Thermodynamic Properties Of Multicomponent Systems Research Articles

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.

Высокотемпературные термодинамические свойства керамики на основе оксидов гафния и редкоземельных элементов

In the review results of thermodynamic properties and vaporization processes of ceramics based on hafnium and rare earth oxides studied during recent years using high temperature mass spectrometry up to the temperature 3000 K were classified. Advantages of semi-empirical and statistical thermodynamic approaches for the prediction of thermodynamic properties of multicomponent systems based on oxides considered were illustrated.

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.

MMA‐EoS: A Computational Framework for Mineralogical Thermodynamics

AbstractWe present a newly developed software framework, MMA‐EoS, that evaluates phase equilibria and thermodynamic properties of multicomponent systems by Gibbs energy minimization, with application to mantle petrology. The code is versatile in terms of the equation‐of‐state and mixing properties and allows for the computation of properties of single phases, solution phases, and multiphase aggregates. Currently, the open program distribution contains equation‐of‐state formulations widely used, that is, Caloric‐Murnaghan, Caloric–Modified‐Tait, and Birch‐Murnaghan–Mie‐Grüneisen‐Debye models, with published databases included. Through its modular design and easily scripted database, MMA‐EoS can readily be extended with new formulations of equations‐of‐state and changes or extensions to thermodynamic data sets. We demonstrate the application of the program by reproducing and comparing physical properties of mantle phases and assemblages with previously published work and experimental data, successively increasing complexity, up to computing phase equilibria of six‐component compositions. Chemically complex systems allow us to trace the budget of minor chemical components in order to explore whether they lead to the formation of new phases or extend stability fields of existing ones. Self‐consistently computed thermophysical properties for a homogeneous mantle and a mechanical mixture of slab lithologies show no discernible differences that require a heterogeneous mantle structure as has been suggested previously. Such examples illustrate how thermodynamics of mantle mineralogy can advance the study of Earth's interior.

Calculations of vapor–liquid equilibria of the H2O-N2 and H2O-H2 systems with improved SAFT-LJ EOS

The SAFT-LJ equation of state (EOS) improved by our previous study, which introduces a multi-polar term to explicitly account for the contribution of multi-polar interactions (including the dipole–dipole, dipole–quadrupole and quadrupole–quadrupole interactions), is applied to the H2O-N2 and H2O-H2 systems. N2 and H2 are modeled as chain molecules with evenly distributing quadrupole moments. The van der Waals one-fluid mixing rule was used to calculate parameters for mixtures and two binary parameters for the interactions of H2O-N2 and H2O-H2 pairs were evaluated from mutual solubility data of binary water–gas systems. Comparison with the experimental data shows that this molecular-based EOS can well represent vapor–liquid equilibria of H2O-N2 and H2O-H2 systems over a wide P–T range (273–623K and 0–1000bar). In addition, the effect of the dipole moment of H2O and quadrupole moments of N2, H2 and CO2 on VLE of the CO2-N2, H2O-N2 and H2O-H2 systems was checked. It was found that the SAFT-LJ model without any polar term gives good prediction (without any binary parameters) for vapor compositions of the CO2-N2, H2O-N2 and H2O-H2 systems except in the critical region and taking account of the contribution of multi-polar interactions does not improve the prediction of this EOS any more. However, taking account of multi-polar interactions indeed significantly improves the prediction of this EOS for compositions of liquid phase. We argue that it is the reason why this EOS can quantitatively represent VLE of highly non-ideal water–gas systems. Comparison of calculations of this EOS with experimental VLE data of the ternary CO2-N2-H2O system confirms the prediction capability of this EOS for thermodynamic properties of multi-component systems.

Phase diagram calculations of Al–Cr–Nb–Ti quaternary system

The phase diagrams and thermodynamics of the complex systems are of great importance for the materials development and processing optimisation. The Calphad method is a powerful tool to predict the phase diagrams and thermodynamic properties of multicomponent systems from the corresponding database. In this work, a reliable thermodynamic database of the Al–Cr–Nb–Ti quaternary system, which is the basis for high performance gamma titanium aluminide alloys, was constructed based on the thermodynamic descriptions of its subsystems. The database contains 27 phases. The thermodynamic models used for each phases were brielfy introduced. The thermodynamic descriptions of the six sub-binary and four sub-ternary sytems were discussed. The effects of the alloying element on the stabilities of phase were predicted.

Thermodynamic Calculations of Phase Equilibria and Phase Fractions of a β-Solidifying TiAl Alloy using the CALPHAD Approach

ABSTRACTThe CALPHAD (CALculation of PHAse Diagrams) method is widely recognized as a powerful tool in both scientific and industrial development of new materials and processes. For the implementation of consistent databases, where each phase is described separately, models are used which are based on physical principles and parameters assessed from experimental data. Such a database makes it possible to perform realistic calculations of thermodynamic properties of multi-component systems. However, a commercial available TiAl database can be applied for thermodynamic calculations to both conventional Ti-base alloys and complex intermetallic TiAl alloys to describe experimentally evaluated phase fractions as a function of temperature. In the present study calculations were done for a β-solidifying TiAl alloy with a nominal composition of Ti-43.5Al-4Nb-1Mo-0.1B (in at. %), termed TNMTM alloy. At room temperature this alloy consists of ordered γ-TiAl, α2-Ti3Al and β0-TiAl phases. At a certain temperature α2 and β0 disorder to α and β, respectively. Using the commercial database the thermodynamic calculations reflect only qualitative trends of phase fractions as a function of temperature. For more exact quantitative calculations the commercial available thermodynamic database had to be improved for TiAl alloys with high Nb (and Mo) contents, as recently reported for Nb-rich γ-TiAl alloys. Therefore, the database was modified by experimentally evaluated phase fractions obtained from quantitative microstructure analysis of light-optical and scanning electron micrographs as well as conventional X-ray diffraction after long-term heat treatments and by means of in-situ highenergy X-ray diffraction experiments. Based on the CALPHAD-conform thermodynamic assessment, the optimized database can now be used to correctly predict the phase equilibria of this multi-component alloying system, which is of interest for applications in automotive and aircraft engine industry.

Phase diagram of CeO2–CoO for nano-sized powders

The CALPHAD (Calculation of Phase Diagrams) framework to calculate the thermodynamic properties of multicomponent systems is extended to account for the change in thermodynamic properties by the size effect in small particle systems. We have applied this framework to the CeO2–CoO binary in order to elucidate the “liquid phase sintering like” fast densification at unusually low temperatures of cobalt oxide doped ceria. The phase diagram for 5 nm particles shows a significant drop of the eutectic from 1645 °C to 1327 °C. The size-dependent thermodynamic stability of intergranular films is examined using CALPHAD approach and melting temperature of 1180 °C is found for 1 mol% CoO doped CeO2 corresponding to an intergranular film thickness between 1 and 4 nm. This result comes close to the unusual low sintering temperatures of 1100 °C, with a “liquid-sintering”-like characteristic that was previously experimentally observed for CeO2 with small amounts of transition metal oxides such as CoO.

Estimation of thermodynamic properties of multicomponent systems on the basis of generalized hole theory

In the present work a generalized hole theory is applied to compute the energy of vaporization, heat of vaporization, cohesive energy density, solubility parameter and van der Waals constant of four ternary [viz., cyclohexane + n-heptane + n-hexane (I), toluene + n-heptane + n-hexane (II), n-hexane + n-heptane + n-decane (III), n-hexane + cyclohexane + benzene (IV)] and four quaternary [n-decane + n-hexane + cyclohexane + benzene (VIII), pentane + hexane + cyclohexane + benzene (V), pentane + hexane + benzene + toluene (VI) , pentane + cyclohexane + heptane + toluene (VII)] liquid systems at 298.15 K. The calculated values are compared with those obtained experimentally. The present study encourages the concept of the existence of holes in mixtures.

Computation of liquid-liquid equilibria and phase stabilities: implications for RH-dependent gas/particle partitioning of organic-inorganic aerosols

Abstract. Semivolatile organic and inorganic aerosol species partition between the gas and aerosol particle phases to maintain thermodynamic equilibrium. Liquid-liquid phase separation into an organic-rich and an aqueous electrolyte phase can occur in the aerosol as a result of the salting-out effect. Such liquid-liquid equilibria (LLE) affect the gas/particle partitioning of the different semivolatile compounds and might significantly alter both particle mass and composition as compared to a one-phase particle. We present a new liquid-liquid equilibrium and gas/particle partitioning model, using as a basis the group-contribution model AIOMFAC (Zuend et al., 2008). This model allows the reliable computation of the liquid-liquid coexistence curve (binodal), corresponding tie-lines, the limit of stability/metastability (spinodal), and further thermodynamic properties of multicomponent systems. Calculations for ternary and multicomponent alcohol/polyol-water-salt mixtures suggest that LLE are a prevalent feature of organic-inorganic aerosol systems. A six-component polyol-water-ammonium sulphate system is used to simulate effects of relative humidity (RH) and the presence of liquid-liquid phase separation on the gas/particle partitioning. RH, salt concentration, and hydrophilicity (water-solubility) are identified as key features in defining the region of a miscibility gap and govern the extent to which compound partitioning is affected by changes in RH. The model predicts that liquid-liquid phase separation can lead to either an increase or decrease in total particulate mass, depending on the overall composition of a system and the particle water content, which is related to the hydrophilicity of the different organic and inorganic compounds. Neglecting non-ideality and liquid-liquid phase separations by assuming an ideal mixture leads to an overestimation of the total particulate mass by up to 30% for the composition and RH range considered in the six-component system simulation. For simplified partitioning parametrizations, we suggest a modified definition of the effective saturation concentration, Cj*, by including water and other inorganics in the absorbing phase. Such a Cj* definition reduces the RH-dependency of the gas/particle partitioning of semivolatile organics in organic-inorganic aerosols by an order of magnitude as compared to the currently accepted definition, which considers the organic species only.

New Parametric Model to Correlate the Gibbs Excess Function and Other Thermodynamic Properties of Multicomponent Systems. Application to Binary Systems

A new empirical mathematical model for the Gibbs excess function, gE = ψ(p,T,x), is presented for a multicomponent system. Dependence on the composition is achieved through the so-called active fraction, zi, which, in turn, is related to the molar fraction xi of the components of a solution and a parameter kij, the determination of which is also indicated. The efficacy of the model in relation to its extension of application is discussed, considering various cases and three possible ways to calculate the parameter kij. This produces different versions of the model for data correlation the advantages of which are discussed. The model proposed for the Gibbs excess function adopts the following generic expression, gE(P,T,x) = z(x)[1 − z(x)]∑i=0gi(P,T)zi where gi(P,T) = gi1 + gi2P2 + gi3PT + gi4/T + gi5T2, which can be applied to a general case of vapor−liquid equilibrium with variation of the three main variables xi, p, and T, or by considering the experimental values for two important situations, isobaric and isothermal, which are also studied here. Other mixing properties are obtained via mathematical derivation, and a simultaneous correlation is carried out on several of them. The model has been applied to various binary systems for which experimental data are available in the literature and over a wide range of p and T. The results obtained can be considered acceptable.

Thermodynamic properties of multicomponent systems and hole theory

For the first time hole theory is applied to calculate isothermal compressibility, thermal expansivity, ultrasonic velocity and internal pressure of ternary and quaternary liquid mixture. The obtained calculated values are compared with experimental findings. A fairly good agreement is found. The results of calculations show that for all the systems under consideration, the calculated values of various thermodynamic parameters show the same trend as observed experimentally.

The development of the COST 531 lead-free solders thermodynamic database

The methods for modeling the thermodynamic properties of multicomponent systems are described in this article. The rules for creating a consistent database for muticomponent systems are described in general terms and documented in relation to the thermodynamic database for lead-free solders, developed within the scope of European Cooperation in the Field of Scientific and Technical Research Action 531. New assessments and reassessments of the Bi-Sn-Zn, Cu-Ni-Sn, and Ag-Cu-Sn systems are shown as examples illustrating the application of the database for the modeling of lead-free solder materials.

Enthalpies of formation for the Al–Cu–Ni–Zr quaternary alloys calculated via a combined approach of geometric model and Miedema theory

A method to extrapolate the thermodynamic properties of quaternary alloys from constitutive binary systems is presented. The method is based on Miedema's theory, and the asymmetry of thermodynamic properties of constitutive binary alloys is considered in the present model. The dependence of asymmetric constituent on the choice in Toop model has been overcome. This method has been applied to calculate the enthalpies of formation for ternary alloys. In the present work, the proposed method is used to calculate the mixing enthalpies of Al–Cu–Ni–Zr quaternary alloys and its constitutive subsystems. The good agreement between calculation and experimental data indicates that the present method is reasonable for predicting the thermodynamic properties of multi-component system.

Thermodynamic description for concentrated metallic solutions using interaction parameters

The integral molar excess Gibbs energy of a multicomponent system is expressed in terms of interaction parameters, from which the analytical formulae of the activity coefficients of the solutes and solvent, as Eqs. [23] and [24], were deduced. This approach, named the e approach, is able to describe quantitatively the thermodynamic properties of multicomponent systems. It features thermodynamic consistency, high accuracy, and a rather small influence of the higher-interaction parameters on the thermodynamic properties of metallic solutions. A simple modification to the first-order interaction parameters extends the e approach, to be applicable to systems with strong interactions between components at both low and concentrated levels.

ChemInform Abstract: GENERAL METHODS FOR CALCULATING THERMODYNAMIC PROPERTIES OF MULTICOMPONENT SYSTEMS FROM KNOWN FUNCTIONS OF ACTIVITY, ACTIVITY RATIO AND ACTIVITY PRODUCT

Chemischer InformationsdienstVolume 16, Issue 23 Physical Inorganic Chemistry ChemInform Abstract: GENERAL METHODS FOR CALCULATING THERMODYNAMIC PROPERTIES OF MULTICOMPONENT SYSTEMS FROM KNOWN FUNCTIONS OF ACTIVITY, ACTIVITY RATIO AND ACTIVITY PRODUCT Z.-C. WANG, Search for more papers by this author Z.-C. WANG, Search for more papers by this author First published: June 11, 1985 https://doi.org/10.1002/chin.198523018AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume16, Issue23June 11, 1985 RelatedInformation

General Methods for Calculating Thermodynamic Properties of Multicomponent Systems from Known Functions of Activity, Activity Ratio and Activity Product

Article General Methods for Calculating Thermodynamic Properties of Multicomponent Systems from Known Functions of Activity, Activity Ratio and Activity Product was published on January 1, 1984 in the journal Zeitschrift für Physikalische Chemie (volume 141, issue 1).

Viscosity, refractive index, and surface tension of multicomponent systems: Mathematical representation and estimation from data for binary systems

An equation previously developed for estimation of the excess thermodynamic properties of multicomponent systems from binary mixing data has been applied to other physical properties through extrathermodynamic properties such as the excess Gibbs free energy of activation for viscous flow, molar refractivity, and exess surface free energy. This equation provides reasonably accurate predictions for viscosity, refractive index and surface tension of ternary and quaternary systems, given the properties of the various binary combinations of the components. The equation also serves quite well as a point-of-departure for mathematical representation of experimental data, in that all of the data considered could be represented within experimental uncertainty with the aid of no more than one adjustable parameter for each multicomponent system.

Matrix Representation of Thermodynamic Properties of Multicomponent Systems

Thermodynamic properties of multicomponent systems can be simply generated from matrices whose elements represent basic data. Although this concept is quite general, it has been applied specifically to generating the entropy, enthalpy, and free energy of multicomponent systems, as functions of composition and temperature. Each of these properties can be generated from the product of three matrices: a row vector whose elements depend only on the composition, a rectangular matrix whose elements remain invariant for a given system, and a column vector whose elements depend only on the temperature. A given row of the rectangular matrix corresponds to one of the species in the system and may be regarded as a thermodynamic-property vector for that species. Thermodynamic-property vectors have been calculated and tabulated for 143 species which are stable at high temperatures. The matrix representation of thermodynamic data has proved to be particularly useful in formulating large multicomponent problems for a digital computer. Two numerical examples illustrate the utility of the method.