Consequences of Crystal Structure Differences between C14, C15, and C36 Laves Phase Polytypes for their Coexistence in T
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Consequences of Crystal Structure Differences between C14, C15, and C36 Laves Phase Polytypes for their Coexistence in Transition-Metal-Based Systems F. Stein Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Str. 1, D-40237 Düsseldorf, Germany ABSTRACT In various binary and ternary transition-metal-based systems, two or even three different polytypes of Laves phases coexist as equilibrium phases. A comparison of different phase diagrams reveals that the coexistence is characterized by some common features. In binary systems with cubic and hexagonal Laves phases existing at the same temperature but different compositions, the cubic C15 polytype always crystallizes at and around the stoichiometric composition whereas the hexagonal C14 and C36 polytypes are observed on the A-rich (C14) and B-rich (C36) side of the stoichiometry, respectively. On replacing the B atoms of an AB2 Laves phase by ternary additions, the highest solubility is always found in the C14 Laves phase. Ternary Laves phases A(B,C)2 in systems where none of the binary boundary systems contains a Laves phase are always of the C14 type. It is discussed how these observations are related to crystallographic differences between the three polytypic structures C14, C15, and C36. INTRODUCTION With far more than 1000 representatives in binary and ternary systems, the Laves phases form the largest group of intermetallic phases. By definition they are topologically close-packed Frank-Kasper phases of composition AB2, where the A and B atoms have an ideal atomic radius ratio rA/rB = (3/2)1/2 ≈ 1.225 in order to fulfill the geometrical requirement of dense sphere packing. Laves phases form a family of crystallographically closely related polytypes. The three fundamental representatives of the polytypic structures are the cubic MgCu2 type (C15) and the two hexagonal types MgZn2 (C14) and MgNi2 (C36). Schemes of these polytypic structures are shown in Fig. 1 revealing their close crystallographic relation. The crystal structures only differ by the particular stacking of a fundamental structural unit which consists of four alternating layers of A atoms and B atoms. As a consequence of the close relation between the stacking variants, the differences between calculated values for the total energies of the three polytypes for a particular Laves phase can be very small. Therefore, it is not too surprising that in many binary or ternary systems two or even three Laves phase polytypes coexist with distinct homogeneity ranges for each structure type [1]. In the following, an example of a binary and a related ternary transition-metal-based system with coexisting C14, C15, and C36 Laves phases is briefly presented. A comparison with similar systems reveals that they show a representative behavior with respect to the polytypedependent extension of the homogeneity ranges and the preferred composition range of each polytype. An attempt is made to explain how the occurrence of the polytypes in distinct composition ranges of the phase diagram is related to differences in
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