Enthalpy of mixing of liquid Al–Cu–Si alloys

Journal of Alloys and Compounds 297 (2000) 176–184

L

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Enthalpy of mixing of liquid Al–Cu–Si alloys V.T. Witusiewicz*, I. Arpshofen, H.-J. Seifert, F. Aldinger ¨ Metallforschung, Institut f ur ¨ Nichtmetallische Anorganische, Materialien and Universitat ¨ Stuttgart, Pulvermetallurgical Max-Planck Institut f ur Laboratorium, Heisenbergstr. 5, D-70569 Stuttgart, Germany Received 31 August 1999; accepted 3 September 1999

Abstract The partial and the integral enthalpies of mixing of liquid Al–Cu–Si alloys have been measured by high temperature calorimetry at 157563 K. Results for three sections with constant concentration ratios of Al and Si are given in tabular form. A least-square regression analysis of the integral enthalpy of mixing data results in the following relationships (in kJ mol 21 ; T5157563 K): DH

5 xAl x Cu aAl – Cu 1 xAl x Si aAl – Si 1 x Cu x Si aCu – Si 1 xAl x Cu x Si aAl – Cu – Si

aAl – Cu aAl – Si

3 5 (275.666.5) 1 (263.868.8)xAl 1 (232633)x 2Al 1 (2131628)x Al 5 2 12.6 1 2.5x Si

aCu – Si

5 (216.262.2) 1 (97.7637.1)x Cu 1 (211386208)x 2Cu 1 (35146489)x 3Cu 1 4 5 (247486515)x Cu 1 (22166199)x Cu

aAl – Cu – Si 5 (2241.768.8) 1 (1165632)xAl 1 (891634)x Si 1 (2935630)x 2Al 1 (2640635)x 2Si 1 1 (21563652)xAl x Si . The minimum of DH changes with composition from 214.5 kJ mol 21 (Cu–25at.%Si) to 217.3 kJ mol 21 (Al–60at.%Cu). The presence of additional ternary interactions or ternary associates in the liquid state could not be observed.  2000 Published by Elsevier Science S.A. All rights reserved. Keywords: Al–Cu–Si alloys; Calorimetry; Enthalpy of mixing

1. Introduction This paper is one in the series [1,2] reporting on the enthalpies of mixing of the constituent ternary liquid alloys of the quaternary system Al–Cu–Ni–Si. The critically assessed phase equilibria of the ternary system Al–Cu–Si are reported in details in Ref. [3], but to our knowledge no thermodynamic data of the liquid state are available. Such data are interesting for the reason of the immense industrial application of aluminum and copper based alloys and they are necessary for further progress in our calorimetric investigations, the eventual goal of each is the thermodynamic optimization of the phase diagrams of the constituent ternaries and the quaternary Al–Cu–Ni–Si system. The measurements in the present paper were performed *Corresponding author.

on the basis of the thermodynamic data for the constituent liquid Al–Cu and Cu–Si alloys reported in our recent works [2,4–6] and the thermodynamically optimized set of the Al–Si system [7].

2. Experimental The partial and the integral enthalpies of mixing of liquid Al–Cu–Si alloys were measured at 157563 K using a high-temperature calorimeter described previously [4]. The experimental arrangements and procedures for the determination of the partial and the integral enthalpies of mixing of liquid ternary alloys simultaneously in the same experimental run have previously been described in [8,9]. Here only some important details are specified. The experiments were carried out under pure argon gas at atmospheric pressure. For the measurements the ther-

0925-8388 / 00 / $ – see front matter  2000 Published by Elsevier Science S.A. All rights reserved. PII: S0925-8388( 99 )00602-7

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 297 (2000) 176 – 184

mocouple was made of Pt–6%Rh / Pt–30%Rh and the thermopile from W–5%Re / W–20%Re. The alloy samples were prepared from copper (Puratronic, purity 99.999%), aluminum (purity 99.9%) and silicon (lumps, purity 99.9999%). Copper and silicon were from Alfa (Johnson Matthey). The measurements in the ternary system were performed along three vertical sections, that is xAl 0.80 xAl 0.50 xAl 0.20 ] 5 ]], ] 5 ]], and ] 5 ]], x Si 0.20 x Si 0.50 x Si 0.80 with 0#x Cu #1using the method described in Ref. [6]. The real compositions, attained in the investigations starting from either liquid Al–Si alloys or from liquid copper, are shown in Fig. 1 as solid and open points, respectively. The partial functions of mixing in the case of the initial Al–Si alloys have been calculated from the area under a temperature–time curve using the following relations [8,9] D s H¯ i (x) 5 2 DH

T 298,i

F

1 W(x)Fi (x), i 5 Al,Cu,Si

FS (x) 2 Q W(x) dW(x) 5 2 ]] dFS (x) 1 ]]] dx 12x FS (x)

G

(1) (2)

and

O x F (x)

FS (x) 5

i

i

(3)

i

where x5x Cu (mole fraction of copper), Q 5 FCu (x), xAl 5 (1 2 y) (1 2 x), x Si 5 y (1 2 x), is the heat content of component i and Fi is the area under a temperature–time curve due to the dissolution of 1 mol of component i in the liquid bath and y is the mole fraction of silicon of an initial

177

Al 12y Si y alloy. The initial condition for a numerical solution of the Eq. (2) is (1 2 y)DH T298,Al 1 yDH T298,Si 1 DHx 50 Wx 50 5 ]]]]]]]]]]], (1 2 y)FAl (x 50 ) 1 yFSi (x 50 )

(4)

where DHx 50 is the integral enthalpy of mixing of the initial Al 12y Si y alloy (the values of this parameter were adopted as mentioned in the first chapter of Ref. [7]). For the measurements performed starting from liquid copper the partial functions were calculated using the same equations, but in this case DH 1575 298,Cu Wx 50 5 ]]]] FCu(xAl 50, x Si 50)

(5)

and if y # 0.5 then x 5 xAl , Q 5 FAl (x), x Si 5 xy /(1 2 y), x Cu 5 1 2 x /(1 2 y) else x 5 x Si , Q 5 FSi (x), xAl 5 x (1 2 y) /y, x Cu 5 1 2 x /y. The measurements were performed at temperatures below the melting temperature of silicon (in this case the standard state is liquid copper, liquid aluminum and solid silicon). These data were converted to the reference states of liquid aluminum, copper and silicon using the following simplified equation DH¯ Si 5 D s H¯ Si 2 D f HSi

(6)

where subscript s indicates the partial enthalpies referred to the solid silicon, D f HSi is the molar heat of fusion of silicon. The values of the heat contents of the components

Fig. 1. Ternary Al–Cu–Si compositions for which the partial and the integral enthalpies of mixing were measured (a–c).

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 297 (2000) 176 – 184

178

as well as the heats of fusion of silicon were taken from SGTE data for the pure elements [10]. The integral enthalpies of mixing were calculated from the partial ones using simultaneously the three following methods:

O

DH(

k

O O

DHx 50 n 0 1 DH¯ k Dn k k Dn k ) 5 ]]]]]]] n 0 1 Dn k

(7)

k

Table 1 Enthalpies of mixing of liquid Al–Cu–Si alloys measured at 157563 K starting from liquid Al–Si alloys Added substance (i)

Added amount (Dn i ) (mmol)

Area (Fi 310 27 ) (mV s mol 21 )

Partial enthalpy Mole fraction (x Cu )

Integral enthalpy ] DHi (kJ mol 21 )

Mole fraction (x Cu )

DHi (kJ mol 21 )

Section Al 80 Si 20 –Cu (run 1); starting amount (mmol): nAl 546.1693, n Si 511.5004 Si 1.2398 7.1018 0 Al 4.7541 4.5338 0 Cu 1.4563 1.6502 0.0112 Si 0.8513 7.2544 0.0222 Al 3.3895 4.5417 0.0216 Cu 2.3950 1.6224 0.0374 Cu 2.4044 1.5922 0.0691 Cu 2.2757 1.6115 0.098 Si 0.9079 6.7886 0.1109 Al 3.8686 3.8983 0.1077 Cu 2.7704 1.8321 0.1199 Cu 2.9073 1.8059 0.1491 Cu 2.5707 1.9105 0.1755 Si 0.8171 6.0816 0.1868 Al 2.9582 3.8846 0.183 Cu 3.9792 1.5800 0.1967 Cu 3.7330 1.8965 0.2281 Cu 4.0145 1.7608 0.2571 Si 1.1055 6.7246 0.2702 Al 4.6054 3.7542 0.2632 Cu 4.8483 1.9648 0.2732 Cu 5.6197 1.2335 0.3052 Cu 6.6560 1.6218 0.3394 Si 1.1743 6.4782 0.3554 Al 4.4708 3.4911 0.3478 Cu 6.5389 1.2919 0.3573 Cu 7.0644 1.4831 0.3877 Cu 7.7356 1.6783 0.4177 Si 1.1771 6.0775 0.431 Al 4.8654 3.0231 0.4229 Cu 8.1723 1.4044 0.4305 Cu 9.4393 1.4764 0.4593

26.9 20.6 231.4 24.0 0.2 231.3 231.2 230.7 24.3 24.2 227.8 227.7 226.0 28.8 22.0 229.7 225.4 226.6 3.6 21.2 223.7 232.9 227.2 5.4 21.9 231.5 228.4 225.1 4.8 26.0 228.8 227.2

0 0 0.0224 0.0221 0.0210 0.0537 0.0844 0.1116 0.1103 0.1051 0.1346 0.1635 0.1876 0.1859 0.1800 0.2135 0.2426 0.2716 0.2688 0.2576 0.2887 0.3217 0.3571 0.3538 0.3419 0.3727 0.4028 0.4327 0.4294 0.4164 0.4446 0.4740

22.0 21.9 22.6 22.6 22.4 23.4 24.3 25.1 25.1 25.0 25.8 26.5 27.1 27.1 26.9 27.9 28.5 29.2 29.1 28.8 29.4 210.5 211.3 211.2 210.9 211.8 212.6 213.3 213.1 212.9 213.7 214.4

Section Al 80 Si 20 –Cu (run 2); starting amount (mmol): nAl 546.3918, n Si 511.6072 Si 1.3423 7.5648 0 Al 4.7912 5.2196 0 Cu 1.3659 2.0653 0.0104 Cu 1.9528 1.9306 0.035 Cu 2.0928 1.8138 0.0635 Si 1.2497 7.3921 0.0771 Al 4.6466 4.9941 0.0741 Cu 2.2486 1.6767 0.0852 Cu 2.7207 2.0756 0.1138 Cu 2.7286 1.9123 0.1434 Al 4.7096 4.5104 0.1535 Cu 3.0134 1.9874 0.1633 Cu 3.6161 1.8731 0.1931 Cu 3.8285 1.7020 0.2243 Si 0.9364 6.8962 0.2386 Cu 4.0504 1.8226 0.2525 Cu 4.1605 1.7273 0.2816 Cu 4.3729 1.9094 0.3095 Si 1.1785 6.8958 0.3216 Al 4.4575 3.8475 0.3139 Cu 4.7931 1.7575 0.3214 Si 1.1963 6.3666 0.3333

211.4 0.2 229.5 230.4 231.2 29.0 0.6 232.3 227.7 229.0 21.4 227.8 228.5 230.0 24.5 228.1 228.7 226.0 1.3 22.7 227.6 24.4

0 0 0.0209 0.0492 0.0778 0.0764 0.0717 0.0986 0.1291 0.1577 0.1492 0.1774 0.2089 0.2397 0.2375 0.2674 0.2957 0.3233 0.3199 0.3078 0.3349 0.3317

22.1 21.9 22.5 23.3 24.2 24.2 24.0 24.8 25.5 26.3 26.1 26.8 27.6 28.5 28.4 29.2 210.0 210.6 210.5 210.2 210.9 210.8

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179

Table 1 (continued) Added substance (i)

Added amount (Dn i ) (mmol)

Area (Fi 310 27 ) (mV s mol 21 )

Partial enthalpy Mole fraction (x Cu )

Integral enthalpy ] DHi (kJ mol 21 )

Mole fraction (x Cu )

DHi (kJ mol 21 )

Section Al 50 Si 50 –Cu; starting amount (mmol): nAl 535.2295, n Si 535.4625 Si 1.0379 15.8072 0 Al 1.0027 8.2713 0 Cu 1.5873 5.1644 0.0107 Cu 2.0785 4.9134 0.0347 Si 1.2433 15.3049 0.0476 Al 1.1744 7.7751 0.0469 Cu 2.7411 4.6341 0.0625 Cu 2.8020 4.6635 0.0939 Si 1.5549 14.9258 0.1082 Al 1.6439 7.4210 0.1062 Cu 2.7411 4.4490 0.1187 Cu 2.8020 4.1741 0.1454 Si 1.6154 14.0864 0.1572 Al 1.4693 6.8837 0.1546 Cu 3.9248 4.3099 0.17 Cu 3.8217 3.3582 0.2016 Si 2.5315 11.8333 0.2139 Al 2.4594 7.0455 0.209 Cu 5.7504 4.0030 0.2264 Cu 5.2096 3.8468 0.2627 Si 2.0587 12.8807 0.2768 Al 1.9810 6.8844 0.2722 Cu 5.1172 3.3997 0.2844 Cu 6.4589 3.6697 0.3156 Si 1.9191 11.5879 0.33 Al 2.0014 5.8136 0.3254 Cu 6.4532 3.7768 0.338 Cu 7.8766 3.2425 0.3695 Si 2.9477 11.1150 0.3825 Al 3.0690 5.8358 0.3752 Cu 7.3517 3.2173 0.3854 Cu 8.3869 2.8142 0.4135

21.2 23.8 220.6 221.5 21.3 25.2 222.5 221.7 0.4 25.3 222.5 223.6 21.2 26.9 222.1 227.5 211.3 23.7 222.5 222.6 1.0 21.8 225.2 222.3 22.9 26.7 220.8 223.8 21.0 24.0 223.5 225.9

0 0 0.0214 0.0480 0.0472 0.0465 0.0786 0.1092 0.1072 0.1052 0.1323 0.1585 0.1558 0.1534 0.1866 0.2165 0.2113 0.2066 0.2463 0.2791 0.2744 0.2700 0.2989 0.3324 0.3277 0.3230 0.3530 0.3861 0.3788 0.3716 0.3992 0.4279

22.8 22.8 23.2 23.7 23.7 23.7 24.3 24.9 24.8 24.8 25.4 25.9 25.8 25.8 26.5 27.3 27.4 27.3 28.0 28.7 28.5 28.4 29.1 29.7 29.6 29.6 210.1 210.8 210.6 210.4 211.0 211.7

Section Al 20 Si 80 –Cu; starting amount (mmol): nAl 510.8285, n Si 542.4055 Al 1.0940 – 0 Si 3.6246 – 0 Cu 2.1180 – 0.0176 Al 1.1941 – 0.0349 Si 4.8992 – 0.0333 Cu 2.5382 3.5222 0.0499 Cu 3.0275 3.3141 0.0875 Cu 2.4957 2.9001 0.1221 Si 4.0732 7.1411 0.1336 Al 0.7491 3.1665 0.1294 Cu 3.6475 2.7311 0.148 Cu 4.0913 3.1079 0.1868 Cu 3.3029 2.2979 0.2211 Si 3.4608 7.6396 0.2312 Al 0.6675 3.0196 0.226 Cu 4.0629 2.5063 0.2412 Cu 5.5075 2.4838 0.277 Cu 5.4823 2.1340 0.3144 Si 3.7207 7.0372 0.3265 Al 0.9976 2.4912 0.3196 Cu 6.1542 1.8598 0.3357 Cu 5.9355 1.7933 0.3684 Cu 6.5712 2.0055 0.3989 Si 3.9237 6.0280 0.4082 Al 0.8715 2.4672 0.401 Cu 8.3745 1.8584 0.4169 Cu 7.5783 1.8860 0.4481 Cu 7.8600 1.6239 0.4752 Si 4.0447 6.0913 0.4824 Al 1.3202 2.1385 0.4745 Cu 9.8033 1.6629 0.4873 Cu 9.0039 1.8589 0.514

– – – – – 211.6 212.8 216.6 27.7 28.8 217.7 212.2 221.3 4.8 27.8 218.2 217.5 221.2 4.1 211.9 224.4 224.7 221.1 23.9 210.0 222.8 221.8 225.1 2.2 212.8 224.3 220.8

0 0 0.0353 0.0346 0.0320 0.0678 0.1071 0.1371 0.1300 0.1288 0.1672 0.2065 0.2356 0.2268 0.2252 0.2573 0.2967 0.3320 0.3210 0.3182 0.3531 0.3836 0.4141 0.4022 0.3997 0.4342 0.4621 0.4883 0.4764 0.4726 0.5019 0.5261

– – – – – 23.1 23.5 24.0 24.2 24.2 24.8 25.2 25.8 25.4 25.4 25.9 26.5 27.3 26.9 26.9 27.8 28.6 29.2 29.1 29.1 29.9 210.5 211.2 210.9 210.9 211.6 212.1

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 297 (2000) 176 – 184

180

Table 2 Enthalpies of mixing of liquid Al–Cu–Si alloys at 157563 K measured starting from liquid copper Added substance (i)

Added amount (Dn i ) (mmol)

Area (Fi 310 27 ) (mV s mol 21 )

Partial enthalpy Mole fraction (x Cu )

Integral enthalpy ] DHi (kJ mol 21 )

Mole fraction (x Cu )

DHi (kJ mol 21 )

Section Cu–Al 80 Si 20 ; starting amount (mmol): n Cu 548.6231 Cu 2.6452 5.8113 Cu 3.5090 5.9543 Cu 3.2148 5.8819 Al 1.9877 23.1147 Si 0.8545 0.2405 Al 1.8801 22.6629 Cu 2.3839 5.6169 Al 2.8221 22.0534 Si 1.4847 1.4845 Al 2.8814 21.1627 Cu 2.9032 5.2148 Al 2.8035 20.6423 Si 1.6200 3.1695 Al 3.3005 0.2598 Cu 2.9111 3.9415 Al 3.0817 0.4489 Si 1.5951 5.3231 Al 3.2115 1.8076 Cu 2.7978 4.2355 Al 4.1274 1.7220 Si 2.0936 6.7475 Al 4.0792 2.7205 Cu 3.1031 3.2360 Al 4.8506 2.7361 Si 2.5458 8.0793 Al 5.3920 3.1291 Cu 3.6806 2.3487 Al 6.6009 3.2604 Si 2.7665 7.7586 Al 5.6738 3.1946 Cu 3.6444 2.1985 Al 5.7739 3.5496 Si 3.0300 6.9960 Al 7.2165 3.3365 Cu 3.5924 1.9993

1 1 1 0.9834 0.9601 0.939 0.9261 0.9082 0.8794 0.8526 0.8384 0.8265 0.8031 0.779 0.7672 0.7579 0.738 0.7188 0.7106 0.7002 0.6785 0.6587 0.6509 0.6421 0.6214 0.601 0.5935 0.5847 0.564 0.547 0.5416 0.537 0.5213 0.5046 0.4985

22.0 20.8 21.4 276 281 272.9 0.5 268.2 269.4 260.2 20.2 255.4 252.5 246.7 210.7 244.7 229.9 230.8 26.5 231.3 213.2 220.3 215.2 219.4 4.3 214.1 223.4 211.4 6.0 211.1 223.5 25.7 1.5 26.8 224.4

1.0000 1.0000 1.0000 0.9669 0.9533 0.9247 0.9275 0.8889 0.8699 0.8352 0.8416 0.8113 0.7948 0.7632 0.7712 0.7445 0.7314 0.7063 0.7148 0.6855 0.6715 0.6459 0.6559 0.6282 0.6145 0.5875 0.5995 0.5698 0.5582 0.5358 0.5474 0.5265 0.5161 0.4930 0.5041

0 0 0 22.7 23.8 25.9 25.7 28.3 29.6 211.6 211.1 212.7 213.5 214.9 214.7 215.8 216.0 216.5 216.2 216.8 216.8 216.9 216.9 217.0 216.5 216.4 216.6 216.3 215.9 215.7 215.9 215.5 215.2 214.8 215.0

Section Cu–Al 50 Si 50 ; starting amount (mmol): n Cu 548.3242 Cu 2.0533 11.8964 Si 1.3889 0.2008 Al 1.2516 27.2859 Cu 1.8815 11.2072 Si 2.1416 0.8515 Al 2.1483 25.5864 Cu 2.4408 10.5803 Si 2.1324 2.4546 Al 2.2098 22.1502 Si 2.3396 7.4079 Al 2.4101 1.4003 Cu 2.1204 9.1961 Si 2.3424 10.9882 Al 2.4423 3.3064 Si 3.2500 14.2543 Al 3.4492 5.4137 Cu 2.4655 6.5814 Si 3.3230 15.2330 Al 3.3008 7.1963 Si 3.5427 16.6511 Al 3.6698 7.0018 Cu 2.4694 4.4400

1 0.9866 0.9617 0.951 0.9341 0.8996 0.8852 0.8727 0.8435 0.8149 0.7871 0.7767 0.7679 0.7439 0.7172 0.6882 0.6785 0.6705 0.6462 0.6231 0.6003 0.5941

0.7 282.2 283.1 2.7 279.1 275.6 0.8 271.4 259.2 248.7 242.8 27.3 232.7 233.8 217.0 222.2 217.0 29.3 211.1 3.2 29.1 224.4

1.0000 0.9732 0.9502 0.9519 0.9162 0.8829 0.8875 0.8579 0.8291 0.8007 0.7734 0.7800 0.7557 0.7320 0.7025 0.6738 0.6831 0.6579 0.6346 0.6115 0.5892 0.5990

0 22.2 24.1 23.9 26.7 29.2 28.8 210.9 212.5 213.7 214.7 214.5 215.1 215.7 215.7 216.0 216.0 215.8 215.6 214.9 214.7 214.9

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 297 (2000) 176 – 184

181

Table 2 (continued) Added substance (i)

Added amount (Dn i ) (mmol)

Si Al Si Al Cu Si Al Si Al Cu

4.1145 4.2390 4.6639 4.6544 2.7509 4.4335 4.5702 5.5547 5.4105 3.1064

Area (Fi 310 27 ) (mV s mol 21 )

Partial enthalpy Mole fraction (x Cu )

14.1563 6.7702 14.8676 6.3816 4.6834 14.1354 6.9401 13.1885 5.6522 3.9580

Section Cu–Al 20 Si 80 ; starting amount (mmol): n Cu 548.1983 Cu 2.3619 6.6875 Cu 2.7238 6.5905 Cu 2.3273 6.4852 Si 1.8871 0.3671 Al 0.7639 23.0373 Si 1.1678 20.3763 Cu 2.1857 6.4747 Si 2.3748 0.2959 Al 1.0680 21.5989 Si 1.8265 1.8737 Cu 2.7868 6.0121 Si 1.8372 2.6359 Al 1.2905 20.1597 Si 2.5778 5.0407 Cu 2.6499 5.3895 Si 2.5529 5.4215 Al 1.3016 1.8066 Si 2.7629 7.0803 Cu 2.1495 4.5422 Si 2.9125 7.9581 Al 1.6836 2.8969 Si 3.7599 9.4098 Cu 2.3242 3.4115 Si 4.0447 9.2434 Al 2.1360 3.3799 Si 4.1337 9.6393 Cu 3.0165 2.9947 Si 5.2375 8.9470 Al 2.3326 3.0910 Si 5.0559 9.2131 Cu 2.6467 2.6150 Si 5.2660 8.2216 Al 2.3214 3.2570 Si 4.3758 8.0384 Cu 2.3084 2.3913

O x DH¯ (x)

DH(x) 5

i

0.5760 0.5541 0.5318 0.5113 0.5222 0.5041 0.4867 0.4672 0.4496 0.4612

214.6 214.3 213.6 213.4 213.5 212.9 212.7 212.1 212.2 212.5

1 1 1 0.9836 0.9608 0.9451 0.9368 0.9206 0.8958 0.8762 0.8669 0.8584 0.8397 0.8179 0.8071 0.7975 0.7785 0.7596 0.7501 0.7411 0.7222 0.7013 0.6909 0.6807 0.6601 0.6406 0.6332 0.6239 0.6035 0.5853 0.5775 0.5702 0.5537 0.5402 0.5353

20.8 21.6 22.3 285.2 272.4 291.0 1.0 285.7 262.0 272.9 20.9 266.6 250.5 246.7 25.3 243.2 234.3 228.8 211.5 220.5 224.7 26.0 219.8 24.7 219.0 2.4 221.7 0.3 219.1 8.2 222.6 2.8 213.9 4.9 222.3

1.0000 1.0000 1.0000 0.9672 0.9545 0.9357 0.9380 0.9032 0.8884 0.8641 0.8696 0.8472 0.8322 0.8037 0.8104 0.7847 0.7723 0.7470 0.7533 0.7289 0.7154 0.6872 0.6946 0.6669 0.6532 0.6281 0.6383 0.6095 0.5975 0.5730 0.5819 0.5586 0.5489 0.5315 0.5392

0 20.1 20.2 23.0 23.9 25.6 25.4 28.4 29.2 211.0 210.6 212.0 212.7 213.9 213.6 214.5 214.8 215.3 215.2 215.4 215.5 215.2 215.3 214.8 214.9 214.3 214.5 213.8 213.9 213.0 213.2 212.6 212.6 212.0 212.2

x51

3

DHi (kJ mol 21 )

25.4 28.3 4.5 28.9 220.1 4.0 25.0 0.4 213.9 224.4

i

DH(x) y / (12y)5const 5 (1 2 x) DHx 50 1

Mole fraction (x Cu )

0.5875 0.5651 0.543 0.5215 0.5168 0.5132 0.4954 0.4769 0.4584 0.4554

(8)

i

Integral enthalpy ] DHi (kJ mol 21 )

DH¯ (x) E ]]] dx , 4 (1 2 x)

check that the measurements were performed without any significant experimental errors and the data received are consistent with the Gibbs–Duhem equation.

Cu

2

x50

(9) where Dn is the mole number of dropped sample, n 0 is the mole number of an initial alloy, k is the number of successive dropped samples and x 5 x Cu . This allowed to

3. Results and discussion The results obtained for the partial and the integral enthalpies of mixing of the liquid ternary Al–Cu–Si alloys starting from liquid Al–Si alloys and liquid copper are

182

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 297 (2000) 176 – 184

summarized in Tables 1 and 2, respectively. Fig. 2 shows the composition dependence of the experimentally determined partial enthalpies of mixing in combination with

Fig. 2. Partial enthalpy of mixing of aluminum (a), silicon (b) and copper (c) of ternary liquid and undercooled liquid Al–Cu–Si alloys at 157563 K: points are experimental data; solid lines result from Eqs. (10)–(18); dotted lines are confidence bands at tolerance 0.05; dashed lines are data for the constituent binary liquid alloys.

the same ones of the constituent binary alloys, i.e., Cu–Si, Al–Cu [4,6] and Al–Si [7]. From Fig. 2a,b it follows that the partial functions of aluminum and silicon change only slightly with the ratio xAl /x Si . This fact is explained by the very small energy of pair Al–Si interactions as the partial enthalpies of mixing chosen for the measurements of the initial Al–Si alloys do not exceed 28 kJ mol 21 . Another interesting fact is that the pair interactions Al–Cu and Si–Cu in ternary alloys are also close regarding the energy. More pronounced are composition variations for the partial enthalpy of mixing of copper (Fig. 2c). Thus, the first value of the partial enthalpy of mixing of copper varies with the compositions of liquid Al–Si alloys from 210 up to 238 kJ mol 21 with some positive deviations from additive values (Fig. 3). Such a phenomenon was pointed out also for the partial enthalpy of mixing at infinitely dilute solution of carbon and boron in liquid Ni–Si–C, Ni–Si–B [11] and for copper in liquid Ni–Si–Cu alloys [2]. Such positive deviation is more distinctly observed for those ternary systems which are characterized by large negative interactions between three pairs of the components. Fig. 4 shows the composition dependence of the integral enthalpy of mixing of the liquid Al–Cu–Si alloys. Points represent the values calculated from Eq. (7). Solid lines are data calculated on the basis of smoothed functions of partial enthalpy of copper using Eq. (9). Similar values, but with somewhat larger scattering of the points around given dependences were obtained using Eq. (8). The good agreement between the results of the three methods of calculations confirms that the partial and the integral functions are determined correctly and their composition variations are consistent with the Gibbs–Duhem equation. A least-square regression analysis of the partial enthalpies of mixing of the ternary Al–Cu–Si alloys result in the following relationships (in kJ mol 21 ): for the vertical section Cu–Al 0.80 Si 0.20

Fig. 3. Variation of the first partial enthalpy of mixing of copper with composition of constituent liquid Al–Si alloys.

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 297 (2000) 176 – 184

183

Fig. 4. Integral enthalpy of mixing of liquid and undercooled liquid Al–Cu–Si alloys at 157563 K: points result from Eq. (7); solid lines result from Eq. (9); dotted lines result from Eq. (19); dashed lines are data for the constituent binary liquid alloys (a,b).

DH¯ Cu 5 (1 2 x)2 f (232.261.0) 1 (234.869.6)x 1 (2641684)x 3 1 (8506168)x 5 g

DH¯ Cu 5 (1 2 x)2 f (212.061.5) 1 (280610)x

DH¯ Al 5 2 75.6x 6

g

3

(11)

F

(28.761.9) 1 (103621)x 1 (29086380)x 3 1 3 (31006889)x 4 1 (223616563) x 5

DH¯ Si 5 2 75.4x 1 (1 2 x)

1 (1 2 x) f (27.861.9) 1 (77614)x 1 (596662)x 3 1 (211086100)x 6 g

(12)

for the vertical section Cu–Al 0.50 Si 0.50

3

F

(20.860.7) 1 (123636)x 1 (214426772)x 3 1 (592761818)x 4 1 (2526461150)x 5

3

1 (2326646)x 1 (16266692)x

14

g

(13)

DH¯ Al 5 2 75.6x 1 (1 2 x) (26.062.3) 1 (115625)x 1 (211486464)x 3 1 (429661101)x 4 1 (236346708)x 5

G

(14) DH¯ Si 5 2 75.4x 1 (1 2 x) 3

F

(22.161.4) 1 (119616)x 1 (213776297)x 3 1 (55636706)x 4 1 (248226453)x 5

G

(15) and for the vertical section Cu–Al 0.20 Si 0.80

G

(18)

DH¯ Cu 5 (1 2 x)2 f (221.561.3) 1 (263610)x

F

G

(17)

DH¯ Si 5 2 75.4x

3

(16)

DH¯ Al 5 2 75.6x 1 (1 2 x)

1 (1 2 x) f (20.961.0) 1 (8569)x 1 (209635)x 1 (2520650)x

1 (2349640)x 3 1 (16126570)x 14 g

(10)

The experimental data points of the integral enthalpy of mixing of the ternary alloys together with the values of the constituent binaries [2,4–6] were treated using regression analysis according to DH 5 xAl x Cu aAl – Cu 1 xAl x Si aAl – Si 1 x Cu x Si aCu – Si 1 xAl x Cu x Si aAl – Cu – Si

(19)

For the other a functions the following relationships were found (in kJ mol 21 ):

aAl – Cu 5 (275.666.5) 1 (263.868.8)xAl 1 (232633)x 2Al 1 (2131628)x 3Al

aAl – Si 5 2 12.6 1 2.5x Si

(20) (21)

184

V.T. Witusiewicz et al. / Journal of Alloys and Compounds 297 (2000) 176 – 184

aCu – Si 5 (216.262.2) 1 (97.7637.1)x Cu 1 (211386208)x 2Cu 1 (35146489)x 3Cu 1 (247486515)x 4Cu 1 (22166199)x 5Cu

(22)

aAl – Cu – Si 5 (2241.768.8) 1 (1165632)xAl 1 (891634)x Si (2935630)x 2Al 2 1 (2640635)x Si 1 (21563652)xAl x Si .

(23)

Eq. (19) describes adequately the experimental results in the whole composition range (see Fig. 4, dashed lines). A projection of the isoenthalpic lines on the Gibbs triangle of liquid and undercooled liquid Al–Cu–Si alloys according to Eq. (19) is shown in Fig. 5a. The minimum of the integral enthalpy of mixing changes with composition of the ternary liquid alloys from 214.5 kJ mol 21 (Cu– 25at.%Si) to 217.3 kJ mol 21 (Al–60at.%Cu). The contribution of the fourth term of Eq. (19), which describes the ternary interactions, is shown separately in Fig. 5b. Obviously, for this liquid alloy small positive deviations of the integral enthalpy of mixing from the regular behavior are present. Thus, occurrence of the additional ternary interactions or ternary associates in the liquid state is not considerable and the thermodynamic functions of mixing in the whole composition region of the Al–Cu–Si system could be successfully described by a regular association model using the model parameters only from the constituent binaries.

References

Fig. 5. Projection of the isoenthalpic lines on the Gibbs triangle (a) and contribution of the fourth term of Eq. (19), which describes the ternary interactions (b) of the integral enthalpy of mixing of liquid and undercooled liquid Al–Cu–Si alloys at 157563 K (in kJ mol 21 ).

[1] U.K. Stolz, I. Arpshofen, F. Sommer, Z. Metallkd. 84 (1993) 552. [2] V. Witusiewicz, I. Arpshofen, H.-J. Seifert, F. Sommer, F. Aldinger, submitted to the Z. Metallkd. [3] Ternary alloys, in: G. Petzow, G. Effenberg (Eds.), A Comprehensive Compendium of Evaluated Constitutional Data and Phase Diagrams, Vol. 5, VCH Verlagsgesellschaft, Weinheim, Germany, 1992. [4] U.K. Stolz, I. Arpshofen, F. Sommer, J. Phase Equilib. 14 (1993) 473. [5] V. Witusiewicz, I. Arpshofen, F. Sommer, Z. Metallkd. 88 (1997) 866. [6] V. Witusiewicz, I. Arpshofen, U.K. Stolz, F. Sommer, Z. Metallkd. 89 (1998) 704. ¨ [7] H. Feufel, T. Godecke, H.L. Lukas, F. Sommer, J. Alloys Comp. 247 (1997) 31. [8] V.T. Witusiewicz, M.I. Ivanov, J. Alloys Comp. 200 (1993) 177. [9] V.T. Witusiewicz, Thermochim. Acta 264 (1995) 41. [10] A.T. Dinsdale, CALPHAD 15 (1991) 317. [11] V.T. Witusiewicz, J. Alloys Comp. 203 (1994) 103.