Research Collection Journal Article Structural building principles of complex face-centered cubic intermetallics Author(s): Dshemuchadse, Julia; Jung, Daniel Y.; Steurer, Walter Publication Date: 2011-08 Permanent Link: https://doi.org/10.3929/ethz-a-009903920 Originally published in: Acta Crystallographica Section B: Structural Science 67(4), http://doi.org/10.1107/ S0108768111025390 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library electronic reprint Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials ISSN 2052-5192 Structural building principles of complex face-centered cubic intermetallics Julia Dshemuchadse, Daniel Y. Jung and Walter Steurer Acta Cryst. (2011). B67, 269–292 Copyright c International Union of Crystallography Author(s) of this paper may load this reprint on their own web site or institutional repository provided that this cover page is retained. Republication of this article or its storage in electronic databases other than as specified above is not permitted without prior permission in writing from the IUCr. For further information see http://journals.iucr.org/services/authorrights.html Acta Crystallographica Section B: Structural Science publishes papers in structural chem- istry and solid-state physics in which structure is the primary focus of the work reported. The central themes are the acquisition of structural knowledge from novel experimental observations or from existing data, the correlation of structural knowledge with physico- chemical and other properties, and the application of this knowledge to solve problems in the structural domain. The journal covers metals and alloys, inorganics and minerals, metal-organics and purely organic compounds. Crystallography Journals Online is available from journals.iucr.org Acta Cryst. (2011). B67, 269–292 Julia Dshemuchadse et al. · Complex face-centered cubic intermetallics feature articles Acta Crystallographica Section B Structural Structural building principles of complex face- Science centered cubic intermetallics ISSN 0108-7681 Julia Dshemuchadse, Daniel Y. Fundamental structural building principles are discussed for Received 14 February 2011 Jung and Walter Steurer* all 56 known intermetallic phases with approximately 400 or Accepted 28 June 2011 more atoms per unit cell and space-group symmetry F443 m, Fd3m, Fd33, Fm3m or Fm3c. Despite fundamental differences Laboratory of Crystallography, Department of in chemical composition, bonding and electronic band Materials, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland structure, their complex crystal structures show striking similarities indicating common building principles. We demonstrate that the structure-determining elements are flat Correspondence e-mail: [email protected] and puckered atomic {110} layers stacked with periodicities 2p. The atoms on this set of layers, which intersect each other, form pentagon face-sharing endohedral fullerene-like clusters arranged in a face-centered cubic packing (f.c.c.). Due to their topological layer structure, all these crystal structures can be described as (p  p  p)=p3-fold superstructures of a common basic structure of the double-diamond type. The parameter p, with p = 3, 4, 7 or 11, is determined by the number of layers per repeat unit and the type of cluster packing, which in turn are controlled by chemical composition. 1. Introduction Why and how do complex intermetallic phases form with up to thousands of atoms per unit cell or even in a quasiperiodic way without a unit cell? How do all these atoms find their sites during crystal growth? How do their structures depend on chemical composition and do they have anything in common? All these questions are in the focus of our long-term study of the crystallography of complex intermetallics, periodic as well as quasiperiodic ones. In this first comprehensive classification of intermetallics with giant unit cells, we discuss all known f.c.c. structures in the range from approximately 400 up to more than 23 000 atoms per unit cell. Structural complexity can result from: (i) atomic size ratios geometrically hindering optimum atomic interactions and preventing the formation of atomic environment types (AETs), which can be packed efficiently; (ii) energetically favorable electronic band structures (e.g. pseudogaps at the Fermi energy, EF) based on odd stoichio- metries or large unit-cell dimensions; (iii) other parameters that are close to optimum but not optimum (pseudosymmetry) for a simple structural arrange- ment or packing such as a misfit between structural subunits as in composite (host/guest) or modulated structures. In some cases complex structures can be described as modulations or superstructures of rather simple basic struc- tures. We distinguish two classes of modulations: a simple modulation is a correlated displacement or substitution of atoms leading to a comparatively small deviation of the actual # 2011 International Union of Crystallography structure from the underlying basic structure, resulting in a Printed in Singapore – all rights reserved (in)commensuratly modulated structure. A complex modula- Acta Cryst. (2011). B67, 269–292 doi:10.1107/S0108768111025390 269 electronic reprint feature articles tion on the other hand results from a correlated displacement We want to emphasize that our goal is the crystallographic or substitution of atoms leading to the local formation of description of complex structures, to identify their structural clusters yielding a cluster-modulated structure; as we will show, building units and connectivities. A detailed analysis of this is the case for all structures discussed in the following. chemical bonding and the identification of chemically relevant There is no unique way to classify, describe and visualize the subunits such as polyanionic frameworks is beyond the scope crystal structure of a complex intermetallic compound. One of this study. should keep in mind that the visualization of a crystal struc- The paper is organized in the following way: in x2we ture in terms of clusters (in the meaning of structural building describe the data basis of the present study and introduce the blocks) or structure modules can be quite arbitrary. There are general packing principles and peculiarities we derived for some conventions and rules, such as the maximum-gap rule f.c.c. structures with giant unit cells; in xx3, 4 and 5 we apply (Brunner & Schwarze, 1971) for the definition of AETs, which our concept of cluster description, layer decomposition and can be seen, in some cases, as the first shell of a multi-shell average structure derivation to the 56 intermetallics grouped cluster. However, there are not usually such simple rules for according to their symmetries F443 m (39), Fd3m (9), Fd3 (1), higher-order cluster shells. Furthermore, even if one finds a Fm3m (4) or Fm3c (3); in x6 we discuss the results of ab initio topologically elucidating cluster-based description, this does calculations of representatives of the two most frequent not mean that it is supported from a crystal-chemical point of structure types and show that chemical bonding and electronic view, i.e. that the chemical bonds between atoms within a band structure differ significantly between all these geome- cluster differ from those outside a cluster. For a more detailed trically closely related structures. discussion of this problem see Steurer (2006) and Henley et al. (2006). In the following we will pragmatically utilize this kind of 2. Some peculiarities of complex f.c.c. intermetallics cluster description that proves to be most useful. This is the Our study is based on structures taken from Pearson’s Crystal case when it allows for a simpler representation of a structure Data database (PCD; Villars & Cenzual, 2009/10). Full which is simpler than any other geometrical description; it is structural information is only available for 10 655 of the 41 788 particularly justified if the clusters used are constituents of intermetallics1 included in this database. However, these more than just a single structure type. A useful cluster-based numbers refer to database entries and not necessarily to description relates complex structures to simpler ones, thereby structures of different compounds; for some compounds, more reducing the degree of complexity and unveiling the under- than one entry may exist based on different structure deter- lying packing principles. In this case of f.c.c. structures, the minations. We restrict our study to the fully determined fundamental endohedral pentagon face-sharing fullerene-like structures and start with the analysis of 1891 entries with cubic clusters form cubic close packing with the octahedral voids symmetry and focus first on the 842 with f.c.c. lattice filled with a second type of cluster. The choice of this kind of symmetry: Fm3 (4 entries), Fd3 (1 entry), F443 m (305 entries), cluster is particularly justified because it allows the family of Fm3m (249 entries), Fm3c (76 entries) and Fd3m (207 2 giant unit-cell structures cF444-Al63:6Ta 36:4, cFð5928 À xÞ- entries). Al56:6Cu3:9Ta 39:5 and cFð23256 À xÞ-Al55:4Cu5:4Ta 39:1 (Weber et The histogram in Fig. 1 lists the number of database entries al., 2009; Conrad et al., 2009) to be described in a unique way. of f.c.c. structures as a function of the number of atoms per unit cell. Obviously, the majority of f.c.c. structures has unit cells with less than 200 atoms. Another significant clustering of structures is found at around 400 atoms per unit cell, while even larger structures are sparse. These are the structures we will focus on in the following, taking into account both their comparably high frequency and complexity. In this survey, we also consider the two recently discovered structures cFð5928 À xÞ-Al56:6Cu3:9Ta 39:5 and cFð23256 À xÞ- Al55:4Cu5:4Ta 39:1 (Weber et al., 2009; Conrad et al., 2009), with space-group symmetry F443 m, which are not included in the databases yet, as well as structures taken directly from the literature and another database, the ICSD (Belsky et al., 2002).