Enthalpies of mixing of liquid Ga-In and Cu-Ga-In alloys

Journal of Molecular Liquids 293 (2019) 111543

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Enthalpies of mixing of liquid Ga-In and Cu-Ga-In alloys Dominika Jendrzejczyk-Handzlik ⁎, Piotr Handzlik Faculty of Non-Ferrous Metals, AGH University of Science and Technology in Krakow, 30 Mickiewicza Ave., 30-059 Krakow, Poland

a r t i c l e

i n f o

Article history: Received 21 May 2019 Received in revised form 6 August 2019 Accepted 7 August 2019 Available online 09 August 2019 Keywords: Calorimetry Ga-In alloys Cu-Ga-In alloys Thermochemistry Heat of mixing

a b s t r a c t A literature overview of Cu-Ga-In system shows that the information about the liquid phase of this system does not exist. Therefore, using MHTC 96 Setaram high temperature drop calorimeter, partial and integral enthalpies of mixing of liquid alloys were determined at first in the binary Ga-In system and next in the ternary Cu-Ga-In system. The ternary liquid alloys were investigated along two cross-sections at three temperatures: 1123 K, 1273 K and 1423 K. Experimental data were used to find ternary interaction parameters by applying the Redlich–Kister–Muggianu model for substitutional solutions, and consequently providing a full set of parameters describing the concentration dependence of the enthalpy of mixing. The experimental data indicate that the heat of mixing in this ternary system is temperature dependent, at least in the measured temperature range. © 2019 Published by Elsevier B.V.

1. Introduction During the last years, one of the most interesting materials applied in solar cells is thin-film material Cu(In,Ga)Se2 (CIGS). The CIGS technology in commercial modules has been on the market for several years. This material has recently reached a power conversion efficiency of 22.6% for small-area solar cells (laboratory-scale) [1]. This value exceeds that of multicrystalline silicon (21.3%) and is comparable with CdTe and perovskite polycrystalline material systems (both of them at 22.1%) [2]. However, commercial CIGS modules typically have efficiencies between 12% and 14% [3]. Nevertheless, there are still open questions concerning basic physical and chemical properties. For a proper preparation of the solar cell materials it is important to be able to control independently each element during deposition. To fulfill this condition, it is necessary to know thermodynamic properties and phase equilibria in the given quaternary metallic system. The Cu-Ga-In system is of interest in developing CuInxGa1-xSe2 based solar cell technologies. Binary phase diagrams Cu-Ga, Cu-In and Ga-In are well known and described in the literature. The recent thermodynamic assessments of these three binary systems based on many experimental results were published by following authors: for Cu-Ga system by JendrzejczykHandzlik et al. [4], for Cu-In system by Cao et al. [5] and for Ga-In system by Reddy and Hajra [6]. In the case of the Cu-Ga-In system, the situation is slightly different. The information about this ternary system, as well as its properties are missing in the monographs of Villars et al. [7] and Petzow and Effenberg [8]. In the literature one can find only three experimental works related to this ternary system. Purwins et al. [9]

⁎ Corresponding author. E-mail address: [email protected] (D. Jendrzejczyk-Handzlik).

https://doi.org/10.1016/j.molliq.2019.111543 0167-7322/© 2019 Published by Elsevier B.V.

carried out the measurements from which the phase relations in the Cu-Ga-In system at 623 K were determined. Measurements were carried out on eight samples with chosen compositions. However, it is puzzling that the samples after being heated from room temperature up to 623 K were held at this temperature only for 2 . Next, the samples were analyzed by X-ray diffraction method. It's hard to say that in these samples the equilibrium state was reached. Next, the Cu-Ga-In system was studied by Kim et al. [10]. But in this work only one sample with chosen composition Cu41Ga19In40 was analyzed (inductively coupled plasma atomic emission spectroscopy ICP-AES, differential thermal analysis DTA and X-ray diffraction). The phase equilibria at 723 K in this ternary system were determined. Finally, Muzillo et al. [11] carried out the DTA/ DSC and X-ray diffraction measurements of the Cu-Ga-In system. Similarly like in the previous studies, the number of samples which were tested was limited only four samples which were studied by DTA/DSC and X-ray diffraction methods. Two of them (Cu71Ga15In14 and Cu82Ga9In9) were investigated by using DTA measurements which were carried out with heating/cooling rates 5 and 10 K/min. Additionally, those samples were annealed at 591 K, 711 K and 950 K. After annealing they were studied by using X-ray diffraction method. The other two samples (Cu476Ga95In429 and Cu55Ga18In27) were investigated by using DSC measurements. From the results of DTA/DSC measurements the temperatures of phase transformations were determined. Finally, the Cu-Ga-In phase diagram was calculated by applying Calphad method. In this calculation information taken from binary systems together with experimental data [9–11] were used. However, in this description of the Cu-Ga-In ternary system there is a lack of information about liquid phase and experimental data about phase equilibria are scarce. In this situation a description of this system is incomplete, and it is difficult to interpret the evolution of phase equilibria with temperature change.

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D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

Thus, to gain the necessary knowledge about the phase diagram and melting behavior of the Cu-Ga-In system, new experimental data are needed. The present work refers to the high-temperature calorimetric measurements, which were carried out on the liquid phase at 1123 K, 1273 K and 1423 K, in order to look for the possible mixing enthalpy temperature dependence. Next, the data obtained for the liquid phase were described by Redlich-Kister-Muggianu polynomial [12]. 2. Literature survey In the literature, one can find a number of results concerning calorimetric measurements conducted on the binary systems: Cu-Ga, Cu-In and Ga-In at various temperatures. They are summarized as follows: 2.1. Cu-Ga system The enthalpy of mixing of the liquid copper gallium system was determined twice. At first, the ΔHmix of liquid Cu-Ga alloys was investigated by Predel and Stein [13] at the single temperature 1423 K, and in the whole concentration range by using high temperature solution calorimeter. Next, the integral enthalpies of mixing of Cu-Ga liquid alloys were determined at three temperatures 1123 K, 1273 K and 1423 K by Jendrzejczyk-Handzlik et al. [14] in order to look for the possible mixing enthalpy temperature dependency. Measurements were carried out using high-temperature drop calorimeter, in the composition range from 0.188 to 0.921 x(Ga). All experimental results obtained from the calorimetric method show negative values of the enthalpy of mixing in the liquid phase. The enthalpy of mixing of the liquid Cu-Ga alloys depends on temperature and experimental results from works [13,14] are in good agreement. 2.2. Cu-In system There are several published papers in which the data of the enthalpy of mixing of liquid copper indium were given. The enthalpy of mixing of this liquid binary system was measured using different types of calorimeters. Using solution calorimeter Kleppa [15] determined the enthalpy of mixing at 723 K within the composition range from 0.211 to 0.9778 x(In). Itagaki and Yazawa [16] measured the enthalpy of mixing at 1373 K in the whole composition range of indium using an adiabatic calorimeter. Kang et al. [17] determined the enthalpy of mixing of liquid copper indium alloys in the temperature range from 903 K to 1348 K. The measurements were carried out in the whole composition range of indium using reaction calorimeter. Next, Knott and Mikula [18] reported enthalpy of mixing in the liquid phase in this binary system at four temperatures: 973 K, 1073 K, 1173 K and 1273 K in the composition range from 0.2 to 0.87 x(In) by using Calvet-type calorimeter. All experimental results obtained from the calorimetric method show negative values and the enthalpy of mixing depends on temperature in the liquid phase. The experimental results obtained by Kleppa [15], Itagaki and Yazawa [16], Kang et al. [17] at 903 K, 955 K, 997 K, 1033 K and Knott and Mikula [18] are compatible with each other. But the results obtained by Kang et al. [17] at 1182 K, 1229 K, 1283 K and 1348 K are more positive than with values reported in [16,18]. 2.3. Ga-In system The enthalpy of mixing of the liquid gallium indium system was determined by several authors. Using high-temperature calorimeter Bros [19,20] measured enthalpy of mixing from 400 to 743 K in the whole composition range of indium. Predel and Stein [21] measured enthalpies of mixing at 743 K in the whole composition range of indium using hightemperature calorimeter. Next, Mechkovskii and Vecher [22] reported the enthalpy of mixing at 443 K. Ansara et al. [23] derived enthalpy of mixing at 995 K using high-temperature Calvet-type calorimeter in the composition range from 0.069 to 0.665 x(In). Additionally, in this

work the equation which describes the enthalpy of mixing in the liquid Ga-In system is given. All experimental results obtained from the calorimetric method show positive values. Small differences between published data obtained in the temperature range from 400 to 743 K show that the enthalpy of mixing does not depend on temperature in the liquid Ga-In system. In the present work, the enthalpy of mixing in liquid Ga-In system was measured at 1123 K, 1273 K and 1423 K. These measurements were done to determine the value of the enthalpy of mixing for the alloy of chosen composition Ga0.5In0.5 at chosen temperatures. These values will be further used in the present work during the investigations of the enthalpy of mixing in ternary Cu-Ga-In system. 3. Experimental procedure In the present work, the problem of temperature dependence of the enthalpy of mixing in liquid Cu-Ga-In systems was considered. Measurements were done at three temperatures: 1223 K, 1323 K and 1423 K. Additionally, the enthalpy of mixing for liquid Ga-In system was determined at these temperatures. Calorimetric measurements were done by using the MHTC hightemperature drop calorimeter from Setaram, France. It is the calorimeter with a thermopile of 20 thermocouples and a graphite tube resistance furnace working up to 1723 K. Control and data evaluation is performed using the SetSoft software provided by the manufacturer. To prevent oxidation of the samples, measurements were conducted in the atmosphere of flowing argon (approx. 20 cm3/min). All measurements were carried out in an alumina crucible. Samples of pure metals (Cu, In) were introduced into a bath of pure liquid gallium or into binary alloys (Cu-Ga, In-Ga). All samples were weighed using Sartorius balance type Cubis with the accuracy equal 10−5 g. Every bath (Ga, Cu-Ga and In-Ga) was formed by placing the weighed pure metals in an alumina crucible, which was then inserted into the calorimetric cell in the furnace. At the end of every series of metallic samples additions the calorimeter was calibrated by using pieces of α-Al2O3 (min 30 mg each). Random errors as well as systematic errors of measurements depend on the construction of the calorimeter, calibration procedure and signal integration. Considering many calibration measurements done by dropping NIST standard sapphire, the standard deviation can be estimated to be less than ±1.5% for the MHTC instrument. The systematic errors are mainly caused by parasitic heat flows, base line problems at signal integration, and dropping and mixing problems. One can estimate that the overall error connected with a specific calorimeter is ± 300 J·mol−1 for the MHTC calorimeter. Until the signal of the recorded heat effect returned to the base line, it took 20 min after α-Al2O3 addition. The signals which were obtained during calorimetric measurements were recorded and integrated. All the substances used in the experiments are listed in Table 1 together with their purity and manufacturers. At first, the enthalpy of mixing in the liquid binary Ga-In alloys was determined at three temperatures 1123 K, 1273 K and 1423 K. The metallic samples of In from 49 to 104 mg, were prepared and introduced into pure Ga bath (approximately 0.5 g). Pieces of indium were introduced into the bath of gallium from room temperature by using a manual drop device. After each series, pieces of standard α-Al2O3 were dropped in order to perform calibration. The system required 20 min after the addition of indium and standard α-Al2O3 until the signal of

Table 1 Materials used in the experiments. Manufacturer

Substance

Purity [wt%]

Alfa Aesar Alfa Aesar Alfa Aesar Air Products NIST

Cu Ga In Ar gas Sapphire rods

99.99 99.99 99.99 99.9999 99.95

D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

the recorded heat effect returned to the base line. Next, the enthalpy of mixing in the liquid ternary Cu-Ga-In alloys was determined at three temperatures 1123 K, 1273 K and 1423 K. The composition was changed in the following way: • along cross-section x(Cu)/x(Ga) = the mole fraction of In varied from 0 to 0.657 by dropping pieces of pure In (53–122 mg) into a liquid binary Cu-Ga bath (approximately 0.6 g) • along cross-section x(Ga)/x(In) = 1:1 the mole fraction of Cu varied from 0 to 0.8724 by dropping pieces of pure Cu (73–153 mg) into a liquid binary Ga-In bath (approximately 0.6 g)

1423 K was obtained from the calorimetric measurements which are also presented in this work. In the case of binary Cu-Ga alloy for chosen composition x(Cu) = 0.5, the starting data of the ΔmixHm at three temperatures 1123 K, 1273 K and 1423 K were taken from our previous work [14]. The measured enthalpy (integrated heat flux at constant pressure) in binary Ga-In system and ternary Cu-Ga-In system can be expressed by the relationship:
 ΔH Reaction ¼ ΔH Signal  H iT D →T M ⋅ni ð1Þ P Δmix H m ¼

The obtained signals were recorded and integrated. The initial value of the enthalpy of mixing ΔmixHm in the binary liquid Ga-In alloy for chosen composition x(In) = 0.5 at temperatures: 1123 K, 1273 K and

3

ΔH Reaction P nbath þ ni

ð2Þ

where ni is the number of moles of either indium or copper and nbath stands for the molar amount of gallium or binary systems

Table 2 Partial and integral enthalpies of mixing of liquid Ga-In alloys at 1123 K, 1273 K and 1423 K. Mole droped

Drop enthalpy

Partial molar enthalpy of mixing

Integral molar enthalpy of mixing

nIn [mol·10−3]

ΔHsignal [J]

x(In)

x(Ga)

Δmix H In [J·mol−1]

ΔmixHm [J·mol−1]

u(ΔmixHm) [J·mol−1]

T = 1123 K: starting amount nGa = 85.38·10−4 mol; calibration constant k = (27.65·10−4 ± 0.24·10−4)[J·μVs−1]; TD = 298 K; TM = 1123 K; HTInD→TM=27,191 [J·mol−1] [24] 0.550 30,147 0.0606 3040 0.9394 184 16 0.575 30,786 0.1164 3679 0.8836 392 31 0.630 30,289 0.1705 3182 0.8295 563 45 0.633 31,016 0.2186 3909 0.7814 757 58 0.672 28,823 0.2638 1716 0.7362 812 69 0.745 29,158 0.3082 2051 0.6918 887 80 0.745 29,466 0.3476 2359 0.6524 971 90 0.766 28,992 0.3837 1885 0.6163 1021 99 0.786 28,519 0.4168 1412 0.5832 1042 107 1.609 28,358 0.4745 1251 0.5255 1063 121 0.829 28,598 0.5000 1491 0.5000 1084 127 0.900 27,800 0.5251 693 0.4749 1064 133 0.906 27,931 0.5478 824 0.4522 1053 138 −4 −4 −4 −1 T = 1273 K: starting amount nGa = 89.08·10 mol; calibration constant k = (27.34·10 ± 0.20·10 )[J·μVs ]; TD = 298 K; TM = 1273 K; HTInD→TM=31,556 [J·mol−1] [24] 0.430 37,817 0.0461 4721 0.9539 218 13 0.466 37,527 0.0914 4431 0.9086 418 25 0.474 37,016 0.1333 3920 0.8667 579 36 0.489 36,116 0.1727 3020 0.8273 690 47 0.496 34,355 0.2091 1259 0.7909 715 56 0.518 37,026 0.2439 3930 0.7561 857 65 0.535 36,041 0.2767 2945 0.7233 947 74 0.564 34,533 0.3084 1437 0.6916 969 82 0.566 35,293 0.3375 2197 0.6625 1020 89 0.578 35,158 0.3648 2062 0.6352 1063 96 1.224 35,045 0.4158 1949 0.5842 1134 109 0.628 34,445 0.4389 1349 0.5611 1143 115 0.628 35,072 0.4602 1976 0.5398 1175 120 0.640 34,611 0.4804 1515 0.5196 1187 125 0.673 34,164 0.5000 1068 0.5000 1183 130 0.689 34,252 0.5186 1156 0.4814 1182 134 0.703 34,053 0.5362 957 0.4638 1174 138 T = 1423 K: starting amount nGa = 91.10·10−4 mol; calibration constant k = (28.34·10−4 ± 0.22·10−4)[J·μVs−1]; TD→T −1 TD = 298 K; TM = 1423 K; HIn M=35,915 [J·mol ] [24] 0.621 41,106 0.0638 5191 0.9362 331 20 0.633 40,520 0.1210 4605 0.8790 592 38 0.684 38,635 0.1754 2720 0.8246 724 54 0.688 38,653 0.2237 2738 0.7763 842 69 0.698 38,846 0.2673 2931 0.7327 959 82 0.704 38,585 0.3066 2670 0.6934 1051 94 0.710 38,245 0.3422 2330 0.6578 1117 104 0.715 37,884 0.3745 1969 0.6255 1158 113 0.725 37,874 0.4041 1959 0.5959 1196 122 0.725 37,690 0.4311 1775 0.5689 1223 130 0.733 37,721 0.4560 1806 0.5440 1248 137 0.734 37,555 0.4788 1640 0.5212 1265 143 0.740 37,355 0.5000 1440 0.5000 1272 149 0.763 37,138 0.5201 1223 0.4799 1270 155 0.774 37,074 0.5389 1159 0.4611 1265 160 0.807 36,882 0.5570 967 0.4430 1254 165 0.821 36,688 0.5740 773 0.4260 1235 170

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D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

(copper gallium or indium gallium) which was already present in the crucible. ΔHSignal is the total heat effect recorded after each drop of metal (Cu or In) which was introduced into the bath of gallium or binary system, TD is the drop temperature, and TM is the calorimeter temperature of the respective measurement in Kelvin. The HTi D→TM is the enthalpy of pure metals (Cu or In) which was obtained from Barin and Knacke [24]. Because of the rather small masses added, the partial enthalpies of indium and copper can be directly given as: Δmix H i ¼

ΔHReaction ni

ð3Þ

After these experiments the microstructure of the sample was checked by optical microscope in order to verify the complete dissolution of the metallic pieces into the bath. Finally, compositions of CuGa-In alloys which were obtained after calorimetric measurements were confirmed by XRF method. The difference between the composition of alloys calculated from weighed metals and determined from the XRF method was found to be negligible. 4. Results and discussion 4.1. Experimental data In case of binary liquid system, the enthalpy of mixing in the liquid Ga-In system was measured at three temperatures 1123 K, 1273 K and 1423 K in three separate experiments. At each temperature one experimental series was performed. All experimental results are summarized in Table 2 and shown in Fig. 1. The Table 2 provides information about: initial amounts, the number of moles of pure metals dropped into the liquid alloys, calorimeter constant, partial molar enthalpies of mixing, integral enthalpies of mixing and standard uncertainty. The experimental data obtained at these three temperatures show positive values in the whole range of gallium concentration in which measurements were done. The maximum value of the enthalpy of mixing in each case is locate about at the composition x(Ga) = 0.50. The values from the present work are in good agreement with the literature data [19–23] and they create a consistent description of the liquid phase in this binary system. In the examined temperature range from

400 K to 1423 K, the enthalpy of mixing in liquid Ga-In system does not exhibit temperature dependence. Similarly to the previous liquid metallic system, the enthalpy of mixing in the liquid Cu-Ga-In system was measured at three temperatures 1123 K, 1273 K and 1423 K along two chosen cross-sections x (Cu)/x(Ga) = 1:1 and x(In)/x(Ga) = 1:1 in twelve separate experiments. All experimental results are summarized in Tables 3 and 4 and they are shown in Figs. 4 and 5. The starting values of the enthalpy of mixing in the binary Cu-Ga system, necessary for the evaluation of results of the measurements in ternary system were taken from the previous work [14]. These values are following: for cross-section where x (Cu)/x(Ga) = 1:1, the enthalpies of mixing for Cu0.5Ga0.5 alloys at chosen temperatures are equal ΔmixHm = −8943 J·mol−1 for x(Cu) = 0.5000 at 1123 K, ΔmixHm = −8320 J·mol−1 for x(Cu) = 0.4960 at 1273 K and ΔmixHm = −8039 J·mol−1 for x(Cu) = 0.5000 at 1423 K. The slight differences seen between mole fractions copper and initial values given in Table 4 are negligible, and these values can be used for ΔmixHm calculations in the liquid ternary system. For cross-section where x(Ga)/x(In) = 1:1, the enthalpies of mixing for Ga0.5In0.5 alloy at chosen temperatures are equal to ΔmixHm = 1084 J·mol−1 for x(In) = 0.5000 at 1123 K, ΔmixHm = 1183 J·mol−1 for x(In) = 0.5000 at 1273 K and ΔmixHm = 1272 J mol−1 for x(In) = 0.5000 at 1423 K. Experimental results for enthalpy of mixing in the liquid Cu-Ga-In system, which are obtained for the cross-section x(Ga)/x(In) = 1:1 at three temperatures 1123 K, 1273 K and 1423 K, show negative values in the whole range of x(Cu) mole fraction in which the experiments were performed. The enthalpy of mixing minimum at 1123 K is equal to about. −8600 J ·mol−1 in the concentration range 0.7484 b x(Cu) b 0.7492 while at 1273 K is equal to about −7600 J·mol−1 in the concentration range 0.7156 b x(Cu) b 0.7477 and at 1423 K is equal to about −6400 J·mol−1 in the concentration range 0.7043 b x(Cu) b 0.7078. This is in agreement with the fact that in the binary Cu-Ga system, a minimum of ΔmixHm is located at x(Cu) about 0.7 which is probably caused by the existence of γ-Cu9In4 phase in the solid state. Similarly like in previous case, in the binary Cu-In system, a minimum of ΔmixHm is located at x(Cu) about 0.75 which is probably caused by the existence of γ phase. The data of the enthalpy of mixing in the liquid Cu-Ga-In system along the cross-section x(Cu)/x(Ga) = 1:1 do not show the minimum value. In the case of In addition from Cu-Ga side, the enthalpy of

Fig. 1. Integral enthalpies of mixing of liquid Cu-Ga alloys; standard states: pure liquid components.

D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

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Table 3 Partial and integral enthalpies of mixing of liquid Cu-Ga-In alloys at 1123 K, 1273 K and 1423 K, cross-section x(Cu)/x(Ga) = 1:1, standard states: pure liquid components. Mole droped

Drop enthalpy

Partial molar enthalpy of mixing

Integral molar enthalpy of mixing

nIn [mol·10−3]

ΔHsignal [J]

x(In)

x(Cu)

Δmix H In [J·mol−1]

x(Ga)

ΔmixHm [J·mol−1]

u(ΔmixHm) [J·mol−1]

T = 1123 K series I: starting amount nCu = 45.32·10−4 mol and nGa = 45.32·10−4 mol; calibration constant k = (29.66·10−4 ± 0.35·10−4) [J·μVs−1]; TD = 298 K; TM = 1123 K; HTInD→TM=27,191 [J·mol−1] [24] 0 0 0 0 0.5000 0.5000 −8943 120 0. 522 40,700 0.0545 13,509 0.4728 0.4728 −7720 26 0. 551 38,364 0.1058 11,173 0.4471 0.4471 −6693 49 0. 635 37,059 0.1585 9868 0.4207 0.4207 −5717 72 0. 686 33,629 0.2089 6438 0.3956 0.3956 −4989 92 0. 693 32,763 0.2540 5572 0.3730 0.3730 −4387 108 0. 702 31,578 0.2948 4387 0.3526 0.3526 −3908 123 0. 704 30,726 0.3314 3535 0.3343 0.3343 −3521 135 0. 705 33,303 0.3645 6112 0.3178 0.3178 −3045 148 0. 737 31,877 0.3957 4686 0.3022 0.3022 −2665 159 0. 776 28,009 0.4254 818 0.2873 0.2873 −2494 168 0. 798 30,385 0.4531 3194 0.2734 0.2734 −2220 177 0. 736 30,410 0.4764 3219 0.2618 0.2618 −1989 185 0. 833 28,706 0.5004 1515 0.2498 0.2498 −1828 192 0. 824 28,861 0.5221 1670 0.2389 0.2389 −1676 198 0. 854 28,847 0.5427 1656 0.2286 0.2286 −1532 204 0.862 28,648 0.5618 1457 0.2191 0.2191 −1408 210 0. 907 28,241 0.5802 1050 0.2099 0.2099 −1305 215 T = 1123 K series II: starting amount nCu = 45.41·10−4 mol and nGa = 45.41·10−4 mol; calibration constant k = (30.11·10−4 ± 0.34·10−4) [J·μVs−1]; TD = 298 K; TM = 1123 −1 TD→T K; HIn M=27,191 [J·mol ] [24] 0 0 0 0 0.5000 0.5000 −8943 120 0. 467 42,251 0.0489 15,060 0.4755 0.4755 −7769 23 0. 479 38,791 0.0943 11,600 0.4528 0.4528 −6844 43 0. 493 34,581 0.1368 7390 0.4316 0.4316 −6177 60 0. 509 36,363 0.1766 9172 0.4117 0.4117 −5469 76 0. 542 36,221 0.2152 9030 0.3924 0.3924 −4790 91 0. 556 33,078 0.2512 5887 0.3744 0.3744 −4300 104 0. 573 34,272 0.2849 7081 0.3575 0.3575 −3787 117 0. 610 31,132 0.3177 3941 0.3411 0.3411 −3433 128 0. 626 29,942 0.3484 2751 0.3258 0.3258 −3155 137 0. 641 31,900 0.3770 4709 0.3115 0.3115 −2809 147 0. 665 30,499 0.4042 3308 0.2979 0.2979 −2542 156 0. 702 30,629 0.4304 3438 0.2848 0.2848 −2279 164 0. 709 29,324 0.4547 2133 0.2727 0.2727 −2091 171 0. 740 29,874 0.4779 2683 0.2611 0.2611 −1888 178 0. 758 29,371 0.4997 2180 0.2502 0.2502 −1718 185 0. 763 27,896 0.5199 705 0.2401 0.2401 −1620 190 0. 794 28,764 0.5392 1573 0.2304 0.2304 −1492 195 0. 828 28,383 0.5578 1192 0.2211 0.2211 −1384 200 T = 1273 K series I: starting amount nCu = 45.46·10−4 mol and nGa = 45.46·10−4 mol; −4 4 −1 −1 TD→T calibration constant k = (27.93·10 ± 0.20·10– ) [J·μVs ]; TD = 298 K; TM = 1273 K; HIn M=31,556 [J·mol ] [24] 0 0 0 0 0.5000 0.5000 −8320 160 0. 567 46,387 0.0000 14,834 0.4706 0.4706 −6961 19 0. 590 42,624 0.0587 11,071 0.4436 0.4436 −5923 36 0. 603 39,852 0.1129 8299 0.4189 0.4189 −5133 50 0.635 39,621 0.1622 8068 0.3958 0.3958 −4403 63 0. 643 38,646 0.2085 7093 0.3748 0.3748 −3793 74 0. 659 37,169 0.2505 5616 0.3555 0.3555 −3309 84 0. 686 36,769 0.2891 5216 0.3374 0.3374 −2875 93 0. 693 36,047 0.3253 4494 0.3209 0.3209 −2514 101 0.708 34,321 0.3583 2768 0.3056 0.3056 −2263 108 0.728 34,514 0.3888 2961 0.2913 0.2913 −2019 115 0. 742 35,413 0.4173 3860 0.2781 0.2781 −1752 121 0. 776 32,670 0.4438 1117 0.2655 0.2655 −1622 126 0. 782 34,123 0.4690 2570 0.2539 0.2539 −1439 131 0. 793 33,460 0.4922 1907 0.2431 0.2431 −1297 136 0. 802 33,645 0.5137 2092 0.2331 0.2331 −1158 140 0. 813 33,162 0.5337 1609 0.2238 0.2238 −1047 144 0. 824 33,052 0.5524 1499 0.2151 0.2151 −948 148 0. 831 32,844 0.5698 1291 0.2069 0.2069 −863 151 T = 1273 K series II: starting amount nCu = 45.46·10−4 mol and nGa = 45.46·10−4 mol; TD→T −4 −4 −1 −1 calibration constant k = (27.58·10 ± 0.20·10 ) [J·μVs ]; TD = 298 K; TM = 1273 K; HIn M=31,556 [J·mol ] [24] 0 0 0 0 0.5000 0.5000 −8320 160 0. 583 44,573 0.0603 13,020 0.4699 0.4699 −7034 19 0. 633 42,546 0.1180 10,993 0.4410 0.4410 −5927 37 0. 646 40,960 0.1700 9407 0.4150 0.4150 −5023 52 0.0768 39,420 0.2244 7867 0.3878 0.3878 −4178 68 0. 738 40,869 0.2703 9316 0.3648 0.3648 −3379 81 0. 849 36,465 0.3169 4912 0.3416 0.3416 −2850 93 0. 876 35,665 0.3590 4112 0.3205 0.3205 −2420 103 (continued on next page)

6

D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

Table 3 (continued) Mole droped

Drop enthalpy

Partial molar enthalpy of mixing

Integral molar enthalpy of mixing

nIn [mol·10−3]

ΔHsignal [J]

x(In)

x(Cu)

Δmix H In [J·mol−1]

x(Ga)

0. 718 34,974 0.3899 3421 0.3050 0.3050 0.766 34,255 0.4197 2702 0.2901 0.2901 1.009 34,263 0.4549 2710 0.2726 0.2726 0. 880 33,748 0.4822 2195 0.2589 0.2589 0. 957 34,159 0.5089 2606 0.2455 0.2455 0. 953 34,607 0.5330 3054 0.2335 0.2335 0.903 31,743 0.5537 190 0.2232 0.2232 0.933 32,239 0.5732 686 0.2134 0.2134 0. 998 33,328 0.5923 1775 0.2038 0.2038 −4 −4 T = 1423 K series I: starting amount nCu = 45.01·10 mol and nGa = 45.01·10 mol; calibration constant k = (29.89·10−4 ± 0.20·10−4) [J·μVs−1]; TD = 298 K; TM = 1423 K; HTInD→TM=35,915 [J·mol−1] [24] 0 0 0 0 0.5000 0.5000 0. 665 50,593 0.0688 14,678 0.4656 0.4656 0. 804 50,687 0.1403 14,772 0.4299 0.4299 0. 891 46,714 0.2077 10,799 0.3961 0.3961 0. 995 44,784 0.2715 8869 0.3642 0.3642 0. 577 39,163 0.3040 3248 0.3480 0.3480 0. 928 40,042 0.3506 4127 0.3247 0.3247 0. 754 40,344 0.3841 4429 0.3080 0.3080 0. 887 39,619 0.4193 3704 0.2903 0.2903 0. 991 39,331 0.4542 3416 0.2729 0.2729 0. 914 36,597 0.4829 682 0.2586 0.2586 0.0967 38,319 0.5101 2404 0.2450 0.2450 1.003 37,030 0.5355 1115 0.2323 0.2323 0. 953 36,169 0.5572 254 0.2214 0.2214 0.892 38,596 0.5758 2681 0.2121 0.2121 0. 985 36,715 0.5947 800 0.2027 0.2027 1.053 37,253 0.6130 1338 0.1935 0.1935 1.064 37,627 0.6299 1712 0.1850 0.1850 −4 −4 T = 1423 K series II: starting amount nCu = 45.41·10 mol and nGa = 45.41·10 mol; −4 −4 −1 TD→T calibration constant k = (29.33·10 ± 0.20·10 ) [J·μVs ]; TD = 298 K; TM = 1423 K; HIn M=35,915 [J·mol−1] [24] 0 0 0 0 0.5000 0.5000 0. 663 52,082 0.0680 16,167 0.4660 0.4660 0. 857 49,714 0.1434 13,799 0.4283 0.4283 0. 913 46,713 0.2113 10,798 0.3944 0.3944 0. 742 43,169 0.2590 7254 0.3705 0.3705 0. 767 41,498 0.3027 5583 0.3487 0.3487 0. 953 40,723 0.3502 4808 0.3249 0.3249 0. 843 41,744 0.3872 5829 0.3064 0.3064 0. 927 38,436 0.4233 2521 0.2884 0.2884 0. 883 39,328 0.4539 3413 0.2731 0.2731 0. 914 37,102 0.4823 1187 0.2588 0.2588 0. 865 37,451 0.5067 1536 0.2467 0.2467 0. 931 37,644 0.5304 1729 0.2348 0.2348 0. 935 37,687 0.5521 1772 0.2240 0.2240 0. 793 36,479 0.5689 564 0.2155 0.2155 0. 756 36,224 0.5839 309 0.2081 0.2081 0. 887 36,611 0.6001 696 0.1999 0.1999 0. 720 37,811 0.6124 1896 0.1938 0.1938 1.091 36,895 0.6296 980 0.1852 0.1852 0. 955 37,097 0.6435 1182 0.1782 0.1782 1.003 37,740 0.6570 1,25 0.1715 0.1715

mixing increases as concentration In increases in ternary system. The integral enthalpy of mixing in Cu-Ga system is more negative than integral enthalpy of mixing in liquid Cu-In and Ga-In systems. The values of the enthalpy of mixing in ternary system increase from about −7700 to −1300 J·mol−1 at 1123 K in the concentration range 0 b x (In) b 0.58 while at 1273 K from about. −7000 to 900 J·mol−1 in the concentration range 0 b x(In) b 0.59 and at 1423 K from about −6500 to 140 J·mol−1 in the concentration range 0 b x(In) b 0.66. One can see that the results of the experimental series for both cross-sections, along which calorimetric measurements were done, are in good agreement with each other at 1123 K, 1273 K and 1423 K. 4.2. Modelling of mixing enthalpy 4.2.1. Binary systems The results obtained for liquid binary systems from calorimetric studies are described by using Redlich-Kister polynomial [25] which is

ΔmixHm [J·mol−1]

u(ΔmixHm) [J·mol−1]

−2139 −1902 −1623 −1432 −1223 −1014 −960 −888 −769

111 117 125 131 137 143 147 150 155

−8039 −6476 −4845 −3618 −2613 −2351 −1917 −1590 −1287 −1005 −916 −741 −645 −603 −465 −409 −330 −241

200 23 48 68 87 95 106 115 123 132 138 144 149 154 158 162 166 170

−8039 −6392 −4760 −3527 −2874 −2376 −1886 −1447 −1214 −968 −856 −743 −624 −514 −473 −446 −401 −331 −273 −218 −141

200 24 50 71 84 96 109 119 127 135 141 146 151 156 160 163 166 169 173 176 179

the standard CALPHAD procedure [26,27]. Excess Gibbs energy Gex is described by using Redlich-Kister polynomial with a set of interaction parameters vL by following formula: Gex i; j ¼ xi x j

X

v

 v Li; j xi −x j

ð4Þ

v

where i, j are equal to 1, 2 for the element in binary alloys (Cu and Ga, Cu and In, Ga and In respectively) and vLi, j can be expressed as: v

L ¼ v a þ v bT þ v cTlnT

ð5Þ

with T expressed in Kelvin. By applying the Gibbs-Helmholtz equa∂G tion H ¼ G−T  , the mixing enthalpy can be described as below: ∂T p

ð Þ

Δmix H ¼ xi x j

Xv v

X   v v v W i; j xi −x j ¼ xi x j a−v cT xi −x j v

ð6Þ

D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

7

Table 4 Partial and integral enthalpies of mixing of liquid Cu-Ga-In alloys at 1123 K, 1273 K and 1423 K, cross-section x(Ga)/x(In) = 1:1, standard states: pure liquid components. Mole droped

Drop enthalpy

Partial molar enthalpy of mixing

Integral molar enthalpy of mixing

nCu [mol·10−3]

ΔHsignal [J]

x(Cu)

x(Ga)

Δmix H Cu [J·mol−1]

x(In)

T = 1123 K series I: starting amount nGa = 31.07·10−4 mol and nIn = 31.07·10−4 mol; TD →T −1 calibration constant k = (30.14·10−4 ± 0.6·10−4) [J·μVs−1]; TD = 298 K; TM = 1123 K; HCu ] [24] M=35,167 [J·mol 0 0 0 0 0.5000 0.5000 1.116 22,016 0.1523 −13,151 0.4239 0.4239 1.229 24,352 0.2740 −10,815 0.3630 0.3630 2.423 21,986 0.4342 −13,181 0.2829 0.2829 1.336 20,938 0.4955 −14,229 0.2522 0.2522 1.193 21,239 0.5401 −13,928 0.2300 0.2300 1.330 20,860 0.5813 −14,307 0.2094 0.2094 1.128 22,455 0.6109 −12,712 0.1946 0.1946 2.476 22,667 0.6631 −12,500 0.1684 0.1684 1.406 23,445 0.6870 −11,722 0.1565 0.1565 3.100 26,050 0.7292 −9117 0.1354 0.1354 1.828 26,031 0.7492 −9136 0.1254 0.1254 1.521 27,544 0.7637 −7623 0.1181 0.1181 1.572 27,573 0.7771 −7594 0.1115 0.1115 1.484 28,696 0.7883 −6471 0.1058 0.1058 T = 1123 K series II: starting amount nGa = 30.91·10−4 mol and nIn = 30.91·10−4 mol; calibration constant k = (29.12·10−4 ± 0.3·10−4) [J·μVs−1]; TD = 298 K; TM = 1123 K; HTCuD →TM=35,167 [J·mol−1] [24] 0 0 0 0 0.5000 0.5000 1.106 22,525 0.1518 −12,642 0.4241 0.4241 1.254 23,544 0.2763 −11,623 0.3619 0.3619 1.259 23,389 0.3692 −11,778 0.3154 0.3154 20,247 0.4430 −14,920 0.2785 0.2785 1.298 1.317 20,220 0.5021 −14,947 0.2490 0.2490 1.414 23,072 0.5530 −12,095 0.2235 0.2235 1.437 20,457 0.5951 −14,710 0.2025 0.2025 1.462 20,990 0.6305 −14,177 0.1848 0.1848 1.495 24,348 0.6608 −10,819 0.1696 0.1696 1.532 25,349 0.6871 −9818 0.1565 0.1565 1.589 24,975 0.7104 −10,192 0.1448 0.1448 1.600 26,723 0.7306 −8444 0.1347 0.1347 1.606 26,302 0.7482 −8865 0.1259 0.1259 1.655 26,706 0.7641 −8461 0.1180 0.1180 1.279 26,917 0.7751 −8250 0.1125 0.1125 1.289 28,785 0.7852 −6382 0.1074 0.1074 1.373 28,101 0.7949 −7066 0.1025 0.1025 1.395 28,213 0.8040 −6954 0.0980 0.0980 1.430 29,939 0.8125 −5228 0.0937 0.0937 2.912 31,652 0.8277 −3515 0.0861 0.0861 1.475 31,276 0.8345 −3891 0.0827 0.0827 1.506 30,779 0.8409 −4388 0.0795 0.0795 1.535 30,459 0.8470 −4708 0.0765 0.0765 1.582 31,091 0.8527 −4076 0.0736 0.0736 1.582 31,297 0.8581 −3870 0.0710 0.0710 1.600 32,671 0.8631 −2496 0.0684 0.0684 1.641 33,320 0.8679 −1847 0.0660 0.0660 1.660 33,471 0.8724 −1696 0.0638 0.0638 T = 1273 K series I: starting amount nGa = 30.55·10−4 mol and nIn = 30.55·10−4 mol; calibration constant k = (27.63·10−4 ± 0.4·10−4) [J·μVs−1]; TD = 298 K; TM = 1273 K; HTCuD →TM=39,874 [J·mol−1] [24] 0 0 0 0 0.5000 0.5000 1.252 30,709 0.1701 −9165 0.4150 0.4150 1.326 27,911 0.2967 −11,963 0.3516 0.3516 1.360 27,756 0.3919 −12,118 0.3040 0.3040 1.392 27,273 0.4659 −12,601 0.2670 0.2670 1.396 26,759 0.5240 −13,115 0.2380 0.2380 1.396 27,129 0.5707 −12,745 0.2147 0.2147 1.421 29,361 0.6097 −10,513 0.1952 0.1952 1.427 29,431 0.6423 −10,443 0.1789 0.1789 1.450 29,730 0.6703 −10,144 0.1649 0.1649 1.472 30,618 0.6945 −9256 0.1527 0.1527 1.479 31,572 0.7156 −8302 0.1422 0.1422 1.518 32,577 0.7343 −7297 0.1328 0.1328 1.548 32,663 0.7511 −7211 0.1245 0.1245 1.547 33,515 0.7658 −6359 0.1171 0.1171 1.555 33,936 0.7790 −5938 0.1105 0.1105 1.582 35,393 0.7910 −4481 0.1045 0.1045 1.602 35,214 0.8018 −4660 0.0991 0.0991 1.687 33,606 0.8121 −6268 0.0939 0.0939 T = 1273 K series II: starting amount nGa = 31.38·10−4 mol and nIn = 31.38·10−4 mol;

ΔmixHm [J·mol−1]

u(ΔmixHm) [J·mol−1]

1084 −1083 −2481 −4841 −5860 −6572 −7265 −7650 −8301 −8543 −8621 −8659 −8599 −8542 −8438

75 67 127 195 219 237 253 267 292 304 333 347 358 369 379

1084 −999 −2559 −3743 −5050

75 35 66 88 102

−6100 −6713 −7466 −8052 −8279 −8398 −8532 −8526 −8548 −8543 −8529 −8433 −8371 −8308 −8174 −7796 −7642 −7516 −7409 −7284 −7160 −6994 −6814 −6639

113 126 134 141 150 159 166 174 180 186 190 194 197 201 205 213 217 220 223 226 229 232 236 239

1183 −577 −2315 −3642 −4732 −5643 −6340 −6719 −7030 −7274 −7420 −7480 −7468 −7452 −7387 −7306 −7153 −7023 −6984

130 76 126 163 191 213 230 248 263 276 288 300 311 321 331 340 349 358 365 (continued on next page)

8

D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

Table 4 (continued) Mole droped

Drop enthalpy

Partial molar enthalpy of mixing

Integral molar enthalpy of mixing

nCu [mol·10−3]

ΔHsignal [J]

x(Cu)

x(Ga)

Δmix H Cu [J·mol−1]

x(In)

calibration constant k = (27.87·10−4 ± 0.2·10−4) [J·μVs−1]; TD = 298 K; TM = 1273 K; HTCuD →TM=39,874 [J·mol−1] [24] 0 0 0 0 0.5000 0.5000 1183 1.181 −9495 0.1584 −9495 0.4208 0.4208 1.218 −11,107 0.2765 −11,107 0.3617 0.3617 1.248 −12,129 0.3675 −12,129 0.3162 0.3162 1.256 −13,733 0.4386 −13,733 0.2807 0.2807 1.281 −13,146 0.4963 −13,146 0.2518 0.2518 1.309 −12,238 0.5442 −12,238 0.2279 0.2279 1.348 −12,562 0.5848 −12,562 0.2076 0.2076 1.355 −10,173 0.6190 −10,173 0.1905 0.1905 1.379 −10,911 0.6484 −10,911 0.1758 0.1758 1.394 −10,287 0.6739 −10,287 0.1631 0.1631 1.395 −8546 0.6959 −8546 0.1520 0.1520 1.396 −9219 0.7152 −9219 0.1424 0.1424 1.416 −7983 0.7324 −7983 0.1338 0.1338 1.426 −7700 0.7477 −7700 0.1261 0.1261 1.432 −7066 0.7615 −7066 0.1193 0.1193 1.470 −6273 0.7741 −6273 0.1130 0.1130 1.492 −5436 0.7856 −5436 0.1072 0.1072 1.533 −5696 0.7963 −5696 0.1019 0.1019 1.571 −4195 0.8062 −4195 0.0969 0.0969 1.642 −3943 0.8155 −3943 0.0922 0.0922 −4 −4 T = 1423 K series I: starting amount nGa = 30.13·10 mol and nIn = 30.13·10 mol; calibration constant k = (28.17·10−4 ± 0.3·10−4) [J·μVs−1]; TD = 298 K; TM = 1423 K; HTCuD →TM=45,570 [J·mol−1] [24] 0 0 0 0 0.5000 0.5000 1.151 38,033 0.1604 −6537 0.4198 0.4198 1.161 34,435 0.2773 −10,135 0.3614 0.3614 1.190 31,775 0.3675 −12,795 0.3162 0.3162 1.262 32,587 0.4415 −11,983 0.2792 0.2792 1.286 33,103 0.5010 −11,467 0.2495 0.2495 1.339 33,514 0.5508 −11,056 0.2246 0.2246 1.368 34,873 0.5924 −9697 0.2038 0.2038 1.386 36,005 0.6273 −8565 0.1863 0.1863 1.389 36,390 0.6568 −8180 0.1716 0.1716 1.406 36,054 0.6822 −8516 0.1589 0.1589 1.414 36,946 0.7043 −7624 0.1479 0.1479 1.425 38,238 0.7236 −6332 0.1382 0.1382 1.427 38,532 0.7406 −6038 0.1297 0.1297 1.445 38,953 0.7558 −5617 0.1221 0.1221 1.465 40,180 0.7695 −4390 0.1153 0.1153 1.495 39,864 0.7819 −4706 0.1090 0.1090 1.496 41,031 0.7931 −3539 0.1034 0.1034 1.539 40,353 0.8035 −4217 0.0982 0.0982 1.651 41,888 0.8136 −2682 0.0932 0.0932 1.689 43,324 0.8228 −1246 0.0886 0.0886 T = 1423 K series II: starting amount nGa = 30.21·10−4 mol and nIn = 30.21·10−4 mol; calibration constant k = (27.59·10−4 ± 0.2·10−4) [J·μVs−1]; TD = 298 K; TM = 1423 K; HTCuD →TM=45,570 [J·mol−1] [24] 0 0 0 0 0.5000 0.5000 1.206 37,800 0.1664 −6770 0.4168 0.4168 1.235 34,728 0.2878 −98,42 0.3561 0.3561 1.235 32,869 0.3783 −11,701 0.3109 0.3109 1.239 33,046 0.4486 −11,524 0.2757 0.2757 1.306 32,244 0.5073 −12,326 0.2464 0.2464 1.332 33,742 0.5556 −10,828 0.2222 0.2222 1.375 34,840 0.5964 −9730 0.2018 0.2018 1.392 35,835 0.6307 −8735 0.1846 0.1846 1.433 36,015 0.6605 −8555 0.1698 0.1698 1.438 36,435 0.6859 −8135 0.1571 0.1571 1.447 37,690 0.7078 −6880 0.1461 0.1461 1.497 38,296 0.7276 −6274 0.1362 0.1362 1.527 38,337 0.7451 −6233 0.1274 0.1274 1.579 39,351 0.7610 −5219 0.1195 0.1195 1.586 40,233 0.7751 −4337 0.1124 0.1124 1.635 39,772 0.7880 −4798 0.1060 0.1060 1.664 40,083 0.7997 −4487 0.1001 0.1001

where vWi, j = va − vcT is the enthalpic part of the interaction parameter depending on temperature. Parameters vWi, j were derived on the basis of calculations performed by using Thermo-Calc software

ΔmixHm [J·mol−1]

u(ΔmixHm) [J·mol−1]

130 −508 −1996 −3271 −4446 −5341 −5996 −6582 −6877 −7189 −7413 −7490 −7599 −7622 −7627 −7596 −7526 −7420 −7334 −7182 −7025

39 62 78 90 100 109 117 125 131 137 143 149 154 159 164 169 173 177 182 186

1272 20 −1394 −2818 −3890 −4697 −5332 −5736 −5978 −6152 −6328 −6418 −6412 −6389 −6344 −6234 −6152 −6017 −5927 −5761 −5537

82 65 107 136 161 181 199 215 229 242 252 262 271 280 288 296 303 310 316 322 329

1272 −66 −1489 −2787 −3775 −4686 −5288 −5696 −5954 −6164 −6311 −6351 −6346 −6338 −6268 −6154 −6077 −5989

82 46 76 96 112 125 137 148 157 166 173 180 187 192 198 204 209 213

[28] and their values are given in J·mol−1. All vWi, j parameters for binary systems (Cu-Ga, Cu-In and Ga-In) are listed in Table 5. The following experimental data were used during this calculations.

D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543 Table 5 Enthalpic part of binary and ternary interaction parameters. System

Literature

Interaction parameters [J·mol−1]

Cu-Ga

This work

0

W = −48,946.717 + 11.359·T W = −92,977.018 + 42.980·T 2 W = −99,661.856 + 66.656·T 0 W = −30,265.595 + 18.046·T 1 W = −64,255.043 + 31.790·T 2 W = −44,367.246 + 23.298·T 0 W = 4573.532 1 W = −36.316 0 W = 591,780.631 + 368.887·T 1 W = −433,238.417 + 368.417·T 2 W = −132,609.446 + 69.309·T

9

in the temperature range from 997 K to 1348 K were not taken in the account in description of the liquid phase in this binary system. The values of the enthalpy of mixing taken from the experimental works [15–18], which were used in calculation, are compared in Fig. 2 with the results of the model calculation. They are in good agreement.

1

Cu-In

This work

Ga-In

This work

Cu-Ga-In

This work

4.2.2. (Cu-Ga) system In the description of the liquid phase in this binary system the data of the enthalpy of mixing in Cu-Ga alloys were taken from literature [13,14]. All of them agree well. These values of the enthalpy of mixing taken from the experimental works [13,14] are compared in Fig. 1 with the results of the model calculation. The agreement between experiment and the calculations is very good.

4.2.4. (Ga-In) system In our calculations, the experimental data from the present work together with the literature data were used [19–23]. The enthalpy of mixing values in liquid Ga-In system are shown in Fig. 3. Experimental results obtained in the present work are compared with the literature data, and with the results of the model calculations. They are in good agreement, similarly like in two previous liquid binary systems. 4.2.5. Ternary system The experimental results of the enthalpy of mixing in the liquid CuGa-In system were described by the least square method by using the Redlich-Kister-Muggianu polynomial [12]. By applying the Gibbs∂G Helmholtz equation H ¼ G−T  to the following formula: ∂T p

ð Þ

Gex i; j;k ¼

XX jNi

i

4.2.3. (Cu-In) system In the description of the liquid phase in this system, the data of the enthalpy of mixing in Cu-In alloys were taken from the literature [15–18]. They agree well with another except of Kang et al. [17] at temperatures from 997 K to 1348 K, which are more positive than experimental data given by Knott and Mikula [18]. Moreover, data given by Knott and Mikula [18] give consistent description of the enthalpy of mixing in this binary system together with the data given by Kleppa [15], Itagaki and Yazawa [16] and Kang et al. [17] at two chosen temperatures at 903 K and 955 K. In this situation, data given by Kang et al. [17]

xi x j

þ xi x j xk




X

v

 v Li; j xi −x j

v

0

Li; j;k xi þ 1 Li; j;k x j þ 2 Li; j;k xk



ð7Þ

where subscripts i, j, k are equal to 1, 2, 3 for the elements Cu, Ga and In respectively, vLi, j are already obtained binary interaction parameters and vLi, j, k are ternary interaction parameters given in J·mol−1, we obtained the expression for the mixing enthalpy: Δmix H ¼

XX i

xi x j

jNi

þ xi x j xk




0

X

v

 v W i; j xi −x j

v

W i; j;k xi þ 1 W i; j;k x j þ 2 W i; j;k xk

Fig. 2. Integral enthalpies of mixing of liquid Cu-In alloys; standard states: pure liquid components.



ð8Þ

10

D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

Fig. 3. Integral enthalpies of mixing of liquid Ga-In alloys; standard states: pure liquid components.

Parameters vWi, j are already obtained enthalpic binary interaction parameters. Finally, vWi, j, k are enthalpic part of ternary interaction parameters which were obtained also on the basis of calculations performed by using Thermo-Calc software [28] and are listed in Table 5. Calculated values of the enthalpy of mixing in liquid Cu-Ga-In system are shown in Figs. 4 and 5 as solid lines. In these figures, the experimental data from the present work are compared with the results of these calculations. The biggest difference between them is ± 250 J mol−1, and they are found to be in very good agreement. The enthalpy of mixing in the liquid Cu-Ga-In system exhibits a temperature dependence similarly to Cu-Ga and Cu-In binary systems.

Finally, Figs. 6,7,8 show calculated three-dimensional plots of the enthalpy of mixing in ternary Cu-Ga-In system at 1123 K, 1273 K and 1423 K, which are compared with the experimental results. These figures were drafted with Statistica 10.0 software [29]. The values of the enthalpy of mixing determined at these temperatures at the intersections point of two cross-sections x(Cu)/x(Ga) = 1:1 and x(Ga)/x(In) = 1:1 agree very well (the biggest difference between them is ±215 J·mol−1). The obtained values of the enthalpies of mixing which are equal: -3440 ± 215 J·mol−1 at 1123 K, −2690 ± 200 J·mol−1 at 1273 K and −2130 ± 100 J·mol−1 at 1423 K, indicate that the results are consistent. It should be mentioned that the

Fig. 4. Integral enthalpies of mixing of liquid Cu-Ga-In alloys along cross-section x(Cu)/x(Ga) = 1:1; standard states: pure liquid components.

D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

11

Enthalpies of mixing determined in this work for liquid Cu-Ga-In solutions are obtained for these alloys for the first time. They will be very helpful in a future optimization of the thermodynamic properties and the phase diagram of this ternary system. Calorimetric measurements were done along two cross-sections x(Cu)/x(Ga) = 1:1 and x(Ga)/x (In) = 1:1 at three temperatures 1123 K, 1273 K and 1423 K. Based on the experimental results, three ternary interaction parameters vLi, j, k were obtained using the Redlich–Kister–Muggianu polynomial [27]. The experimental results are consistent and they are in good agreement with the calculated values. The values obtained in the present work showed that the enthalpy of mixing in this ternary system exhibits

temperature dependence. Moreover, sharp decrease of the enthalpy of mixing near the composition x(In)~0.25 in the Cu-In system indicates interactions between unlike atoms. Recent studies of the viscosity and the structure of this alloy conducted by Mudry et al. [30] leads to the conclusion that chemical ordering resulting in the formation of cluster with chemical compound-like structure takes place in the liquid state. Since the decrease of the enthalpy is even more pronounced in the Cu-Ga alloy, one may speculate that similar cluster appear also in this system. It seems that both binary systems in the liquid state behave similarly to Cu-Sn and Cu-Sb systems. According to Waseda's classification [31] based on the structure data they belong to group III were the partial structure factor of unlike-atom pairs is very clause to either of the two like-atom pairs. Consequently it is interesting to follow the change of those interactions with the ternary alloy composition. Since structural changes can be induced in Ga-In alloy only under very high pressure [32], it can be assume that no chemical ordering takes place between Ga-In atoms under normal condition. Therefore, clusters formation in the ternary alloy can be caused only by either

Enthalpy of mixing [J·mol-1]

Enthalpy of mixing [J·mol-1]

Fig. 5. Integral enthalpies of mixing of liquid Cu-Ga-In alloys along cross-section x(Ga)/x(In) = 1:1; standard states: pure liquid components.

agreement between the mixing enthalpy values from different crosssections in the vicinity of points of intersection is a valuable check of the quality of the experimental data.

5. Summary

□ ♦ Δ ○

x(Cu)/x(Ga)=1:1 series I x(Cu)/x(Ga)=1:1 series II x(Ga)/x(In)=1:1 series I x(Ga)/x(In)=1:1 series II

Fig. 6. 3D surface representation of the enthalpy of mixing of liquid Cu-Ga-In alloys at 1123 K; standard state: pure liquid components.

□ ♦ Δ ○

x(Cu)/x(Ga)=1:1 series I x(Cu)/x(Ga)=1:1 series II x(Ga)/x(In)=1:1 series I x(Ga)/x(In)=1:1 series II

Fig. 7. 3D surface representation of the enthalpy of mixing of liquid Cu-Ga-In alloys at 1273 K; standard state: pure liquid components.

Enthalpy of mixing [J·mol-1]

12

D. Jendrzejczyk-Handzlik, P. Handzlik / Journal of Molecular Liquids 293 (2019) 111543

□ ♦ Δ ○

x(Cu)/x(Ga)=1:1 series I x(Cu)/x(Ga)=1:1 series II x(Ga)/x(In)=1:1 series I x(Ga)/x(In)=1:1 series II

Fig. 8. 3D surface representation of the enthalpy of mixing of liquid Cu-Ga-In alloys at 1423 K; standard state: pure liquid components.

Cu-In or Cu-Ga interactions. The minimum of the enthalpy of mixing detected along x(Ga)/x(In) = 1 cross-section (Fig. 5) does not differ much from that one on Cu-In side. This may mean that in the liquid state there is no tendency towards formation of more stable ternary clusters. Only binary clusters may exist in the liquid state. Therefore, no ternary compound can be expected to appear in the solid state in this ternary system. Acknowledgements This work was realized at AGH University of Science and Technology, Faculty of Non-Ferrous Metals under grant number 11.11.180.959 and was supported by the Ministry of Science and Higher Education. References [1] P. Jackson, R. Wuerz, D. Hariskos, E. Lotter, W. Witte, M. Powalla, Effects of heavy alkali elements in Cu(In,Ga)Se2 solar cells with efficiencies up to 22.6%, Phys. Status Solidi-Rapid Res. Lett 10 (2016) 583–586. [2] M.A. Green, K. Emery, Y. Hishikawa, W. Warta, E.D. Dunlop, Solar cell efficiency tables (version 48), Prog. Photovolt. Res. Appl. 24 (2016) 905–913. [3] www.energy.gov/eere/solar/copper-indium-gallium-diselenide. [4] D. Jendrzejczyk-Handzlik, K. Fitzner, W. Gierlotka, On the Cu–Ga system: electromotive force measurement and thermodynamic reoptimization, J. Alloys and Compd. 621 (2015) 287–294. [5] S. Cao, S. Huang, M. Chu, Q. Yue, J. Shen, Thermodynamic optimization of Cu-In system, Xiyou Jinshu 31 (2007) 807–815.

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