Partial Enthalpies Of Mixing Research Articles

Enthalpies of Mixing in Al−Ce−Co Liquid Alloys

AbstractThe enthalpies of mixing in liquid alloys of the ternary Al−Ce−Co system were determined along four sections (with a constant mole fraction ratio xCe/xCo=0.77/0.23 and xCe/xCo=0.35/0.65 up to xAl=0.2 at 1700 K; with xAl/xCo=0.76/0.24 up to xCe=0.3 and xAl/xCe=0.30/0.70 up to xCo=0.23 at 1823 K) via isoperibolic calorimetry. The enthalpies of mixing in the liquid Al−Ce−Co alloys are large exothermic values. A comparison of the experimentally obtained results for the enthalpies of mixing of liquid alloys and those calculated by the regular Redlich‐Kister‐Muggianu model, taking into account only the data for binary constituent systems, indicates the specific exothermic ‘ternary’ contribution to the energy of formation of Al−Ce−Co ternary alloys. Data on the partial enthalpy of mixing of cobalt at infinite dilution indicate the involvement of cerium 4 f‐electron in the process of alloy formation.

Thermodynamic studies in the Ce-Te binary system

Vapour pressure measurements in the Ce-Te system were carried out employing the isopiestic method. Four sets of isopiestic experimental runs were performed for the temperature range 805 – 1035 K for the composition span from ∼65 to ∼75 at% Te covering the Ce-Te phase diagram region encompassing the intermetallic compounds CeTe2, Ce2Te5 and CeTe3. Activity measurements, partial enthalpy of mixing of tellurium for CeTe2 intermetallic compound and Gibbs energy of the reaction between CeTe2 and Ce2Te5 are reported. A few phase boundaries of the Ce-Te phase diagram were redefined with the measured data and reported.

Hydrogen bonding in glassy trehalose-water system: Insights from density functional theory and molecular dynamics simulations.

We report a detailed density functional theory and molecular dynamics study of hydrogen bonding between trehalose and water, with a special emphasis on interactions in the amorphous solid state. For comparison, water-water interactions in water dimers and tetramers are evaluated using quantum calculations. The results show that the hydrogen bonding energy is dependent not only on the geometry (bond length and angle) but also on the local environment of the hydrogen bond. This is seen in quantum calculations of complexes in vacuum as well as in amorphous solid states with periodic boundary conditions. The temperature-induced glass transition in the trehalose-water system was studied using molecular dynamics simulations with varying cooling and heating rates. The obtained parameters of the glass transition are in good agreement with the experiments. Moreover, the dehydration of trehalose in the glassy state was investigated through a gradual dehydration with multiple small steps under isothermal conditions. From these simulations, the values of water sorption energy at different temperatures were obtained. The partial molar enthalpy of mixing of water value of -18 kJ/mol found in calorimetric experiments was accurately reproduced in these simulations. These findings are discussed in light of the hydrogen bonding data in the system. We conclude that the observed exothermic effect is due to different responses of liquid and glassy matrices to perturbations associated with the addition or removal of water molecules.

Calorimetric study of the enthalpy of mixing in the liquid systems Li-Zn and Li-Sn-Zn

Partial and integral molar enthalpies of mixing of binary liquid Li-Zn alloys and ternary liquid Li-Sn-Zn alloys were determined by drop calorimetry at 823 K. The binary system was investigated up to xZn = 0.85 and the integral mixing enthalpy was described with a Redlich-Kister-polynomial. Li-Zn shows an exothermic behavior and a minimum molar mixing enthalpy of about ΔHmix = -11.7 kJ⋅mol−1 at xZn = 0.6. The mixing enthalpy along nine ternary sections of Li-Sn-Zn (A: xLi/xSn ≈ 9:11, B: xLi/xSn ≈ 1:4, C: xSn/xZn ≈ 9:1, D: xSn/xZn ≈ 7:3, E: xSn/xZn ≈ 1:1, F: xLi/xZn ≈ 1:3, G: xLi/xZn ≈ 1:1, H: xLi/xZn ≈ 3:2, I: xLi/xZn ≈ 7:3) was investigated. Solid pieces of Li, Sn, and Zn respectively were dropped to the liquid binary starting alloys in the calorimeter at 823 K. The integral values at the crossing points of the various sections show excellent agreement. The course of the partial and integral enthalpy values along the sections A, D, E, F, G, H, and I indicate multiple-phase regions. The occurrence of such partially liquid and de-mixed liquid regions is discussed and compared with a calculated version of the isothermal section at 823 K which exhibits a large ternary liquid miscibility gap. The experimental ternary data allocated to the fully liquid monophasic regions was numerically fitted based on a Redlich-Kister-Muggianu polynomial for substitutional solutions including ternary interactions. In addition, a comparison with enthalpy values from the extrapolation methods based on binary data according to the Muggianu and Toop model, respectively, is shown. Both models fail to accurately reproduce the experimental values. Iso-enthalpy plots of calculated integral mixing enthalpy for stable and metastable fully homogeneous liquid alloys for the entire ternary system are shown.

THERMODYNAMIC PROPERTIES OF MELTS OF THE Eu-Ge AND Al-Eu-Ge SYSTEMS

The thermochemical properties of the melts of the Eu–Ge and Al–Eu–Ge systems at 1200–1400 K were determined for the first time by the method of calorimetry. It was established that the minimum value of the enthalpy of mixing of the melts of the Eu–Ge system is -49.1±4.4 for an alloy with xGe = 0.45, ΔH̅∞Eu = -145.7 ± 22.3; ΔH̅∞Ge = −166.8 ± 19.8 kJ/mole at T = 1400 K. The curve of enthalpy of mixing of the studied melts is almost symmetrical, which correlates with the behavior of alloys of this and similar systems in the solid state. The obtained data make it possible to consider the entire spectrum of Ge–Ln systems (lanthanides) and to explain what determines the thermodynamic properties of melts of the Eu–Ge system, in particular, and Ge–Ln, in general. Using the defined thermochemical properties of melts and the known phase diagram of the Eu–Ge system, the Gibbs energy, enthalpy, and entropy of formation of melts, associates in melts, and compounds of the Eu–Ge system were optimized and calculated according to the ideal associated solution (IAS) model. The calculated activities of the components in the melts of this system show large negative deviations from ideal solutions. Using the obtained thermochemical data, the temperatureconcentration dependences of Gibbs energies, enthalpies and entropies of the formation of melts and intermetallics, and the coordinates of the liquidus curve of the state diagram of the Eu–Ge system were also calculated according to the IAS model. The calculated liquidus curve and the one known from experimental data do not fully agree with each other. Comparison of ΔHmin of melts with enthalpies of formation, temperatures of melting Ln5Ge3 compounds, and differences in molar volumes and electronegativities of components of Ge–Ln systems depending on the serial number of Ln showed that they are correlated with each other, and ΔHmin of melts and Ln5Ge3 compounds differ little from each other. In addition, all dependences, with the exception of Δχ, are symbiotic and monotonic, with the exception of compounds and melts of binary Ge–Eu(Yb) systems. It was established that the integral and partial enthalpies of mixing of melts of radial sections with xEu/xGe = 0.85/0.15 and 0.3/0.7 of the Al–Eu–Ge system at 1400 K are exothermic. When aluminum is added to GexEu1-x melts, the thermal effect of its dissolution in the first section initially decreases, and then it increases, and in the second – it increases. This is due to the breaking of strong Eu–Ge bonds and the formation of lower energy bonds between Al and Eu. The thermodynamic properties of melts of the Al–Eu–Ge system were calculated using the “geometric” models and the Redlich-Kister-Mujianu model based on similar data for limiting binary systems. It is shown that those calculated according to the Redlich-Kister-Mujianu model with the ternary contribution L = -220 kJ/mole are in the best agreement with the experimental data. Therefore, the same model was used to calculate other thermodynamic properties of melts of the Al–Eu–Ge system.

Thermochemical investigations in the praseodymium-tellurium system

Vapour pressure measurements were carried out over the praseodymium-tellurium samples using a non-isothermal isopiestic method in the temperature range from 764 to 1210 K. From these results, thermodynamic activities of Te were derived as a function of temperature for the composition range ∼65–75 at% Te. This study revealed the existence of non-stoichiometry in the compounds PrTe1.9 and PrTe3. Further, it is found that the thermal stability of PrTe3 is extended beyond 728 K. Using an adapted Gibbs-Helmholts equation, partial molar enthalpies of mixing of Te were obtained for the composition range of PrTe1.9, which was used to convert the activity values of Te to a common average temperature of 1000 K. The relatively large variation of the activity across the homogeneity ranges of the phase PrTe1.9, indicates that it probably belong to the most stable intermetallic compound in this system. Gibbs energies of reaction between selected intermetallic compounds were also determined.

Measurement of mixing enthalpies for Bi-Zn lead-free solder system

Integral mixing enthalpy, partial mixing enthalpy & interaction parameters of the Bi-Zn alloys system has been calculated at 823 K and 923 K by using the drop calorimetric technique. This will help to predict the thermodynamic properties of multi-component systems by using values of interaction parameters of the Bi-Zn binary system. It is widely recognized that high concentrations of any elements can lead to toxicity; however, Sn and Zn are relatively less hazardous due to their essential roles in the human diet. Bi is low-risk metal with a history of medical use. So it may be a good replacement for lead-based solder alloys as lead is a very toxic element. Argon gas is used as a carrier and auxiliary gas to provide an inert atmosphere in the furnace. It is also visible that the enthalpy of mixing is asymmetrical with a composition of Zn. The integral enthalpy of mixing of the Bi-Zn system at 823 K and 923 K is endothermic in nature all through the composition, and its most value at xZn = 0.79 is 3717.035349 Jmol−1 and 3780.695484 Jmol−1 respectively. The theoretical Redlich-Kister polynomial substitutional solution model was applied to the data from these measurements in order to find the binary interaction parameter by least-square fitting. When the estimated and measured values are compared, it is found that there is a good agreement between them.

Experimental and theoretical partial and integral enthalpies of mixing of liquid quaternary Cu-In-Sn-Zn alloys

Experimental and theoretical partial and integral enthalpies of mixing of liquid quaternary Cu-In-Sn-Zn alloys

Дослідження і моделювання термодинамічних властивостей розплавів систем Bi—Cu—Eu і Cu—Eu

The partial and integral enthalpies of mixing of the melts of the Bi—Cu—Eu system were determined for the first time by the method of calorimetry on three radial sections with a constant ratio of two components: xCu/xEu = 0,3/0,7, xEu/xBi = 0,23/0,77, xEu/xBi = = 0,8/0,2 at T = 1400 ± 1 K. It is shown that the partial and integral enthalpies of mixing of the studied melts are mainly exothermic. Moreover, when adding bismuth to CuхEu1-х melt, the thermal effect of dissolution of the latter increases. This is due to the formation of strong bonds between Bi and Eu. In the other two sections, the opposite happens. Using the literature enthalpies of mixing of melts of the Cu—Eu system, investigated by the method of calorimetry at 1313—1480 K in the entire range of compositions, Gibbs energies, enthalpies and entropies of the formation of melts and intermetallics, their temperature-concentration dependences, and from them — the liquidus curve of the state diagram were calculated of the studied system according to the model of the ideal associated solution. It is shown that the activities of the components in these melts exhibit small negative deviations from ideal solutions and a small amount of associates, especially Eu5Cu, is formed in them. The maximum mole fraction of the EuCu associate reaches a value of 0,09, and the other two (Eu2Cu, EuCu5) — 0,05 and 0,02. From the critically analyzed thermodynamic properties of melts of the Cu—Eu, Bi—Cu and Bi—Eu systems, their reliable data were derived, from which similar parameters for liquid alloys of the ternary system Bi—Cu—Eu were calculated according to various known models. It is shown that the experimental mixing enthalpies of melts of the Bi—Cu—Eu system best agree with those calculated according to the Redlich—Kister—Mujianu model. It was established that ΔHmin = = −61,5 kJ/mol at xBi = 0,5. According to the same model, G, S of these melts were calculated. It was established that Gmin = –40 kJ/mol, and Smin = –18 J/mol•K, the minima of which also fall on the boundary subsystem Bi—Eu, i.e., the main contribution to the interaction energy between different-named atoms of melts of the Bi—Cu—Eu system contribute to the components of this subsystem. Keywords: calorimetry, melts, intermetallics, thermodynamic properties, systems, Bi—Cu—Eu, Cu—Eu, ideal associated solution model, phase equilibria.

The magnesium-palladium-silver system: Thermodynamic properties of the liquid phase

A drop calorimetry method was used to measure the partial and integral mixing enthalpies of Ag-Mg-Pd liquid solutions. The experiments were performed for six separate series of liquid alloys starting from the binary alloys with constant xAg/xMg ratios equal to 1/9, 1/3, 1/1, and 3/1 for (Ag0.10Mg0.90)1-xPdx and (Ag0.25Mg0.75)1-xPdx at 1116 K and (Ag0.50Mg0.50)1-xPdx and (Ag0.75Mg0.25)1-xPdx at 1279 K and xMg/xPd ratios of 9/1 and 8/1 for (Mg0.90Pd0.10)1-xAgx and (Mg0.80Pd0.20)1-xAgx at 1116 K. Then, using the thermodynamic properties of the binary systems in the form of the Redlich-Kister equations and the changes in mixing enthalpies provided by this study, the ternary interaction parameters were determined with the Muggianu model and our own software (TerGexHm). Based on the binary and ternary interaction parameters, the partial mixing enthalpies of Ag, Mg, and Pd were calculated for the same cross-sections where the measurements were conducted. These studies were the first step of an investigation of the Ag-Mg-Pd system before the calculation of the phase diagram for this ternary system.

Calorimetric studies and thermodynamic modelling of liquid Mg-Pb-Pd alloys

The thermodynamic properties of liquid Mg-Pb-Pd alloys had not yet been studied. Therefore, with the use of a MHTC 96 drop calorimeter, the first time, calorimetric measurements of the partial and integral mixing enthalpies of liquid Mg-Pb-Pd alloys were performed. Calorimetric measurements of five series of liquid alloys with compositions (Mg0.75Pb0.25)1-xPdx, (Mg0.50Pb0.50)1-xPdx (two series of this alloy were evaluated), (Mg0.25Pb0.75)1-xPdx, and (Pb0.90Pd0.10)1-xMgx were performed at a temperature of 1012 K. Thereafter, based on the obtained data on the mixing enthalpy and taking into account the thermodynamic properties of binary subsystems described by the Redlich-Kister equation, ternary excess term of the Mg-Pb-Pd liquid phase was evaluated by the Muggianu model. Using home-made software (TerGexHm), thermodynamic optimization resulting in ternary optimized parameters was done. The presented calorimetric measurements represent the first step in the investigation and assessment of ternary Mg-Pb-Pd system. Overall, the intention of the authors is to model the phase equilibria in both binary and ternary systems.

Термодинамічні властивості розплавів систем Cu—Yb і Cu—In—Yb

The partial and integral enthalpies of mixing of the melts the Cu-Yb system in the composition range 0 < xCu <0,7 and for 5 sections of Cu – In – Yb system with a constant ratio of the other two components (xCu/xIn=0,36/0,64; xCu/xIn= 0,62/0,38; xIn/xYb= 0,62/0,38; xCu/xYb =0,64/0,36; xCu/xYb =0,21/0,79) to x3 = 0.3 by method isoperibolical calorimetry in the temperature range 1453-1473K first were determined. Using the model of ideal associated solutions (IAR), all the thermodynamic properties (Gibbs energies of mixing melts, enthalpy and entropy of formation of intermetallic compounds and associates) of the Cu–Yb system were calculated. It turned out that the activity of the components in the melts of this system exhibit small negative deviations from ideal solutions. Calculations using the IAR model also made it possible to establish that with increasing temperature it increases slightly, but more significantly. Also were obtained the coordinates of the liquidus curve of the diagram state of the studied system. The principal contribution to the enthalpies of mixing in the liquid alloysof the Cu–In–Yb system gives the border subsystem In–Yb. Because the minimum of the mixing enthalpies in the ternary sysytem Cu–In–Yb shifts towards the equiatomic alloy concentration of subsystem In–Yb (-36,5±1,0) at Т= 1453 К. Using the experimental partial and integral enthalpies of mixing, the activities of the components in the melts of binary limiteyted system of melts of the Cu–In–Yb ternary system, calculated according to «geometric» and the Redlich-Kister-Mujian models in a wide range of concentrations. It is established that the experimental ∆H, and calculated analogical datas according to the Redlich-Kister-Mujianu model agree between. It is shown that the activities of the components in the melts of this system, calculated according to the Redlich-Kister model, show small negative deviations from ideal solutions at 1453 K. From these of data calculated G, S. It was found that Gmin = –19 kJ/mol, Smin = –15 J/mol*K for the alloy In0,5Yb0,5. This correlates with the determined thermochemical properties of the melts Cu –In– Yb system. Keywords: calorimetry, the melts, intermetallic, thermodynamic properties, Cu, Yb, In, the model of ideal associated solutions, the Redlich—Kister—Mujianu model, phase equilibria.

Термодинамічні властивості і фазові рівноваги в сплавах системи Eu—Pb

Firstthe partial and integral enthalpies of mixing of the melts of the Eu—Pb system were determined at a temperature of 1100—1350 K in everything range the composition by method isoperibolical calorimetry. It was established that of the melts of the Eu—Pb system are formed with the release of a big amount of heat: the minimum H = –51,7  ± 0,8 (at xPb = 0,4). Using the model of ideal associated solutions, all the thermodynamic properties (Gibbs energies, enthalpy and entropy of formation of melts, intermetallic compounds and associates) of the Eu—Pb system were calculated. It turned out that the activity of the components in the melts of this system exhibit moderate negative deviations from ideal solutions. According to the IAR model, the temperature-concentration dependences of the Gibbs energies, enthalpies and entropies formation of melts and intermetallics were calculated, and from them were obtained the coordinates of the liquidus curve of the diagram state of the studied system. As a result, the temperature-concentration dependences of the thermodynamic properties of all phases and the liquidus of the Eu—Pb system are obtained, those a thermodynamic description of this system is made. Keywords: calorimetry, melts, intermetallics, thermodynamic properties, Eu, Pb, model of ideal associated solutions, phase equilibria.

Role of mixing thermodynamic properties on the Soret effect.

We demonstrate that the modified Kempers model, a recently developed theoretical model for the Soret effect in oxide melts, is applicable for predicting the composition dependence of the Soret coefficient in three binary molecular liquids with negative enthalpies of mixing. We compared the theoretical and experimental values for water/ethanol, water/methanol, water/ethylene glycol, water/acetone, and benzene/n-heptane mixtures. In water/ethanol, water/methanol, and water/ethylene glycol, which have negative enthalpies of mixing across the entire mole fraction range, the modified Kempers model successfully predicts the signchange of the Soret coefficient with high accuracy, whereas, in water/acetone and benzene/n-heptane, which have composition ranges with positive enthalpies of mixing, it cannot predict the signchange of the Soret coefficient. These results suggest that the model is applicable in composition ranges with negative enthalpies of mixing and provides a framework for predicting and understanding the Soret effect from the equilibrium thermodynamic properties of mixing, such as the partial molar volume, partial molar enthalpy of mixing, and chemical potential.

Mixing Enthalpies of Liquid Ag-Mg-Pb Alloys: Experiment vs. Thermodynamic Modeling.

A drop calorimetric method was used to measure liquid Ag–Mg–Pb alloys. The partial and integral mixing enthalpies of the investigated alloys were determined at a temperature of 1116 K. The experiments were performed for four separate series starting from binary alloys with a constant xMg/xPb ratio of 1/3, 1, 3 ((Mg0.25Pb0.75)1−xAgx, (Mg0.50Pb0.50)1−xAgx, (Mg0.75Pb0.25)1−xAgx) and xAg/xMg ratio of 1/3 (Ag0.25Mg0.75)1−xPbx. Next, the ternary interaction parameters were determined using the Muggianu model, the thermodynamic properties of binary systems in the form of the Redlich-Kister equations and the values of the mixing enthalpy changes, which were determined in this study. The partial mixing enthalpies of Ag, Mg, and Pb were calculated based on the binary and elaborated ternary interaction parameters for the same intersections in which the measurements were conducted. It was found that the ternary Ag-Mg-Pb liquid solutions are characterized by negative deviations from the ideal solutions, with a maximal value slightly lower than –13 kJ/mol for alloys with the ratio (Mg0.75Pb0.25) and xAg = 0.4166.

Interaction of the components in liquid glass-forming Fe–Hf–Ni alloys

The enthalpies of mixing of liquid Fe–Hf–Ni alloys were studied at 1873 K by means of a high-temperature isoperibolic calorimeter. The investigations were performed along the section xFe/xNi = 3/1 at xHf = 0–0.18 and sections xFe/xNi = 1/1 and 1/3 at xHf = 0–0.46. The limiting partial enthalpies of mixing of undercooled liquid hafnium in liquid Fe–Ni alloys are (–135 ± 10) kJ mol−1 (at xFe/xNi = 3/1), (–155 ± 14) kJ mol−1 (at xFe/xNi = 1/1), and (–203 ± 15) kJ mol−1 (at xFe/xNi = 1/3). The integral mixing enthalpies are negative over the studied composition range. The integral mixing enthalpies show negative deviations from ideal mixing in the entire composition range. The thermodynamic properties of liquid ternary alloys are modeled using the associate solution model. The amorphization range in the ternary system is predicted by considering a total molar fraction of associates in undercooled liquid alloys.

Composition-dependent signinversion of the Soret coefficient of SiO2 in binary borosilicate melts.

Using a laser-induced local-heating experiment combined with temperature analysis, we observed the composition-dependent signinversion of the Soret coefficient of SiO2 in binary silicate melts, which was successfully explained by a modified Kempers model used for describing the Soret effect in oxide melts. In particular, the diffusion of SiO2 to the cold side under a temperature gradient, which is an anomaly in silicate melts, was observed in the SiO2-poor compositions. The theoretical model indicates that the thermodynamic mixing properties of oxides, partial molar enthalpy of mixing, and partial molar volume are the dominant factors for determining the migration direction of the SiO2 component under a temperature gradient.

Enthalpies of mixing of liquid Al–Fe–Ge alloys

Abstract The partial and integral enthalpies of mixing of Al–Fe–Ge melts have been measured by high-temperature calorimetry at 1740 ± 5 K. The integral enthalpies of mixing at 1173 K, are about 4 to 6 kJ mol–1 less negative than determined by electromotive force measurement [9]. The integral enthalpies of mixing have been also estimated on the basis of the Bonnier geometric model. The calculated values show a reasonable agreement with experimental data for x Ge > 0.3. A difference between experimental and estimated integral enthalpies of mixing (up to 2.5 kJ mol–1) is observed for ternary alloys with low germanium content.

Mixing enthalpy of the Co–Ti–Hf liquid alloys and regularities of the function change in the row of the ternary (Co, Ni, Cu)–Ti–Hf glass-forming melts

The partial molar mixing enthalpies of titanium and hafnium in liquid Co–Ti–Hf alloys were studied at 1900 K by high-temperature isoperibolic calorimetry along xCo/xHf = 3 and xCo/xHf = 3 sections. The partial mixing enthalpies of undercooled liquid titanium and hafnium in liquid alloys and the integral mixing enthalpy are negative over the studied composition range. The thermodynamic mixing functions of liquid (Co, Ni, Cu)–Ti–Hf alloys were modeled in the framework of the associate solution model. Regularities in the change of thermodynamic mixing functions in liquid glass-forming (Co, Ni, Cu)–Ti–Hf alloys are discussed considering donor–acceptor interaction of the components in the melts.

Drop Calorimetric Measurement of In-Zn system for Lead-Free solder applications

Circuit boards installed inside vehicles in the automotive industry are subjected to significant thermal stress due to temperatures above 150 °C. It can be reduced by using In-Zn solder alloys instead of hazardous Pb-based solder alloys, representing Pb-free solder alloys' development. The formation of an alloy is determined by its phase diagram, which is then measured to determine its thermodynamic properties. Using a drop calorimeter, the mixing heat effect (mixing enthalpy) as partial enthalpies and integral enthalpies of mixing in the liquid phase of In-Zn systems were investigated at 800 K and 900 K. The plots of mixing enthalpies are plotted versus zinc composition. When the Redlich–Kister polynomial is fitted, it is compared to our experimental data to identify the binary interaction parameters. This will help to predict the thermodynamic properties of multicomponent systems by using values of interaction parameters of the binary system (In-Zn). For all compositions at 800 K and 900 K, the model value was found to be close to the experimental values. The integral enthalpy of mixing of In-Zn system at 800 K and 900 K is endothermic in nature all through the composition and its most value in the range of XZn ∼ 0.48–0.52. It is also visible that the enthalpy of mixing is symmetrical with the composition of Zn.