Experimental investigation and thermodynamic calculation of excess enthalpies in the Ga–In–Te system

Journal of Alloys and Compounds 305 (2000) 144–152

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Experimental investigation and thermodynamic calculation of excess enthalpies in the Ga–In–Te system Roger Blachnik*, Erwin Klose ¨ Osnabruck ¨ , Postfach 4469, D-49069 Osnabruck ¨ , Germany Anorganische Chemie, Universitat Received 9 December 1999; accepted 5 January 2000

Abstract The excess enthalpies of liquid alloys in the ternary system Ga–In–Te were determined at 1173 K in a heat flow calorimeter for five sections Ga y In 12y Te with y 5 0.2, 0.4, 0.5, 0.6 and 0.8 and, in addition, for the section Ga 0.5 In 0.5 –Te at 973 and 1073 K. The enthalpy surface in the ternary system is determined by a valley of exothermic minima stretching from a minimum at the composition Ga 2 Te 3 to a minimum at composition In 2 Te 3 in the binaries. The excess enthalpies in the binary systems were adapted using the Lukas program. Ternary interactions were taken into account for the analytical description of excess enthalpies of the ternary system.  2000 Elsevier Science S.A. All rights reserved. Keywords: Thermodynamics; Enthalpies of mixing; High-temperature calorimetry; Ga–In–Te system; Liquid alloys

1. Introduction Thermodynamic excess functions of liquid mixtures provide information on interactions in the liquid state. For this reason the excess enthalpies of liquid alloys in systems with tellurium were measured in previous investigations [1–8]. The excess enthalpies in binary metal–tellurium systems are often nearly triangular-shaped functions of the concentration. The exothermic minima of these curves are found at, or close to, the composition of congruently melting compounds. Wagner [9] assumed the formation of associates in the melt to explain this behaviour. Based on this idea, Sommer [10,11] developed a thermodynamic formalism, which allows a fit of the experimental data in such systems. The optimized data sets of the binaries can be used to calculate the phase diagrams of multicomponent systems of technical relevance. As part of a systematic investigation of systems with chalcogens we have measured the excess enthalpies of liquid Ga–In–Te alloys.

2. Experimental The measurements were performed with the aid of a *Corresponding author. E-mail address: [email protected] (R. Blachnik)

high-temperature heat flow calorimeter [12] using the isoperibolic procedure. The experimental arrangement and the procedure for the determination of H E have been described previously [1–4]. Ga (Ingal, Stade, 99.999%), In (Preussag, 99.999%) and Te (Fluka, 99.999%) were used in the calorimetric work. The binary alloys were prepared by melting appropriate amounts of Ga and In in evacuated and sealed silica tubes. The heat effect DQ of mixing was determined for five sections with a constant concentration ratio of the two metals ( y Ga /y In 5 0.2, 0.4, 0.5, 0.6 and 0.8) at 1173 K and for one section with y Ga /y In 5 0.5 at 1073 and 973 K. Measurements started on the metal-rich side of the sections Ga y In 12y –Te. Binary Gay In 12y alloys were placed in the calorimeter tube and heated to the measurement temperature. Small pieces of pure Te were consecutively added from ambient temperature (T 5 298 K) after temperature equilibration of the calorimeter cell. On the tellurium-rich part of the system small amounts of Ga y In 12y were successively added to liquid tellurium. In these cases the low-melting Ga y In 12y alloys had to be cooled below room temperature (T 5 283 K) under dry conditions to keep them in the solid state. The enthalpy increments H(T ) 2 H(283 K) of Ga y In 12y and H(T ) 2 H(298 K) of Te, which were needed to calculate the heat effect of alloying, were determined by dropping Ga y In 12y in liquid Ga y In 12y , or Te in liquid Te, at the measurement

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R. Blachnik, E. Klose / Journal of Alloys and Compounds 305 (2000) 144 – 152

temperature. Calibration of the calorimeter was carried out after each measurement by dropping pieces of tin into a second tube, which ends in the liquid alloy. The enthalpy increments H(T 2 298 K) of tin were taken from Barin [13]. The reproducibility of the heat effects was better than 65%. All experiments were carried out under argon gas at atmospheric pressure.

3. Binary systems

3.1. The Ga–Te system The system Ga–Te has four intermediate compounds: GaTe and Ga 2 Te 3 melt congruently at 1108 and 1071 K, respectively; Ga 3 Te 4 decomposes in a peritectic reaction at 1057 K; the high-temperature phase Ga 2 Te 5 is formed in a eutectoid reaction at 681 K and decomposes peritectically at 757 K. A miscibility gap is found between 8 and 28 mol% Te with a monotectic temperature of 1020 K [23]. The system has been assessed twice, namely by Oh and Lee [14] and by Irle et al. [4]. The thermodynamic properties of the melt have been studied by several authors. The results are given in Table 1 [15–22]. In the optimization of Irle [4], 10 coefficients were used for the description of the liquid phase. These coefficients could not be used in our calculation because of another formal-

Table 1 Previous thermodynamic investigations in the systems Ga–Te, In–Te and Ga–In Authors

Method, function

Ref.

Ga–Te Irle et al. Castanet and Bergman Said and Castanet Glazov et al. Alfer et al. Katayama et al. Srikanth and Jacob Predel et al. Takeda et al.

Optimization, calorimetry, H E Calorimetry, H E Calorimetry, H E Calorimetry, H E Calorimetry, H E Emf, mGa Emf, mGa Vapour pressure, mTe Calorimetry, c p

[4] [15] [16] [17] [18] [19] [20] [21] [22]

In–Te Maekawa et al. Predel et al. Karpenko et al. Naoi et al. Said and Castanet Takeda et al. Glazov et al. Lee and Lee Schlieper

Calorimetry, H E Vapour pressure, mTe DTA, H E Emf, mIn Calorimetry, H E Calorimetry, c p Emf, mIn Calorimetry, H E Calorimetry, H E

[25] [26] [27] [28] [29] [30] [17] [31] [32]

Ga–In Anderson and Ansara Hayes and Kubaschewski Rao Ansara et al. Rugg and Chart

Optimization Optimization Optimization Optimization Optimization

[34] [35] [36] [37] [38]

145

Table 2 Coefficients for the analytical description of the liquid binary systems Ga–Te, In–Te and Ga–In System: i, j:

Ga–Te 2,3

In–Te 2,3

Ga–In 0,0

DH 0A i B j (kJ mol 21 ) DS 0A i B j (J K 21 mol 21 ) C HA,B (kJ mol 21 ) C SA,B (J K 21 mol 21 ) C HA,A i B j (kJ mol 21 ) C SA,A i B j (J K 21 mol 21 ) C HB,A i B j (kJ mol 21 ) C SB,A i B j (J K 21 mol 21 )

2292.4 2173.7 – – 184.5 210.7 124.8 126.2

2248.8 2145.2 258.0 22.9 73.8 177.4 62.7 295.5

– – 4.5 21.2 – – – –

ism in our software. Therefore, thermodynamic functions of the melt were again optimized, based on literature data, the assumption of Ga 2 Te 3 associates in the liquid, and additional phase equilibrium data to describe the miscibility gap. The exothermic minimum of the excess enthalpies is found near the composition Ga 2 Te 3 at 239.5 kJ mol 21 (T 5 1173 K). These data were presented in a paper by Blachnik et al. [24].

3.2. The In–Te system This system contains the compounds In 4 Te 3 , InTe, In 3 Te 4 , In 2 Te 3 , In 3 Te 5 and In 2 Te 5 : InTe and In 2 Te 3 melt congruently, the other phases decompose peritectically. In 2 Te 3 and In 3 Te 5 exist in two modifications. A liquid miscibility gap appears between 6 and 28 mol% Te with a monotectic temperature of 691 K. Other relevant points are the three eutectics between InTe–In 3 Te 4 at T 5 922 K, In 2 Te 5 –Te at T 5 700 K and In 4 Te 3 –In at T 5 429 K. An overview of the thermodynamic investigations is given in Table 1 [25–32]. Optimized coefficients for the description of thermodynamic functions of the liquid system were ¨ given by Romermann [33] using all the available literature data. The minimum of the exothermic excess enthalpy is found near the composition In 2 Te 3 with 229.4 kJ mol 21 at 1173 K.

3.3. The Ga–In system The Ga–In system is a simple eutectic with a eutectic temperature of 288 K and a low terminal solubility of In in solid Ga. Because of its technical importance for semiconducting devices, the system has often been optimized

Table 3 Ternary interaction parameters of the association model of the system Ga–In–Te Ga–In–Te

kJ mol 21

C HGa,In 2 Te 3 C HIn,Ga 2 Te 3 C HGa 2 Te 3 ,In 2 Te 3

20.0 6.6 48.0

R. Blachnik, E. Klose / Journal of Alloys and Compounds 305 (2000) 144 – 152

146

Table 4 Heat effects DQ, experimental excess enthalpies according to Eq. (1) and ternary excess enthalpies according to Eq. (2) in the Ga–In–Te system at 1173 K of the sections Ga y In 12y –Te, and at 1073 and 973 K of the section Ga 0.5 In 0.5 –Te Starting amount n Ga y In 12y (mol)

Added amount n Te (mol)

Mole fraction x Te

Ga0.2 In0.8 –Te ( T 51173 K) 0.022779 0.001181 0.001223 0.002036 0.002147 0.002498 0.012675 0.000901 0.001071 0.001198 0.001743 0.002154 0.002433 0.014428 0.001050 0.001306 0.001296 0.001948 0.002190 0.001701 0.002234 0.014095 0.000900 0.001089 0.001384 0.000705

0 0.049 0.095 0.163 0.224 0.285 0 0.066 0.135 0.200 0.279 0.358 0.428 0 0.068 0.140 0.202 0.280 0.351 0.397 0.448 0 0.060 0.124 0.193 0.224

Ga0.4 In0.6 –Te ( T 51173 K) 0.013408 0.000507 0.001758 0.000814 0.002178 0.001928 0.001059 0.002431 0.015897 0.001118 0.001327 0.000880 0.001144 0.001574 0.001660 0.002131 0.002082 0.001602 0.016762 0.001142 0.000817 0.000903 0.001230 0.001806 0.002384 0.001329 0.002538

0 0.036 0.145 0.187 0.282 0.349 0.381 0.443 0 0.066 0.133 0.173 0.219 0.275 0.326 0.382 0.428 0.460 0 0.064 0.105 0.146 0.196 0.260 0.331 0.364 0.420

Heat effect DQ (J)

21.4 27.8 222.9 237.8 257.4 21.9 211.0 219.9 267.9 260.7 244.3 26.3 227.5 221.7 254.1 258.1 238.2 240.4 25.8 213.8 226.1 216.1

0.6 27.9 29.8 246.9 250.0 225.2 240.8 230.3 26.6 29.5 215.6 231.9 243.6 260.3 244.7 228.7 0.7 24.6 28.8 214.6 235.6 257.3 234.4 249.9

Experimental excess E enthalpy H exp (J mol 21 )

Ternary excess enthalpy H E (J mol 21 )

0 22246 24600 28415 212 328 216 640 0 23084 26849 210 943 218 113 224 047 228 273 0 23415 28238 212 026 217 868 223 093 226 200 229 295 0 23048 26700 211 178 213 350

722.8 21559 23946 27810 211 767 216 123 722.8 22409 26223 210 364 217 592 223 583 227 860 722.8 22741 27617 211 449 217 347 222 623 225 764 228 896 722.8 22368 26067 210 594 212 789

0 21572 26876 29322 215 922 221 010 223 317 227 132 0 24696 27923 210 088 212 776 216 493 220 297 224 631 227 713 229 593 0 22790 24850 27117 210 012 214 317 219 463 222 020 225 707

1066.2 2545 25964 28455 215 156 220 316 222 657 226 539 1066.2 23700 26999 29206 211 944 215 720 219 579 223 972 227 103 229 017 1066.2 21792 23896 26206 29155 213 529 218 750 221 342 225 089

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147

Table 4. Continued Starting amount n Ga y In 12y (mol)

Added amount n Te (mol)

Mole fraction x Te

Ga0.5 In0.5 –Te ( T 51173 K) 0.016678 0.000679 0.000829 0.000806 0.000859 0.000887 0.001017 0.001034 0.013660 0.000690 0.001539 0.001491 0.001187 0.001298 0.001164 0.012475 0.000832 0.000975 0.000871 0.001677 0.001497 0.001660 0.001871 0.001322 0.001502

0 0.039 0.083 0.122 0.160 0.196 0.233 0.268 0 0.048 0.140 0.214 0.264 0.312 0.350 1 0.062 0.126 0.177 0.259 0.319 0.376 0.429 0.462 0.495

Ga0.6 In0.4 –Te ( T 51173 K) 0.015920 0.001328 0.001327 0.001939 0.001959 0.001746 0.001567 0.014921 0.000748 0.000874 0.001567 0.001344 0.001897 0.001369 0.001146 0.000974 0.015828 0.001246 0.001311 0.000844 0.001349 0.001706 0.001576

0 0.077 0.143 0.224 0.292 0.343 0.383 0 0.048 0.098 0.176 0.233 0.301 0.343 0.375 0.399 0 0.073 0.139 0.177 0.231 0.290 0.337

Ga0.8 In0.2 –Te ( T 51173 K) 0.024789 0.001314 0.001719 0.001519 0.002337 0.002811

0 0.050 0.109 0.155 0.217 0.281

Heat effect DQ (J)

Experimental excess E enthalpy H exp (J mol 21 )

Ternary excess enthalpy H E (J mol 21 )

0 21297 23270 25167 27363 29477 211 682 213 795 0 21991 26519 210 777 214 131 217 562 220 347 0 22754 27414 210 141 215 723 220 056 224 028 227 526 229 447 231 148

1112.5 2228 22249 24190 26429 28582 210 829 212 981 1112.5 2932 25563 29903 213 313 216 797 219 624 1112.5 21711 26443 29225 214 898 219 299 223 334 226 891 228 848 230 585

2.6 20.9 25.9 216.9 230.6 240.1

0 23113 26300 210 952 215 524 219 568 222 724 0 21439 23708 27574 210 967 215 232 218 368 221 163 223 078 0 23084 26077 28064 211 262 215 168 218 778

1066.2 22129 25387 210 125 214 769 218 868 222 066 1066.2 2424 22746 26695 210 150 214 486 217 667 220 497 222 437 1066.2 22095 25159 27186 210 442 214 411 218 070

10.8 4.1 20.2 29.5 229.4

21817 24298 26377 29478 213 171

722.8 21131 23654 25766 28913 212 651

7.6 20.2 22.9 210.0 211.0 212.5 214.4 2.0 26.8 217.6 222.5 228.9 227.4 0.2 226.0 29.1 236.6 236.6 239.1 238.5 222.3 219.6

5.2 24.5 221.6 237.3 247.6 242.5 10.6 20.0 26.3 216.6 227.7 231.4 237.0 225.0

R. Blachnik, E. Klose / Journal of Alloys and Compounds 305 (2000) 144 – 152

148 Table 4. Continued Starting amount n Ga y In 12y (mol)

Added amount n Te (mol)

0.015563 0.001401 0.000701 0.001410 0.002134 0.001437 0.001913 0.001397 0.001404 0.001328 0.016791 0.000578 0.001041 0.001697 0.000719 0.001062 Starting amount n Te (mol)

Added amount n Ga y In 12y (mol)

Mole fraction x Te 0 0.083 0.119 0.184 0.266 0.313 0.366 0.400 0.431 0.457 0 0.033 0.088 0.165 0.194 0.233 Mole fraction x Te

Heat effect DQ (J)

Experimental excess enthalpy H Eexp (J mol 21 )

16.0 20.3 24.3 237.0 239.6 259.7 248.7 255.6 245.4

22718 24386 27564 213 010 216 748 221 327 224 443 227 495 229 856

10.3 7.5 22.1 22.3 24.3

2882 22933 26536 27954 29917

Heat effect DQ (J)

Ternary excess enthalpy H E (J mol 21 ) 722.8 22055 23749 26975 212 480 216 251 220 869 224 009 227 084 229 464 722.8 2184 22274 25932 27371 29362

Experimental excess enthalpy H Eexp (J mol 21 )

Ternary excess enthalpy H E (J mol 21 )

257.0 222.5 254.1 246.4 239.2

0 28493 214 462 224 741 230 731 230 697 0 27747 210 808 216 556 220 923 224 311

0 28411 214 324 224 520 230 443 230 372 0 27682 210 709 216 406 220 728 224 067

Te–Ga0.2 In0.8 ( T 51173 K) 0.012098 0.001552 0.001300 0.002489 0.002669 0.001898 0.010268 0.001009 0.000624 0.001052 0.001106 0.001457

1 0.886 0.809 0.694 0.602 0.550 1 0.910 0.863 0.793 0.730 0.662

Te–Ga0.4 In0.6 ( T 51173 K) 0.010160 0.001087 0.001523 0.001476 0.002424 0.001946 0.002171

1 0.903 0.796 0.713 0.609 0.546 0.489

246.6 279.2 282.4 2103.3 16.0 60.3

0 27295 216 514 223 964 231 411 230 671 227 968

0 27192 216 297 223 658 230 995 230 187 227 423

Te–Ga0.5 In0.5 ( T 51173 K) 0.011047 0.001771 0.001098 0.001301 0.001191 0.001904 0.002523 0.001070

1 0.862 0.794 0.726 0.673 0.603 0.530 0.504

289.2 265.0 274.9 264.3 252.6 29.4 30.2

0 211 512 217 875 224 088 228 650 231 968 230 677 229 409

0 211 359 217 646 223 784 228 286 231 527 230 154 228 857

Te–Ga0.6 In0.4 ( T 51173 K) 0.010336 0.001527 0.001188 0.001265 0.002149 0.001700 0.001782

1 0.872 0.792 0.722 0.628 0.570 0.519

278.7 272.7 274.2 297.7 12.2 59.0

0 210 797 218 333 224 761 231 696 231 102 228 271

0 210 660 218 112 224 465 231 300 230 643 227 758

269.2 261.1 2140.3 2106.1 20.4

R. Blachnik, E. Klose / Journal of Alloys and Compounds 305 (2000) 144 – 152

149

Table 4. Continued Starting amount n Ga y In 12y (mol)

Added amount n Te (mol)

Te–Ga0.8 In0.2 ( T 51173 K) 0.011925 0.001077 0.002111 0.002215 0.000988 0.002788 0.010796 0.000838 0.001364 0.002112 Starting amount n Ga y In 12y (mol)

Added amount n Te (mol)

Ga0.5 In0.5 –Te ( T 51073 K) 0.020180 0.000949 0.000987 0.001440 0.001396 0.014387 0.001460 0.000713 0.001301 0.001868 0.001787 0.001754 0.001856 0.001998 0.001190 0.000857 Starting amount n Te (mol)

Added amount n Ga y In 12y (mol)

Mole fraction x Te

1 0.917 0.789 0.688 0.651 0.565 1 0.928 0.831 0.714 Mole fraction x Te

0 0.045 0.088 0.143 0.191 0 0.092 0.131 0.195 0.271 0.331 0.382 0.427 0.470 0.492 0.507 Mole fraction x Te

Te–Ga0.5 In0.5 ( T 51073 K) 0.010766 0.000767 0.001362 0.001302 0.001772 0.0100520 0.000749 0.001069 0.002053 0.001929 0.001333 0.002093

1 0.933 0.835 0.758 0.674 1 0.934 0.853 0.731 0.645 0.596 0.533

Ga0.5 In0.5 –Te ( T 5973 K) 0.014073 0.000636 0.001457 0.001080 0.001009 0.001253 0.001902 0.001337

0 0.043 0.129 0.184 0.229 0.279 0.343 0.381

Heat effect DQ (J)

Experimental excess enthalpy H Eexp (J mol 21 )

Ternary excess enthalpy H E (J mol 21 )

240.2 255.5 2124.2

0 26579 218 940 229 577 232 675 234 854 0 25594 212 391 223 029

0 26519 218 787 229 351 232 423 234 539 0 25542 212 269 222 822

Heat effect DQ (J)

Experimental excess enthalpy H Eexp (J mol 21 )

Ternary excess enthalpy H E (J mol 21 )

0 21834 23779 26724 29484 0 24072 26074 29665 214 482 219 068 223 117 227 168 231 215 232 990 234 102

1112.5 2772 22764 25771 28584 1112.5 23062 25107 28769 213 671 218 324 222 430 226 531 230 624 232 425 233 554

Experimental excess enthalpy H Eexp (J mol 21 )

Ternary excess enthalpy H E (J mol 21 )

249.5 257.4 2129.5 2116.6 228.3 231.0

0 25342 214 383 223 181 230 723 0 26202 212 680 223 758 231 317 232 616 233 620

0 25268 214 199 222 912 230 361 0 26128 212 516 223 459 230 922 232 167 233 100

21.2 222.2 225.9 223.6 237.6 263.5 263.6

0 21799 26600 210 181 213 112 216 756 221 772 225 627

1112.5 2735 25632 29274 212 255 215 953 221 041 224 939

253.6 2138.1 2160.5 256.6 254.3

1.5 22.9 213.7 219.0 22.6 25.8 216.8 233.8 248.7 253.3 265.9 279.3 236.9 224.4 Heat effect DQ (J)

240.7 286.7 2108.1 2113.2

R. Blachnik, E. Klose / Journal of Alloys and Compounds 305 (2000) 144 – 152

150 Table 4. Continued Starting amount n Ga y In 12y (mol)

Added amount n Te (mol)

0.015353 0.001039 0.001674 0.001087 0.000882 0.001564 0.013746 0.001515 0.001038 0.002536 0.001878 Starting amount n Te (mol)

Added amount n Ga y In 12y (mol)

Te–Ga0.5 In0.5 ( T 5973 K) 0.010275 0.000522 0.001249 0.001327 0.000909 0.010878 0.001347 0.001576 0.001801 0.001972 0.002231

Mole fraction x Te 0 0.063 0.150 0.198 0.234 0.289 0 0.099 0.157 0.270 0.336 Mole fraction x Te

1 0.952 0.853 0.768 0.719 1 0.890 0.788 0.697 0.619 0.549

Heat effect DQ (J) 213.1 224.3 224.5 217.9 247.4 225.5 236.4 279.2 270.7 Heat effect DQ (J)

231.7 279.0 281.6 273.3 281.2 2112.3 2145.8 2103.7 231.9

(Table 1) [34–38] and thermodynamic investigations have frequently been performed. For the description of thermodynamic functions of the liquid, the data set of the most recent assessment by Anderson [34] was used. H E data have a maximum of about 1.0 kJ mol – 1 at x In 5 0.5 with almost no temperature dependence.

Experimental excess enthalpy H Eexp (J mol 21 )

Ternary excess enthalpy H E (J mol 21 )

0 23324 28050 211 129 213 287 217 404 0 25622 210 034 218 246 223 613

1112.5 22282 27104 210 237 212 434 216 613 1112.5 24620 29096 217 434 222 874

Experimental excess enthalpy H Eexp (J mol 21 )

Ternary excess enthalpy H E (J mol 21 )

0 24143 212 856 220 157 225 598 0 29393 219 306 229 303 234 717 235 229

0 24089 212 692 219 899 225 285 0 29270 219 071 228 966 234 293 234 727

functions of the liquid binary tellurium alloys were described using the association model of Sommer [10,11]. The formation of short-range ordered Ga 2 Te 3 and In 2 Te 3

4. The ternary system Ga–In–Te The GaTe–InTe section of the system was investigated using DTA and X-ray methods by Kuliev et al. [39] and is eutectic. Wooley et al. [40] investigated the section Ga 2 Te 3 –In 2 Te 3 using thermal and X-ray methods. It was found that a complete solid solution occurs throughout the whole composition range, but that the section is not quasibinary.

5. Analytical descriptions

5.1. Binary systems Calculation of the thermodynamic functions was carried out by means of the software ‘‘BINGSS’’ and ‘‘BINFKT’’ developed by Lukas et al. [41–43]. The thermodynamic

Fig. 1. Measured and calculated excess enthalpies of the ternary system Ga–In–Te at T 5 1173 K for the section Ga y In 12y Te with y 5 0.4. Different Symbols represent the different series of measurements.

R. Blachnik, E. Klose / Journal of Alloys and Compounds 305 (2000) 144 – 152

Fig. 2. Measured and calculated excess enthalpies of the ternary system Ga–In–Te at T 5 1173 K for the section Ga y In 12y Te with y 5 0.6. Different Symbols represent the different series of measurements.

associates in the melt was assumed. The thermodynamic functions of the limiting Ga–In system were expressed by a Redlich–Kister formalism. The resulting coefficients, which were fitted to the experimental data by a least squares method, are given in Table 2. The SGTE description of the temperature dependence of the Gibbs energy function for the elements Ga and In was taken from Dinsdale [44] and for Te from Feutelais et al. [45].

5.2. Ternary system For the analytical description of the system Ga–In–Te the association model was used with three additional

151

Fig. 3. Projection of the calculated isoenthalpies (kJ mol 21 ) on the Gibbs triangle in the Ga–In–Te system at T 5 1173 K.

parameters for interactions between the associates Ga 2 Te 3 and In 2 Te 3 and between these associates and the nonconstituent elements. The procedure is analogous to the calculation of the ternary excess enthalpies in the Ge–Sn– Te system reported by Schlieper and Blachnik [46]. The parameters obtained by a numerical optimization are given in Table 3.

6. Results The experimental enthalpies H Eexp of the reaction (1 2 x)Ga y In 12y (liq) 1 xTe(liq) → Ga y( 12x) In ( 12y)(12x) Te x (liq)

Fig. 4. Temperature dependence for the minima of the ternary excess enthalpies of liquid Ga 0.5 In 0.5 –Te alloys at x Te 5 0.6.

(1)

R. Blachnik, E. Klose / Journal of Alloys and Compounds 305 (2000) 144 – 152

152

and the ternary excess enthalpies H E of the reaction (1 2 x)yGa(liq) 1 (1 2 x)(1 2 y)In(liq) 1 xTe(liq) → Ga y( 12x) In ( 12x)(12y) Te x (liq)

(2)

are presented in Table 4 and in Figs. 1 and 2 for two sections. A projection of the isoenthalpic lines on the Gibbs triangle (Fig. 3) shows that the exothermic values decrease smoothly from the maximum at Ga 2 Te 3 to the corners of the ternary system. The H E values of the ternary system were first calculated from the H E data of the constituent binaries without considering ternary interaction. However, the enthalpy curves of the ternary mixtures were not well reproduced (Figs. 1 and 2, dashed line). The best fit was obtained when the ternary interactions Ga 2 Te 3 ↔In, In 2 Te 3 ↔Ga and Ga 2 Te 3 ↔In 2 Te 3 (Figs. 1 and 2, full line) were assumed. The results for the section Ga 0.5 In 0.5 –Te alloys show that the excess enthalpies are temperature dependent. The values decrease in the range from 973 to 1173 K more with increasing temperature than in most other tellurium systems (Fig. 4). This effect is due to the dissociation of associates at higher temperatures.

Acknowledgements The authors wish to express their gratitude to the Fonds der Chemie and the Deutsche Forschungsgemeinschaft for financial support. The authors would like to express their thanks to ‘‘Ingal Stade GmbH’’ for the metallic gallium.

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