Cluster disorder and ordering principles in Al-stabilized "LaI"

Angewandte Chemie - International Edition

Volumn 44, Issue 25, 2005, Pages 3917-3921

  Oeckler, Oliver ^b   Weber, Thomas ^c   Kienle, Lorenz ^a   Mattausch, Hansjürgen ^a   Simon, Arndt ^a  

^a MAX PLANCK INSTITUT FÜR FESTKÖRPERFORSCHUNG   (Germany)

^b UNIVERSITY OF MUNICH   (Germany)

^c ETH ZURICH   (Switzerland)

Author keywords

Cluster compounds; Diffuse scattering; Disorder; Lanthanum; Subiodides

Indexed keywords

COMPOSITION; CRYSTAL LATTICES; DATA REDUCTION; DIFFRACTION; DIFFUSION; STATISTICAL METHODS;

CLUSTER COMPOUNDS; CLUSTER DISORDERS;

MOLECULAR STRUCTURE;

EID: 21244444342     PISSN: 14337851     EISSN: None     Source Type: Journal    
DOI: 10.1002/anie.200500594     Document Type: Article

References (43)

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.
2. Simulation methods are discussed in R. T. Welberry, Diffuse X-ray Scattering and Models of Disorder, Oxford University Press, Oxford, 2004.
3. 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. Bürgi, Acta Crystallogr. Sect. A 2002, 58, 526;
4. b) T. Proffen, T. R. Welberry, Acta Cryslallogr. Sect. A 1997, 53, 202;
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20. [5a,c] and a few Al-containing octahedral clusters are known as well.
21. Other disordered cluster compounds have been discussed, cf. for example: J. Köhler, G. Svensson, A. Simon, Angew. Chem. 1992, 104, 1463;
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27. 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.
28. A new generation is created from the parent population by recombination and variation ("mutation") of the parameters ("genes"). Here, we used so-called differential evolution (K. Price, R. Storn, Dr Dobb's J. 1997, April issue, 18 ;
29. 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.
30. max = 45°, beam normal to oscillation axis and normal to detector, 492 frames, Δφ = 0.5°/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.
31. 2).
32. Atom shifts from Bragg data are just a mean displacement ("octahedral" split position) from the atom positions of the NaCl type: 0.25(1) Å for La and 0.22(1) Å 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 Å. A "repulsive force" between La and 1 (avoiding short contacts) leads to an average distance of 3.3 Å for the inner and 3.5 Å for the outer ligands. The root-mean-square displacements as obtained from the Monte Carlo modeling were 0.40 Å for La and 0.19 Å for 1 (based on diffuse data only).
33. 2 = 0.068/0.066, GooF = 1.14 for 41 observed reflections [I > 2σ(1)] 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: crysdata@fiz-karlsruhe.de), on quoting the depository number CSD-391280.
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