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Thermodynamic properties of liquid Si–Ga–Y ternary alloys
Journal of Alloys and Compounds 367 (2004) 36–40
Thermodynamic properties of liquid Si–Ga–Y ternary alloys V.M. Dubyna∗ , O.A. Bieloborodova, T.M. Zinevich, N.V. Kotova Department of Chemistry, Kyiv National Taras Shevchenko University, Volodimirska st. 64, 03017 Kyiv, Ukraine
Abstract The mixing enthalpies of Si–Ga–Y ternary melts have been determined using high-temperature isoperibolic calorimetry at 1750 K. The formation of these melts is accompanied by large exothermic heat effects. The thermodynamic behavior of Si–Ga–Y liquid alloys and the phase equilibria in the solid state have been compared. The thermodynamic properties of Si–Ga–Y melts were modeled by a regular associated solution theory, and Gibbs free energies of alloy formation have been evaluated. The liquid Si–Ga–Y alloys are characterized by well-developed short-range order of chemical compound type. © 2003 Published by Elsevier B.V. Keywords: Silicon–gallium–yttrium ternary melts; Mixing enthalpy; High-temperature isoperibolic calorimetry; Regular associated solution model; Short range order
1. Introduction At present no thermodynamic data for Si–Ga–Y melts exist. Phase equilibrium data on the Si–Ga–Y ternary system at 1073 K are reported in [1]. Three ternary compounds were observed. The ternary compounds and solid solutions have wide homogeneity regions parallel to the Si–Ga boundary. This means that the properties of Si–Ga–Y solid alloys change strongly with respect to the yttrium content, but gradually on changing the silicon to gallium ratio. Two ternary compounds were found to be similar in structure to solid solutions based on yttrium silicides. The gallium solubility in yttrium silicides was observed to be considerably higher than the silicon solubility in yttrium gallides. Thus, the Si–Ga–Y solid alloy properties are mainly caused by the interaction between silicon and yttrium atoms. It would be interesting to find a relationship between the structure of Si–Ga–Y solid alloys and the thermodynamic properties of Si–Ga–Y melts. Since the experimental investigation of multicomponent systems is relatively difficult, the calculation of thermodynamic properties of these systems on the basis of data for the boundaries is of great importance. The regular associated solution model developed by Sommer and coworkers [2] can be used for the calculations of thermodynamic prop-
∗
Corresponding author. E-mail address: [email protected] (V.M. Dubyna).
0925-8388/$ – see front matter © 2003 Published by Elsevier B.V. doi:10.1016/j.jallcom.2003.08.007
erties in ternary systems with different types of interaction in the boundaries. The aim of this work is to investigate the mixing enthalpies in Si–Ga–Y melts at 1750 K using the isoperibolic calorimetry method and to calculate the thermodynamic properties of these melts using the regular associated solution model.
2. Experimental details The partial mixing enthalpies of yttrium have been measured along five intersections with constant silicon to gallium atomic fraction ratios: xSi /xGa = 0.15/0.85; 0.3/0.7; 0.5/0.5; 0.7/0.3; 0.85/0.15. The atomic fraction of yttrium was 0–0.6 or 0–0.3 (for intersections with xSi /xGa = 0.7/0.3; 0.85/0.15). In this case, the experimental investigation of alloys with higher yttrium content is impossible, because of the existence of yttrium silicides with high melting points [3]. The experiments were carried out using a high-temperature isoperibolic calorimeter [4], similar to that described in [5]. Silicon (99.999% purity), gallium (99.99% purity), yttrium (99.976% purity) and tungsten (99.98% purity) were used. All experiments were conducted under high-purity argon atmosphere. The alumina crucible, in which the component mixing process was performed, was covered with yttria to avoid any interaction with yttrium. After melting pure silicon in a crucible and heating it up to the appropriate temperature, eight silicon samples
V.M. Dubyna et al. / Journal of Alloys and Compounds 367 (2004) 36–40
were added for calorimeter calibration. Then about six gallium drops were introduced, until the desired silicon to gallium ratio was reached. After that, about 30–50 yttrium samples were added. At the end of the experiment the calorimeter was calibrated with tungsten. The initial silicon mass in the crucible was about 1 g. The
37
drop masses varied from 0.0050 to 0.0600 g for silicon, from 0.0072 to 0.1162 g for gallium, from 0.0104 to 0.1545 g for yttrium, from 0.2739 to 0.3066 g for tungsten. Immediately before dropping, each sample was at standard temperature. The time dependence of the temperature difference between the crucible and the coat of the
Fig. 1. Yttrium partial mixing enthalpies (in kJ mol−1 ) obtained from experiment (points and solid lines) and calculated using a regular associated solution model (dashed lines) at 1750 K.
38
V.M. Dubyna et al. / Journal of Alloys and Compounds 367 (2004) 36–40
calorimeter was recorded during the introduction of each sample. The dependence of the calibration factor with respect to the melt mass was approximated by a linear function using the least squares method. The dissolution of yttrium was accompanied by exothermic (at xY < 0.45) and endothermic heat effects. The partial mixing enthalpies for yttrium were calculated using the expression: k τ∞ T ¯ Y = −H298 H + T dt, (1) nY 0 T is the difference between the enthalpies of where H298 1 mol undercooled liquid yttrium at the experimental temperature and 1 mol solid ␣-yttrium at the standard temperature, k is the calibration factor, nY is the yttrium amount in the sample, τ ∞ is the time necessary for the temperature to return to the equilibrium value, T is the difference between the actual crucible temperature and the equilibrium crucible temperature, t is the time. Enthalpy data as a function of temperature for the pure elements were taken from the handbook [6]. The integral mixing enthalpies were calculated from partial ones using the Darken equation: xY H = (1 − xY ) αY dxY + HxY =0 , (2) 0
where xY is the atomic fraction of yttrium; αY is the function ¯ Y /(1 − xY )2 ), HxY =0 is enthalpy for yttrium (αY = H for the Si–Ga boundary system. For this purpose the concentration dependence of αY was approximated by a polynomial using the least squares method: αY = j Qj xj . The best polynomial power was adjusted using Fischer criteria. The polynomials obtained this way are reported in Table 1. The H values for the Si–Ga boundary were taken from [7].
3. Results The experimental data and the fitting curves for all investigated intersections are shown in Fig. 1. The scattering of experimental points can be explained by the high melting point of yttrium and by its low diffusion rate in silicon-containing melts. The smoothed values of the partial mixing enthalpy for yttrium are listed in Table 2.
Table 1 Coefficients of the polynomials approximating the concentration dependence of αY along five intersections in Si–Ga–Y melts xSi /xGa
j
0.15/0.85
0 1 2 3
−250.8233 319.3937 −8986.8409 25836.8012
0.30/0.70
0 1 2 3
−210.8304 −1138.8721 −3311.7168 8304.0938
0.50/0.50
0 1 2
−235.5475 −192.9956 −1575.4731
0.70/0.30
0 1 2
−236.5467 −164.6818 −1495.6896
0.85/0.15
0 1
−218.2456 −586.6644
Qj
The integral mixing heats are reported in Table 3. It can be seen that the formation of Si–Ga–Y ternary melts is accompanied by large exothermic heat effects (except for a small concentration range along the Si–Ga border binary).
4. Discussion The projection of isoenthalpic lines on the Gibbs triangle was constructed (Fig. 2). It can be seen that at high silicon content in Si–Ga–Y ternary melts the isoenthalpic lines are nearly parallel to the Si–Ga boundary. In this region the energetics of alloy formation are determined by the interaction between yttrium and silicon atoms. At high gallium concentration the projections of isoenthalpies have non-linear form. In this concentration area, the mixing heats change from values observed in the Si–Y limiting system [3] to those of the Ga–Y binary system [8]. Such thermodynamic behavior can be explained on the basis of boundary thermodynamic characteristics. In the Si–Ga boundary small positive deviations from ideality are observed [9]. The mixing enthalpies have positive values and can be described in a satisfactory way using a
Table 2 The yttrium partial mixing enthalpies (in kJ mol−1 ) in Si–Ga–Y liquid alloys (standard state for yttrium is undercooled liquid yttrium) ¯ Y ± 2σ H
xY
0.15/0.85a −240.27 −234.23 −216.36 −189.61
0.0 0.1 0.2 0.3 a
xSi /xGa .
± ± ± ±
0.30/0.70a 12.92 7.07 8.13 10.07
−210.83 −202.12 −194.97 −159.90
± ± ± ±
0.50/0.50a 13.10 6.67 5.89 7.58
−235.55 −219.19 −215.79 −213.27
± ± ± ±
0.70/0.30a 14.66 7.56 6.43 9.59
−236.55 −217.06 −210.76 −206.08
± ± ± ±
0.85/0.15a 10.97 5.86 4.95 15.07
−218.25 −224.30 −214.77 −192.18
± ± ± ±
7.17 3.77 5.68 7.31
V.M. Dubyna et al. / Journal of Alloys and Compounds 367 (2004) 36–40
39
Table 3 Mixing enthalpies (H) (in kJ mol−1 ) of Si–Ga–Y melts at 1750 K measured by calorimetry and calculated using a regular associated solution (RAS) model 0.15/0.85a
xY
0.30/0.70a
Calorimetry 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 a
2.30 −21.76 −44.43 −64.25 – – – – – –
± ± ± ±
0.40 1.15 2.37 4.63
0.50/0.50a
RAS model
Calorimetry
2.35 −16.80 −36.16 −55.58 −69.74 −68.79 −58.96 −45.61 −30.92 −15.61
3.90 −16.90 −37.24 −55.01 – – – – –
± ± ± ±
0.60 1.29 1.98 3.72
0.70/0.30a
RAS model
Calorimetry
3.86 −15.82 −35.94 −56.38 −74.06 −74.55 −63.29 −48.57 −32.75 −16.49
4.60 −18.40 −40.46 −62.25 – – – – – –
± ± ± ±
0.80 1.57 2.28 4.74
0.85/0.15a
RAS model
Calorimetry
4.60 −15.67 −36.42 −57.39 −77.36 −82.19 −68.93 −52.42 −35.16 −17.64
3.90 −18.97 −40.55 −61.56 – – – – – –
± ± ± ±
0.60 1.20 1.74 6.93
RAS model
Calorimetry
3.86 −16.85 −37.75 −58.67 −79.22 −89.70 −74.37 −56.14 −37.53 −18.79
2.30 −20.21 −42.47 −62.70 – – – – – –
± ± ± ±
RAS model
0.40 0.78 1.75 3.45
2.35 −18.41 −39.15 −59.87 −80.43 −95.12 −78.25 −58.84 −39.26 −19.64
xSi /xGa .
regular solution model [7]. In contrast, the Ga–Y boundary is characterized by strong component interaction of associated solution type [8]. In the Si–Y binary system, the heats of mixing [3,10] are larger in absolute value than those in the Ga–Y limiting system. The melting points of yttrium silicides [3] are higher than those of yttrium gallides [11]. Based on these facts it can be concluded that the associate stability in the Si–Y system is higher than that in the Ga–Y system. This is why the energetics of the formation of Si–Ga–Y alloy is determined mainly by the interaction in the Si–Y boundary. A similar conclusion can be drawn from X-ray data for Si–Ga–Y solid alloys. It can be concluded that the type of component interaction does not change during the melting of these alloys. This means that Si–Ga–Y melts are characterized by a well developed short range order of a chemical compound type. For this reason, the thermodynamic properties of these melts should be modeled by the associated solution theory [2]. According to this model either non-associated atoms or associates exist in the melt. When the formation enthalpy of associate Hlf is independent with respect to temperature, the equilibrium constant depends on temperature according to the following expression: Hlf 1 Kl,T2 1 ln = . (3) − Kl,T1 R T1 T2
To calculate the thermodynamic properties of Si–Ga–Y melts we modeled these values in the Si–Y boundary. Unfortunately, there are no experimental thermodynamic data in the middle region of concentration, because of the high melting points of yttrium silicides. Thus, the modeling was made based on the mixing Gibbs free energy obtained from solid alloys thermodynamics [12] and phase diagram [3] data at the temperature 2132 K for the yttrium concentration 0.625. The associate formula was assumed to be YSi, according to the phase diagram [3]. The solution of yttrium, silicon and YSi was treated as an ideal solution. In this case, the partial mixing enthalpy of each component at infinite dilution can be expressed as ¯ i∞ = H
f K HYSi YSi . KYSi + 1
(4)
f ,K The model parameters (HYSi YSi ) were calculated by solving a system of Eqs. (3) and (4), expressions for G and equilibrium conditions, and material balance equations. ¯ ∞ value for yttrium at 1870 K was taken from [10]. The H Y The Si–Ga binary melts were treated as regular solutions. According to Golovataya [7], the interaction parameter is equal to −18.4 kJ mol−1 . The parameters of interaction between other species (associates and non-associated atoms) are assumed to be equal to zero. The model parameters for associates of the Ga–Y boundary were taken from [9]. The thermodynamic properties of all associates present in the Si–Ga–Y ternary system are listed in Table 4. To obtain the thermodynamic properties of the Si–Ga–Y ternary melts, the system of material balance equations,
Table 4 Thermodynamic properties, formation enthalpy (in kJ mol−1 ) and stability constant, of associates present in the Si–Ga–Y ternary system at 1750 K
Fig. 2. Projection of the integral mixing enthalpy surface (in kJ mol−1 ) onto the Gibbs triangle at 1750 K.
Associate
Hlf
Kl
YGa2 YGa YSi
−185.875 −149.528 −205.003
4.012 × 103 198.234 1.67 × 103
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V.M. Dubyna et al. / Journal of Alloys and Compounds 367 (2004) 36–40
xSi/xGa:
Sum of associate concentrations
1,0
0.15/0.85 0.30/0.70 0.50/0.50 0.70/0.30 0.85/0.15
0,8
0,6
0,4
0,2
0,0 0,0
0,2
0,4
XY
0,6
0,8
1,0
Fig. 3. The sum of associate concentrations as a function of the composition of Si–Ga–Y melts according to a regular associated solution model.
equilibrium conditions and expressions for activity coefficients was solved. The calculated mixing enthalpies are in satisfactory agreement with those obtained from experiment (see Fig. 1 and Table 3). This confirms the validity of this model for the Si–Ga–Y system. The sum of associate concentration with respect to composition (Fig. 3) illustrates the highly developed short range order of chemical compound type. References [1] M.V. Speka, N.M. Belyavina, V.Ya. Markiv, Visn. Kiiv. Univ. Ser. Fiz.-Mat. Nauk 2 (1998) 455. [2] W.T. Witusiewicz, I. Arpshofen, H.-J. Seifert, F. Sommer, Z. Metallkd. 91 (2002) 128.
[3] I. Ansara, A.T. Dinsdale, M.H. Rand, COST 507 2 (1998) 274. [4] I.V. Nikolaenko, M.A. Turchanin, G.I. Batalin, E.A. Bieloborodova, Ukr. Khim. Zh. 53 (1987) 795. [5] M.A. Turchanin, I.V. Nikolaenko, J. Alloys Comp. 235 (1996) 128. [6] V.A. Kireyev, Methods of Practical Calculations in Thermodynamic of Chemical Reactions, Khimiya, Moscow, 1970. [7] N.V. Golovataya, Ph.D. Thesis, Kiev, 1999. [8] V.M. Dubyna, O.A. Bieloborodova, T.M. Zinevich, N.V. Kotova, Ukr. Khim. Zh., in press. [9] C.D. Thurmond, M. Kowalchik, Bell Syst. Technol. J. 7 (1960) 169. [10] G.M. Ryss, Yu.O. Esin, A.I. Stroganov, P.V. Geld, Reduction Processes in Ferroalloy Production, Nauka, Moscow, 1977. [11] S.P. Yatsenko, A.A. Semjannikov, C.G. Semenov, K.A. Chuntonov, J. Less-Common Met. 64 (1979) 185. [12] V.T. Witusiewicz, V.D. Sidorko, M.V. Bulanova, J. Alloys Comp. 248 (1997) 233.
Thermodynamic properties of liquid Si–Ga–Y ternary alloys V.M. Dubyna∗ , O.A. Bieloborodova, T.M. Zinevich, N.V. Kotova Department of Chemistry, Kyiv National Taras Shevchenko University, Volodimirska st. 64, 03017 Kyiv, Ukraine
Abstract The mixing enthalpies of Si–Ga–Y ternary melts have been determined using high-temperature isoperibolic calorimetry at 1750 K. The formation of these melts is accompanied by large exothermic heat effects. The thermodynamic behavior of Si–Ga–Y liquid alloys and the phase equilibria in the solid state have been compared. The thermodynamic properties of Si–Ga–Y melts were modeled by a regular associated solution theory, and Gibbs free energies of alloy formation have been evaluated. The liquid Si–Ga–Y alloys are characterized by well-developed short-range order of chemical compound type. © 2003 Published by Elsevier B.V. Keywords: Silicon–gallium–yttrium ternary melts; Mixing enthalpy; High-temperature isoperibolic calorimetry; Regular associated solution model; Short range order
1. Introduction At present no thermodynamic data for Si–Ga–Y melts exist. Phase equilibrium data on the Si–Ga–Y ternary system at 1073 K are reported in [1]. Three ternary compounds were observed. The ternary compounds and solid solutions have wide homogeneity regions parallel to the Si–Ga boundary. This means that the properties of Si–Ga–Y solid alloys change strongly with respect to the yttrium content, but gradually on changing the silicon to gallium ratio. Two ternary compounds were found to be similar in structure to solid solutions based on yttrium silicides. The gallium solubility in yttrium silicides was observed to be considerably higher than the silicon solubility in yttrium gallides. Thus, the Si–Ga–Y solid alloy properties are mainly caused by the interaction between silicon and yttrium atoms. It would be interesting to find a relationship between the structure of Si–Ga–Y solid alloys and the thermodynamic properties of Si–Ga–Y melts. Since the experimental investigation of multicomponent systems is relatively difficult, the calculation of thermodynamic properties of these systems on the basis of data for the boundaries is of great importance. The regular associated solution model developed by Sommer and coworkers [2] can be used for the calculations of thermodynamic prop-
∗
Corresponding author. E-mail address: [email protected] (V.M. Dubyna).
0925-8388/$ – see front matter © 2003 Published by Elsevier B.V. doi:10.1016/j.jallcom.2003.08.007
erties in ternary systems with different types of interaction in the boundaries. The aim of this work is to investigate the mixing enthalpies in Si–Ga–Y melts at 1750 K using the isoperibolic calorimetry method and to calculate the thermodynamic properties of these melts using the regular associated solution model.
2. Experimental details The partial mixing enthalpies of yttrium have been measured along five intersections with constant silicon to gallium atomic fraction ratios: xSi /xGa = 0.15/0.85; 0.3/0.7; 0.5/0.5; 0.7/0.3; 0.85/0.15. The atomic fraction of yttrium was 0–0.6 or 0–0.3 (for intersections with xSi /xGa = 0.7/0.3; 0.85/0.15). In this case, the experimental investigation of alloys with higher yttrium content is impossible, because of the existence of yttrium silicides with high melting points [3]. The experiments were carried out using a high-temperature isoperibolic calorimeter [4], similar to that described in [5]. Silicon (99.999% purity), gallium (99.99% purity), yttrium (99.976% purity) and tungsten (99.98% purity) were used. All experiments were conducted under high-purity argon atmosphere. The alumina crucible, in which the component mixing process was performed, was covered with yttria to avoid any interaction with yttrium. After melting pure silicon in a crucible and heating it up to the appropriate temperature, eight silicon samples
V.M. Dubyna et al. / Journal of Alloys and Compounds 367 (2004) 36–40
were added for calorimeter calibration. Then about six gallium drops were introduced, until the desired silicon to gallium ratio was reached. After that, about 30–50 yttrium samples were added. At the end of the experiment the calorimeter was calibrated with tungsten. The initial silicon mass in the crucible was about 1 g. The
37
drop masses varied from 0.0050 to 0.0600 g for silicon, from 0.0072 to 0.1162 g for gallium, from 0.0104 to 0.1545 g for yttrium, from 0.2739 to 0.3066 g for tungsten. Immediately before dropping, each sample was at standard temperature. The time dependence of the temperature difference between the crucible and the coat of the
Fig. 1. Yttrium partial mixing enthalpies (in kJ mol−1 ) obtained from experiment (points and solid lines) and calculated using a regular associated solution model (dashed lines) at 1750 K.
38
V.M. Dubyna et al. / Journal of Alloys and Compounds 367 (2004) 36–40
calorimeter was recorded during the introduction of each sample. The dependence of the calibration factor with respect to the melt mass was approximated by a linear function using the least squares method. The dissolution of yttrium was accompanied by exothermic (at xY < 0.45) and endothermic heat effects. The partial mixing enthalpies for yttrium were calculated using the expression: k τ∞ T ¯ Y = −H298 H + T dt, (1) nY 0 T is the difference between the enthalpies of where H298 1 mol undercooled liquid yttrium at the experimental temperature and 1 mol solid ␣-yttrium at the standard temperature, k is the calibration factor, nY is the yttrium amount in the sample, τ ∞ is the time necessary for the temperature to return to the equilibrium value, T is the difference between the actual crucible temperature and the equilibrium crucible temperature, t is the time. Enthalpy data as a function of temperature for the pure elements were taken from the handbook [6]. The integral mixing enthalpies were calculated from partial ones using the Darken equation: xY H = (1 − xY ) αY dxY + HxY =0 , (2) 0
where xY is the atomic fraction of yttrium; αY is the function ¯ Y /(1 − xY )2 ), HxY =0 is enthalpy for yttrium (αY = H for the Si–Ga boundary system. For this purpose the concentration dependence of αY was approximated by a polynomial using the least squares method: αY = j Qj xj . The best polynomial power was adjusted using Fischer criteria. The polynomials obtained this way are reported in Table 1. The H values for the Si–Ga boundary were taken from [7].
3. Results The experimental data and the fitting curves for all investigated intersections are shown in Fig. 1. The scattering of experimental points can be explained by the high melting point of yttrium and by its low diffusion rate in silicon-containing melts. The smoothed values of the partial mixing enthalpy for yttrium are listed in Table 2.
Table 1 Coefficients of the polynomials approximating the concentration dependence of αY along five intersections in Si–Ga–Y melts xSi /xGa
j
0.15/0.85
0 1 2 3
−250.8233 319.3937 −8986.8409 25836.8012
0.30/0.70
0 1 2 3
−210.8304 −1138.8721 −3311.7168 8304.0938
0.50/0.50
0 1 2
−235.5475 −192.9956 −1575.4731
0.70/0.30
0 1 2
−236.5467 −164.6818 −1495.6896
0.85/0.15
0 1
−218.2456 −586.6644
Qj
The integral mixing heats are reported in Table 3. It can be seen that the formation of Si–Ga–Y ternary melts is accompanied by large exothermic heat effects (except for a small concentration range along the Si–Ga border binary).
4. Discussion The projection of isoenthalpic lines on the Gibbs triangle was constructed (Fig. 2). It can be seen that at high silicon content in Si–Ga–Y ternary melts the isoenthalpic lines are nearly parallel to the Si–Ga boundary. In this region the energetics of alloy formation are determined by the interaction between yttrium and silicon atoms. At high gallium concentration the projections of isoenthalpies have non-linear form. In this concentration area, the mixing heats change from values observed in the Si–Y limiting system [3] to those of the Ga–Y binary system [8]. Such thermodynamic behavior can be explained on the basis of boundary thermodynamic characteristics. In the Si–Ga boundary small positive deviations from ideality are observed [9]. The mixing enthalpies have positive values and can be described in a satisfactory way using a
Table 2 The yttrium partial mixing enthalpies (in kJ mol−1 ) in Si–Ga–Y liquid alloys (standard state for yttrium is undercooled liquid yttrium) ¯ Y ± 2σ H
xY
0.15/0.85a −240.27 −234.23 −216.36 −189.61
0.0 0.1 0.2 0.3 a
xSi /xGa .
± ± ± ±
0.30/0.70a 12.92 7.07 8.13 10.07
−210.83 −202.12 −194.97 −159.90
± ± ± ±
0.50/0.50a 13.10 6.67 5.89 7.58
−235.55 −219.19 −215.79 −213.27
± ± ± ±
0.70/0.30a 14.66 7.56 6.43 9.59
−236.55 −217.06 −210.76 −206.08
± ± ± ±
0.85/0.15a 10.97 5.86 4.95 15.07
−218.25 −224.30 −214.77 −192.18
± ± ± ±
7.17 3.77 5.68 7.31
V.M. Dubyna et al. / Journal of Alloys and Compounds 367 (2004) 36–40
39
Table 3 Mixing enthalpies (H) (in kJ mol−1 ) of Si–Ga–Y melts at 1750 K measured by calorimetry and calculated using a regular associated solution (RAS) model 0.15/0.85a
xY
0.30/0.70a
Calorimetry 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 a
2.30 −21.76 −44.43 −64.25 – – – – – –
± ± ± ±
0.40 1.15 2.37 4.63
0.50/0.50a
RAS model
Calorimetry
2.35 −16.80 −36.16 −55.58 −69.74 −68.79 −58.96 −45.61 −30.92 −15.61
3.90 −16.90 −37.24 −55.01 – – – – –
± ± ± ±
0.60 1.29 1.98 3.72
0.70/0.30a
RAS model
Calorimetry
3.86 −15.82 −35.94 −56.38 −74.06 −74.55 −63.29 −48.57 −32.75 −16.49
4.60 −18.40 −40.46 −62.25 – – – – – –
± ± ± ±
0.80 1.57 2.28 4.74
0.85/0.15a
RAS model
Calorimetry
4.60 −15.67 −36.42 −57.39 −77.36 −82.19 −68.93 −52.42 −35.16 −17.64
3.90 −18.97 −40.55 −61.56 – – – – – –
± ± ± ±
0.60 1.20 1.74 6.93
RAS model
Calorimetry
3.86 −16.85 −37.75 −58.67 −79.22 −89.70 −74.37 −56.14 −37.53 −18.79
2.30 −20.21 −42.47 −62.70 – – – – – –
± ± ± ±
RAS model
0.40 0.78 1.75 3.45
2.35 −18.41 −39.15 −59.87 −80.43 −95.12 −78.25 −58.84 −39.26 −19.64
xSi /xGa .
regular solution model [7]. In contrast, the Ga–Y boundary is characterized by strong component interaction of associated solution type [8]. In the Si–Y binary system, the heats of mixing [3,10] are larger in absolute value than those in the Ga–Y limiting system. The melting points of yttrium silicides [3] are higher than those of yttrium gallides [11]. Based on these facts it can be concluded that the associate stability in the Si–Y system is higher than that in the Ga–Y system. This is why the energetics of the formation of Si–Ga–Y alloy is determined mainly by the interaction in the Si–Y boundary. A similar conclusion can be drawn from X-ray data for Si–Ga–Y solid alloys. It can be concluded that the type of component interaction does not change during the melting of these alloys. This means that Si–Ga–Y melts are characterized by a well developed short range order of a chemical compound type. For this reason, the thermodynamic properties of these melts should be modeled by the associated solution theory [2]. According to this model either non-associated atoms or associates exist in the melt. When the formation enthalpy of associate Hlf is independent with respect to temperature, the equilibrium constant depends on temperature according to the following expression: Hlf 1 Kl,T2 1 ln = . (3) − Kl,T1 R T1 T2
To calculate the thermodynamic properties of Si–Ga–Y melts we modeled these values in the Si–Y boundary. Unfortunately, there are no experimental thermodynamic data in the middle region of concentration, because of the high melting points of yttrium silicides. Thus, the modeling was made based on the mixing Gibbs free energy obtained from solid alloys thermodynamics [12] and phase diagram [3] data at the temperature 2132 K for the yttrium concentration 0.625. The associate formula was assumed to be YSi, according to the phase diagram [3]. The solution of yttrium, silicon and YSi was treated as an ideal solution. In this case, the partial mixing enthalpy of each component at infinite dilution can be expressed as ¯ i∞ = H
f K HYSi YSi . KYSi + 1
(4)
f ,K The model parameters (HYSi YSi ) were calculated by solving a system of Eqs. (3) and (4), expressions for G and equilibrium conditions, and material balance equations. ¯ ∞ value for yttrium at 1870 K was taken from [10]. The H Y The Si–Ga binary melts were treated as regular solutions. According to Golovataya [7], the interaction parameter is equal to −18.4 kJ mol−1 . The parameters of interaction between other species (associates and non-associated atoms) are assumed to be equal to zero. The model parameters for associates of the Ga–Y boundary were taken from [9]. The thermodynamic properties of all associates present in the Si–Ga–Y ternary system are listed in Table 4. To obtain the thermodynamic properties of the Si–Ga–Y ternary melts, the system of material balance equations,
Table 4 Thermodynamic properties, formation enthalpy (in kJ mol−1 ) and stability constant, of associates present in the Si–Ga–Y ternary system at 1750 K
Fig. 2. Projection of the integral mixing enthalpy surface (in kJ mol−1 ) onto the Gibbs triangle at 1750 K.
Associate
Hlf
Kl
YGa2 YGa YSi
−185.875 −149.528 −205.003
4.012 × 103 198.234 1.67 × 103
40
V.M. Dubyna et al. / Journal of Alloys and Compounds 367 (2004) 36–40
xSi/xGa:
Sum of associate concentrations
1,0
0.15/0.85 0.30/0.70 0.50/0.50 0.70/0.30 0.85/0.15
0,8
0,6
0,4
0,2
0,0 0,0
0,2
0,4
XY
0,6
0,8
1,0
Fig. 3. The sum of associate concentrations as a function of the composition of Si–Ga–Y melts according to a regular associated solution model.
equilibrium conditions and expressions for activity coefficients was solved. The calculated mixing enthalpies are in satisfactory agreement with those obtained from experiment (see Fig. 1 and Table 3). This confirms the validity of this model for the Si–Ga–Y system. The sum of associate concentration with respect to composition (Fig. 3) illustrates the highly developed short range order of chemical compound type. References [1] M.V. Speka, N.M. Belyavina, V.Ya. Markiv, Visn. Kiiv. Univ. Ser. Fiz.-Mat. Nauk 2 (1998) 455. [2] W.T. Witusiewicz, I. Arpshofen, H.-J. Seifert, F. Sommer, Z. Metallkd. 91 (2002) 128.
[3] I. Ansara, A.T. Dinsdale, M.H. Rand, COST 507 2 (1998) 274. [4] I.V. Nikolaenko, M.A. Turchanin, G.I. Batalin, E.A. Bieloborodova, Ukr. Khim. Zh. 53 (1987) 795. [5] M.A. Turchanin, I.V. Nikolaenko, J. Alloys Comp. 235 (1996) 128. [6] V.A. Kireyev, Methods of Practical Calculations in Thermodynamic of Chemical Reactions, Khimiya, Moscow, 1970. [7] N.V. Golovataya, Ph.D. Thesis, Kiev, 1999. [8] V.M. Dubyna, O.A. Bieloborodova, T.M. Zinevich, N.V. Kotova, Ukr. Khim. Zh., in press. [9] C.D. Thurmond, M. Kowalchik, Bell Syst. Technol. J. 7 (1960) 169. [10] G.M. Ryss, Yu.O. Esin, A.I. Stroganov, P.V. Geld, Reduction Processes in Ferroalloy Production, Nauka, Moscow, 1977. [11] S.P. Yatsenko, A.A. Semjannikov, C.G. Semenov, K.A. Chuntonov, J. Less-Common Met. 64 (1979) 185. [12] V.T. Witusiewicz, V.D. Sidorko, M.V. Bulanova, J. Alloys Comp. 248 (1997) 233.