Explanation of Cr-C eutectic points using the cluster-plus-glue-atom model

Abstract

Cr-C system is an important protective coating material for its high hardness, good corrosion resistance and electrical conductivity. It is also a typical eutectic system, where all stable phases are involved in the eutectic reactions. According to our previous work, binary eutectic liquids satisfy the dual-cluster short-range-order structural model, i.e., a eutectic liquid is composed of two stable liquid subunits respectively issued from the two eutectic phases and each one formulates the same ideal metallic glass [cluster] (glue atom)1 or 3, where the nearest-neighbor cluster is derived from a devitrification phase. Therefore a eutectic liquid can always be formulated as two nearest-neighbor clusters plus two, four, or six glue atoms. The key step towards understanding a eutectic composition is then to obtain the right clusters from the two eutectic phases for use in the formulation of the glassy/eutectic composition, which we call the principal clusters. In this paper, Friedel oscillation and atomic dense packing theories are adopted to identify the principal clusters of Cr-C eutectic phases for the objective of establishing the dual cluster formulas for the eutectic compositions. First, clusters in eutectic phases Cr, Cr23C6, Cr7C3 and Cr3C2 are defined by assuming that all the nearest neighbors are located within the first negative potential minimum zone in Friedel oscillation, which causes a cutoff distance to be less than 1.5 times the innermost shell distance. Second, by comparing all the radial distribution profiles of total atomic density centered by each cluster in a given phase structure, the one exhibiting the most distinct spherical periodicity feature is selected as the principal cluster. Moreover, the principal clusters are the most separated from each other among all the clusters in the same phase, showing the highest degree of cluster isolation. Under the criteria of the cluster distribution following spherical periodicity order and of the cluster isolation, the following principal clusters are derived: rhombidodecahedron CN14 [Cr-Cr14] from Cr, capped trigonal prism CN9 [C-Cr9] from Cr23C6 and Cr7C3, and [C-Cr8] from Cr3C2. Via these examples, the principal cluster identification procedures are detailed. Third, the thus selected principal clusters are matched with appropriate glue atoms to construct the dual cluster formulas for the Cr-C eutectics Cr86C14 and Cr67.4C32.6, i.e., [Cr-Cr14+C-Cr9]CrC3Cr86.2C13.8 and [C-Cr9+C-Cr8]C6Cr68.0C32.0, respectively. This work proves the universality of the cluster-plus-glue-atom model in explaining the composition of binary eutectics and lays a theoretical foundation for the composition design of Cr-C based materials.