Cluster formulas of Co-Al-W-base superalloys
Authors: Ma Qi-Hui , Zhang Yu , Wang Qing , Dong Hong-Gang , Dong Chuang ,   Key Laboratory of Materials Modification by Laser, Ion and Electron Beams Ministry of Education, Dalian University of Technology, Dalian 116024, China
Published: December 2020

Having a <inline-formula><tex-math id="M23">\begin{document}$\gamma /\gamma′ $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M23.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M23.png"/></alternatives></inline-formula> microstructure similar to Ni-base superalloys and also including various alloying elements such as Al and W, new Co-base superalloy, namely Co-Al-W-base alloy, has been widely studied as a kind of potential alternative of Ni-base superalloy, which is the most important high-temperature structural material in industrial applications. Besides, Co-Al-W-base alloy has also excellent mechanical properties, for example, creep properties comparable to those of the first-generation Ni-base single crystal superalloys. In our previous work, the ideal composition formula of Ni-base superalloy has been obtained by applying the cluster-plus-glue-atom structure model of faced centered cubic solid solution, which shows that the most stable chemical short-range-order unit is composed of a nearest-neighbor cluster and three next-neighbor glue atoms. In this paper, the ideal cluster formula of Co-Al-W-base superalloy is addressed by using the same approach. Based on cluster-plus-glue-atom model theory, according to lattice constants and atom radii, calculations are carried out. The results show that the atom radius of Al is equal to Covalent radius (0.126 nm) and for <inline-formula><tex-math id="M24">\begin{document}$\gamma′ $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M24.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M24.png"/></alternatives></inline-formula> phase the atom radius of W changes obviously (0.1316 nm). After analyzing atomic radii, the chemical formula for Co-Al-W ternary alloy is calculated to be [Al-Co<sub>12</sub>](Co,Al,W)<sub>3</sub>, which signifies an Al centered atom and twelve Co nearest-neighbored cluster atoms plus three glue atoms, which is in good consistence with that for Ni-base single crystal superalloy. For multi-element alloy, the alloying elements are classified, according to the heat of mixing between the alloying elements and Co as well as partition behavior of alloying elements, as solvent elements-Co-like elements <inline-formula><tex-math id="M25">\begin{document}$\overline {{\rm{Co}}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M25.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M25.png"/></alternatives></inline-formula> (Co, Ni, Ir, Ru, Cr, Fe, and Re) and solute elements-Al-like elements <inline-formula><tex-math id="M26">\begin{document}$\overline {{\rm{Al}}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M26.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M26.png"/></alternatives></inline-formula> (Al, W, Mo, Ta, Ti, Nb, V, etc.). The solvent elements can be divided into two kinds according to partition behaves: <inline-formula><tex-math id="M27">\begin{document}${\overline {{\rm{Co}}} ^{\gamma }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M27.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M27.png"/></alternatives></inline-formula> (Cr, Fe, and Re) and <inline-formula><tex-math id="M28">\begin{document}${\overline {{\rm{Co}}} ^{\gamma′}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M28.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M28.png"/></alternatives></inline-formula> (Ni, Ir, and Ru). The latter is further grouped into Al, <inline-formula><tex-math id="M29">\begin{document}${\overline {\rm{W}} }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M29.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M29.png"/></alternatives></inline-formula> (W and Mo, which have weaker heat of mixing than Al-Co ) and <inline-formula><tex-math id="M30">\begin{document}${\overline {{\rm{Ta}}} }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M30.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M30.png"/></alternatives></inline-formula> (Ta, Ti, Nb, V, etc., which have stronger heat of mixing than Al-Co). Then all chemically complex Co-Al-W-base superalloys are simplified into <inline-formula><tex-math id="M31">\begin{document}$\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M31.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M31.png"/></alternatives></inline-formula> pseudo-binary or <inline-formula><tex-math id="M32">\begin{document}$\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M32.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M32.png"/></alternatives></inline-formula> pseudo-ternary system. Within the framework of the cluster-plus-glue-atom formulism and by analyzing the compositions of alloy, it is shown that the Co-Al-W-base superalloy satisfies the ideal formula <inline-formula><tex-math id="M33">\begin{document}$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{1.0}}{{\overline {{\rm{Al}}} }_{2.0}}} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M33.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M33.png"/></alternatives></inline-formula> (or <inline-formula><tex-math id="M34">\begin{document}$\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}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M34.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M34.png"/></alternatives></inline-formula> = <inline-formula><tex-math id="M35">\begin{document}${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{9.375}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M35.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M35.png"/></alternatives></inline-formula> at.%). In the same way, those of <inline-formula><tex-math id="M36">\begin{document}$\gamma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M36.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M36.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M37">\begin{document}$\gamma′ $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M37.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M37.png"/></alternatives></inline-formula> phases are respectively <inline-formula><tex-math id="M38">\begin{document}$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{1.5}}{{\overline {{\rm{Al}}} }_{1.5}}} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M38.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M38.png"/></alternatives></inline-formula> (or <inline-formula><tex-math id="M39">\begin{document}$\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}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M39.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M39.png"/></alternatives></inline-formula> = <inline-formula><tex-math id="M40">\begin{document}${\overline {{\rm{Co}}} _{84.375}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{6.250}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M40.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M40.png"/></alternatives></inline-formula> at.%) and <inline-formula><tex-math id="M41">\begin{document}$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{0.5}}{{\overline {{\rm{Al}}} }_{2.5}}} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M41.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M41.png"/></alternatives></inline-formula> (or <inline-formula><tex-math id="M42">\begin{document}$\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}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M42.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M42.png"/></alternatives></inline-formula> = <inline-formula><tex-math id="M43">\begin{document}${\overline {{\rm{Co}}} _{78.125}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{12.500}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M43.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M43.png"/></alternatives></inline-formula> at.%). For example, alloy Co<sub>82</sub>Al<sub>9</sub>W<sub>9</sub> and its <inline-formula><tex-math id="M44">\begin{document}$\gamma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M44.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M44.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M45">\begin{document}$\gamma′ $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M45.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20181030_M45.png"/></alternatives></inline-formula> phases are formulated respectively as [Al-Co<sub>12</sub>]Co<sub>1.1</sub>Al<sub>0.4</sub>W<sub>1.4</sub> (～ [Al-Co<sub>12</sub>]Co<sub>1.0</sub>Al<sub>0.5</sub>W<sub>1.5</sub>), [Al-Co<sub>12</sub>]Co<sub>1.6</sub>Al<sub>0.4</sub>W<sub>1.0</sub> (～ [Al-Co<sub>12</sub>]Co<sub>1.5</sub>Al<sub>0.5</sub>W<sub>1.0</sub>), and [Al-Co<sub>12</sub>]Co<sub>0.3</sub>Al<sub>0.5</sub>W<sub>2.2</sub> (～[Al-Co<sub>12</sub>]Co<sub>0.5</sub>Al<sub>0.5</sub>W<sub>2.0</sub>).