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Thermodynamics of liquid Al–Ni–Zr and Al–Cu–Ni–Zr alloys
Journal of Alloys and Compounds 289 (1999) 152–167
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Thermodynamics of liquid Al–Ni–Zr and Al–Cu–Ni–Zr alloys V.T. Witusiewicz, F. Sommer* ¨ Metallforschung, Seestr. 92, 70174 Stuttgart, Germany Max-Planck-Institut f ur Received 22 March 1999
Abstract The partial and the integral enthalpies of mixing of liquid Al–Ni–Zr alloys and liquid Al–Cu–Ni–Zr alloys have been measured by high temperature calorimetry at 156565 K. A least square treatment of the data results in the following relationships (kJ mol 21 ): for Al–Ni–Zr DH 5 aAl – Ni xAl x Ni 1 aNi – Zr x Ni x Zr 1 aAl – Zr xAl x Zr 1 aAl – Ni – Zr xAl x Ni x Zr 2 aAl – Ni 5 2 129.6 2 331.6xAl 1 331.0x Al 2 3 4 aNi – Zr 5 2 83.1 2 217.8x Ni 1 419.9x Ni 2 1195.2x Ni 1 810.6x Ni
aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x 2Zr aAl – Ni – Zr 5 2 1955.9 1 5842.2x Zr 1 4620.5xAl 2 3760.2x 2Zr 2 2399.9x 2Al 2 5964.0x Zr xAl for the quasiternary cut Al–Cu 0.63 Ni 0.37 –Zr DH 5 DHCu 0.63 Ni 0.37 xAl 1 aCu 0.63 Ni 0.37 – Al xAl x 1 aCu 0.63 Ni 0.37 – Zr x x Zr 1 aAl – Zr xAl x Zr 1 aAl – Cu 0.63 Ni 0.37 – Zr xAl x x Zr
with x 5 x Cu 0.63 Ni 0.37
DHCu 0.63 Ni 0.37 5 2.7
aCu 0.63 Ni 0.37 – Al 5 2 132.4 2 132.8xAl 1 197.4x 2Al aCu 0.63 Ni 0.37 – Zr 5 2 64.2 2 181.1x 1 539.1x 2 2 575.5x 3 aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x 2Zr 2 aAl – Cu 0.63 Ni 0.37 – Zr 5 2 531 1 2020.3x Zr 1 3079.0xAl 2 832.8x 2Zr 2 2749.7x Al 2 5530.1x Zr xAl
The DH(a (x)) relations of the enthalpy show the existence of essential contributions of ternary and quaternary interactions among the alloy components. The excess entropy and Gibbs energy of mixing are estimated on the basis of the DH-values data using an empirical relation. The results confirm that the liquid Al–Cu–Ni–Zr alloys exhibits near the ternary composition Al 0.42 Ni 0.42 Zr 0.16 the strongest tendency toward chemical short-range ordering. 1999 Elsevier Science S.A. All rights reserved. Keywords: Al–Cu–Ni–Zr; Calorimetry; Enthalpy of mixing; Excess entropy; Gibbs energy
1. Introduction *Corresponding author. Tel.: 149-711-209-5417; fax: 149-711-209420. E-mail address: [email protected] (F. Sommer)
Specific liquid alloys of the quaternary Al–Cu–Ni–Zr system possess an extraordinary glass-forming ability and
0925-8388 / 99 / $ – see front matter 1999 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 99 )00180-2
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
are widely used for the production of bulk amorphous materials [1,2]. Data on the temperature and composition dependencies of the thermodynamic properties of these liquid alloys are important to achieve a better understanding of this phenomenon. We have already performed an extensive series of investigations of the thermodynamic properties of liquid constituent binaries such as Al–Cu, Al–Ni, Cu–Ni [3], Cu–Zr [4], Al–Zr [5], Ni–Zr [6] and constituent ternaries Al–Cu–Ni [7], Al–Cu–Zr [5] and Ni–Cu–Zr [6] alloys of this quaternary system. The present paper is devoted to a
153
calorimetric study of the partial and integral enthalpies of mixing for the lacking constituent ternary Al–Ni–Zr system and for one quasi-ternary cut Al–Cu 0.63 Ni 0.37 –Zr.
2. Experimental The partial and the integral enthalpies of mixing of the liquid alloys were measured with the high temperature calorimeter described previously [3]. The experiments were carried out under pure argon at atmospheric pressure.
Fig. 1. Calibration factor as a function of the mole number of the liquid bath for ternary Al–Ni–Zr (a) and quaternary Al–Cu–Ni–Zr (b) alloys (numbers of runs are given in Tables 1–4). Solid lines correspond to zirconia reaction crucibles while dashed and dotted line correspond to yttria and alumina reaction crucible, respectively.
154
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
Table 1 Experimental data of liquid Ni 0.64 Zr 0.36 –Al alloys at 1565 K Added element (i)
Added amount (Dn i ), mmol
Run 1. Starting amount (mmol): nAl 5 84.264 Al 4.877 ZrO 2 1.611 Al 4.699 ZrO 2 1.115 Zr 1.595 Ni 2.642 Ni 4.667 Zr 2.576 Al 4.202 Ni 4.155 Zr 2.394 Zr 2.226 Ni 3.902 Al 4.325 Zr 3.454 Ni 5.926 Ni 7.245 Zr 4.074 Al 4.340 ZrO 2 1.319 Ni 6.609 Zr 3.801 Zr a 4.341 Ni a 7.655 Al a 4.792 Zr a 4.274 Ni a 6.781 Ni a 8.943 Zr a 4.655 Al a 4.929 Ni a 7.626 Zr 5.340 Ni 6.218 Al 5.159 ZrO 2 1.600
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
1 1 1 1 0.9916 0.9700 0.9351 0.9022 0.8931 0.8788 0.8535 0.8367 0.8155 0.8056 0.7983 0.7703 0.7341 0.7052 0.6997 0.6997 0.6893 0.6667 0.6501 0.6274 0.6185 0.6164 0.5982 0.5741 0.5545 0.5534 0.5489 0.5325 0.5188 0.5171 0.5171
2023 3563 2057 3503 24637 23590 23449 24839 1936 23393 25346 26063 22331 1847 25586 21141 21504 24632 1557 3336 2975 23945 – – – – – – – – – 21289 2498 476 2112
0 – 0 – 2170.9 2144.3 2141.1 2176.4 22.1 2139.7 2188.6 2206.0 2114.7 23.8 2195.9 286.5 296.6 2181.9 27.4 – 284.6 2170.4 – – – – – – – – – 2111.1 278.9 228.8 –
0 – 0 – 21.5 25.3 211.2 216.9 218.4 221.0 224.1 227.2 229.7 230.5 231.1 232.9 239.4 240.6 241.4 – 242.2 244.9 – – – – – – – – – 258.1 259.4 259.6 –
2822 627.3 2135 21447 23081 369 78 23812 – – – – – – – 35 16 2473 2372 2419 239
– 239.6 264.6 292.3 2143.1 247.1 258.1 2166.9 – – – – – – – 257.3 260.0 – 261.2 263.0 249.9
– 248.6 248.7 249.9 256.7 260.8 260.4 263.2 – – – – – – – 262.2 262.5 – 260.2 261.8 258.6
Run 2. Starting amount (mmol): n Ni 5 41.554; n Zr 5 23.740 ZrO 2 1.252 0 Ni 2.822 0 Zr 1.695 0 Al 3.621 0.0247 Al 3.473 0.0708 Ni 2.462 0.0908 Zr 1.407 0.0886 Al 2.617 0.1021 Al a 3.632 0.1349 Al a 3.672 0.1704 Ni a 2.235 0.1854 Zr a 1.171 0.1819 Al a 3.954 0.1973 Al a 4.310 0.2304 Al a 4.436 0.2626 Ni 2.271 0.2753 Zr 1.197 0.2710 ZrO 2 1.080 0.2710 Al 3.836 0.2818 Al 3.476 0.3046 Al 3.824 0.3257
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
155
Table 1. Continued Added element (i)
Added amount (Dn i ), mmol
Mole fraction (xAl )
Ni Zr Al Al Al Ni Zr Al Al Al Ni Zr Al Al Ni Zr ZrO 2
2.107 1.109 4.503 4.288 4.403 1.933 1.242 5.170 4.866 5.356 1.806 1.142 5.241 4.766 2.854 1.678 1.182
0.3336 0.3293 0.3395 0.3617 0.3821 0.3895 0.3850 0.3942 0.4147 0.4342 0.4415 0.4374 0.4448 0.4615 0.4653 0.4591 0.4591
Run 3. Starting amount (mmol): n Ni 5 48.405; ZrO 2 1.441 Ni 3.665 Zr 2.123 Al 2.846 Al 3.024 Ni 2.743 Zr 1.581 Al 2.535 Al a 3.024 Ni a 3.107 Zr a 1.831 Al a 3.328 Al a 3.280 Al a 3.621 Ni a 2.877 Zr a 1.635 Al a 4.903 Al a 5.096 Al a 5.481 ZrO 2 1.095 Ni a 3.189 Zr a 1.865 Al a 5.411 Al 6.626 Al 6.422 Al 5.381 Ni 2.854 Zr 1.580 Al 5.811 Al 6.282 Al 6.941 Al 7.186 Ni 3.291 Zr 1.909 ZrO 2 1.645 a
Solid–liquid phase region.
n Zr 5 27.560 0 0 0 0.0168 0.0503 0.0659 0.0644 0.0764 0.1030 0.1154 0.1125 0.1255 0.1524 0.1788 0.1898 0.1861 0.2011 0.2332 0.2644 0.2644 0.2766 0.2715 0.2834 0.3128 0.3421 0.3667 0.3741 0.3691 0.3780 0.3995 0.4213 0.4430 0.4498 0.4438 0.4439
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
2275 262 2328 269 2195 2434 169 330 106 347 2474 2595 424 594 2519 2840 2107
268.2 262.7 260.1 251.0 255.6 274.4 254.4 236.3 244.5 235.4 276.5 283.1 232.3 225.5 278.6 292.9 –
260.6 261.1 262.6 260.6 263.6 260.7 259.4 256.8 261.5 259.3 259.1 261.1 258.8 257.4 255.4 256.3 –
2423 349 265 22476 23329 513 223 22339 – – – – – – – – – – – 1844 – – – 2182 2132 253 235 2144 279 100 113 159 2177 2267 1340
– 245.9 250.9 2137.0 2172.2 238.7 251.9 2138.1 – – – – – – – – – – – – – – – 257.9 255.6 251.3 260.3 268.6 252.9 242.3 241.2 238.1 269.6 277.4 –
– 248.2 247.9 246.2 247.3 248.5 249.7 247.6 – – – – – – – – – – – – – – – 260.7 260.4 259.1 259.1 259.0 259.8 256.0 256.4 256.5 252.9 254.4 –
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
156
For the measurements the thermocouples and a thermopile were made of Pt–6%Rh / Pt–30%Rh and of W–5%Re / W– 20%Re, respectively. Starting materials for the alloy preparation were aluminum with a purity 99.999% (2 mm wire, Goodfellow), copper with a purity 99.999% (1 mm wire, Alfa / Johnson Matthey GmbH), nickel with a purity
99.981% (2 mm wire, Goodfellow) and zirconium with purity 99.81% (2 mm wire, Goodfellow). The heat effects were measured by successive dropping of solid samples (pure components) from 298 K through a charging tube into a zirconia reaction crucible containing the bath substance. One experimental run was performed
Table 2 Experimental data of liquid Ni 0.36 Zr 0.64 –Al alloys at 1565 K Added element (i)
Added amount (Dn i ), mmol
Run 4. Starting amount (mmol): nAl 5 75.533 Al 3.409 ZrO 2 1.352 Al 4.262 ZrO 2 1.798 Ni 2.354 Zr 2.386 Zr 1.613 Al 3.962 Ni 2.989 Zr 2.467 Zr 2.786 Al 3.287 Ni 2.456 Zr 2.662 Zr 1.989 Al 3.461 ZrO 2 1.831 Ni a 3.226 Zr a 2.729 Run 5. Starting amount (mmol): n Ni 5 22.726; Ni 1.814 Zr 1.993 Zr 1.175 ZrO 2 1.537 Al 3.280 Al 3.239 Al 3.780 Ni 2.455 Zr 2.338 Zr 1.904 Al 3.758 Al 3.632 Al 4.021 ZrO 2 1.876 Ni 2.808 Zr 2.176 Zr 2.931 Al 4.781 Al 4.228 Al 4.095 Ni 3.440 Zr 2.965 Zr 3.075 Al 4.984 Al a 4.784 ZrO 2 a 1.833 a
Solid–liquid phase region.
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
1 1 1 1 0.9862 0.9592 0.9375 0.9305 0.9176 0.8919 0.8686 0.8588 0.8512 0.8311 0.8137 0.8093 0.8588 0.8012 0.7813
1571 2899 1554 2542 22567 23685 23478 1553 22568 24336 24495 1472 21853 24495 24005 1584 2556 21172 21652
0 – 0 – 2143.2 2182.2 2175.3 2.8 2143.3 2203.6 2208.9 0.1 2119.7 2208.9 2192.7 3.8 – 297.2 2115.1
0 – 0 – 21.2 28.3 210.8 29.9 213.9 216.2 219.2 223.9 220.4 225.3 227.2 225.9 – 229.3 224.9
2520 1841 1795 2822 21125 21528 21682 2325 1490 1349 21024 2971 2994 1649 2157.6 1095.9 1100.9 2874.3 2877.3 2566 2207 837 922 2642 2581 1129
274.0 25.6 24.4 – 283.7 2101.4 2113.6 271.8 20.2 26.5 291.6 293.7 299.4 – 266.9 23.1 23.7 295.5 2100.2 284.5 272.0 27.1 22.8 289.9 288.7 –
230.2 230.2 230.9 – 230.9 233.8 237.8 237.5 235.6 238.9 236.8 238.7 241.5 – 241.8 241.3 241.2 241.7 245.5 244.6 245.3 246.8 245.3 246.8 251.8 –
n Zr 5 40.206 0 0 0 0 0.0230 0.0668 0.1096 0.1296 0.1258 0.1226 0.1399 0.1751 0.2085 0.2085 0.2222 0.2166 0.2113 0.2256 0.2571 0.2839 0.2924 0.2848 0.2779 0.2882 0.3142 0.3142
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
157
Table 3 Experimental data of liquid Cu 0.41 Ni 0.24 Zr 0.35 –Al alloys at 1565 K Added element (i)
Added amount (Dn i ), mmol
Run 1. Starting amount (mmol): nAl 5 75.385 ZrO 2 1.1728 Al 3.339 ZrO 2 1.4214 Ni 1.945 Cu 3.345 Zr 2.819 Al 3.632 Ni 2.146 Cu 3.573 Zr 3.157 Al 4.095 Ni 1.923 Cu 3.287 Zr 2.831 Al 3.343 Ni 1.931 Cu 3.287 Zr 2.799 Al 4.477 ZrO 2 1.3029 Ni 2.504 Cu 4.280 Zr 3.669 Al 3.665 Ni 1.986 Cu 3.204 Zr 2.861 Al 4.380 Ni 2.224 Cu 3.724 Zr 3.287 Al 4.336 Ni 2.449 ZrO 2 1.7103 Run 2. Starting amount (mmol): n Cu 5 28.746; ZrO 2 1.6280 Ni 1.914 Cu 3.281 Zr 2.799 Al 2.612 Al 3.002 Al 3.013 Al 2.846 Ni 1.959 Cu 3.366 Zr 2.818 Al 3.483 Al 2.853 Al 3.317 Al 3.884 Ni 1.919 Cu 3.296
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
1 1 1 0.9879 0.9564 0.9218 0.9084 0.8998 0.8727 0.8426 0.8323 0.8281 0.8081 0.7855 0.7787 0.7755 0.7585 0.7394 0.7356 0.7356 0.7332 0.7145 0.6936 0.6883 0.6876 0.6753 0.6615 0.6600 0.6602 0.6478 0.6337 0.6321 0.6323 0.6323
2930 1688 2890 22899 579 23601 1643 22720 540 23667 1589 22646 556 24061 1540 22231 465 24750 1470 2310 21245 1122 24668 1222 2901 1507 24522 1259 2224 1506 23592 1046 2263 2113
– 0 – 2142.3 232.4 2168.0 1.0 2140.8 232.7 2176.3 2.1 2143.0 231.3 2195.4 3.0 2133.3 233.5 2225.8 2.9 – 2102.1 29.2 2232.2 23.5 291.7 6.9 2231.3 20.6 267.0 8.7 2201.6 27.3 268.8 –
– 0 – 21.4 24.5 27.5 28.6 29.5 212.2 215.5 216.9 217.2 219.3 222.3 223.2 223.9 226.4 228.4 227.7 – 228.2 230.3 231.6 234.4 233.1 232.9 234.2 232.2 233.5 234.5 234.6 235.2 234.8 –
n Ni 5 16.790; n Zr 5 24.528 0 2869 0 2235 0 1715 0 1153 0.0161 2981 0.0497 2806 0.0833 2772 0.1138 2913 0.1267 2112 0.1231 1749 0.1192 915 0.1326 2973 0.1595 2863 0.1840 2712 0.2108 2644 0.2230 2359 0.2179 1671
– 265.4 0.8 226.8 277.6 273.1 272.8 278.0 262.2 7.6 230.8 280.4 277.5 272.9 271.1 271.3 9.7
– 224.8 224.8 224.6 225.2 226.1 227.3 229.2 229.2 229.3 230.1 230.6 231.8 232.5 233.9 235.9 235.2
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
158 Table 3. Continued Added element (i)
Added amount (Dn i ), mmol
Mole fraction (xAl )
ZrO 2 Zr Al Al Al Al Ni Cu Zr Al Al Al Al Al Ni Cu Zr ZrO 2
1.904 2.759 5.692 6.037 5.670 6.278 1.933 3.323 2.784 6.749 6.574 7.623 7.086 7.827 1.875 3.016 2.774 1.516
0.2179 0.2123 0.2278 0.2632 0.2955 0.3256 0.3385 0.3324 0.3256 0.3371 0.3646 0.3914 0.4169 0.4407 0.4504 0.4446 0.4380 0.4380
Run 3. Starting amount (mmol): n Cu 5 35.160; ZrO 2 1.194 Ni 1.921 Cu 3.589 Zr 2.919 ZrO 2 1.135 Al 6.485 Al 7.145 Al 7.783 Al 8.264 Ni 2.076 Cu 3.469 Zr 2.936 Al 8.643 Al 9.439 Al 9.439 Al 9.591 Ni 2.870 Cu 4.977 Zr 4.138 ZrO 2 1.243 Al 7.768
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
2355 804 2887 2571 2391 2272 2232 1676 153 2295 2143 2158 2137 138 2437 1531 2430 1965
n Ni 5 20.516, n Zr 5 30.014; nAl 5 49.819 0.3650 2416 0.3650 2832 0.3578 1629 0.3496 433 0.3496 2310 0.3602 250 0.3884 21 0.4167 85 0.4443 65 0.4551 2789 0.4481 1554 0.4401 2428 0.4493 223 0.4747 188 0.4989 332 0.5212 457 0.5285 2588 0.5193 1481 0.5089 21090 0.5089 1978 0.5124 397
using an alumina crucible and another one using an yttria crucible (see Fig. 1). The masses of the dropping samples of the pure components were so small that the composition change in the bath did not exceed 1–3 at.%. This allows us to determine directly the partial enthalpy of mixing of all components in the same experimental run. At the beginning, in the middle and at the end of each series of measurements the calorimeter has been calibrated using cylindrical zirconia samples. The value of the standard heat content of the used zirconia ceramic at 156565 K referred to 298 K was determined previously [6] (DH 1565 298,ZrO 2 5 84.0860.66 kJ mol 21 ). The performed calibrations confirm our earlier observation [6] that the calibration factor varies linearly with the mole number of the bath, o k Dn k , (see Fig. 1). Therefore, the calibration factor W of our calorimeter depends on the composition and the amount of
Integral enthalpy (DH ), kJ mol 21
– 232.2 280.1 269.5 263.3 259.1 267.6 16.1 254.6 260.1 254.2 255.0 254.2 242.6 277.4 16.5 278.9 –
– 233.5 237.1 237.2 237.9 238.8 239.7 239.8 240.3 240.0 240.0 242.4 244.1 240.8 242.2 242.2 242.0 –
– 287.9 7.8 245.5 – 250.2 247.7 245.3 245.9 289.7 11.5 277.2 239.7 240.8 234.5 228.7 284.2 14.5 2106.9 – 231.5
– 240.5 239.9 239.4 – 240.4 241.8 242.9 245.1 244.0 243.9 243.9 242.7 244.7 242.9 240.8 240.5 241.3 242.2 – 241.9
the bath alloys and on the material of the reaction crucibles. Thus, for an initial alloy of about 60 mmol the calibration factor is 0.022, 0.028 and 0.034 for alumina, zirconia and yttria crucibles, respectively. A linear fit of the mole number-dependent calibration factors enables an easy calculation of DH¯ i and DH using the following relationships:
SO Dn D
W
k
k
DH 1565 298,ZrO 2 5 ]]]]] FZrO 2 Dn k
SO D
(1)
k
DH¯ i
SO Dn D 5 2 DH k
k
i 5 Al, Cu, Ni, Zr
1565 298,i
SO Dn D F SO Dn D,
1W
k
k
i
k
k
(2)
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
159
Table 4 Experimental data of liquid Cu 0.19 Ni 0.11 Zr 0.70 –Al alloys at 1565 K Added element (i)
Added amount (Dn i ), mmol
Run 4. Starting amount (mmol): nA1 5 76.842 ZrO 2 1.091 Al 3.739 Al 3.432 ZrO 2 1.094 Ni 1.546 Cu 2.566 Zr 3.566 Zr 3.322 Zr 2.930 Al 3.561 Ni 1.678 Cu 3.086 Zr 3.651 Zr 3.983 Zr 2.769 Al 3.891 Ni 1.260 Cu 2.209 Zr 2.581 ZrO 2 1.055 Zr 2.933 Zr 2.351 Al 3.858 Ni 1.523 Cu 2.499 Zr 3.028 Zr 3.729 Zr 3.200 Al 3.565 Ni 1.422 Cu 2.360 Zr 5.021 Zr 5.349 Al 4.132 ZrO 2 1.152 Run 5. Starting amount (mmol): n Cu 5 11.821; ZrO 2 1.692 Ni 1.432 Cu 2.454 Zr 3.113 Zr 3.384 ZrO 2 1.633 Zr 2.952 Al 2.898 Al 4.295 Al 4.443 Al 4.410 Ni 1.442 Cu 2.451 Zr 4.560 Zr 4.574 Al 3.913 Al 4.562 Ni 1.391 Cu 2.407 Zr 4.439 ZrO 2 1.700
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
1 1 1 1 0.9909 0.9676 0.9347 0.9002 0.8709 0.8602 0.8557 0.8363 0.8103 0.7827 0.7597 0.7546 0.7547 0.7441 0.7298 0.7298 0.7141 0.6997 0.6977 0.6982 0.6881 0.6747 0.6589 0.6435 0.6408 0.6420 0.6343 0.6197 0.6002 0.5954 0.5954
2919 1730 1710 2971 23232 549 23716 23538 23419 1476 22579 1040 24351 24641 24772 1421 2539 1183 24003 2395 23147 23337 956 2131 968 22004 22123 22050 900 442 1054 21091 21012 219 2012
– 0 0 – 2151.8 233.4 2170.6 2167.5 2166.1 22.5 2139.0 216.4 2201.7 2215.1 2223.1 0.2 276.9 28.4 2201.2 – 2173.1 2181.8 213.7 263.3 213.7 2135.5 2141.4 2140.1 213.4 241.3 28.0 2104.1 2102.0 239.4 –
– 0 0 – 20.7 25.1 223.5 211.6 216.3 219.7 224.1 227.1 231.1 236.9 242.1 236.7 238.5 239.9 243.6 – 240.9 245.6 249.4 245.2 245.9 240.7 245.7 249.3 244.5 248.2 248.4 246.8 252.4 249.0 –
2382 2881 871 1474 1595 2358 1546 21238 21385 21447 21530 2734 844 1435 1353 21474 21490 2711 810 1306 1915
– 290.0 218.3 27.9 23.6 – 25.4 293.2 2100.28 2105.13 2111.33 289.348 214.057 20.92396 24.8139 2110.03 2113.13 290.358 212.747 23.8719 –
– 217.329 217.329 218.934 215.905 – 217.136 218.229 221.007 224.882 229.522 231.441 231.047 229.154 230.678 230.69 234.502 234.0065 234.146 234.635 –
n Ni 5 6.8552; n Zr 43.801 0 0 0 0 0 0 0 0.0184 0.0617 0.1098 0.1538 0.1733 0.1697 0.1637 0.1564 0.1682 0.1998 0.2150 0.2115 0.2055 0.2055
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
160 Table 4. Continued Added element (i)
Added amount (Dn i ), mmol
Run 6. Starting amount (mmol): n Cu 5 11.815; ZrO 2 1.628 Ni 1.192 Cu 2.058 Zr 4.009 Zr 3.508 Al 4.076 Al 3.880 Al 5.218 Al 5.144 Ni 1.345 Cu 2.327 Zr 4.172 Zr 4.396 Al 4.336 Al 4.414 Al 4.484 Al 5.207 Al 5.062 ZrO 2 1.904 Ni 1.260 Cu 2.196 Zr 3.949 Zr 3.727 Al a 5.763 ZrO 2 a 1.516 a
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
n Ni 5 6.8552, n Zr 5 43.799; nAl 5 14.677 0.1888 2548 0.1888 21074 0.1849 1008 0.1782 1708 0.1704 1656 0.1854 21824 0.2199 21902 0.2558 21544 0.2930 21506 0.3086 2148 0.3034 896 0.2947 1560 0.2838 1404 0.2912 21256 0.3160 21397 0.3395 21037 0.3633 2729 0.3868 2533 0.3868 1748 0.3962 317 0.3914 728 0.3833 1321 0.3736 609 0.3805 – 0.3805 1636
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
– 295.2 215.0 22.5 24.5 2110.6 2115.2 2105.3 2107.6 264.5 213.4 25.2 25.2 297.6 2105.9 293.5 282.0 274.5 – 242.6 213.4 29.5 231.8 – –
– 234.4 234.1 232.7 233.3 233.9 237.7 238.2 242.5 242.6 242.2 237.5 240.3 239.3 245.1 245.2 246.6 250.8 – 251.6 251.0 242.2 248.9 – –
Solid–liquid phase region.
3. Results and discussion
3,4
DH(x) 5
O x DH¯ (x) i
(3)
i
i 51
3.1. Liquid Al–Ni–Zr alloys
where Fi is the area under a temperature–time curve due to the dissolution of 1 mole of component i in liquid bath and x i is the mole fraction of component i of the ternary and the quaternary alloy. The measurements of the ternary Al–Ni–Zr and quaternary Al–Cu–Ni–Zr alloys were performed at temperatures below the melting temperature of Ni and Zr. The standard state of the data given in column 4 of the Tables 1–4 is liquid Al, Cu and solid Ni, Zr. DH¯ i , and DH given in column 5 and 6 of the Tables 1–4 are referred to liquid Al, Cu, Ni and Zr: DH¯ j 5 D s H¯ j 2 Df Hj ;
j 5 Ni, Zr
(4)
where subscript s indicates the partial enthalpy refers to the solid metals; Df Hj is the molar heat of fusion of metal j. The standard values of heat content of the components and heat of fusion of Ni and Zr were taken from Ref. [8]. The simplified Eq. (4) is used because the heat capacity of undercooled liquid nickel and undercooled liquid zirconium is not known.
The results obtained for the partial and the integral enthalpies of mixing of liquid Al–Ni–Zr alloys of the vertical composition sections with x Ni /x Zr 5 0.64 / 0.36 and x Ni /x Zr 5 0.36 / 0.64 are summarized in Tables 1 and 2, respectively. Fig. 2 shows the partial functions of the components along the sections with the experimental data of the constituent binary Al–Zr [5], Al–Ni [3] and Ni–Zr [6] alloys. Analyzing our measurements we could determine the homogeneity ranges of the liquid phase at 1565 K along the vertical section x Ni /x Zr 5 0.64 / 0.36 as 0 # xAl # 0.08, 0.28 # xAl # 0.54 and 0.66 # xAl # 1. The homogeneity ranges of the liquid phase along the vertical section x Ni /x Zr 5 0.36 / 0.64 are 0 # xAl # 0.29 and 0.81 # xAl # 1. Obviously, the partial enthalpies of the components gradually change with the increasing mole fractions of aluminum with the exception of DH¯ Al of the Ni 0.64 Zr 0.36 –Al isopleth (see Fig. 2c, curve 2). This DH¯ Al is characterized by a sharp minimum near 5 at.% Al. The experimental data points of the ternary alloys together with the values for constituent binaries [3–6] were treated by means of least square procedure according to
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
161
Fig. 2. Composition dependencies of the partial enthalpies of mixing (nickel (a), zirconium (b) and aluminum (c)) and integral enthalpy of mixing (d) of the ternary liquid and undercooled liquid Al–Ni–Zr alloys at 156565 K: points are from Tables 1 and 2; solid lines result from Eq. (5); dashed lines in (d) result from Eq. (6).
DH 5 xA xB aA – B 1 xA x C aA – C 1 xB x C aB – C 1 xA xB x C aA – B – C (5) The a -functions of Al–Ni–Zr are collected in Table 5. These relationships adequately describe the experimental values of the integral enthalpy of mixing in the whole composition range. Fig. 2d shows DH versus the mole fraction of Al of the liquid Al–Ni–Zr alloys. Points are from Tables 1 and 2. Dashed lines are calculated only on the basis of smoothed functions of the partial enthalpy of aluminum (see Fig. 2c, curves 2 and 3) using the relation: DHy / ( 12y2z)5const,z / ( 12y2z)5const 5 (1 2 x) x
3
DH¯ (x) E ]]] dx 4 (1 2 x) Al
3 DHx 50 1
2
(6)
x50
where x 5 xAl , y 5 x Ni and z 5 x Zr . Considering the scatter of the experimental data points there is good agreement between the results of both methods of calculations. The
partial and the integral functions are therefore determined correctly and their composition variation is consistent with the Gibbs–Duhem equation.
3.2. Liquid Al–Cu–Ni–Zr alloys The measured partial and the integral enthalpies of mixing of the liquid Al–Cu–Ni–Zr alloys of the vertical sections with x Cu :x Ni :x Zr 5 0.41:0.24:0.35 and x Cu :x Ni :x Zr 5 0.19:0.11:0.70 are presented in Tables 3 and 4, respectively. The homogeneity ranges of the liquid phase at 1565 K of the vertical sections are 0 # xAl # 1 and 0 # xAl # 0.38 and 0.57 # xAl # 1, respectively. The resulting DH¯ i values for three components are shown in Fig. 3 as functions of composition together with the smoothed curves (solid lines) and the experimental data for constituent binary and ternary alloys (broken lines). DH¯ i change gradually as a function of the zirconium composition. The same data plotted versus aluminum composition show evident maxima (DH¯ i of Cu and Ni) and
162
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
Table 5 Parameters of Eqs. (5) and (7) System A–B–C
Constituent ternary systems: DH 5 aA – B xA xB 1 aB – C xB x C 1 aA – C xA x C 1 aA – B – C xA xB x C [kJ mol 21 ]
Al–Cu–Ni
aAl – Cu 5 2 75.6 2 63.8xAl 1 231.8x 2Al 2 130.6x 3Al aCu – Ni 5 12.1 2 1.1x Cu 2 aAl – Ni 5 2 130.2 2 330.4x Ni 1 331.0x Ni aAl – Cu – Ni 5 2 215.8 1 597.1x Ni 2 460.5xAl 3 aAl – Cu 5 2 75.6 2 63.8xAl 1 231.8x 2Al 2 130.6x Al aCu – Zr 5 2 40.9 1 67.5x Cu 2 926.6x 2Cu 1 2541.7x 3Cu 2 2895.3x 4Cu 1 1202.6x 5Cu 2 aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x Zr 2 2 aAl – Cu – Zr 5 459.3 2 1395.8x Zr 2 1853.9xAl 1 1576.7x Zr 1 1301.9x Al 1 986.9x Zr xAl 2 aAl – Ni 5 2 129.6 2 331.6xAl 1 331.0x Al 2 3 4 aNi – Zr 5 2 83.1 2 217.8x Ni 1 419.9x Ni 2 1195.2x Ni 1 810.6x Ni 2 aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x Zr 2 2 aAl – Ni – Zr 5 2 1955.9 1 5842.2x Zr 1 4620.5xAl 2 3760.2x Zr 2 2399.9x Al 2 5964.0x Zr xAl aCu – Ni 5 11.1 1 1.1x Ni aCu – Zr 5 2 40.9 1 67.5x Cu 2 926.6x 2Cu 1 2541.7x 3Cu 2 2895.3x 4Cu 1 1202.6x 5Cu aNi – Zr 5 2 193.6 2 422.8x Zr 1 1769.9x 2Zr 2 2047.2x 3Zr 1 810.6x 4Zr 2 aCu – Ni – Zr 5 2 720.6 1 3342.7x Zr 1 566.9x Ni 2 3436.3x 2Zr 2 1357.8x Ni 2 985.5x Zr x Ni
Al–Cu–Ni
Al–Ni–Cu
Cu–Ni–Zr
System Al–Cu 0.63 Ni 0.37 –Zr
Quasiternary cut A–BC–D: DH 5 DHBC xA 1 aA – BC xA xBC 1 aBC – D xBC x D 1 aA – C xA x C 1 aA – BC – D xA xBC x D [kJ mol 21 ] DHCu 0.63 Ni 0.37 5 2.7 aCu 0.63 Ni 0.37 – Zr 5 2 64.2 2 181.1x 1 539.1x 2 2 575.5x 3 aCu 0.63 Ni 0.37 – Al 5 2 132.4 2 132.8xAl 1 197.4x 2Al 2 aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x Zr 2 2 aAl – Cu 0.63 Ni 0.37 – Zr 5 2 531 1 2020.3x Zr 1 3079.0xAl 2 832.8x Zr 2 2749.7x Al 2 5530.1x Zr xAl
Fig. 3. Partial enthalpies of mixing of copper (a), nickel (b), zirconium (c) and aluminum (d) of liquid Al–Cu–Ni–Zr alloys at 156565 K: points are from Tables 3 and 4; lines result from fitted a -functions.
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
minima (DH¯ i of Zr and Al). These peculiarities were also observed in some constituent binary and ternary alloys, but they became more visible in quaternary alloys. The integral enthalpy of mixing of the liquid Al–Cu– Ni–Zr alloys as functions of mole fraction of aluminum are illustrated in Fig. 4. Points are from Tables 3 and 4. Dashed lines are calculated on the basis of smoothed partial enthalpy of aluminum data (see Fig. 4d, curves 3 and 5) using Eq. (6). The values of both methods of calculations are in proper agreement, this confirms the self-consistency of the measured functions. The experimental integral enthalpy values of the quaternary alloys along the quasiternary cut were treated by means of least square procedure according to DH 5 DHBC xA 1 aA – BC xA xBC 1 aBC – D xBC x D 1 aA – D xA x D 1 aA – BC – D xA xBC x D
(7)
The results represented by the a -functions are collected in Table 5. These relationships adequately describe the experimental results in the whole composition range (see Fig. 4, solid lines).
4. Discussion The enthalpies of mixing of liquid alloys of three constituent ternary systems, i.e. Al–Cu–Ni, Al–Cu–Zr and
163
Ni–Cu–Zr have been presented in our previous works [5–7]. In order to compare the integral enthalpy of mixing and to estimate excess thermodynamic functions of these systems we have treated the results of Ref. [7] by means of least square procedure according to Eq. (5). The relationships obtained together with the ones for liquid and undercooled liquid Al–Cu–Zr and Ni–Cu–Zr alloys from Refs. [5,6] are given in Table 5. Fig. 5 illustrates the enthalpy of mixing according to the relationships given in Table 5. Obviously, the minimum value of the enthalpy of mixing gradually decreases from the binary Al 0.53 Zr 0.47 alloy (DHmin 5 251.7 kJ mol 21 ) via quaternary compositions to the ternary Al 0.35 Ni 0.47 Zr 0.18 alloy (DHmin 5 261.5 kJ mol 21 ). The Al–Ni–Zr system reveals the highest interaction energy between the components of the quaternary Al–Cu–Ni–Zr system. To analyze the quaternary interactions the contribution of the fifth term of Eq. (7) to the enthalpy of mixing of liquid Al–Cu–Ni–Zr alloys is shown in Fig. 6. Obviously, these results indicate the existence of repulsive and attractive quaternary interactions among the components of the liquid alloy. The glass forming ability of liquid alloys by rapid solidification is determined by thermodynamic and kinetic factors [9]. Quantitative statements about the Gibbs energy of liquid and undercooled liquid alloys are very important. Activity data of liquid Al–Cu–Ni–Zr alloys and the constituent liquid ternary alloys are not given in the
Fig. 4. Integral enthalpy of mixing as a function of mole fraction of Al of liquid quaternary Al–Cu–Ni–Zr alloys: points are experimental data; solid lines are values according to Eq. (7); dashed lines are data according to Eq. (5) and smoothed DH¯ Al (xAl ) functions (see Fig. 3d, curves 3 and 5).
164
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
Fig. 5. Enthalpy of mixing (kJ mol 21 ) of liquid and undercooled liquid alloys of the constituent ternary systems and of the quasiternary cut Al–Cu 0.63 Ni 0.37 –Zr at 156565 K.
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
165
Fig. 6. Contribution of the fifth term of Eq. (7), which describes the quaternary interactions of the integral enthalpy of mixing of liquid and undercooled liquid Al–Cu 0.63 Ni 0.37 –Zr alloys at 156565 K (in kJ mol 21 ).
literature. A reasonable approximation for activities and the Gibbs energy can be obtained using an empirical model proposed earlier [10]. This model was successfully applied to various liquid metallic binary alloys [4,10] and liquid ternary Al–Cu–Zr and Ni–Cu–Zr [5,6] alloys as well as to solid intermetallic binary compounds [11]. In a case of a ternary A–B–C system the relationship for the excess entropy can be written as DS ex 5 xA xB (A AB 1 B AB aA – B ) 1 xA x C (A AC 1 B AC aA – C ) 1 xB x C (A
BC
BC
1 B aB – C ) 1 xA xB x C (A
ABC
1 B ABC aA – B – C )
(8)
and for a quasiternary A–B12y Cy –D cut of the quaternary A–B–C–D as ABC DS ex 5 xA DS ex 1 B ABC aA – BC ) BC 1 xA x BC (A
S D
Tˆ m ??? A 5R 2 ] Tˆ b
OT
5/2
;B
???
n Tˆ m 5 2 ]2 ; Tˆ m 5 T m,i /n; Tˆ b i 51
O
n
Tˆ b 5
b,i
/n
(10)
i 51
where T m,i and T b,i are melting and boiling temperatures of the component i (i 5 A, B, C . . . ) of an appropriate constituent 2-, 3- or 4-component system (n52, 3 or 4 respectively); xBC and DS ex BC are mole fraction and excess entropy of mixing of binary composition B12y Cy . The resulting Gibbs energies at 1565 K are shown in Fig. 7. The minimal values of Gibbs energy show up near the compositions of the minima of the enthalpy of mixing and amount to 241.4 for the constituent ternary Al–Cu– Ni system and 252.7 kJ mol 21 for the constituent ternary Al–Ni–Zr system.
1 xA x D (A AD 1 B ADaA – D ) 1 xBC x D (ABCD 1 B BCDaBC – D ) 1 xA xBC x D (A ABCD 1 B ABCDaA – BC – D )
Acknowledgements
(9) with
This work is partly supported by DFG, SPP: ‘Undercooled liquid metals: phase selection and glass transition’.
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V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
Fig. 7. Estimated values of the excess Gibbs energy of mixing (kJ mol 21 ) of liquid and undercooled liquid alloys of the constituent ternary systems and of the quasiternary cut Al–Cu 0.63 Ni 0.37 –Zr at 156565 K.
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
References [1] T. Masumoto, Sci. Rep. RITU A 39 (1994) 91. [2] A. Inoue, T. Zhang, T. Masumoto, Mater. Trans. JIM 31 (1990) 177. [3] U.K. Stolz, I. Arpshofen, F. Sommer, B. Predel, J. Phase Equil. 14 (1993) 473. [4] V. Witusiewicz, I. Arpshofen, F. Sommer, Z. Metallkd. 88 (1997) 866. [5] V. Witusiewicz, I. Arpshofen, U.K. Stolz, F. Sommer, Z. Metallkd. 89 (1998) 704.
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[6] V. Witusiewicz and F. Sommer, Submitted to Metall. Trans. B. [7] U.K. Stolz, I. Arpshofen, F. Sommer, Z. Metallkd. 84 (1993) 552. [8] O. Knacke, O. Kubaschewski, K. Hesselmann, in: 2nd ed, Thermochemical Properties of Inorganic Substances, Springer, Berlin, 1991. [9] F. Sommer, Metallic glass forming ability, in: S. Steeb, H. Warlimont (Eds.), Rapidly Quenched Metals, Elsevier Science, Amsterdam, 1985, p. 153. [10] V.T. Witusiewicz, J. Alloys Comp. 221 (1995) 74. [11] V.T. Witusiewicz, V.R. Sidorko, M.V. Bulanova, J. Alloys Comp. 248 (1997) 233.
L
Thermodynamics of liquid Al–Ni–Zr and Al–Cu–Ni–Zr alloys V.T. Witusiewicz, F. Sommer* ¨ Metallforschung, Seestr. 92, 70174 Stuttgart, Germany Max-Planck-Institut f ur Received 22 March 1999
Abstract The partial and the integral enthalpies of mixing of liquid Al–Ni–Zr alloys and liquid Al–Cu–Ni–Zr alloys have been measured by high temperature calorimetry at 156565 K. A least square treatment of the data results in the following relationships (kJ mol 21 ): for Al–Ni–Zr DH 5 aAl – Ni xAl x Ni 1 aNi – Zr x Ni x Zr 1 aAl – Zr xAl x Zr 1 aAl – Ni – Zr xAl x Ni x Zr 2 aAl – Ni 5 2 129.6 2 331.6xAl 1 331.0x Al 2 3 4 aNi – Zr 5 2 83.1 2 217.8x Ni 1 419.9x Ni 2 1195.2x Ni 1 810.6x Ni
aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x 2Zr aAl – Ni – Zr 5 2 1955.9 1 5842.2x Zr 1 4620.5xAl 2 3760.2x 2Zr 2 2399.9x 2Al 2 5964.0x Zr xAl for the quasiternary cut Al–Cu 0.63 Ni 0.37 –Zr DH 5 DHCu 0.63 Ni 0.37 xAl 1 aCu 0.63 Ni 0.37 – Al xAl x 1 aCu 0.63 Ni 0.37 – Zr x x Zr 1 aAl – Zr xAl x Zr 1 aAl – Cu 0.63 Ni 0.37 – Zr xAl x x Zr
with x 5 x Cu 0.63 Ni 0.37
DHCu 0.63 Ni 0.37 5 2.7
aCu 0.63 Ni 0.37 – Al 5 2 132.4 2 132.8xAl 1 197.4x 2Al aCu 0.63 Ni 0.37 – Zr 5 2 64.2 2 181.1x 1 539.1x 2 2 575.5x 3 aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x 2Zr 2 aAl – Cu 0.63 Ni 0.37 – Zr 5 2 531 1 2020.3x Zr 1 3079.0xAl 2 832.8x 2Zr 2 2749.7x Al 2 5530.1x Zr xAl
The DH(a (x)) relations of the enthalpy show the existence of essential contributions of ternary and quaternary interactions among the alloy components. The excess entropy and Gibbs energy of mixing are estimated on the basis of the DH-values data using an empirical relation. The results confirm that the liquid Al–Cu–Ni–Zr alloys exhibits near the ternary composition Al 0.42 Ni 0.42 Zr 0.16 the strongest tendency toward chemical short-range ordering. 1999 Elsevier Science S.A. All rights reserved. Keywords: Al–Cu–Ni–Zr; Calorimetry; Enthalpy of mixing; Excess entropy; Gibbs energy
1. Introduction *Corresponding author. Tel.: 149-711-209-5417; fax: 149-711-209420. E-mail address: [email protected] (F. Sommer)
Specific liquid alloys of the quaternary Al–Cu–Ni–Zr system possess an extraordinary glass-forming ability and
0925-8388 / 99 / $ – see front matter 1999 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 99 )00180-2
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
are widely used for the production of bulk amorphous materials [1,2]. Data on the temperature and composition dependencies of the thermodynamic properties of these liquid alloys are important to achieve a better understanding of this phenomenon. We have already performed an extensive series of investigations of the thermodynamic properties of liquid constituent binaries such as Al–Cu, Al–Ni, Cu–Ni [3], Cu–Zr [4], Al–Zr [5], Ni–Zr [6] and constituent ternaries Al–Cu–Ni [7], Al–Cu–Zr [5] and Ni–Cu–Zr [6] alloys of this quaternary system. The present paper is devoted to a
153
calorimetric study of the partial and integral enthalpies of mixing for the lacking constituent ternary Al–Ni–Zr system and for one quasi-ternary cut Al–Cu 0.63 Ni 0.37 –Zr.
2. Experimental The partial and the integral enthalpies of mixing of the liquid alloys were measured with the high temperature calorimeter described previously [3]. The experiments were carried out under pure argon at atmospheric pressure.
Fig. 1. Calibration factor as a function of the mole number of the liquid bath for ternary Al–Ni–Zr (a) and quaternary Al–Cu–Ni–Zr (b) alloys (numbers of runs are given in Tables 1–4). Solid lines correspond to zirconia reaction crucibles while dashed and dotted line correspond to yttria and alumina reaction crucible, respectively.
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V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
Table 1 Experimental data of liquid Ni 0.64 Zr 0.36 –Al alloys at 1565 K Added element (i)
Added amount (Dn i ), mmol
Run 1. Starting amount (mmol): nAl 5 84.264 Al 4.877 ZrO 2 1.611 Al 4.699 ZrO 2 1.115 Zr 1.595 Ni 2.642 Ni 4.667 Zr 2.576 Al 4.202 Ni 4.155 Zr 2.394 Zr 2.226 Ni 3.902 Al 4.325 Zr 3.454 Ni 5.926 Ni 7.245 Zr 4.074 Al 4.340 ZrO 2 1.319 Ni 6.609 Zr 3.801 Zr a 4.341 Ni a 7.655 Al a 4.792 Zr a 4.274 Ni a 6.781 Ni a 8.943 Zr a 4.655 Al a 4.929 Ni a 7.626 Zr 5.340 Ni 6.218 Al 5.159 ZrO 2 1.600
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
1 1 1 1 0.9916 0.9700 0.9351 0.9022 0.8931 0.8788 0.8535 0.8367 0.8155 0.8056 0.7983 0.7703 0.7341 0.7052 0.6997 0.6997 0.6893 0.6667 0.6501 0.6274 0.6185 0.6164 0.5982 0.5741 0.5545 0.5534 0.5489 0.5325 0.5188 0.5171 0.5171
2023 3563 2057 3503 24637 23590 23449 24839 1936 23393 25346 26063 22331 1847 25586 21141 21504 24632 1557 3336 2975 23945 – – – – – – – – – 21289 2498 476 2112
0 – 0 – 2170.9 2144.3 2141.1 2176.4 22.1 2139.7 2188.6 2206.0 2114.7 23.8 2195.9 286.5 296.6 2181.9 27.4 – 284.6 2170.4 – – – – – – – – – 2111.1 278.9 228.8 –
0 – 0 – 21.5 25.3 211.2 216.9 218.4 221.0 224.1 227.2 229.7 230.5 231.1 232.9 239.4 240.6 241.4 – 242.2 244.9 – – – – – – – – – 258.1 259.4 259.6 –
2822 627.3 2135 21447 23081 369 78 23812 – – – – – – – 35 16 2473 2372 2419 239
– 239.6 264.6 292.3 2143.1 247.1 258.1 2166.9 – – – – – – – 257.3 260.0 – 261.2 263.0 249.9
– 248.6 248.7 249.9 256.7 260.8 260.4 263.2 – – – – – – – 262.2 262.5 – 260.2 261.8 258.6
Run 2. Starting amount (mmol): n Ni 5 41.554; n Zr 5 23.740 ZrO 2 1.252 0 Ni 2.822 0 Zr 1.695 0 Al 3.621 0.0247 Al 3.473 0.0708 Ni 2.462 0.0908 Zr 1.407 0.0886 Al 2.617 0.1021 Al a 3.632 0.1349 Al a 3.672 0.1704 Ni a 2.235 0.1854 Zr a 1.171 0.1819 Al a 3.954 0.1973 Al a 4.310 0.2304 Al a 4.436 0.2626 Ni 2.271 0.2753 Zr 1.197 0.2710 ZrO 2 1.080 0.2710 Al 3.836 0.2818 Al 3.476 0.3046 Al 3.824 0.3257
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
155
Table 1. Continued Added element (i)
Added amount (Dn i ), mmol
Mole fraction (xAl )
Ni Zr Al Al Al Ni Zr Al Al Al Ni Zr Al Al Ni Zr ZrO 2
2.107 1.109 4.503 4.288 4.403 1.933 1.242 5.170 4.866 5.356 1.806 1.142 5.241 4.766 2.854 1.678 1.182
0.3336 0.3293 0.3395 0.3617 0.3821 0.3895 0.3850 0.3942 0.4147 0.4342 0.4415 0.4374 0.4448 0.4615 0.4653 0.4591 0.4591
Run 3. Starting amount (mmol): n Ni 5 48.405; ZrO 2 1.441 Ni 3.665 Zr 2.123 Al 2.846 Al 3.024 Ni 2.743 Zr 1.581 Al 2.535 Al a 3.024 Ni a 3.107 Zr a 1.831 Al a 3.328 Al a 3.280 Al a 3.621 Ni a 2.877 Zr a 1.635 Al a 4.903 Al a 5.096 Al a 5.481 ZrO 2 1.095 Ni a 3.189 Zr a 1.865 Al a 5.411 Al 6.626 Al 6.422 Al 5.381 Ni 2.854 Zr 1.580 Al 5.811 Al 6.282 Al 6.941 Al 7.186 Ni 3.291 Zr 1.909 ZrO 2 1.645 a
Solid–liquid phase region.
n Zr 5 27.560 0 0 0 0.0168 0.0503 0.0659 0.0644 0.0764 0.1030 0.1154 0.1125 0.1255 0.1524 0.1788 0.1898 0.1861 0.2011 0.2332 0.2644 0.2644 0.2766 0.2715 0.2834 0.3128 0.3421 0.3667 0.3741 0.3691 0.3780 0.3995 0.4213 0.4430 0.4498 0.4438 0.4439
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
2275 262 2328 269 2195 2434 169 330 106 347 2474 2595 424 594 2519 2840 2107
268.2 262.7 260.1 251.0 255.6 274.4 254.4 236.3 244.5 235.4 276.5 283.1 232.3 225.5 278.6 292.9 –
260.6 261.1 262.6 260.6 263.6 260.7 259.4 256.8 261.5 259.3 259.1 261.1 258.8 257.4 255.4 256.3 –
2423 349 265 22476 23329 513 223 22339 – – – – – – – – – – – 1844 – – – 2182 2132 253 235 2144 279 100 113 159 2177 2267 1340
– 245.9 250.9 2137.0 2172.2 238.7 251.9 2138.1 – – – – – – – – – – – – – – – 257.9 255.6 251.3 260.3 268.6 252.9 242.3 241.2 238.1 269.6 277.4 –
– 248.2 247.9 246.2 247.3 248.5 249.7 247.6 – – – – – – – – – – – – – – – 260.7 260.4 259.1 259.1 259.0 259.8 256.0 256.4 256.5 252.9 254.4 –
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
156
For the measurements the thermocouples and a thermopile were made of Pt–6%Rh / Pt–30%Rh and of W–5%Re / W– 20%Re, respectively. Starting materials for the alloy preparation were aluminum with a purity 99.999% (2 mm wire, Goodfellow), copper with a purity 99.999% (1 mm wire, Alfa / Johnson Matthey GmbH), nickel with a purity
99.981% (2 mm wire, Goodfellow) and zirconium with purity 99.81% (2 mm wire, Goodfellow). The heat effects were measured by successive dropping of solid samples (pure components) from 298 K through a charging tube into a zirconia reaction crucible containing the bath substance. One experimental run was performed
Table 2 Experimental data of liquid Ni 0.36 Zr 0.64 –Al alloys at 1565 K Added element (i)
Added amount (Dn i ), mmol
Run 4. Starting amount (mmol): nAl 5 75.533 Al 3.409 ZrO 2 1.352 Al 4.262 ZrO 2 1.798 Ni 2.354 Zr 2.386 Zr 1.613 Al 3.962 Ni 2.989 Zr 2.467 Zr 2.786 Al 3.287 Ni 2.456 Zr 2.662 Zr 1.989 Al 3.461 ZrO 2 1.831 Ni a 3.226 Zr a 2.729 Run 5. Starting amount (mmol): n Ni 5 22.726; Ni 1.814 Zr 1.993 Zr 1.175 ZrO 2 1.537 Al 3.280 Al 3.239 Al 3.780 Ni 2.455 Zr 2.338 Zr 1.904 Al 3.758 Al 3.632 Al 4.021 ZrO 2 1.876 Ni 2.808 Zr 2.176 Zr 2.931 Al 4.781 Al 4.228 Al 4.095 Ni 3.440 Zr 2.965 Zr 3.075 Al 4.984 Al a 4.784 ZrO 2 a 1.833 a
Solid–liquid phase region.
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
1 1 1 1 0.9862 0.9592 0.9375 0.9305 0.9176 0.8919 0.8686 0.8588 0.8512 0.8311 0.8137 0.8093 0.8588 0.8012 0.7813
1571 2899 1554 2542 22567 23685 23478 1553 22568 24336 24495 1472 21853 24495 24005 1584 2556 21172 21652
0 – 0 – 2143.2 2182.2 2175.3 2.8 2143.3 2203.6 2208.9 0.1 2119.7 2208.9 2192.7 3.8 – 297.2 2115.1
0 – 0 – 21.2 28.3 210.8 29.9 213.9 216.2 219.2 223.9 220.4 225.3 227.2 225.9 – 229.3 224.9
2520 1841 1795 2822 21125 21528 21682 2325 1490 1349 21024 2971 2994 1649 2157.6 1095.9 1100.9 2874.3 2877.3 2566 2207 837 922 2642 2581 1129
274.0 25.6 24.4 – 283.7 2101.4 2113.6 271.8 20.2 26.5 291.6 293.7 299.4 – 266.9 23.1 23.7 295.5 2100.2 284.5 272.0 27.1 22.8 289.9 288.7 –
230.2 230.2 230.9 – 230.9 233.8 237.8 237.5 235.6 238.9 236.8 238.7 241.5 – 241.8 241.3 241.2 241.7 245.5 244.6 245.3 246.8 245.3 246.8 251.8 –
n Zr 5 40.206 0 0 0 0 0.0230 0.0668 0.1096 0.1296 0.1258 0.1226 0.1399 0.1751 0.2085 0.2085 0.2222 0.2166 0.2113 0.2256 0.2571 0.2839 0.2924 0.2848 0.2779 0.2882 0.3142 0.3142
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
157
Table 3 Experimental data of liquid Cu 0.41 Ni 0.24 Zr 0.35 –Al alloys at 1565 K Added element (i)
Added amount (Dn i ), mmol
Run 1. Starting amount (mmol): nAl 5 75.385 ZrO 2 1.1728 Al 3.339 ZrO 2 1.4214 Ni 1.945 Cu 3.345 Zr 2.819 Al 3.632 Ni 2.146 Cu 3.573 Zr 3.157 Al 4.095 Ni 1.923 Cu 3.287 Zr 2.831 Al 3.343 Ni 1.931 Cu 3.287 Zr 2.799 Al 4.477 ZrO 2 1.3029 Ni 2.504 Cu 4.280 Zr 3.669 Al 3.665 Ni 1.986 Cu 3.204 Zr 2.861 Al 4.380 Ni 2.224 Cu 3.724 Zr 3.287 Al 4.336 Ni 2.449 ZrO 2 1.7103 Run 2. Starting amount (mmol): n Cu 5 28.746; ZrO 2 1.6280 Ni 1.914 Cu 3.281 Zr 2.799 Al 2.612 Al 3.002 Al 3.013 Al 2.846 Ni 1.959 Cu 3.366 Zr 2.818 Al 3.483 Al 2.853 Al 3.317 Al 3.884 Ni 1.919 Cu 3.296
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
1 1 1 0.9879 0.9564 0.9218 0.9084 0.8998 0.8727 0.8426 0.8323 0.8281 0.8081 0.7855 0.7787 0.7755 0.7585 0.7394 0.7356 0.7356 0.7332 0.7145 0.6936 0.6883 0.6876 0.6753 0.6615 0.6600 0.6602 0.6478 0.6337 0.6321 0.6323 0.6323
2930 1688 2890 22899 579 23601 1643 22720 540 23667 1589 22646 556 24061 1540 22231 465 24750 1470 2310 21245 1122 24668 1222 2901 1507 24522 1259 2224 1506 23592 1046 2263 2113
– 0 – 2142.3 232.4 2168.0 1.0 2140.8 232.7 2176.3 2.1 2143.0 231.3 2195.4 3.0 2133.3 233.5 2225.8 2.9 – 2102.1 29.2 2232.2 23.5 291.7 6.9 2231.3 20.6 267.0 8.7 2201.6 27.3 268.8 –
– 0 – 21.4 24.5 27.5 28.6 29.5 212.2 215.5 216.9 217.2 219.3 222.3 223.2 223.9 226.4 228.4 227.7 – 228.2 230.3 231.6 234.4 233.1 232.9 234.2 232.2 233.5 234.5 234.6 235.2 234.8 –
n Ni 5 16.790; n Zr 5 24.528 0 2869 0 2235 0 1715 0 1153 0.0161 2981 0.0497 2806 0.0833 2772 0.1138 2913 0.1267 2112 0.1231 1749 0.1192 915 0.1326 2973 0.1595 2863 0.1840 2712 0.2108 2644 0.2230 2359 0.2179 1671
– 265.4 0.8 226.8 277.6 273.1 272.8 278.0 262.2 7.6 230.8 280.4 277.5 272.9 271.1 271.3 9.7
– 224.8 224.8 224.6 225.2 226.1 227.3 229.2 229.2 229.3 230.1 230.6 231.8 232.5 233.9 235.9 235.2
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
158 Table 3. Continued Added element (i)
Added amount (Dn i ), mmol
Mole fraction (xAl )
ZrO 2 Zr Al Al Al Al Ni Cu Zr Al Al Al Al Al Ni Cu Zr ZrO 2
1.904 2.759 5.692 6.037 5.670 6.278 1.933 3.323 2.784 6.749 6.574 7.623 7.086 7.827 1.875 3.016 2.774 1.516
0.2179 0.2123 0.2278 0.2632 0.2955 0.3256 0.3385 0.3324 0.3256 0.3371 0.3646 0.3914 0.4169 0.4407 0.4504 0.4446 0.4380 0.4380
Run 3. Starting amount (mmol): n Cu 5 35.160; ZrO 2 1.194 Ni 1.921 Cu 3.589 Zr 2.919 ZrO 2 1.135 Al 6.485 Al 7.145 Al 7.783 Al 8.264 Ni 2.076 Cu 3.469 Zr 2.936 Al 8.643 Al 9.439 Al 9.439 Al 9.591 Ni 2.870 Cu 4.977 Zr 4.138 ZrO 2 1.243 Al 7.768
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
2355 804 2887 2571 2391 2272 2232 1676 153 2295 2143 2158 2137 138 2437 1531 2430 1965
n Ni 5 20.516, n Zr 5 30.014; nAl 5 49.819 0.3650 2416 0.3650 2832 0.3578 1629 0.3496 433 0.3496 2310 0.3602 250 0.3884 21 0.4167 85 0.4443 65 0.4551 2789 0.4481 1554 0.4401 2428 0.4493 223 0.4747 188 0.4989 332 0.5212 457 0.5285 2588 0.5193 1481 0.5089 21090 0.5089 1978 0.5124 397
using an alumina crucible and another one using an yttria crucible (see Fig. 1). The masses of the dropping samples of the pure components were so small that the composition change in the bath did not exceed 1–3 at.%. This allows us to determine directly the partial enthalpy of mixing of all components in the same experimental run. At the beginning, in the middle and at the end of each series of measurements the calorimeter has been calibrated using cylindrical zirconia samples. The value of the standard heat content of the used zirconia ceramic at 156565 K referred to 298 K was determined previously [6] (DH 1565 298,ZrO 2 5 84.0860.66 kJ mol 21 ). The performed calibrations confirm our earlier observation [6] that the calibration factor varies linearly with the mole number of the bath, o k Dn k , (see Fig. 1). Therefore, the calibration factor W of our calorimeter depends on the composition and the amount of
Integral enthalpy (DH ), kJ mol 21
– 232.2 280.1 269.5 263.3 259.1 267.6 16.1 254.6 260.1 254.2 255.0 254.2 242.6 277.4 16.5 278.9 –
– 233.5 237.1 237.2 237.9 238.8 239.7 239.8 240.3 240.0 240.0 242.4 244.1 240.8 242.2 242.2 242.0 –
– 287.9 7.8 245.5 – 250.2 247.7 245.3 245.9 289.7 11.5 277.2 239.7 240.8 234.5 228.7 284.2 14.5 2106.9 – 231.5
– 240.5 239.9 239.4 – 240.4 241.8 242.9 245.1 244.0 243.9 243.9 242.7 244.7 242.9 240.8 240.5 241.3 242.2 – 241.9
the bath alloys and on the material of the reaction crucibles. Thus, for an initial alloy of about 60 mmol the calibration factor is 0.022, 0.028 and 0.034 for alumina, zirconia and yttria crucibles, respectively. A linear fit of the mole number-dependent calibration factors enables an easy calculation of DH¯ i and DH using the following relationships:
SO Dn D
W
k
k
DH 1565 298,ZrO 2 5 ]]]]] FZrO 2 Dn k
SO D
(1)
k
DH¯ i
SO Dn D 5 2 DH k
k
i 5 Al, Cu, Ni, Zr
1565 298,i
SO Dn D F SO Dn D,
1W
k
k
i
k
k
(2)
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
159
Table 4 Experimental data of liquid Cu 0.19 Ni 0.11 Zr 0.70 –Al alloys at 1565 K Added element (i)
Added amount (Dn i ), mmol
Run 4. Starting amount (mmol): nA1 5 76.842 ZrO 2 1.091 Al 3.739 Al 3.432 ZrO 2 1.094 Ni 1.546 Cu 2.566 Zr 3.566 Zr 3.322 Zr 2.930 Al 3.561 Ni 1.678 Cu 3.086 Zr 3.651 Zr 3.983 Zr 2.769 Al 3.891 Ni 1.260 Cu 2.209 Zr 2.581 ZrO 2 1.055 Zr 2.933 Zr 2.351 Al 3.858 Ni 1.523 Cu 2.499 Zr 3.028 Zr 3.729 Zr 3.200 Al 3.565 Ni 1.422 Cu 2.360 Zr 5.021 Zr 5.349 Al 4.132 ZrO 2 1.152 Run 5. Starting amount (mmol): n Cu 5 11.821; ZrO 2 1.692 Ni 1.432 Cu 2.454 Zr 3.113 Zr 3.384 ZrO 2 1.633 Zr 2.952 Al 2.898 Al 4.295 Al 4.443 Al 4.410 Ni 1.442 Cu 2.451 Zr 4.560 Zr 4.574 Al 3.913 Al 4.562 Ni 1.391 Cu 2.407 Zr 4.439 ZrO 2 1.700
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
1 1 1 1 0.9909 0.9676 0.9347 0.9002 0.8709 0.8602 0.8557 0.8363 0.8103 0.7827 0.7597 0.7546 0.7547 0.7441 0.7298 0.7298 0.7141 0.6997 0.6977 0.6982 0.6881 0.6747 0.6589 0.6435 0.6408 0.6420 0.6343 0.6197 0.6002 0.5954 0.5954
2919 1730 1710 2971 23232 549 23716 23538 23419 1476 22579 1040 24351 24641 24772 1421 2539 1183 24003 2395 23147 23337 956 2131 968 22004 22123 22050 900 442 1054 21091 21012 219 2012
– 0 0 – 2151.8 233.4 2170.6 2167.5 2166.1 22.5 2139.0 216.4 2201.7 2215.1 2223.1 0.2 276.9 28.4 2201.2 – 2173.1 2181.8 213.7 263.3 213.7 2135.5 2141.4 2140.1 213.4 241.3 28.0 2104.1 2102.0 239.4 –
– 0 0 – 20.7 25.1 223.5 211.6 216.3 219.7 224.1 227.1 231.1 236.9 242.1 236.7 238.5 239.9 243.6 – 240.9 245.6 249.4 245.2 245.9 240.7 245.7 249.3 244.5 248.2 248.4 246.8 252.4 249.0 –
2382 2881 871 1474 1595 2358 1546 21238 21385 21447 21530 2734 844 1435 1353 21474 21490 2711 810 1306 1915
– 290.0 218.3 27.9 23.6 – 25.4 293.2 2100.28 2105.13 2111.33 289.348 214.057 20.92396 24.8139 2110.03 2113.13 290.358 212.747 23.8719 –
– 217.329 217.329 218.934 215.905 – 217.136 218.229 221.007 224.882 229.522 231.441 231.047 229.154 230.678 230.69 234.502 234.0065 234.146 234.635 –
n Ni 5 6.8552; n Zr 43.801 0 0 0 0 0 0 0 0.0184 0.0617 0.1098 0.1538 0.1733 0.1697 0.1637 0.1564 0.1682 0.1998 0.2150 0.2115 0.2055 0.2055
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
160 Table 4. Continued Added element (i)
Added amount (Dn i ), mmol
Run 6. Starting amount (mmol): n Cu 5 11.815; ZrO 2 1.628 Ni 1.192 Cu 2.058 Zr 4.009 Zr 3.508 Al 4.076 Al 3.880 Al 5.218 Al 5.144 Ni 1.345 Cu 2.327 Zr 4.172 Zr 4.396 Al 4.336 Al 4.414 Al 4.484 Al 5.207 Al 5.062 ZrO 2 1.904 Ni 1.260 Cu 2.196 Zr 3.949 Zr 3.727 Al a 5.763 ZrO 2 a 1.516 a
Mole fraction (xAl )
Area (Fi ), 21 mV s mol
n Ni 5 6.8552, n Zr 5 43.799; nAl 5 14.677 0.1888 2548 0.1888 21074 0.1849 1008 0.1782 1708 0.1704 1656 0.1854 21824 0.2199 21902 0.2558 21544 0.2930 21506 0.3086 2148 0.3034 896 0.2947 1560 0.2838 1404 0.2912 21256 0.3160 21397 0.3395 21037 0.3633 2729 0.3868 2533 0.3868 1748 0.3962 317 0.3914 728 0.3833 1321 0.3736 609 0.3805 – 0.3805 1636
Partial enthalpy (DH¯ i ), kJ mol 21
Integral enthalpy (DH ), kJ mol 21
– 295.2 215.0 22.5 24.5 2110.6 2115.2 2105.3 2107.6 264.5 213.4 25.2 25.2 297.6 2105.9 293.5 282.0 274.5 – 242.6 213.4 29.5 231.8 – –
– 234.4 234.1 232.7 233.3 233.9 237.7 238.2 242.5 242.6 242.2 237.5 240.3 239.3 245.1 245.2 246.6 250.8 – 251.6 251.0 242.2 248.9 – –
Solid–liquid phase region.
3. Results and discussion
3,4
DH(x) 5
O x DH¯ (x) i
(3)
i
i 51
3.1. Liquid Al–Ni–Zr alloys
where Fi is the area under a temperature–time curve due to the dissolution of 1 mole of component i in liquid bath and x i is the mole fraction of component i of the ternary and the quaternary alloy. The measurements of the ternary Al–Ni–Zr and quaternary Al–Cu–Ni–Zr alloys were performed at temperatures below the melting temperature of Ni and Zr. The standard state of the data given in column 4 of the Tables 1–4 is liquid Al, Cu and solid Ni, Zr. DH¯ i , and DH given in column 5 and 6 of the Tables 1–4 are referred to liquid Al, Cu, Ni and Zr: DH¯ j 5 D s H¯ j 2 Df Hj ;
j 5 Ni, Zr
(4)
where subscript s indicates the partial enthalpy refers to the solid metals; Df Hj is the molar heat of fusion of metal j. The standard values of heat content of the components and heat of fusion of Ni and Zr were taken from Ref. [8]. The simplified Eq. (4) is used because the heat capacity of undercooled liquid nickel and undercooled liquid zirconium is not known.
The results obtained for the partial and the integral enthalpies of mixing of liquid Al–Ni–Zr alloys of the vertical composition sections with x Ni /x Zr 5 0.64 / 0.36 and x Ni /x Zr 5 0.36 / 0.64 are summarized in Tables 1 and 2, respectively. Fig. 2 shows the partial functions of the components along the sections with the experimental data of the constituent binary Al–Zr [5], Al–Ni [3] and Ni–Zr [6] alloys. Analyzing our measurements we could determine the homogeneity ranges of the liquid phase at 1565 K along the vertical section x Ni /x Zr 5 0.64 / 0.36 as 0 # xAl # 0.08, 0.28 # xAl # 0.54 and 0.66 # xAl # 1. The homogeneity ranges of the liquid phase along the vertical section x Ni /x Zr 5 0.36 / 0.64 are 0 # xAl # 0.29 and 0.81 # xAl # 1. Obviously, the partial enthalpies of the components gradually change with the increasing mole fractions of aluminum with the exception of DH¯ Al of the Ni 0.64 Zr 0.36 –Al isopleth (see Fig. 2c, curve 2). This DH¯ Al is characterized by a sharp minimum near 5 at.% Al. The experimental data points of the ternary alloys together with the values for constituent binaries [3–6] were treated by means of least square procedure according to
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
161
Fig. 2. Composition dependencies of the partial enthalpies of mixing (nickel (a), zirconium (b) and aluminum (c)) and integral enthalpy of mixing (d) of the ternary liquid and undercooled liquid Al–Ni–Zr alloys at 156565 K: points are from Tables 1 and 2; solid lines result from Eq. (5); dashed lines in (d) result from Eq. (6).
DH 5 xA xB aA – B 1 xA x C aA – C 1 xB x C aB – C 1 xA xB x C aA – B – C (5) The a -functions of Al–Ni–Zr are collected in Table 5. These relationships adequately describe the experimental values of the integral enthalpy of mixing in the whole composition range. Fig. 2d shows DH versus the mole fraction of Al of the liquid Al–Ni–Zr alloys. Points are from Tables 1 and 2. Dashed lines are calculated only on the basis of smoothed functions of the partial enthalpy of aluminum (see Fig. 2c, curves 2 and 3) using the relation: DHy / ( 12y2z)5const,z / ( 12y2z)5const 5 (1 2 x) x
3
DH¯ (x) E ]]] dx 4 (1 2 x) Al
3 DHx 50 1
2
(6)
x50
where x 5 xAl , y 5 x Ni and z 5 x Zr . Considering the scatter of the experimental data points there is good agreement between the results of both methods of calculations. The
partial and the integral functions are therefore determined correctly and their composition variation is consistent with the Gibbs–Duhem equation.
3.2. Liquid Al–Cu–Ni–Zr alloys The measured partial and the integral enthalpies of mixing of the liquid Al–Cu–Ni–Zr alloys of the vertical sections with x Cu :x Ni :x Zr 5 0.41:0.24:0.35 and x Cu :x Ni :x Zr 5 0.19:0.11:0.70 are presented in Tables 3 and 4, respectively. The homogeneity ranges of the liquid phase at 1565 K of the vertical sections are 0 # xAl # 1 and 0 # xAl # 0.38 and 0.57 # xAl # 1, respectively. The resulting DH¯ i values for three components are shown in Fig. 3 as functions of composition together with the smoothed curves (solid lines) and the experimental data for constituent binary and ternary alloys (broken lines). DH¯ i change gradually as a function of the zirconium composition. The same data plotted versus aluminum composition show evident maxima (DH¯ i of Cu and Ni) and
162
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
Table 5 Parameters of Eqs. (5) and (7) System A–B–C
Constituent ternary systems: DH 5 aA – B xA xB 1 aB – C xB x C 1 aA – C xA x C 1 aA – B – C xA xB x C [kJ mol 21 ]
Al–Cu–Ni
aAl – Cu 5 2 75.6 2 63.8xAl 1 231.8x 2Al 2 130.6x 3Al aCu – Ni 5 12.1 2 1.1x Cu 2 aAl – Ni 5 2 130.2 2 330.4x Ni 1 331.0x Ni aAl – Cu – Ni 5 2 215.8 1 597.1x Ni 2 460.5xAl 3 aAl – Cu 5 2 75.6 2 63.8xAl 1 231.8x 2Al 2 130.6x Al aCu – Zr 5 2 40.9 1 67.5x Cu 2 926.6x 2Cu 1 2541.7x 3Cu 2 2895.3x 4Cu 1 1202.6x 5Cu 2 aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x Zr 2 2 aAl – Cu – Zr 5 459.3 2 1395.8x Zr 2 1853.9xAl 1 1576.7x Zr 1 1301.9x Al 1 986.9x Zr xAl 2 aAl – Ni 5 2 129.6 2 331.6xAl 1 331.0x Al 2 3 4 aNi – Zr 5 2 83.1 2 217.8x Ni 1 419.9x Ni 2 1195.2x Ni 1 810.6x Ni 2 aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x Zr 2 2 aAl – Ni – Zr 5 2 1955.9 1 5842.2x Zr 1 4620.5xAl 2 3760.2x Zr 2 2399.9x Al 2 5964.0x Zr xAl aCu – Ni 5 11.1 1 1.1x Ni aCu – Zr 5 2 40.9 1 67.5x Cu 2 926.6x 2Cu 1 2541.7x 3Cu 2 2895.3x 4Cu 1 1202.6x 5Cu aNi – Zr 5 2 193.6 2 422.8x Zr 1 1769.9x 2Zr 2 2047.2x 3Zr 1 810.6x 4Zr 2 aCu – Ni – Zr 5 2 720.6 1 3342.7x Zr 1 566.9x Ni 2 3436.3x 2Zr 2 1357.8x Ni 2 985.5x Zr x Ni
Al–Cu–Ni
Al–Ni–Cu
Cu–Ni–Zr
System Al–Cu 0.63 Ni 0.37 –Zr
Quasiternary cut A–BC–D: DH 5 DHBC xA 1 aA – BC xA xBC 1 aBC – D xBC x D 1 aA – C xA x C 1 aA – BC – D xA xBC x D [kJ mol 21 ] DHCu 0.63 Ni 0.37 5 2.7 aCu 0.63 Ni 0.37 – Zr 5 2 64.2 2 181.1x 1 539.1x 2 2 575.5x 3 aCu 0.63 Ni 0.37 – Al 5 2 132.4 2 132.8xAl 1 197.4x 2Al 2 aAl – Zr 5 2 177.1 2 170.0x Zr 1 230.0x Zr 2 2 aAl – Cu 0.63 Ni 0.37 – Zr 5 2 531 1 2020.3x Zr 1 3079.0xAl 2 832.8x Zr 2 2749.7x Al 2 5530.1x Zr xAl
Fig. 3. Partial enthalpies of mixing of copper (a), nickel (b), zirconium (c) and aluminum (d) of liquid Al–Cu–Ni–Zr alloys at 156565 K: points are from Tables 3 and 4; lines result from fitted a -functions.
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
minima (DH¯ i of Zr and Al). These peculiarities were also observed in some constituent binary and ternary alloys, but they became more visible in quaternary alloys. The integral enthalpy of mixing of the liquid Al–Cu– Ni–Zr alloys as functions of mole fraction of aluminum are illustrated in Fig. 4. Points are from Tables 3 and 4. Dashed lines are calculated on the basis of smoothed partial enthalpy of aluminum data (see Fig. 4d, curves 3 and 5) using Eq. (6). The values of both methods of calculations are in proper agreement, this confirms the self-consistency of the measured functions. The experimental integral enthalpy values of the quaternary alloys along the quasiternary cut were treated by means of least square procedure according to DH 5 DHBC xA 1 aA – BC xA xBC 1 aBC – D xBC x D 1 aA – D xA x D 1 aA – BC – D xA xBC x D
(7)
The results represented by the a -functions are collected in Table 5. These relationships adequately describe the experimental results in the whole composition range (see Fig. 4, solid lines).
4. Discussion The enthalpies of mixing of liquid alloys of three constituent ternary systems, i.e. Al–Cu–Ni, Al–Cu–Zr and
163
Ni–Cu–Zr have been presented in our previous works [5–7]. In order to compare the integral enthalpy of mixing and to estimate excess thermodynamic functions of these systems we have treated the results of Ref. [7] by means of least square procedure according to Eq. (5). The relationships obtained together with the ones for liquid and undercooled liquid Al–Cu–Zr and Ni–Cu–Zr alloys from Refs. [5,6] are given in Table 5. Fig. 5 illustrates the enthalpy of mixing according to the relationships given in Table 5. Obviously, the minimum value of the enthalpy of mixing gradually decreases from the binary Al 0.53 Zr 0.47 alloy (DHmin 5 251.7 kJ mol 21 ) via quaternary compositions to the ternary Al 0.35 Ni 0.47 Zr 0.18 alloy (DHmin 5 261.5 kJ mol 21 ). The Al–Ni–Zr system reveals the highest interaction energy between the components of the quaternary Al–Cu–Ni–Zr system. To analyze the quaternary interactions the contribution of the fifth term of Eq. (7) to the enthalpy of mixing of liquid Al–Cu–Ni–Zr alloys is shown in Fig. 6. Obviously, these results indicate the existence of repulsive and attractive quaternary interactions among the components of the liquid alloy. The glass forming ability of liquid alloys by rapid solidification is determined by thermodynamic and kinetic factors [9]. Quantitative statements about the Gibbs energy of liquid and undercooled liquid alloys are very important. Activity data of liquid Al–Cu–Ni–Zr alloys and the constituent liquid ternary alloys are not given in the
Fig. 4. Integral enthalpy of mixing as a function of mole fraction of Al of liquid quaternary Al–Cu–Ni–Zr alloys: points are experimental data; solid lines are values according to Eq. (7); dashed lines are data according to Eq. (5) and smoothed DH¯ Al (xAl ) functions (see Fig. 3d, curves 3 and 5).
164
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
Fig. 5. Enthalpy of mixing (kJ mol 21 ) of liquid and undercooled liquid alloys of the constituent ternary systems and of the quasiternary cut Al–Cu 0.63 Ni 0.37 –Zr at 156565 K.
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
165
Fig. 6. Contribution of the fifth term of Eq. (7), which describes the quaternary interactions of the integral enthalpy of mixing of liquid and undercooled liquid Al–Cu 0.63 Ni 0.37 –Zr alloys at 156565 K (in kJ mol 21 ).
literature. A reasonable approximation for activities and the Gibbs energy can be obtained using an empirical model proposed earlier [10]. This model was successfully applied to various liquid metallic binary alloys [4,10] and liquid ternary Al–Cu–Zr and Ni–Cu–Zr [5,6] alloys as well as to solid intermetallic binary compounds [11]. In a case of a ternary A–B–C system the relationship for the excess entropy can be written as DS ex 5 xA xB (A AB 1 B AB aA – B ) 1 xA x C (A AC 1 B AC aA – C ) 1 xB x C (A
BC
BC
1 B aB – C ) 1 xA xB x C (A
ABC
1 B ABC aA – B – C )
(8)
and for a quasiternary A–B12y Cy –D cut of the quaternary A–B–C–D as ABC DS ex 5 xA DS ex 1 B ABC aA – BC ) BC 1 xA x BC (A
S D
Tˆ m ??? A 5R 2 ] Tˆ b
OT
5/2
;B
???
n Tˆ m 5 2 ]2 ; Tˆ m 5 T m,i /n; Tˆ b i 51
O
n
Tˆ b 5
b,i
/n
(10)
i 51
where T m,i and T b,i are melting and boiling temperatures of the component i (i 5 A, B, C . . . ) of an appropriate constituent 2-, 3- or 4-component system (n52, 3 or 4 respectively); xBC and DS ex BC are mole fraction and excess entropy of mixing of binary composition B12y Cy . The resulting Gibbs energies at 1565 K are shown in Fig. 7. The minimal values of Gibbs energy show up near the compositions of the minima of the enthalpy of mixing and amount to 241.4 for the constituent ternary Al–Cu– Ni system and 252.7 kJ mol 21 for the constituent ternary Al–Ni–Zr system.
1 xA x D (A AD 1 B ADaA – D ) 1 xBC x D (ABCD 1 B BCDaBC – D ) 1 xA xBC x D (A ABCD 1 B ABCDaA – BC – D )
Acknowledgements
(9) with
This work is partly supported by DFG, SPP: ‘Undercooled liquid metals: phase selection and glass transition’.
166
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
Fig. 7. Estimated values of the excess Gibbs energy of mixing (kJ mol 21 ) of liquid and undercooled liquid alloys of the constituent ternary systems and of the quasiternary cut Al–Cu 0.63 Ni 0.37 –Zr at 156565 K.
V.T. Witusiewicz, F. Sommer / Journal of Alloys and Compounds 289 (1999) 152 – 167
References [1] T. Masumoto, Sci. Rep. RITU A 39 (1994) 91. [2] A. Inoue, T. Zhang, T. Masumoto, Mater. Trans. JIM 31 (1990) 177. [3] U.K. Stolz, I. Arpshofen, F. Sommer, B. Predel, J. Phase Equil. 14 (1993) 473. [4] V. Witusiewicz, I. Arpshofen, F. Sommer, Z. Metallkd. 88 (1997) 866. [5] V. Witusiewicz, I. Arpshofen, U.K. Stolz, F. Sommer, Z. Metallkd. 89 (1998) 704.
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[6] V. Witusiewicz and F. Sommer, Submitted to Metall. Trans. B. [7] U.K. Stolz, I. Arpshofen, F. Sommer, Z. Metallkd. 84 (1993) 552. [8] O. Knacke, O. Kubaschewski, K. Hesselmann, in: 2nd ed, Thermochemical Properties of Inorganic Substances, Springer, Berlin, 1991. [9] F. Sommer, Metallic glass forming ability, in: S. Steeb, H. Warlimont (Eds.), Rapidly Quenched Metals, Elsevier Science, Amsterdam, 1985, p. 153. [10] V.T. Witusiewicz, J. Alloys Comp. 221 (1995) 74. [11] V.T. Witusiewicz, V.R. Sidorko, M.V. Bulanova, J. Alloys Comp. 248 (1997) 233.