Integral Enthalpies Of Mixing Research Articles

Enthalpies of mixing of Al-Ni-La ternary alloys

Partial (for nickel) and integral enthalpies of mixing of liquid alloys of the Al-Ni-La ternary system of three radial sections with a constant ratio of molar fractions of aluminum and lanthanum xAl/xLa = 0.3/0.7 at 1770 ± 5 K and 0.5/0.5 and 0.8/0.2 at 1870 ± 5 K up to molar fractions of nickel in ternary alloys of approximately 0.5–0.6 are studied by means of high-temperature calorimetry in isoperibolic mode. It is found that the enthalpies of mixing of the melts are essentially exothermic values. Based on the energetics of alloy formation of this ternary system, it is concluded that the main contribution is made by interaction between the components of melts of the boundary Ni-Al binary system.

Enthalpies of mixing of liquid Ag–Ga, Cu–Ga and Ag–Cu–Ga alloys

Abstract Using MHTC 96 Setaram high temperature drop calorimeter, partial and integral enthalpies of mixing of liquid alloys were determined in the Ag–Ga, Cu–Ga and in the ternary Ag–Cu–Ga system. The ternary alloys were investigated along two cross-sections at two different temperatures: 1128 K and 1273 K, respectively. Experimental data were used to find ternary interaction parameters by applying the Redlich–Kister–Muggianu model for substitutional solutions, and a full set of parameters describing the concentration dependence of the enthalpy of mixing was derived. The experimental data indicate that the heat of mixing in this system is slightly temperature dependent, at least in the measured temperature range.

Calorimetric studies of Cu–Li, Li–Sn, and Cu–Li–Sn

Integral molar enthalpies of mixing were determined by drop calorimetry for Cu–Li–Sn at 1073K along five sections xCu/xSn≈1:1, xCu/xSn≈2:3, xCu/xSn≈1:4, xLi/xSn≈1:1, and xLi/xSn≈1:4. The integral and partial molar mixing enthalpies of Cu–Li and Li–Sn were measured at the same temperature, for Li–Sn in addition at 773K. All binary data could be described by Redlich–Kister-polynomials. Cu–Li shows an endothermic mixing effect with a maximum in the integral molar mixing enthalpy of ∼5300J·mol−1 at xCu=0.5, Li–Sn an exothermic minimum of ∼ −37,000J·mol−1 at xSn∼0.2. For Li–Sn no significant temperature dependence between 773K and 1073K could be deduced. Our measured ternary data were fitted on the basis of an extended Redlich–Kister–Muggianu model for substitutional solutions. Additionally, a comparison of these results to the extrapolation model of Chou is given.

Mixing enthalpies in binary Ce-Sb and ternary Ce-Co-Sb liquid alloys

AbstractThe enthalpies of mixing in liquid alloys in the binary Ce-Sb and ternary Ce-Co-Sb systems were determined over a wide range of composition by means of isoperibolic calorimetry in the temperature range 1 600-1 723 K. The minimum value of the integral enthalpy of mixing (ΔHmin) in the Ce-Sb system was evaluated to be −123 kJ mol-1 at xCe = 0.55. The enthalpies of mixing in liquid ternary alloys were found to increase smoothly from the binary boundary systems Co-Ce and Co-Sb towards the Ce-Sb system reaching the value of approximately −123 kJ mol-1 in the vicinity of the phase CeSb.

Thermodynamic properties of melts of Mn-Sc(Y, Ln) systems

Partial and integral mixing enthalpies of melts of binary systems Mn-Sc and Mn-Y at 1873 and 1830 K, respectively, are determined by calorimetry. It is found that the minima of the mixing enthalpies are −7.1 ± 0.4 and -3.2 ± 0.2 kJ/mol at xMn = 0.60 and 0.61, respectively. The initial partial mixing enthalpies of Sc and Y are −33.2 ± 2.1 and −16.6 ± 0.8 kJ/mol, respectively. The thermodynamic properties of melts of binary Mn-Sc(Y) systems are calculated using the ideal associated solution (IAS) model. It is found that the activities of the components exhibit slight negative deviations from the ideal solutions, and the excess Gibbs energies reach −3.0 and −1.6 kJ/mol, respectively.

Mixing enthalpies of liquid Au–Sb–Sn alloys

Using a MHTC 96 Setaram high-temperature drop calorimeter, partial and integral enthalpies of liquid alloy mixing were determined in the ternary Au–Sb–Sn system. The alloys were investigated along three cross sections at two different temperatures: 923 and 1,078 K. Experimental data were used to find ternary interaction parameters by applying the Redlich-Kister-Muggianu model for substitutional solutions, and a full set of parameters describing the concentration dependence of the mixing enthalpy was derived. It was found that the entire system shows exothermic mixing enthalpy at the given temperature. Moreover, experimental data indicate that the mixing heat in this system is temperature independent, at least in the measured temperature range. .

Calorimetric investigations of liquid gold–antimony–tin alloys

Abstract Calorimetric investigations have been done on the Au–Sb–Sn system with a Calvet-type micro-calorimeter. The partial and integral enthalpies of mixing in the ternary system were determined at six cross-sections at 873 K. Three additional cross-sections were measured at 1073 K to check if there are any temperature dependencies. No temperature dependence could be found. The substitutional solution model of Redlich–Kister–Muggianu was used for a least-square fit of the experimental data in order to get an analytical expression for the integral enthalpy of mixing. The isoenthalpy curves for the Au–Sb–Sn system were constructed at 873 K. The Chou model was used to calculate the enthalpies of mixing for the ternary system. The calculated values were then compared with the experimental data. The calculated data are in very good agreement with the experimentally determined values.

Mixing enthalpies of liquid nickel–gallium alloys

The partial mixing enthalpies of melt components in the Ni–Ga system are measured using hightemperature isoperibolic calorimetry at 1770 ± 5 K in a wide composition range. The partial mixing enthalpy of gallium in liquid nickel is –96 kJ/mol. for infinite dilution, while the same function of nickel in liquid gallium is –75 kJ/mol. The integral mixing enthalpy of liquid alloys in this system is calculated from partial enthalpies for the entire composition range (∆m H min = –32 kJ/mol. at xNi = = 0.5). The mixing enthalpies ∆m H of Ni–B (Al, Ga, In) binary alloys are compared. It is shown that the indicated systems are arranged in the Ni–In → Ni–Ga → Ni–B → Ni–Al series according to the increase in interaction energy of dissimilar components. The ∆m H min values of liquid Ni–B(Al, Ga, In) alloys are compared with the values of electrochemical and size factors.

Enthalpy of mixing of liquid systems for lead free soldering: Ni–Sb–Sn system

The partial and integral enthalpies of mixing of liquid ternary Ni–Sb–Sn alloys were determined along five sections xSb/xSn=3:1, xSb/xSn=1:1, xSb/xSn=1:3, xNi/xSn=1:4, and xNi/xSb=1:4 at 1000°C in a large compositional range using drop calorimetry techniques. The mixing enthalpy of Ni–Sb alloys was determined at the same temperature and described by a Redlich–Kister polynomial. The other binary data were carefully evaluated from literature values. Our measured ternary data were fitted on the basis of an extended Redlich–Kister–Muggianu model for substitutional solutions. Additionally, a comparison of these results to the extrapolation model of Toop is given. The entire ternary system shows exothermic values of ΔmixH ranging from approx. −1300J/mol, the minimum in the Sb–Sn binary system down to approx. −24,500J/mol towards Ni–Sb. No significant ternary interaction could be deduced from our data.

Enthalpies of mixing of liquid systems for lead free soldering: Co–Sb–Sn

The partial and integral enthalpy of mixing of molten ternary Co–Sb–Sn alloys was determined performing high temperature drop calorimetry in a large compositional range at 1273 K. Measurements have been done along five sections, xSb/xSn ≈ 1:1, xSb/xSn ≈ 1:3, xSb/xSn ≈ 3:1, xCo/xSn ≈ 1:4, and xCo/xSb ≈ 1:5. Additionally, binary alloys of the constituent systems Co–Sb and Co–Sn were investigated at the same temperature. All the binary data were evaluated by means of a standard Redlich–Kister polynomial fit whereas ternary data were fitted on the basis of an extended Redlich–Kister–Muggianu model for substitutional solutions. An iso-enthalpy plot of the ternary system was constructed. In addition, the extrapolation Model of Toop was applied and compared to our data.

Thermodynamic properties of Eu-Pd melts

Partial and integral enthalpies of mixing of melts of the Eu-Pd system were determined by calorimetry at 1300 K in the concentration interval of 0 < xPd < 0.37. It was established that the first partial enthalpy of mixing of Pd was −158 ± 2 kJ/mol. The thermodynamic properties of Eu-Pd melts were simulated according to the theory of ideal associated solutions over a wide interval of concentrations and temperatures. It was shown that the activities of components display strong negative deviations from Raoult’s law, and the minima of the integral Gibbs energies and enthalpies of mixing were found at xPd = 0.65.

The Effect of Sb Addition on Sn-Based Alloys for High-Temperature Lead-Free Solders: an Investigation of the Ag-Sb-Sn System

Today there is renewed interest in alloys belonging to the Sb-Sn-X (X = Cu, Ag, Bi) ternary systems and their phase equilibria, phase transformations, and thermodynamic properties because of their possible use as high-temperature lead-free solders in the electronics industry. The integral mixing enthalpy of Ag-Sb-Sn liquid alloys has been measured along five different sections (Ag0.25Sn0.75, Ag0.50Sn0.50, Sb0.30Sn0.70, Sb0.50Sn0.50, and Sb0.70Sn0.30) at 530°C, 600°C, and 630°C, using a high-temperature Calvet calorimeter by dropping pure elements (Ag or Sb) in the binary alloy liquid bath. The ternary extrapolation models of Muggianu and Toop were used to calculate the integral enthalpy of mixing and to compare measured and extrapolated values. Selected ternary alloys have been prepared for thermal investigation by using a differential scanning calorimeter at different heating/cooling rates in order to clarify the temperature of the invariant reactions and the crystallization path.

Partial and integral enthalpies of mixing of Ag–Ga–Sn liquid alloys

A Calvet type calorimeter was used for measurement of partial and integral enthalpies of mixing of Ag–Ga–Sn alloys. The Ag–Ga binary alloys have been studied with 0 < x Ag < 0.79 composition and in the 803–1073 K temperature range. The mixing enthalpies at 803 K of Ga–Sn binary alloys have been determined for x Sn < 0.35. The Ag–Ga–Sn ternary liquid alloys have been investigated at 803 K along the following sections: x Ag/ x Ga = 1/3, x Ag/ x Ga = 0.36/0.64, x Ag/ x Ga = 1/1, x Ga/ x Sn = 1/3, x Ga/ x Sn = 1/1, x Ga/ x Sn = 0.65/0.35 and x Ga/ x Sn = 3/1. Experimental data were used to obtain the binary interaction parameters by using the Redlich–Kister polynomial for the Ag–Ga binary system, while the Redlich–Kister–Muggianu method was used to determine the ternary interaction parameters for the Ag–Ga–Sn system. The experimental values and the fitted curves were compared with those predicted from the Muggianu and Toop methods.

Thermodynamic properties of Al-Y system melts

The thermochemical properties of Al-Y melts were determined by isoperibolic calorimetry. It was established that the minimal value of integral mixing enthalpies is equal to −40.8 + 0.4 kJ/mol at 1770 K and xY = 0.41. The thermodynamic properties of liquid alloys were modeled by the developed procedure using the coordinates of a liquidus line in the phase diagram of the Al-Y system, and by the theory of ideal associated solutions. The component activities exhibit high negative deviations from the Raoult law. The Gibbs energies of mixing of Al-Y melts have a minimum of −30.6 kJ/mol at xY = 0.48.

Thermodynamic properties of Ni–Hf melts

Isoperibolic calorimetry is used to determine the integral and partial mixing enthalpies of Ni–Hf melts at 1770 ± 5 K. It is established that Ni–Hf melts form with release of a great amount of heat. Temperature dependence of mixing enthalpies for binary Ni–Hf melts is established. Activities of the melt components are determined from coordinates of the liquidus lines in the phase diagram of this system. The calculated and experimental activities of the Ni–Hf melt components agree well. These data and the mixing enthalpies are used to calculate the Gibbs energies and mixing entropies of Ni–Hf melts. It is shown that they are negative and their absolute value is high.

Enthalpies of mixing of liquid systems for lead-free soldering: Cu–Sb–Sn system

Using two different types of high temperature drop calorimeters, partial and integral enthalpies of mixing of liquid alloys were determined in the ternary Cu–Sb–Sn system. The system was investigated along four sections at 1100 K. Experimental data were used to find ternary interaction parameters by applying the Redlich–Kister–Muggianu model for substitutional solutions, and a full set of parameters describing the concentration dependence of the enthalpy of mixing was derived. From these, the isoenthalpy curves were constructed for 1100 K. The entire system shows exothermic enthalpy of mixing at the given temperature.

Thermodynamic properties of liquid Ga-Si-Mn alloys

The partial enthalpies of mixing of the constituent components (Δmix\( \bar H_i \)) have been determined by high-temperature calorimetry and then used to evaluate the integral enthalpies of mixing (ΔmixH) of Ga-Si-Mn alloys along three cuts at 1770 ± 5 K. The results demonstrate that, in the composition region studied, the formation of Ga-Si-Mn alloys is an exothermic process. ΔmixH is calculated over the entire composition region by the Bonnier-Caboz method.

Thermodynamic properties of liquid silver–gallium alloys determined from e.m.f. and calorimetric measurements

The thermodynamic properties of the liquid Ag–Ga alloys were determined using e.m.f. and calorimetric methods. In the e.m.f. method, solid oxide galvanic cells were used with zirconia electrolyte. The cells of the type W, Ag x Ga ( 1 - x ) , Ga 2 O 3 / / ZrO 2 + ( Y 2 O 3 ) / / FeO,Fe,W were used in the temperature range from 1098 K to 1273 K, and in the range of mole fraction from x Ga = 0.1 to x Ga = 1.0. At first, the Gibbs free energy of formation of pure solid gallium oxide, Ga 2O 3, from pure elements was derived. Using values of the measured e.m.f. for the cell with x Ga = 1.0, the following temperature dependence was obtained: Δ f G m, Ga 2 O 3 ∘ ( ± 4 kJ · mol - 1 J ) = - 1061.7235 + 0.2899 T / K. Next, the activity of the gallium was derived as a function of the alloy composition from the values of the measured e.m.f. Activities of silver were calculated using the Gibbs–Duhem equation. The drop calorimetric measurements were carried out at two temperatures, viz. 923 K and 1123 K, using a Setaram MHTC calorimeter. Integral enthalpies of mixing of liquid binary alloys were determined at those temperatures. Finally, thermodynamic properties of the liquid alloys were described with the Redlich–Kister equation using ThermoCalc software.

Calculation of the viscosity of the liquid ternary Ag–Au–Sn system

Abstract The viscosity of the ternary Ag–Au–Sn system has been calculated using two different semi-empirical models which apply universal parameters valid for all metals. Experimental values of the integral enthalpy of mixing were used as inputs. The theoretical results are represented as iso-lines of the excess viscosity. Additional calculations based on a geometrical model fitted to the experimental viscosities of the binary systems were applied in order to discuss the physical significance of the results predicted for the ternary system.

Calorimetric study and description of the composition dependence of the mixing enthalpy of liquid Cu—Fe—Co aloys

The partial enthalpy of cobalt in ternary liquid Cu-Fe-Co alloys is studied at a temperature of 1873 K along sections characterized by ratios xCu/xFe = 3, 1, and 1/3 in the composition range xCo = 0–0.55. The experiments have been carried out on a high-temperature isoperibolic calorimeter. The composition dependences of the partial mixing enthalpy of the cobalt and the integral mixing enthalpy of Cu-Fe-Co melts are described using the Muggianu-Redlich-Kister equation over the entire concentration triangle. The contributions of a ternary interaction to the partial mixing enthalpy of cobalt and the integral mixing enthalpy of Cu-Fe-Co melts are calculated.