Cluster formulas of Co-Al-W-base superalloys

Having a \begin{document}$\gamma /\gamma′ $\end{document}microstructure similar to Ni-base superalloys and also including various alloying elements such as Al and W, new Co-base superalloy, namely Co-Al-W-base alloy, has been widely studied as a kind of potential alternative of Ni-base superalloy, which is the most important high-temperature structural material in industrial applications. Besides, Co-Al-W-base alloy has also excellent mechanical properties, for example, creep properties comparable to those of the first-generation Ni-base single crystal superalloys. In our previous work, the ideal composition formula of Ni-base superalloy has been obtained by applying the cluster-plus-glue-atom structure model of faced centered cubic solid solution, which shows that the most stable chemical short-range-order unit is composed of a nearest-neighbor cluster and three next-neighbor glue atoms. In this paper, the ideal cluster formula of Co-Al-W-base superalloy is addressed by using the same approach. Based on cluster-plus-glue-atom model theory, according to lattice constants and atom radii, calculations are carried out. The results show that the atom radius of Al is equal to Covalent radius (0.126 nm) and for \begin{document}$\gamma′ $\end{document}phase the atom radius of W changes obviously (0.1316 nm). After analyzing atomic radii, the chemical formula for Co-Al-W ternary alloy is calculated to be [Al-Co 12 ](Co,Al,W) 3 , which signifies an Al centered atom and twelve Co nearest-neighbored cluster atoms plus three glue atoms, which is in good consistence with that for Ni-base single crystal superalloy. For multi-element alloy, the alloying elements are classified, according to the heat of mixing between the alloying elements and Co as well as partition behavior of alloying elements, as solvent elements-Co-like elements \begin{document}$\overline {{\rm{Co}}} $\end{document}(Co, Ni, Ir, Ru, Cr, Fe, and Re) and solute elements-Al-like elements \begin{document}$\overline {{\rm{Al}}} $\end{document}(Al, W, Mo, Ta, Ti, Nb, V, etc.). The solvent elements can be divided into two kinds according to partition behaves: \begin{document}${\overline {{\rm{Co}}} ^{\gamma }}$\end{document}(Cr, Fe, and Re) and \begin{document}${\overline {{\rm{Co}}} ^{\gamma′}}$\end{document}(Ni, Ir, and Ru). The latter is further grouped into Al, \begin{document}${\overline {\rm{W}} }$\end{document}(W and Mo, which have weaker heat of mixing than Al-Co ) and \begin{document}${\overline {{\rm{Ta}}} }$\end{document}(Ta, Ti, Nb, V, etc., which have stronger heat of mixing than Al-Co). Then all chemically complex Co-Al-W-base superalloys are simplified into \begin{document}$\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $\end{document}pseudo-binary or \begin{document}$\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)$\end{document}pseudo-ternary system. Within the framework of the cluster-plus-glue-atom formulism and by analyzing the compositions of alloy, it is shown that the Co-Al-W-base superalloy satisfies the ideal formula \begin{document}$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{1.0}}{{\overline {{\rm{Al}}} }_{2.0}}} \right)$\end{document}(or \begin{document}$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{1.5}}$\end{document}= \begin{document}${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{9.375}}$\end{document}at.%). In the same way, those of \begin{document}$\gamma $\end{document}and \begin{document}$\gamma′ $\end{document}phases are respectively \begin{document}$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{1.5}}{{\overline {{\rm{Al}}} }_{1.5}}} \right)$\end{document}(or \begin{document}$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{1.0}}$\end{document}= \begin{document}${\overline {{\rm{Co}}} _{84.375}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{6.250}}$\end{document}at.%) and \begin{document}$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{0.5}}{{\overline {{\rm{Al}}} }_{2.5}}} \right)$\end{document}(or \begin{document}$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{0.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{2.0}}$\end{document}= \begin{document}${\overline {{\rm{Co}}} _{78.125}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{12.500}}$\end{document}at.%). For example, alloy Co 82 Al 9 W 9 and its \begin{document}$\gamma $\end{document}and \begin{document}$\gamma′ $\end{document}phases are formulated respectively as [Al-Co 12 ]Co 1.1 Al 0.4 W 1.4 ( [Al-Co 12 ]Co 1.0 Al 0.5 W 1.5 ), [Al-Co 12 ]Co 1.6 Al 0.4 W 1.0 ( [Al-Co 12 ]Co 1.5 Al 0.5 W 1.0 ), and [Al-Co 12 ]Co 0.3 Al 0.5 W 2.2 ([Al-Co 12 ]Co 0.5 Al 0.5 W 2.0 ).