Structure and stability of Laves phases. Part I. Critical assessment of factors controlling Laves phase stability F. Stein * , M. Palm, G. Sauthoff Max-Planck-Institut fu ¨r Eisenforschung GmbH, Postfach 140444, D-40074 Du ¨sseldorf, Germany Available online 1 April 2004 Abstract Laves phases form the largest group of intermetallic phases. Although they are well known since long, there are still unsolved problems concerning the stability of the respective crystal structures. The Laves phases crystallize with a cubic MgCu 2 - or a hexagonal MgZn 2 - or MgNi 2 -type structure which differ only by the particular stacking of the same four-layered structural units. It is still not possible to predict which of the structure types is the stable one for a Laves phase compound AB 2 . Phase transformations from a cubic low-temperature structure to a hexagonal high-temperature structure were observed as well as stress-induced transformations from the hexagonal structure to the cubic one. In addition, deviations from the stoichiometric composition were reported to result in a change of the stable polytype in various systems. In this first of two consecutive papers dealing with fundamental aspects of the stability of Laves phases, some factors which are known to affect the occurrence and structure type of Laves phases are discussed and it is shown that, at least up to now, the existing models and calculations are not well suited to give a general description of the stability of Laves phases. q 2004 Published by Elsevier Ltd. Keywords: A. Laves phases; A. Intermetallics, miscellaneous; B. Phase transformation; B. Bonding 1. Introduction Laves phases form the largest group of intermetallic compounds. More than 1400 binary and ternary Laves phases are reported in ‘Pearson’s Handbook of Crystal- lographic Data for Intermetallic Phases’ [1,2]. The discus- sion on the special properties of the crystal structure of Laves phases started in the 1920s and 1930s [3–9]. It was the work of Laves that gave the first valuable insight into the characteristics and properties of this class of intermetallics. This led Schulze [9] to introduce the term ‘Laves phases’ in 1939, which is commonly used today. Since it was Friauf, who was the first one to study the crystallographic structures of MgCu 2 and MgZn 2 [3,4], these intermetallic phases are also referred to as ‘Friauf-Laves phases’. Especially in the last 10 years there is a renewed interest in Laves phases as they have become candidates for several functional as well as structural applications [10,11]. The most prominent example for the first group of applications is the utilization of Laves phases as hydrogen storage materials especially in nickel–metal hydride batteries on the basis of the Laves phase Zr(V,Mn,Ni) 2 [12–27]. In view of structural applications, Laves phases are attractive because of their high strength up to high temperatures [10,11,28 – 37]. The principal shortcoming is their pro- nounced brittleness at ambient temperatures which has been tried to overcome by combining Laves phases with a ductile phase; see e.g. [35,38 – 53]. Laves phases belong to the class of Frank – Kasper phases showing topologically close-packed structures. They have the general composition AB 2 with the larger A atoms in the centre of a 16-atom Frank–Kasper polyhedron and the smaller B atoms in the centres of icosahedra. The coordination number for the A atoms is 16 (4 A and 12 B atoms) and 12 (6 A and 6 B atoms) for the B atoms. The closest packing of hard spheres of types A and B is obtained for the radius ratio r A =r B ¼ð3=2Þ 1=2 < 1:225: Three different polytypes of the Laves phase structure are generally observed: the cubic MgCu 2 type (C15), the hexagonal MgZn 2 type (C14), and the hexagonal MgNi 2 type (C36). The crystallographic structures of the three polytypes are closely related as is visualised in Fig. 1a [54]. The Laves phase polytypes can be built up by a particular stacking of fundamental atomic layers which are iso- oriented or rotated by 1808 with axis perpendicular to the layer interface and shifted by ^ 1/3 [2 110]. These layers, 0966-9795/$ - see front matter q 2004 Published by Elsevier Ltd. doi:10.1016/j.intermet.2004.02.010 Intermetallics 12 (2004) 713–720 www.elsevier.com/locate/intermet * Corresponding author. Tel.: þ49-211-6792-557; fax: þ 49-211- 6792-537. E-mail address: stein@mpie.de (F. Stein).