A geometric analysis of solubility ranges in Laves phases

Abstract

Laves phases nominally occur at the AB2 stoichiometry but can exhibit a range of solubility involving non-stoichiometric compositions in binary alloys. The solubility trends in the reported binary C14, C15 and C36 structures have been analyzed in terms of the atom size requirements that are known to stabilize the Laves phases. For example, Laves phases exist at metallic diameter ratios (DA/DB) between ∼1.05 and 1.68 with the ideal diameter ratio existing at ∼ 1.225. Although less than 25% of the Laves phases within the DA/DB ratios of 1.05–1.68 have defined ranges of homogeneity, the frequency of the number of intermetallic phases exhibiting any solubility range is increased by a factor of approximately two to three within specific DA/DB ratios of 1.12–1.26 (C14 and C36 phases) and 1.1–1.35 (C15 phases). The upper and lower bounds for the C15 structures can be physically defined as the limits at which the A-B atom distance contractions are greater than the A-A atom distance and B-B atom distance contractions, respectively. For all three main polytypes the occurrence of solubility corresponds to a lattice-adjusted contraction between 0–15%. The contraction size rule is a geometric argument based upon the contraction of the atoms forming the intermetallic structure and appears to be an important relationship in describing ranges of homogeneity in Laves phases. The relationships developed are applied to interpret potential defect mechanisms and alloying behavior in binary and ternary Laves phases. In addition, extended ternary solubility ranges normal to a pseudobinary direction can be predicted with suitable solute additions having a metallic diameter between that of the A and B atoms.