Measurement of the Density of Binary Ni-X (X=Co, W, Ta, Al) Alloys

Transcription

1 Materials Transactions, Vol. 45, No. 5 (004) pp to 1763 #004 The Japan Institute of Metals Measurement of the Density of Binary Ni-X (X=Co, W, Ta, Al) Alloys Kusuhiro Mukai, Liang Fang* 1, Zushu Li* and Feng Xiao Department of Materials Science and Engineering, Faculty of Engineering, Kyushu Institute of Technology, Kitakyushu , Japan The modified sessile drop method () and modified pycnometric method () have been employed to measure the densities of liquid Ni-Co, Ni-W, Ni-Ta and Ni-Al alloys precisely. In the case of Ni-Al alloys measurements were also made in the mushy state where both solid and liquid coexist. There was a good agreement between the values measured by the two methods. The density of liquid Ni-base binary alloys from the melting points to 133 K and that of Ni-Al alloys in the mushy state decrease linearly with increasing temperature. The temperature coefficient of the density of Ni-base binary alloys measured in this work was regressed as a quadratic function of the concentration of alloy element. The measured density of Ni-base binary alloys at any required temperature can also be expressed as a quadratic function of the concentration of alloy element. The recommended equations for the density of Ni-base binary alloys were obtained as a function of composition and temperature by regressing the density values measured by both and. The calculated values from the recommended density equations show good agreement with those obtained with both methods. (Received January 0, 004; Accepted March 19, 004) Keywords: nickel-base binary alloy, density, modified sessile drop method, modified pycnometric method, superalloys 1. Introduction Accurate measurements of the density () and its temperature dependency (d=dt) are needed to eliminate problems encountered in the solidification of Ni-base superalloys, such as spurious grain growth and freckle formation. A literature review indicated that although the density of liquid nickel has been measured by a variety of techniques, there is a large scatter in the reported density values and its temperature dependency for liquid nickel because of the experimental uncertainties associated with different methods. 1,) Furthermore, there are very few reports on the measurement of the density of Ni-base alloys in relation to the effects of composition and temperature. Eremenko and Naidich 3) measured the density of Ni-Cr alloys in liquid and mushy (ie solid+liquid) states for Cr concentrations between 9 and 57 mass% using the large drop method. Watanabe et al. 4) and Dizhemilev et al. 5) measured the densities of liquid Ni-Co alloys. Watanabe et al. 4) reported that densities of liquid Ni-Co alloys (for Co concentrations between 0 and 0 mass%) decreased with increasing temperature in the range ( K). The densities of liquid Ni-Co alloys at 13 K, 173 K and 193 K changed with Co concentration in the form of wavy lines but decreased with increasing Co concentration below 40 mass %. The densities of liquid Ni-Co alloys at 13 K reported by Dizhemilev et al. 5) also changed with Co concentration in the form of a wavy line but increased slightly with increasing the Co concentration below 16 mass%. This is in contradiction with the results reported by Watanabe et al. 4) Sung et al. 6) cited measured densities of five Ni-base superalloys but did not indicate any details of the measurement method. We have developed two methods, denoted the modified sessile drop method () and modified pycnometric * 1 Present address: Department of Applied Physics, Chongqing University, Chongqing , P. R. China * Present address: Department of Materials, Imperial College London, Prince Consort Road, London SW7 BP, UK method () to measure accurately the densities of liquid nickel and Ni-base model alloys and commercial alloys in liquid and mushy states. The principles of the two methods and their advantages have been detailed in previous papers. 1,) The densities of liquid nickel and Ni-Cr alloys in liquid and mushy states have been measured precisely by both methods. These two methods ( and ) have the following advantages over the traditional sessile drop method and pycnometric method,. Higher precision, with a continuous measurement of density for a large variety of materials over a wide temperature range (including the mushy state).. The possibility of determining the solidus and liquidus temperatures of some multi-component alloys. Total maximum relative error have been estimated to be 0:75% for and 0:30% for by rigorous calculation of the errors associated with the measurement of sample mass and volume. There is good mutual agreement between the density data obtained by and, differences in density values being less than 0.16% for liquid Nickel and 0.5% for liquid Ni-Cr alloys. This difference was considered to be the result of the systematic errors associated with the two methods. In order to minimize the influence of the systematic errors of the two methods on the measured value of density, a least-square analysis was carried out on the density data (obtained with the two methods) for liquid nickel and Ni-Cr alloy and equations were recommended. These recommended equations for the densities of Ni-Cr alloys in the mushy state were obtained by combining the density value at the liquidus temperature (calculated from the recommended equation of liquid nickel-chromium alloy) with the value of (d=dt) obtained by since the measurement accuracy of is higher than that of. It was found that the solidus (T sol ) and liquidus (T liq ) temperatures of alloy can be evaluated by the observation of drop profile and an analysis of the change of density value with the temperature since the surface of the drop changes from smooth into rough around T sol in measurement

2 Measurement of the Density of Binary Ni-X (X=Co, W, Ta, Al) Alloys 1755 and (d=dt) for the alloy changes possibly at T sol and T liq. The solidus and liquidus temperatures of Ni-Cr alloys evaluated by the two methods were in good agreement with those derived from the phase diagram of Ni-Cr alloy. Ni-base superalloys are mainly composed of nickel and alloy elements such as chromium, cobalt, tungsten, tantalum, aluminum, etc. In this work, the densities of liquid Ni-Co, Ni- W and Ni-Ta alloys and Ni-Al alloys in liquid and mushy states have been measured by both and as a function of composition and temperature.. Experimental Both methods ( and ) were employed to measure accurately the densities of liquid Ni-Co, Ni-W and Ni-Ta alloys and Ni-Al alloys in the liquid and mushy states. The experimental procedures used have been described in detail in previous papers. 1,) The experimental samples of Ni-base binary alloys are composed of Ni (0 mass%)-x (0 mass%, X=Co, W, Ta, Al) master alloy discs cut from high purity Ni (0 mass%)-x (0 mass%) master alloy ingot rods, and the insufficient nickel mass is replenished by nickel disc cut from high purity nickel rod. The chemical compositions of the alloy elements in the alloys after experiments were analysed by radio frequency inductively coupled plasma (I.C.P.) emission spectrometry. The infrared adsorption and thermal conductimetric method after fusion in a He gas flow was adopted to analyse oxygen concentration in the alloys, and the infrared adsorption method after combustion in an induction furnace for sulphur concentration in the alloys. It should be mentioned that in this work all the T sol and T liq values were obtained from the phase diagrams of binary Nibase alloys. 7 14) For Ni-Co alloys, the temperature range of the mushy phase is very narrow, only a few degrees or even less (e.g., about 0.3 K at 50 mass% Ni alloy).,1) The densities of Ni-W and Ni-Ta alloys below the liquidus temperature were measured but the temperature coefficient (d=dt) below T liq was almost identical to that in liquid state. Consequently, only the densities of liquid Ni-Co, Ni-W and Ni-Ta alloys were discussed. In Ni-Al alloys the mushy range extends over a relatively wide temperature, so densities were determined in both the liquid and mushy states. The absolute values for Ni-Al alloys of the temperature coefficients of densities in the mushy state are larger than those for the liquid state (this is described in section 3.5). Therefore, the densities of Ni-Al alloys are expressed with two separate equations for the liquid and mushy states respectively. The linear thermal expansion of alumina crucibles was remeasured because all the alumina crucibles used in this work for and may be slightly different from those reported in previous papers. 1,) Using a gauging microscope (minimum gauge unit is mm), it was measured by comparing the photographed image on nega film of crucible between the experimental temperature of K and room temperature. The average values of the linear thermal expansion for all the crucibles were used to calculate the sample volume in both and. Linear Thermal Expansion, α L /% Temperature, T/K 3. Results and Discussion Previous data 1,) Present α L /%= T Present α L /% = 0.0 Fig. 1 Temperature dependence of the linear thermal expansion of alumina crucible. 3.1 Thermal expansion of alumina crucible As shown in Fig. 1, the measured linear thermal expansion of crucibles had an experimental uncertainty of 0:0. The average value can be expressed by eq. (1): L =% ¼ :96 þ 0:004T 0:0 ð1þ where L (%) is the linear thermal expansion of crucibles, T (K) temperature. In this work, the average thermal expansion was used to calculate the sample volume at the experimental temperature for both and, where the maximum difference between the real value and the average value of linear thermal expansion is 0:0%. Therefore, the maximum uncertainty in the measurement of density arising from uncertainties in the thermal expansion of the alumina crucible in this work is calculated to be 0:17% for and 0:4% for using the estimation method reported previously. 1,) Consequently, the total maximum relative error of density in this study is estimated as 0:% for and 0:4% for when the other sources of uncertainty are taken into account. 1,) 3. Density of Liquid Ni-Co Alloys The density of liquid Ni-Co alloys with Co between 0 and 1.70 mass% were measured by both and and the results are shown in Fig. along with the density of liquid Ni-Co alloys reported by Watanabe et al. 4) The densities of liquid Ni-Co alloys measured in this work were found to decrease linearly with increasing temperature. The densities of liquid Ni-Co alloys with mass%co reported by Watanabe et al. 4) also decreased with increasing the temperature ranging from 174 K to 194 K, but the temperature coefficient is smaller than that obtained in this work. The measured densities of liquid Ni-Co alloys for Co concentrations between 0 and 1.70 mass% can be expressed

3 1756 K. Mukai, L. Fang, Z. Li and F. Xiao Density, ρ / Mg m Fig : Pure nickel,.54mass%co, 5.40mass%Co, 10.6mass%Co, 16.50mass%Co, 1.70mass%Co; : Pure nickel, 6.00mass%Co, 11.55mass%Co, 14.3mass%Co, 1.19mass%Co; Watanabe 60.1mass%Co 0.1mass%Co 0.1mass%Co 40.1mass%Co Temperature, T/K Densities of liquid Ni-Co alloys as measured by and K Watanabe 13K Watanabe K Dzhemilev 193K Watanabe Cobalt concentration, (mass%) : 1753K, : 1773K, 1793K, 113K, 133K, 1773K, 113K, 14K, 16K, 193K. Fig. 3 Effect of Co concentration on the densities of liquid Ni-Co alloys reported by various investigators. Table 1 Density of liquid Ni-Co alloys as a function of temperature at different Co concentrations. Method, mass%, Mgm 3, 10 4 K 1 0 ¼ 7:91 1: ðt 17Þ ¼ 7: 1: ðt 179Þ ¼ 7:5 1: ðt 1730Þ ¼ 7: 1: ðt 173Þ ¼ 7:7 1: ðt 1734Þ ¼ 7:77 1: ðt 1735Þ ¼ 7:9 1: ðt 17Þ ¼ 7:5 1: ðt 1730Þ ¼ 7: 1: ðt 1733Þ ¼ 7:0 1: ðt 1734Þ ¼ 7:76 1: ðt 1735Þ 1.60 : Co concentration in the alloy, mass%. as a function of temperature as shown in Table 1. The volume thermal expansion coefficient for the liquid alloy with various Co concentrations lies in the range of 1: : K 1 for and 1: : K 1 for. The effect of Co concentration on the densities of liquid Ni-Co alloys at various temperatures obtained in this work are shown in Fig. 3 along with those obtained by Watanabe et al. 4) and Dizhemilev et al., 5) and can be expressed as a quadratic function of Co concentration (Table ). As shown in Fig. 3, the dependencies of densities of liquid Ni-Co alloys reported by Watanabe et al. 4) with Co concentration (between 0 and 100 mass%) have the form of a wavy line and decreased with increasing Co concentration between 0 and 40 mass%. The densities of liquid Ni-Co alloys measured by Dzhemilev et al. 5) increased with increasing Co concentration between 0 and 16 mass% at 13 K. Temperature coefficients of the density for liquid Ni-Co alloys, k ¼ðd=dTÞ p (Mgm 3 K 1 ) as shown in Table 1 and Fig. 4, were found to increase with increasing the Co concentration. It can be expressed as a quadratic function of Co concentration using least-square method, and the results are shown in eq. () for and eq. (3) for, respectively. The values of k obtained by two methods are similar. k 10 3 ¼ 1:43 4: þ: k 10 3 ¼ 1:51 þ 1: C CO þ7: Therefore, a least-square analysis of the data obtained by and gives the equations for the densities of liquid Ni-Co alloys as functions of both Co concentration and temperature as eqs. (4) and (5) for and, respectively. : ¼ð7:91 1:05 10 þ 1: C Co Þ ð1:43 þ 4: : C Co Þ 10 3 ðt Þ ð T 133 KÞ ð4þ ðþ ð3þ

4 Measurement of the Density of Binary Ni-X (X=Co, W, Ta, Al) Alloys 1757 Table Density of liquid Ni-Co alloys as a function of Co concentration at different temperatures. Method Temperature/K, Mgm ¼ 7:7 1:06 10 þ : ¼ 7:5 1:14 10 þ : ¼ 7: 1:0 10 þ 3: ¼ 7:79 1:07 10 þ : ¼ 7:76 1:16 10 þ 3: ¼ 7:3 9: þ 1: ¼ 7:77 : þ 1: ¼ 7:7 6: þ 1: ¼ 7:66 6: þ 0: ¼ 7:60 4: þ 0: Temperature Coefficient, k 10 3 /Mg m K : Ni W:6.09% W :10.00% W:15.00% : Ni W:6.06% W :10.03% W:14.95% Cobalt concentration, (mass%) Temperature, T/K Fig. 4 Temperature coefficient of the densities of liquid Ni-Co alloys as a function of Co concentration as measured by and. Fig. 5 Densities of liquid Ni-W alloys measured by and. : ¼ð7:90 6: : C Co Þ ð1:51 1: C CO 7: C Co Þ 10 3 ðt Þ ð T 193 KÞ ð5þ where is the liquidus temperature of the alloy. There is a good agreement between the data measured by and, and the difference between the density values measured by the two methods is less than 0.13%, which can be regarded as the systematic errors of the two methods. Then in order to offset the influence of the systematic error of the two methods on the measured value of density, all the data for the densities of liquid Ni-Co alloys obtained by the two methods were subjected to a least-square analysis and the resulting equation (eq. (6)) is recommended. ¼ð7:91 : þ 5: C Co Þ ð1:46 þ 3: : C Co Þ 10 3 ðt Þ ð T 133 KÞ ð6þ The difference between the calculated value obtained with eq. (6) and the measured value is smaller than 0:90%. 3.3 Densities of liquid Ni-W alloys The effects of both W concentration and temperature on the densities of liquid Ni-W alloys were determined by both and. The experimental results are shown in Fig. 5 and in Table 3. The densities of liquid Ni-W alloys for W concentrations between 0 and 15.0 mass% was found to decrease linearly with increasing temperature from the liquidus temperature of the alloy to 173 K. The volume thermal expansion coefficients of liquid Ni-W alloys were found to be in the range of 1: to 1: K 1. The temperature coefficients k of the density for liquid Ni- W alloys are given in Table 3 and Fig. 6. Least-square analysis produced the quadratic function of W concentration shown in eq. (7) for and eq. () for. The temperature coefficients obtained by two methods are in good agreement. k 10 3 ¼ 1:43 þ 3:69 10 C W 1: CW ð7þ k 10 3 ¼ 1:51 þ 1: C W 6: CW ðþ As shown in Fig. 7 and Table 4, the densities of liquid Ni-W alloys increase with W concentration in the form of a quadratic function of W concentration for temperatures between 1773 K and 133 K. The densities of liquid Ni-W alloys as functions of both composition and temperature can be expressed by eq. (9) for and eq. (10) for.

5 175 K. Mukai, L. Fang, Z. Li and F. Xiao Table 3 Density of liquid Ni-W alloys as a function of temperature at different W concentrations. Method C W, mass%, Mgm 3, 10 4 K 1 0 ¼ 7:91 1: ðt 17Þ ¼ :1 1: ðt 1745Þ ¼ :46 1: ðt 1753Þ ¼ :6 1: ðt 1763Þ ¼ 7:9 1: ðt 17Þ ¼ :10 1: ðt 1745Þ ¼ :40 1: ðt 1753Þ ¼ :66 1: ðt 1763Þ 1.74 C W : W concentration in the alloy, mass%. Temperature coefficient, 3 k /Mg m 10 K : K 1793K 113K 133K : 1773K 1793K 113K 133K Tungsten concentration, C W (mass%) Fig. 6 Temperature coefficients of the densities of liquid NI-W alloys as a function of W concentration as measured by and. Fig Tungsten concentration, C W (mass%) Effect of W concentration on the densities of liquid Ni-W alloys. Table 4 Density of liquid Ni-W alloys as a function of W concentration at different temperatures. Method Temperature/K, Mgm ¼ 7:5 þ 4:97 10 C W þ 4: C W 1793 ¼ 7: þ 4:97 10 C W þ 7: C W 113 ¼ 7:79 þ 4:71 10 C W þ 6: C W 133 ¼ 7:76 þ 4:40 10 C W þ : C W 1773 ¼ 7: þ 3: 10 C W þ 1: C W 1793 ¼ 7:79 þ 3: 10 C W þ 1: C W 113 ¼ 7:76 þ 3:95 10 C W þ 9: C W 133 ¼ 7:73 þ 4:97 10 C W þ 4: C W 153 ¼ 7:70 þ 3:96 10 C W þ : C W 173 ¼ 7:67 þ 4:49 10 C W þ 6: C W : ¼ð7:91 þ 4:01 10 C W þ : CW Þ ð1:43 3:69 10 C W þ 1: CW Þ 10 3 ðt Þ ð T 133 KÞ ð9þ ¼ð7:9 þ 3:30 10 C W þ 1: CW Þ ð1:51 1: C W þ 6: CW Þ 10 3 ðt Þ ð T 173 KÞ ð10þ where is the liquidus temperature of Ni-W alloy. The values obtained by the two methods are in good agreement with the difference between the density values measured by the two methods being smaller than 0.5% which can be regarded as the result from the systematic errors of the two methods. The effect of the systematic errors of the two methods on the measured density, was minimised by carrying out least-square analysis on all the density data for liquid Ni-W alloys obtained by the two methods. The following equation is recommended.

6 Measurement of the Density of Binary Ni-X (X=Co, W, Ta, Al) Alloys 1759 Table 5 Density of liquid Ni-Ta alloys as a function of temperature at different Ta concentrations. Method C Ta, mass%, Mgm 3, 10 4 K 1 0 ¼ 7:91 1: ðt 17Þ ¼ 7:99 : ðt 171Þ ¼ :15 1: ðt 1713Þ ¼ :4 : ðt 1704Þ ¼ 7:9 1: ðt 17Þ ¼ 7:9 9: ðt 171Þ ¼ :14 1: ðt 1713Þ ¼ :45 1: ðt 1704Þ 1.0 C Ta : Ta concentration in the alloy, mass%..5 : Ni Ta:.95% Ta:6.0% Ta:10.0% : Ni Ta:3.04% Ta:6.01% Ta:9.99% Temperature coefficient, k 10 3 /Mg m K : Tantalum concentration, C Ta (mass%) Fig. Temperature, T/K Densities of liquid Ni-Ta alloys as measured by and. Fig. 9 Temperature coefficients of the densities of liquid Ni-Ta alloys as a function of Ta concentration. ¼ð7:90 þ 3:66 10 C W þ 1: CW Þ ð1:47 7:15 10 C W þ 4: CW Þ 10 3 ðt Þ ð T 133 KÞ ð11þ The difference between the calculated value obtained with eq. (11) and the measured value is smaller than 0:65%. 3.4 Densities of liquid Ni-Ta alloys The densities of liquid Ni-Ta alloys with Ta contents between 0 and 10.0 mass% were measured by both and. The densities decreased linearly with increasing temperature from the melting point to 173 K as shown in Fig. and can be expressed by the equations in Table 5. The volume thermal expansion coefficients of liquid Ni-Ta alloys were found to be in the range of 1: : K 1. The temperature coefficients k of the densities of liquid Ni- Ta alloys are given in Table 5 and Fig. 9. Least-square analyses yielded quadratic function of Ta concentration, namely, eq. (1) for and eq. (13) for. The temperature coefficients obtained by two methods are in good agreement. k 10 3 ¼ 1:43 þ 1: C Ta 1:5 10 C Ta ð1þ k 10 3 ¼ 1:51 þ 1: C Ta 1: 10 CTa ð13þ The relationship between the densities of liquid Ni-Ta alloys and Ta concentration was obtained using the leastsquare method as a quadratic function of Ta concentration, and the results were shown in Table 6 and Fig. 10. The densities of liquid Ni-Ta alloys as functions of Ta concentration and temperature can be expressed by eq. (14) for and eq. (15) for. ¼ð7:91 þ :0 10 C Ta þ 3: CTa Þ ð1:43 1: C Ta þ 1:5 10 CTa Þ 10 3 ðt Þ ð T 133 KÞ ð14þ ¼ð7:9 þ 1:61 10 C Ta þ 3: CTa Þ ð1:51 1: C Ta þ 1: 10 CTa Þ 10 3 ðt Þ ð T 173 KÞ ð15þ There is a good agreement between the data measured by both and. The difference between the density values measured by the two methods is less than 0.35%. A least square analysis of all density data for liquid Ni-Ta alloys obtained with the two methods resulted in eq. (16).

7 1760 K. Mukai, L. Fang, Z. Li and F. Xiao Table 6 Density of liquid Ni-Ta alloys as a function of Ta concentration at different temperatures. Method Temperature/K, Mgm ¼ 7:90 þ : 10 C Ta þ : C Ta 1753 ¼ 7:7 þ :13 10 C Ta þ : C Ta 1773 ¼ 7:5 þ :9 10 C Ta þ : C Ta 1793 ¼ 7: þ 3:46 10 C Ta þ 1: C Ta 113 ¼ 7:79 þ 3:14 10 C Ta þ : CTa 133 ¼ 7:76 þ 3:41 10 C Ta þ 1: CTa 1733 ¼ 7: þ 1:57 10 C Ta þ 3: CTa 1753 ¼ 7:5 þ :3 10 C Ta þ : CTa 1773 ¼ 7: þ :0 10 C Ta þ : CTa 1793 ¼ 7:79 þ :5 10 C Ta þ : C Ta 113 ¼ 7:76 þ :9 10 C Ta þ : C Ta 133 ¼ 7:73 þ 3:53 10 C Ta þ 1: C Ta 153 ¼ 7:70 þ 4:09 10 C Ta þ 9: C Ta 173 ¼ 7:67 þ 3:56 10 C Ta þ 1: C Ta : K 1773K 113K 133K : 1733K 1773K 113K 133K Tantalum concentration, C Ta (mass%) : Ni Al:3.06mass% Al:6.06mass% Al:10.1mass% : Ni Al:3.04mass% Al:6.00mass% Al:10.03mass% Temperature, T/K Fig. 10 Effect of Ta concentration on the densities of liquid Ni-Ta alloys measured by and. Fig. 11 Densities of Ni-Al alloys in liquid and mushy states measured by and. ¼ð7:90 þ 1: 10 C Ta þ 3: CTa Þ ð1:47 1: C Ta þ 1:54 10 CTa Þ 10 3 ðt Þ ð T 133 KÞ ð16þ The difference between the calculated density by eq. (16) and the measured value is less than 0:7%. 3.5 Densities of Ni-Al alloys in liquid and mushy states The densities of Ni-Al alloys in both liquid and mushy states were measured by both and as functions of Al concentration and temperature. The experimental results are shown in Fig Densities of liquid Ni-Al alloys The densities of liquid Ni-Al alloys containing 010:1 mass% Al decrease linearly with increasing the temperature (from the melting point to 173 K) as can be seen from Fig. 11. The densities are expressed by the equations in Table 7. The volume thermal expansion coefficients of liquid Ni-Al alloys were found to be in the range of 1: : K 1. The temperature coefficients k of the densities of liquid Ni- Al alloys are given by the equations in Table and shown in Fig. 1. It can be expressed as a quadratic function of Al concentration using the least-square analysis by eq. (17) for and eq. (1) for. The temperature coefficients obtained by two methods are in good agreement. : : k 10 3 ¼ 1:43 þ 1:76 10 C Al 1: 10 3 C Al k 10 3 ¼ 1:51 þ :04 10 C Al ð17þ 1: CAl ð1þ As shown in Fig. 13 and equations in Table, the densities of liquid Ni-Al alloys (in the temperature range K) obtained by both and decrease with increasing Al concentration as a quadratic function of Al content. The densities of liquid Ni-Al alloys are expressed as a function of Al concentration and temperature by eq. (19) for and eq. (0) for, respectively.

8 Measurement of the Density of Binary Ni-X (X=Co, W, Ta, Al) Alloys 1761 Table 7 Density of liquid Ni-Al alloys as a function of temperature at different Al concentrations. Method C Al, mass%, Mgm 3, 10 4 K 1 0 ¼ 7:91 1: ðt 17Þ 1.1 C Al : Al concentration in the alloy, mass% ¼ 7:55 : ðt 171Þ ¼ 7:0 9: ðt 1703Þ ¼ 6:7 9: ðt 16Þ ¼ 7:9 1: ðt 17Þ ¼ 7:50 9: ðt 171Þ ¼ 7:1 9: ðt 1703Þ ¼ 6:1 9: ðt 16Þ 1.35 Table Density of liquid Ni-Al alloys as a function of Al concentration at different temperatures. Method Temperature/K, Mgm ¼ 7:90 1: C Al þ : C Al 1753 ¼ 7:7 1: C Al þ : C Al 1773 ¼ 7:5 1: C Al þ : C Al 1793 ¼ 7: 1: C Al þ : C Al 113 ¼ 7:79 1: C Al þ 1: 10 3 CAl 133 ¼ 7:76 1: C Al þ : CAl 1733 ¼ 7: 1: C Al þ : CAl 1753 ¼ 7:5 1: C Al þ : CAl 1773 ¼ 7: 1: C Al þ : CAl 1793 ¼ 7:79 1: C Al þ : C Al 113 ¼ 7:76 1: 10 1 C Al þ : 10 3 C Al 133 ¼ 7:73 1: C Al þ 1: C Al 153 ¼ 7:70 : 10 1 C Al þ : C Al 173 ¼ 7:67 1: C Al þ 1: C Al 5 : Liquid state : Liquid state Solid-liquid coexistence state Solid-liquid coexistence state : K 1773K 113K 133K : 1733K 1773K 113K 153K Temperature coefficient, k 10 /Mg m K Aluminum concentration, C Al (mass%) Aluminum concentration, C Al (mass%) Fig. 1 Temperature coefficients of the densities of Ni-Al alloys in liquid and mushy states measured by SDM and. ¼ð7:91 1: C Al þ : CAl Þ ð1:43 1:76 10 C Al þ 1: 10 3 CAl Þ 10 3 ðt Þ ð T 133 KÞ ð19þ Fig. 13 Effect of Al concentration on the densities of liquid Ni-Al alloys measured by and. ¼ð7:9 1: C Al þ : CAl Þ ð1:51 :04 10 C Al þ 1: CAl Þ 10 3 ðt Þ ð T 173 KÞ ð0þ At identical compositions and temperature the difference in the density of liquid Ni-Al alloys obtained by and

9 176 K. Mukai, L. Fang, Z. Li and F. Xiao Table 9 Density of Ni-Al alloys in the mushy state as a function of temperature at different Al con centrations. Method C Al, mass%, Mgm 3, 10 3 K ¼ :11 7:30 10 ðt 1711Þ ¼ 7:7 5:5 10 ðt 1693Þ ¼ 6:96 :43 10 ðt 166Þ ¼ 7:6 4:51 10 ðt 1711Þ ¼ 7:40 : ðt 1693Þ ¼ 6:6 1: ðt 166Þ.6 is less than 0.4%. The effect of systematic errors associated with the two methods on the measured value of density was minimized by carrying out a least-square analysis on all the density data of liquid Ni-Al alloys obtained with the two methods. The following equation was obtained: ¼ð7:90 1: C Al þ : CAl Þ ð1:47 1:90 10 C Al þ 1: CAl Þ 10 3 ðt Þ ð T 133 KÞ ð1þ 3.5. Densities of Ni-Al alloys in the mushy state The temperature dependencies of the densities of Ni-Al alloys in the mushy state are shown in Fig. 11 and by the equations in Table 9. As shown in Fig. 1, the absolute values of the temperature coefficients of densities in the mushy state are larger than those for the liquid Ni-Al alloys. It can be seen from the equations in Table 9 that the temperature coefficients of the densities of Ni-Al alloys in the mushy state increase with increasing Al concentration. The differences in temperature coefficients obtained with the two methods may arise from the error caused by the solid particles in the sample in the mushy state. The following equations for k were obtained by the least-square method. k 10 ¼ 9:30 þ 6:55 10 C Al þ3:09 10 C Al ðþ k 10 ¼ :17 þ 1:47 10 C Al :3 10 CAl ð3þ Least-square analyses of our data obtained with both and give the following equations for the densities of Ni-Al alloys in the mushy state as a function of both temperature and aluminum concentration: ¼ð:16 1:49 10 C Al 7: CAl Þ ð9:30 6:55 10 C Al 3: CAl Þ 10 ðt T S Þ ðt S T Þ ð4þ ¼ð7:5 3:9 10 C Al 5: CAl Þ ð:17 1:47 10 C Al þ : CAl Þ 10 ðt T S Þ ðt S T Þ ð5þ where T S is the solidus temperature of Ni-Al alloys. The data determined by the two methods are in good agreement. Since the measurement accuracy in the mushy state of the alloy is higher for than that for, the influence of the systematic error of the two methods on the measured density values was minimized in the following manner. The recommended densities of liquid Ni-Al alloys at the liquidus temperature were calculated from the recommended equation (eq. (1)) and then combined with the temperature coefficient of Ni-Al alloys obtained by for the mushy state to give the following equation. ¼ð:01 :74 10 C Al 6: CAl Þ ð:17 1:47 10 C Al þ : CAl Þ 10 ðt T S Þ ðt S T Þ ð6þ The density values measured in present work and those calculated from eq. (6) show good agreement and the difference between the calculated values by eq. (6) and the measured values is less than 0:5%. 4. Conclusions The densities of liquid Ni-Co, Ni-W and Ni-Ta alloys and those of Ni-Al alloys in liquid and mushy states have been precisely measured by two methods, ie the modified sessile drop method () and modified pycnometric method (). The following results were obtained. (1) There is a good agreement between the density values measured by the two methods for all the Ni-base binary systems investigated in this work. The difference in the density of the alloys at the identical composition and temperature measured by and is less than 0.13% for Ni-Co alloy, 0.5% for Ni-W alloy, 0.35% for Ni-Ta alloy, and 0.4% for Ni-Al alloy. () The densities of Ni-base binary alloys investigated in this work decrease linearly with increasing temperature in the experimental temperature range. The relationship between the densities of Ni-base binary alloy and the concentration of alloy element is a quadratic function of the alloy element content at a certain temperature. The temperature coefficient of the density of the Ni-base binary alloys can be also expressed as a quadratic function of the concentration of the alloy element. The absolute value of the temperature coefficient of density in the mushy state is larger than that of the liquid alloy for Ni-Al alloys. (3) The recommended equations for the densities of Nibase binary alloys investigated in this work were obtained by subjecting the combined density data (measured by both and ) to least-square analysis.

10 Measurement of the Density of Binary Ni-X (X=Co, W, Ta, Al) Alloys 1763 The difference between the calculated values (from recommended equations) and measured values (by both and ) is less than 0:90% for Ni-Co alloy, 0:65% for Ni-W alloy, 0:7% for Ni-Ta alloy and 0:5% for Ni-Al alloy in the mushy state. Acknowledgments This work was performed as a part of Research and Development of Innovative Casting Simulation supported by New Energy and Industrial Technology Development Organization, Japan. The authors would like to sincerely thank Prof. Kenneth C Mills of Imperial College London for his kind suggestions. REFERENCES 1) K. Mukai and F. Xiao: Mater. Trans. 43 (00) ) K. Mukai, F. Xiao and K. Nogi: Mater. Trans. (to be submitted.) 3) V. N. Eremenko and Y. V. Naidich: Fiz. Met. i Metalloved. 11 (1961) ) S. Watanabe, M. Amatatu and T. Saito: Trans. JIM 1 (1971) ) N. K. Dzhemilev, S. I. Popel and B. V. Tsarevskii: Zhur. Fiz. Khim. 1 (1967) ) P. K. Sung, D. R. Poirier and E. McBride: Mater. Sci. Eng. A31 (1997) ) M. Hansen: Constitution of binary alloys, (McGraw-Hill book company, 195) pp ) M. Hansen: Constitution of binary alloys, (McGraw-Hill book company, 195) pp ) M. Hansen: Constitution of binary alloys, (McGraw-Hill book company, 195) pp ) M. Hansen: Constitution of binary alloys, (McGraw-Hill book company, 195) pp ) P. Nash: Phase diagrams of binary nickel alloys, (Materials Park, OH: ASM International, 1991) pp ) P. Nash: Phase diagrams of binary nickel alloys, (Materials Park, OH: ASM International, 1991) pp ) P. Nash: Phase diagrams of binary nickel alloys, (Materials Park, OH: ASM International, 1991) pp ) P. Nash: Phase diagrams of binary nickel alloys, (Materials Park, OH: ASM International, 1991) pp