Prediction of the densities of liquid Ni-based superalloys
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I. INTRODUCTION
ACCURATE values of the density () and its temperature dependency (d/dT) are needed to eliminate problems encountered in the solidification of Ni-based superalloys, such as spurious grain growth and “freckle” formation. An investigation of the literature indicated that although the density of liquid nickel has been measured by a variety of techniques, there still remains a large scatter in the reported values of the density and its temperature dependency; this is due to the experimental uncertainties associated with the different methods.[1,2] Furthermore, there are very few reports on the measurement of the densities of liquid Ni-based alloys in relation to the effects of composition and temperature. Density measurements on liquid Ni-binary alloys have been reported for (1) Ni-Cr (9 to 57 mass pct Cr) by Eremenko and Naidich,[3] using the large drop method, and for (2) NiCo alloys by Watanabe et al.[4] and Dizhemilev et al.[5] Sung et al.[6] cited measured densities of five Ni-based superalloys but did not indicate any details of the measurement. Sung et al.[6] reported a method to estimate the densities of liquid transition metals and liquid Ni-based superalloys. These investigators collated and reviewed data for density () and its temperature dependency (d/dT) for the elements used in Ni-based superalloys. A simple linear correlation was applied to these data. The densities of 16 quaternary Ni-rich alloys (Ni-Al-Cr-Ta) for three different temperatures were calculated by assuming that the Ni-Al-Cr-Ta quaternary alloys exhibited ideal mixing. The regression equations for the densities of the Ni-Al-Cr-Ta alloys as a function of element composition and temperature were obtained by relating the calculated density values to the element composition and temperature (a multilinear regression). The densities of five liquid Ni-based superalloys were estimated to validate the KUSUHIRO MUKAI, Professor Emeritus, Department of Materials Science and Engineering, Kyushu Institute of Technology, Kitakyushu-shi, 8048550 Japan, is Visiting Professor, Department of Materials, Imperial College London, London SW7 2AZ, United Kingdom. ZUSHU LI, Postdoctoral Research Associate, and KENNETH C. MILLS, Professor, are with the Department of Materials, Imperial College London, London SW7 2AZ, United Kingdom. Contact e-mail: [email protected] or [email protected] Manuscript submitted November 1, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS B
method. The errors of the estimated values are somewhat greater (8.59 to 3.24 pct) than those expected compared with the measured density values of the five Ni-based superalloys. They considered that the largest error resulted from uncertainties in the mixing volume. This was calculated from the difference between the molar volume of the alloy (calculated from its measured density) and the calculated molar volume (by the method outlined previously). A compositiondependent correction term was then applied to the molar mixing volume. The corrected estimations of the densities o
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