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Cluster Disorder and Ordering Principles in Al-Stabilized УLaIФ.

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6.323 ) can be refined down to R 5 %.[4] In spite of the
convincing value, this structural characterization is incomplete and even misleading. A correct structural model can be
derived only by taking into account the pronounced diffuse
scattering that shows up as sections of hollow spheres in
Figure 1.
Analysis of X-ray Data
Cluster Disorder and Ordering Principles in
Al-Stabilized “LaI”**
Oliver Oeckler, Thomas Weber, Lorenz Kienle,
Hansjrgen Mattausch, and Arndt Simon*
Diffuse X-ray scattering is frequently dismissed in conventional structure analyses. However, it contains valuable
information in many respects, particularly concerning the
chemical constitution of a crystal. Most investigations on
diffuse scattering so far have been restricted to qualitative
discussions, trial-and-error simulations, and analytical Fourier
calculations.[1] The quantitative measurement of the continuous intensity distribution in reciprocal space has become
routinely feasible with the advent of area detectors. As
computing power is still a bottleneck for complex numerical
methods, quantitative structure refinement against diffuse
data has been performed in only a few investigations.[2] Such
refinements will become more and more accessible in the
future. Here we present a case where only the refinement
against diffuse scattering data led to detailed insight into the
chemical nature of a compound.
Some time ago the preparation and structure of LaI was
described in this journal.[3] It crystallizes in the hexagonal
NiAs structure type. Now we have found a phase with the
approximate composition (La1 xAlx)I (x < 0.15) for which on
the basis of sharp Bragg reflections a NaCl-type structure (a =
[*] Dr. L. Kienle, Dr. H. Mattausch, Prof. Dr. A. Simon
Max-Planck-Institut fr Festkrperforschung
Heisenbergstrasse 1, 70569 Stuttgart (Germany)
Fax: (+ 49) 711-689-1642
Dr. O. Oeckler
Department Chemie und Biochemie
Lehrstuhl fr Anorganische Festkrperchemie
Butenandtstrasse 5–13(D), 81377 Munich (Germany)
Dr. T. Weber
Laboratorium fr Kristallographie
Wolfgang-Pauli-Strasse 10, 8093 Zurich (Switzerland)
[**] O. Oeckler thanks the Max Planck Society for supporting his stay in
Zurich. The authors are indebted to R. Eger for preparative work and
V. Duppel for recording SAED patterns and HRETM images.
Angew. Chem. Int. Ed. 2005, 44, 3917 –3921
Figure 1. Experimental (a, c) and calculated (b, d) X-ray diffraction
patterns for La0.7I1 xAlx (x 0.14); first layer perpendicular [100] (a, b)
and zero layer perpendicular [111] (c, d). The calculated images are
based on the best refinement result.
A hint to the correct interpretation of the diffraction data
comes from the extended cluster chemistry of the rare-earth
metals.[5] Their metal-rich halides are composed of discrete or
condensed clusters, and the M6X12-type cluster stabilized by
an endohedral atom Z is frequently observed. The M6X12Z
entity can be viewed as a section of the rock-salt structure.[6]
Hence, one way of addressing the disorder problem is to start
from a hypothetical NaCl-type LaI, in which some iodine
atoms are replaced by endohedral atoms Z = Al, and the La
atoms that are not part of the La6Al units are removed. If we
assume the presence of such La6I12Al clusters[7] in the title
compound, the occurrence of structured and narrow diffuse
scattering indicates their nonrandom distribution, which is
quite common with metal-rich cluster compounds of lanthanoids and other elements.[8]
Some conclusions can be drawn from the qualitative
analysis of the diffuse intensity. Generally speaking, the
presence of spheres and their location only around odd Bragg
reflections can be interpreted as due to some spherical
modulation[9] characterized by the complementary behavior
of cation and anion sites, and the higher intensity on the large-
DOI: 10.1002/anie.200500594
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
angle side indicates lattice distortions due to a “size effect”,[10]
where a smaller structural motif (e.g. a cluster) is a stronger
scatterer than a larger structural motif. However, from these
and other possible qualitative considerations no reliable
statements can be made concerning the kind of chemical
entities, their interconnection, and their nonrandom arrangement. Here we demonstrate a quantitative structure solution
by a new, very efficient evolutionary algorithm.[2a, 11]
The first important step is the modeling of the disorder
with a realistic atom arrangement using as few parameters as
possible, because diffuse data contain limited information and
precision in comparison to Bragg data. A (defect-)NaCl-type
structure can be derived starting from a fcc lattice of I atoms
by statistically substituting a variable number of atoms (11–
15 %) by La6Al units to create a set of 80 different structures,
each defined by a specific set of parameters. In Monte Carlo
(MC) calculations we used a set of 13 parameters, including
“interaction energies” for edge- and corner-sharing octahedrons and all possible relative cluster positions up to a
distance of 13.4 . Furthermore, the cluster concentration
and local relaxation around vacancies and interstitial atoms
are parameters of the disorder model obtained by “energy
minimization” with respect to the specific parameter set.
The pixelwise comparison of the scattering intensities
calculated for these model structures with observed intensities is quantified by an R-factor for each structure (“individual”). Then the next generation of structures strictly
related to the specific parents, and hence comprising the same
number of individuals as the starting set, is created by
admixing a certain percentage of another parents parameter
set, and those members of the new generation are dismissed
whose structures lead to an inferior fit with the experimental
data. In a later generation the calculation converges to a set of
statistically identical structures which optimally represents
the experimental scattering pattern. This final structure
model is analyzed in terms of the structural features actually
Figure 2 illustrates that the final structure model exhibits a
uniform cluster distribution in contrast to the random
arrangement for the refined cluster concentration x. This
refinement yields x = 0.136 and the chemical formula
La0.69I0.86Al0.14, which is confirmed by chemical analyses. The
deviation of La and I atoms from the ideal NaCl-type
positions as refined from diffuse data is in good agreement
Figure 2. Representative parts of the model crystal (x = 0.136; shaded:
La6Al octahedrons, spheres: I atoms) before MC calculation and the
final model crystal (after MC simulation with the refined parameters).
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
with the corresponding numbers derived from Bragg data;[13]
however, now the displacements can be interpreted directly in
terms of a contraction of the clusters. The cluster geometry is
in very good agreement with that of La6I12Al or related
clusters in other compounds.[7]
Based on this result, a reasonable interpretation of Bragg
data can be obtained, too, in a constrained refinement[14]
assuming one anion site with x Al and (1 x) I and implying
La6Al octahedrons by placing 6x La on the cation site. In
accordance with the result from diffuse data, x amounts to
0.110(1). However, information on the interconnection of
clusters can only be derived from the final structure model.
From Table 1 we conclude that edge- or corner-sharing
octahedrons are very unfavorable in this compound as their
frequency amounts to 49 % and 31 %, respectively, of the
Table 1: Comparison of relative cluster positions (characterized by lattice
vectors corresponding to a NaCl unit cell) for a) random cluster
distribution with x = 0.136 before MC calculation and b) the final model
crystal. The frequencies of intercluster arrangements are denoted ni for
(a) and nf for (b).
Relative cluster positions
55 856
27 108
111 602
95 275
55 976
59 479
111 759
148 168
37 203
59 708
[a] Face centered (fc) in a 2a2b2c supercell. [b] Bod centered (bc) in a
2a2b2c supercell.
random arrangement. Double octahedrons have been frequently observed in other systems;[5a, d] however, the present
disordered NaCl-type matrix obviously cannot adjust to the
high degree of strain induced by the contraction due to metal–
metal bonding in such an entity. Configurations that do not
allow complete relaxation are observed less frequently, and
the tendency to avoid local strain is evident from the most
favorable relative cluster position in which the centers are on
opposite corners in the [111] direction of the NaCl cell as
shown in Figure 3. Short La I contacts are avoided (3.16 in
the average NaCl structure instead of 3.28–3.40 in comparable compounds) both by contraction of the La6 unit as
well as by displacement of the I atoms towards the void.
Angew. Chem. Int. Ed. 2005, 44, 3917 –3921
However, allowing for slight compositional variations,
ordered variants of this structure are sometimes observed in
electron diffraction patterns (cf. Figure 5) which show the
diffuse scattering to develop into superstructure reflections.
Figure 3. Pair of clusters in the relative position [111] of the average
NaCl cell (cell dimensions are outlined). Short La I distances can be
avoided by both cluster contraction and displacement of I atoms
towards the void.
Additional evidence for the preference of this relative
cluster orientation has also been obtained from high-resolution electron microscopy (HRTEM) studies.[15] Images
taken along the zone axis [111] (Figure 4) show the disordered
Figure 4. Electron diffraction pattern (top, left) and HRTEM image
(bottom) of disordered crystal along the zone axis [111]. The hexagonal arrangement of dots results from the average symmetry of the
structure along [111]. The bright and dark contrasts of the experimental image can be correlated with the projection of the real structure
(top, right). Simulated images (Df = 65) indicate that bright dots
correspond to rows of the heavy atoms La and I, while dark dots
indicate a sequence of these atoms replaced by Al and voids.
structure as light spots for rows of La and I, and dark spots for
rows in which Al and voids alternate statistically. Prolonged
exposure to the electron beam as well as long annealing times
does not remove the disorder. Based on our investigations we
explain this behavior as a consequence of the impossibility of
the title compound to order in small unit cells with high
Angew. Chem. Int. Ed. 2005, 44, 3917 –3921
Figure 5. Electron diffraction patterns (zone axis [110]) of several
crystals in one sample of the approximate composition La0.7I1 xAlx
(x 0.14). a) The most frequently observed pattern, corresponding to
X-ray single-crystal diffraction, b) a crystallite with partial ordering,
c) an ordered crystallite with a distinct superstructure.
All reasonable refinements from X-ray Bragg data[16] lead to
structure models in which a certain degree of disorder
remains; however, a body centering of ordered clusters in a
2a2b2c NaCl-type cell is a feature common to all models. This
partial ordering corresponds exactly to the preferred cluster
arrangement in the disordered structure of the title compound.
Summing up, the title compound and its disorder can be
well understood. The cluster distribution is far from a
statistically random function. The uniform (not random)
distribution avoids short intercluster distances which leads to
an approximately harmonic radial distribution function of
intercluster vectors that is reflected in the diffuse spheres. The
preferred relative cluster arrangement (Figure 2) allows a
unique possibility to avoid short distances in a dense packing
by contraction of both Ln6 units around endohedral Al atoms
and of I6 octahedrons around voids.
Finally, we point out that our investigation, though
addressing a special system, is quite relevant to the extended
structural chemistry of NaCl-type transition-metal oxides,
nitrides, and carbides. They form ordered cluster structures in
a few instances, for example, NbO[17] and TiO,[6a, 18] and
frequently show diffuse scattering effects due to local order
and long-range disorder.[19]
Experimental Section
Single crystals of La0.7I1 xAlx (x 0.14) were first obtained from La,
LaI3, and Al in different reactions (e.g. the nominal composition
La3Al2I2) during a systematic investigation of the La/I/Al system.
EDX analyses (Tescan scanning electron microscope, Oxford EDX
detector) of several crystals confirmed the given composition. The
best method for obtaining pure samples was by heating a stoichiometric mixture of La, LaI3, and AlI3 in a tantalum ampule at 875 8C
for 7 days. These samples are single phase according to X-ray powder
diagrams (Stoe STADI P diffractometer, MoKa radiation). Since the
starting materials as well as the product are very moisture sensitive,
all manipulations must be carried out in a glove box or by Schlenk
techniques under purified argon atmosphere. Elemental analysis
(double determinations) by the Mikroanalytisches Labor Pascher,
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Remagen, La0.7I0.86Al0.14 (212.1 amu) calcd (in wt %): La 46.2, I 51.9,
Al 1.8; found: La 43.7, I 54.4, Al 1.8.
Received: February 17, 2005
Published online: May 13, 2005
Keywords: cluster compounds · diffuse scattering · disorder ·
lanthanum · subiodides
[1] A good overview including many references has been given by
H. Jagodzinski, F. Frey in International Tables for Crystallography, Vol. B (Ed.: H. Shmueli), Kluwer, Dordrecht, 2001,
pp. 407 – 442. Simulation methods are discussed in R. T. Welberry, Diffuse X-ray Scattering and Models of Disorder, Oxford
University Press, Oxford, 2004.
[2] Methods that have been used for a quantitative fit of diffuse data
include reverse Monte Carlo, least-squares, and evolutionary
(genetic) algorithms: a) T. Weber, H.-B. Brgi, Acta Crystallogr.
Sect. A 2002, 58, 526; b) T. Proffen, T. R. Welberry, Acta
Crystallogr. Sect. A 1997, 53, 202; c) T. R. Welberry, T. Proffen,
M. Bown, Acta Crystallogr. Sect. A 1998, 54, 661.
[3] J. D. Martin, J. D. Corbett, Angew. Chem. 1995, 107, 234; Angew.
Chem. Int. Ed. Engl. 1995, 34,233.
[4] Split positions and variation of site occupancies further reduce
R1 to about 3 %; however, the mixed La/Al occupation of the
cation site assumed here is not consistent with the correct
average structure.[14]
[5] a) A. Simon, H. Mattausch, G. J. Miller, W. Bauhofer, R. K.
Kremer in Handbook on the Physics and Chemistry of Rare
Earths, Vol. 15 (Eds.: K. A. Gschneidner, L. Eyring), Elsevier,
Amsterdam, 1991, p. 191; b) J. D. Corbett, J. Chem. Soc. Dalton
Trans. 1996, 575; c) G. Meyer, Chem. Rev. 1998, 98, 3295; d) H.
Mattausch, E. Warkentin, O. Oeckler, A. Simon, Z. Anorg. Allg.
Chem. 2000, 626, 2117; e) H. Mattausch, G. V. Vajenine, O.
Oeckler, R. K. Kremer, A. Simon, Z. Anorg. Allg. Chem. 2001,
627, 2542.
[6] a) A. Simon, Angew. Chem. 1981, 93, 23; Angew. Chem. Int. Ed.
Engl. 1981, 20, 1; b) A. Simon, Angew. Chem. 1988, 100, 164;
Angew. Chem. Int. Ed. Engl. 1988, 27, 160; c) H. G. von Schnering, Angew. Chem. 1981, 93, 44; Angew. Chem. Int. Ed. Engl.
1981, 20, 33.
[7] Compounds are well characterized with Al-centering trigonal
Ln6 prisms (H. Mattausch, O. Oeckler, C. Zheng, A. Simon, Z.
Anorg. Allg. Chem. 2001, 627, 1523). Octahedral clusters have
been observed in comparable compounds, e.g. boride halides,[5a,e]
and a few Al-containing octahedral clusters are known as well.
[8] Other disordered cluster compounds have been discussed, cf. for
example: J. Khler, G. Svensson, A. Simon, Angew. Chem. 1992,
104, 1463; Angew. Chem. Int. Ed. Engl. 1992, 31, 1437; O.
Oeckler, L. Kienle, H. Mattausch, A. Simon, Angew. Chem.
2002, 114, 4431; Angew. Chem. Int. Ed. 2002, 41, 4257. In the
latter case, a reasonable structural model was not evident from
the averaged structure, but a “semiquantitative” analysis of
diffuse diffraction data was successful.
[9] T. R. Welberry, Acta Crystallogr. Sect. A 2001, 57, 244.
[10] T. R. Welberry, J. Appl. Crystallogr. 1986, 19, 382.
[11] This algorithm mimics the principles of Darwinism (for a
detailed overview, cf. Z. Michalewicz, Genetic Algorithms +
Data Structures = Evolution Programs, Springer, Berlin, 1996). It
starts from a “population” of diverse structure models, each one
characterized by its “genes”, that is, a set of parameters defining
a model crystal as the “phenotype”. Its “fitness” corresponds to
the crystallographic R factor based on all individual pixels of the
diffraction image and not only on a set of Bragg intensities. A
new generation is created from the parent population by
recombination and variation (“mutation”) of the parameters
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
(“genes”). Here, we used so-called differential evolution (K.
Price, R. Storn, Dr Dobbs J. 1997, April issue, 18; R. Storn, K.
Prince, J. Global Optimization 1997, 11, 341; and ref. [2a])
replacing parents by “fitter” children (models with better R
factors) and discarding “unfit” members of each new generation.
Refinement of the disordered structure based on diffuse data:
Measurement of diffuse data: Huber four-circle goniometer,
MAR345 image-plate detector, AgKa (l = 0.56086 ), graphite
monochromator, 2#max = 458, beam normal to oscillation axis
and normal to detector, 492 frames, Df = 0.58/frame, reconstruction of undistorted reciprocal layers with XCAVATE
(M. A. Estermann, W. Steurer, Phase Transitions 1998, 67,
165). Monte Carlo model: An initial model structure containing
a random distribution of clusters was modified by swapping
cluster and noncluster positions. The energy difference between
the old and the new configuration was calculated based on the
model parameters, and the new configuration was accepted with
a probability following a Boltzmann distribution. Finally, local
relaxations around vacancies and interstitial atoms were applied.
Neither the cluster interaction nor the total energy can be
interpreted as actual energy values, and the parameters of the
structure model cannot be directly analyzed. All “interactions”
are simply abstract parameters, but the result of the corresponding MC simulation bears physical significance. The model
parameters were refined in analogy to T. Weber, H.-B. Brgi,
Acta Crystallogr. Sect. A 2002, 58, 526 with fm = fr = 0.6. The
number of lots was subsequently increased after no improvement was found during one generation. The final results are
based on 125 lots, R(final) = 0.09 (based on F2).
Atom shifts from Bragg data are just a mean displacement
(“octahedral” split position) from the atom positions of the NaCl
type: 0.25(1) for La and 0.22(1) for I. They can be compared
only approximately with the results from diffuse data, which
model the actual situation more clearly: an “attractive force”
between Al and La yields a refined La–Al distance of 2.8 . A
“repulsive force” between La and I (avoiding short contacts)
leads to an average distance of 3.3 for the inner and 3.5 for
the outer ligands. The root-mean-square displacements as
obtained from the Monte Carlo modeling were 0.40 for La
and 0.19 for I (based on diffuse data only).
Refinement of the average structure of La0.7I1 xAlx (x 0.14):
Enraf Nonius CAD4 four-circle diffractometer, MoKa (l =
0.70173 ), 2#max = 708, crystal dimensions 0.11 0.09 0.08 mm3, cubic, space group Fm3̄m (No. 225), a = 6.323(1) ,
V = 252.80(7) 3, Z = 4, calcd density 1 = 5.44 g cm 3, m(MoKa) =
21.7 mm 1, 590 measured reflections, 48 independent (Rint =
0.055), least-squares refinement based on F2 (G. M. Sheldrick,
SHELXL-97, Program for the Refinement of Crystal Structures,
Universitt Gttingen, Gttingen (Germany), 1997); R values
[all data/data with I > 2s(I)]: R1 = 0.033/0.029, wR2 = 0.068/0.066,
GooF = 1.14 for 41 observed reflections [I > 2s(I)] and 6
parameters. Further details on the crystal structure investigations may be obtained from the Fachinformationszentrum
Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax:
(+ 49) 7247-808-666; e-mail:, on
quoting the depository number CSD-391280.
HRTEM along several zone axes was performed with a Philips
CM30 ST electron microscope (300 kV, LaB6 cathode, Gatan
multiscan CCD camera). The multislice formalism (P. A. Stadelmann, Ultramicroscopy 1987, 21, 131 – 146) was used for
image simulations.
A quantitative analysis of the diffuse data from crystals with
partial long-range ordering could not be performed due to
moderate crystal quality and very weak diffuse intensity as well
as limited computational resources. As it is common for many
partially ordered cubic structures, the space group assignment
(including possible twinning) remains ambiguous in this case.
Angew. Chem. Int. Ed. 2005, 44, 3917 –3921
[17] H. Schfer, H. G. Schnering, Angew. Chem. 1964, 76, 833.
[18] D. Watanabe, J. R. Castles, A. Jostsons, A. S. Malin, Acta
Crystallogr. 1967, 23, 307.
[19] a) J. Billingham, P. S. Bell, M. H. Lewis, Acta Crystallogr. Sect. A
1972, 28, 602; b) M. Sauvage, E. Parth, Acta Crystallogr. Sect. A
1972, 28, 607; c) R. DeRidder, G. van Tendeloo, S. Amelinckx,
Acta Crystallogr. Sect. A 1976, 32, 216; d) K. Oshima, J. Harada,
M. Morinaga, P. Georgopoulus, J. B. Cohen, Acta Crystallogr.
Sect. A 1988, 44, 167; e) S. Matsumura, T. Hino, S. Hata, K. Oki,
Mater. Trans. 1996, 37, 1748; f) P. Li, J. M. Howe, Acta Mater.
2003, 51, 1261.
Angew. Chem. Int. Ed. 2005, 44, 3917 –3921
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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clusters, stabilizer, ordering, disorder, уlaiф, principles
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