The relationship between the cross-sectional shape of W fibers and kinetic undercooling in directionally solidified (DS) NiAl–W eutectic alloys was investigated. When the growth rate was less than 8 µm/s, the cross-sectional shape of W fibers was hexagonal (faceted); conversely, when the growth rate was more than 8 µm/s, their cross-sectional shape was elliptical (nonfaceted). Meanwhile, the NiAl matrix and W fibers in DS NiAl–W eutectic alloys presented a particular crystallographic orientation. The crystallographic orientation between NiAl matrix and W fibers was [1¯\documentclass[12pt]{minimal}
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\begin{document}$$ \bar{1} $$\end{document}11]NiAl//[200]W in the growth rate of 6 µm/s, and [1¯\documentclass[12pt]{minimal}
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\begin{document}$$ \bar{1} $$\end{document}11]NiAl//[1¯\documentclass[12pt]{minimal}
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\begin{document}$$ \bar{1} $$\end{document}11]W in the growth rate of 8 µm/s. A critical kinetic undercooling ΔTk,Wc\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta T_{k,W}^{c} $$\end{document} can be used to predict the transition from the faceted to nonfaceted growth of W fibers in DS NiAl–W eutectic alloys. When the kinetic undercooling ΔTk\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta T_{k} $$\end{document} of the W phase was less than ΔTk,Wc\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta T_{k,W}^{c} $$\end{document}, the W fibers’ growth was faceted with a hexagonal shape, whereas when ΔTk>ΔTk,Wc\documentclass[12pt]{minimal}
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\begin{document}$$ \Delta T_{k} > \Delta T_{k,W}^{c} $$\end{document}, the W fibers exhibited nonfaceted growth with elliptical shape.