FeF3 and CrF3 compounds
(VF3 and GaF3 compounds would have very similar cell
parameters with FeF3 and CrF3, respectively). Physical
properties prediction (magnetic behaviour, etc.) for these
hypothetical compounds remains to be done. At least
structure prediction would help to solve the structures if
the samples occur only in powder form, as is frequently the
case for metastable compounds obtained after decomposi-
tion of a precursor.
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