Ternary Parameters Research Articles

Topological and Thermodynamic Investigations of Ternary Mixtures Containing Cyclic Ethers: Excess Molar Volumes

Excess molar volumes, \(V_{123}^{\mathrm{E}}\), of 1,3-dioxolane or 1,4-dioxane (1) + aniline (2) + benzene or toluene (3) ternary mixtures have been determined over the entire mole fraction range at 308.15 K. \(V_{123}^{\mathrm{E}}\) data have been fitted to the Redlich-Kister equation to evaluate ternary adjustable parameters and standard deviations. The observed \(V_{123}^{\mathrm{E}}\) data have been analyzed in terms of (i) Graph theory, (ii) Prigogine-Flory-Patterson theory, and (iii) Sanchez and Lacombe theory. It has been observed that \(V_{123}^{\mathrm{E}}\) values predicted by Graph theory compare well with the corresponding experimental values.

Phase Relations in the ZrO2-Nd2O3-Y2O3 System: Experimental Study and Advanced Thermodynamic Modeling

Phase equilibria in the ZrO2-Nd2O3-Y2O3 system at 1523-1873 K have been investigated by x-ray diffraction (XRD) and scanning electron microscopy combined with energy dispersive x-ray spectroscopy (SEM/EDX). Temperatures of phase transformations were determined by differential thermal analysis. Temperatures of invariant reactions in the ZrO2-Nd2O3 system F = A + Pyr and H = F + A were determined as 1763 and 2118 K respectively and thermodynamic parameters of phases were re-assessed. Phase transformations in ternary systems were determined at 1732 K for composition ZrO2-48.46Nd2O3-5.38Y2O3 (mol%) and at 1744 and 1881 K for composition ZrO2-79.09Nd2O3-2.75Y2O3 (mol%). They were interpreted using XRD investigation before and after DTA as Pyr + B → F, Pyr → F and A → B, respectively. The solubility of the Y2O3 in pyrochlore phase was found to exceed 10 mol%. The thermodynamic parameters of the ZrO2-Nd2O3-Y2O3 system were reassessed taking into account solubility of Y2O3 in the Nd2Zr2O7 pyrochlore phase (Pyr). It is assumed that Y3+ substitutes Nd3+ and Zr4+ in their preferentially occupied sublattices. Ternary parameter was introduced into fluorite phase (F) for better reproducing of phase equilibria. Mixing parameters were reassessed for phase A (Nd2O3 based solution), monoclinic phase B and cubic phase C (Y2O3 based solution). The isothermal sections calculated for the ZrO2-Nd2O3-Y2O3 system are in the reasonable agreement with experimental results.

Oscillatory testing of o/w emulsions containing mixed emulsifiers of the surfactant-long chain alcohol type: self-bodying action

Abstract Liquid paraffin-in-water emulsions stabilized by cationic (cetrimide) or non-ionic (cetomacrogol) surfactants and cetostearyl alcohol were examined at 25° in oscillatory mode, using the Weissenberg Rheogoniometer with parallel plates coupled to a digital transfer function analyser. Ternary systems, formed by dispersing the mixed emulsifiers in water, were similarly investigated. Each preparation was tested in the linear viscoelastic region, and fundamental rheological parameters, the storage modulus (G') and the real viscosity (ẽ') were derived as functions of frequency over the range 7.91 times 10−4to 25 Hz. All ternary systems behaved similarly with respect to frequency. As this increased, G' rose and ẽ' fell. These trends were related to the viscoelastic nature of the systems. Both mixed emulsifiers exhibited self-bodying mechanisms, so that emulsion consistency increased as the mixed emulsifier concentration rose. This was shown by increases in G' and ẽ' at each frequency. The shapes of the plots and other rheological properties were related to viscoelastic gel networks formed in the emulsion continuous phases. The ternary system parameters implied that emulsion networks were similar to ternary gels, that is, they formed by the interaction of long chain alcohol and aqueous surfactant solution. The oscillatory data were compared and correlated with creep data derived for similar ionic and non-ionic dispersed systems, previously described.

Oscillatory testing of o-w emulsions containing mixed emulsifiers of the surfactant-long chain alcohol type: influence of surfactant chain length.

Abstract A Weissenberg Rheogoniometer with parallel plates coupled to a Solartron Digital Transfer Function Analyser was used at 25° in oscillatory mode to investigate liquid paraffin-in-water emulsions stabilized by alkyltrimethylammonium bromides (of C12-C18 chain lengths) and cetostearyl alcohol. Ternary systems, formed by dispersing the quaternary surfactants and cetostearyl alcohol in water, were similarly examined. Each preparation was tested in the linear viscoelastic region and fundamental rheological parameters, the storage modulus (G') and the dynamic viscosity (η′), were derived as functions of frequency over the range 7.91 × 10−4 to 25 Hz. The rheological properties of the emulsions were related to viscoelastic gel networks present in the continuous phases. The corresponding ternary system parameters implied that these networks were formed by the interaction of cetostearyl alcohol and aqueous surfactant solution. Ternary systems and emulsions behaved similarly with respect to frequency. As this increased, G' rose and η′ fell, the latter through several logarithmic decades. At low frequencies, G' and η′ rose as the quaternary alkyl chain length increased. Formulations containing quaternary surfactants of medium chain lengths (C14 and C16) formed strong viscoelastic networks. The C12 systems contained tenuous networks, and networks formed from the C18 surfactant were not as rigid as predicted by the trend of the lower homologues. The oscillatory data were compared and correlated with creep data described previously.

Topological investigations of excess molar volumes and excess isentropic compressibilities of ternary mixtures containing 1-methyl pyrrolidin-2-one at 308.15 K

Excess molar volumes and speeds of sound, of 1-methyl pyrrolidin-2-one ( i) + benzene or methyl benzene or cyclohexane ( j) + propan-1-ol ( k) ternary mixtures have been measured as a function of composition at 308.15 K using dilatometer and interferometer. The observed speeds of sound data have been utilized to calculate excess isentropic compressibilities of the studied mixtures. The observed excess molar volumes and excess isentropic compressibility values have been fitted to the Redlich–Kister equation to predict ternary adjustable parameters and standard deviations. The resulting data have also been analyzed in terms of Graph theory and Flory–Prigogine–Patterson theory. It has been observed that excess molar volumes and excess isentropic compressibility values determined by the Graph theory compare well with their corresponding experimental values.

Thermodynamic assessment of the ternary AgNO 3–LiNO 3–NaNO 3 system

Based on the available experimental information, the AgNO 3–LiNO 3–NaNO 3 ternary system and its low order AgNO 3–LiNO 3, AgNO 3–NaNO 3 and LiNO 3–NaNO 3 binary systems are thermodynamically assessed using the Calphad method. A set of parameters describing the Gibbs energies of the different phases is presented. Ternary parameters are necessary to describe the liquid phase in a neutral species model where each nitrate is treated as a constituent. Calculated phase diagrams and thermodynamical functions for the three limiting binary systems show good agreement with experimental data. In the ternary AgNO 3–LiNO 3–NaNO 3 system we have calculated two vertical sections which are in reasonable agreement with the reported experimental data. Also, several isothermal sections are calculated.

Excess molar volumes of ternary liquid mixtures composed of 1, 4-dioxane, o-toluidine, and aromatic hydrocarbon at temperature of 308.15 K

Excess molar volumes, V ijk E , of 1,4-dioxane ( i) + o-toluidine ( j) + benzene or toluene or m- or p-xylene ( k) ternary mixtures have been measured dilatometrically as a function of composition at 308.15 K. The resulting V ijk E data have been fitted to Redlich–Kister equation to evaluate ternary adjustable parameters and standard deviations σ( V ijk E ). The observed V ijk E data have been analyzed in terms of (i) Graph theory; and (ii) Prigogine–Flory–Patterson theory. It has been observed that Graph theory correctly predicts the sign and magnitude of V ijk E values.

Topological Investigations of Excess Molar Volumes and Excess Isentropic Compressibilities of Ternary Mixtures Containing Pyrrolidin-2-one at 308.15 K

Excess molar volumes, $${V^{\rm E}_{ijk}}$$ , and speeds of sound, u ijk , of pyrrolidin-2-one (2-Py) (i)+benzene or methyl benzene (j)+propan-1-ol (k) ternary mixtures and speeds of sound, u ij , of benzene or methyl benzene (i)+propan-1-ol (j) binary mixtures have been measured dilatometrically and interferrometrically over the complete mole fraction range at 308.15 K. Speed-of-sound data have been utilized to evaluate excess isentropic compressibilities for binary and ternary mixtures. $${V^{\rm E}_{ijk}}$$ and $${\left({\kappa_S^{\rm E}}\right)_{ijk}}$$ values have been fitted to a Redlich–Kister equation to predict ternary adjustable parameters and standard deviations. Topological investigations employed for predicting excess molar volumes and excess isentropic compressibilities, $${\left({\kappa _S^{\rm E}} \right)_{ij}}$$ , of 2-Py + benzene or methyl benzene or propan-1-ol binary mixtures have been extended to ternary mixtures (by employing the concept of a connectivity parameter of third degree, 3 ξ, of a molecule) to obtain an expression that describes well the measured $${V^{\rm E}_{ijk}}$$ and $${\left({\kappa_S^{\rm E}}\right)_{ijk}}$$ values.

Excess Molar Volumes of Ternary Mixtures of a Cyclic Ether with Aromatic Hydrocarbons at 308.15 K

Excess molar volumes, \(V_{ijk}^{E}\), are reported for ternary mixtures of tetrahydropyran (i)+benzene (j)+toluene or o- or p-xylenes (k) and tetrahydropyran (i)+toluene (j)+o- or p-xylenes (k) as a function of composition at 308.15 K. These \(V_{ijk}^{E}\) values have been fitted to the Redlich–Kister equation to predict ternary adjustable parameters and standard deviations. The measured \(V_{ijk}^{E}\) data have been analyzed in terms of Graph theory (which involves the topology of the constituents of mixtures). It has been observed that \(V_{ijk}^{E}\) values predicted by Graph theory compare well with their corresponding experimental values.

Thermodynamics study of the Cs2SO4-MgSO4-H2O system at the temperature 298.15 K

The Pitzer ion-interaction model has been used for thermodynamics simulation of the ternary system Cs2SO4-MgSO4-H2O at 298.15 K. The Pitzer ternary mixing parameter $$ \psi _{CsMgSO_4 } $$ and thermodynamic characteristics for double salt Cs2SO4 · MgSO4 · 6H2O have been calculated and the theoretical solubilities isotherm has been plotted.

Thermodynamic analysis of phase equilibria in the Cr–Mo–B ternary system

A thermodynamic analysis of the phase equilibria in the Cr–Mo–B ternary system has been carried out by combining first-principles calculations with the CALPHAD approach. The thermodynamic descriptions of three binary systems relevant to this ternary phase diagram were taken from previous studies. The enthalpy of formation of the (Cr,Mo) 2B (Al 2Cu-type, tI12, space group I 4 / m c m ), (Cr,Mo) 3B 2 (U 3Si 2-type, tP10, space group P 4 / m b m ), (Cr,Mo)B (CrB-type, oC8, space group Cmcm), (Cr,Mo) 3B 4 (Ta 3B 4-type, oI14, space group Immm), and (Cr,Mo)B 2 (AlB 2-type, hP3, space group P 6 / m m m ) phases were obtained from first-principles calculations. The ternary thermodynamic parameters evaluated using these theoretical values, as well as the available experimental information on the phase boundaries, enabled us to calculate the phase equilibria in the Cr–Mo–B ternary system over the entire composition and temperature ranges.

Thermodynamic and acoustic properties for binary and ternary mixtures of cyclic ethers with industrially important solvents at 308.15 K

Speeds of sound data, u ijk of 1,3-dioxolane or 1,4-dioxane( i) + benzene or toluene ( j) + formamide or N,N-dimethylformamide ( k) ternary mixtures and their sub-binary mixtures, u ij of 1,3-dioxolane or 1,4-dioxane ( i) + benzene or toluene or formamide or N,N-dimethylformamide ( j); benzene or toluene ( i) + formamide or N,N-dimethylformamide ( j) have been measured using a quartz crystal interferometer as a function of composition at 308.15 K. The experimental data have been utilized to evaluate excess isentropic compressibilities of binary, ( κ S E ) ij and ternary, ( κ S E ) ijk mixtures and the same have been fitted to Redlich–Kister equation to predict binary and ternary adjustable parameters along with standard deviations. ( κ S E ) ij and ( κ S E ) ijk data have also been analyzed in terms of Graph and Flory theories. It has been observed that predicted ( κ S E ) ij and ( κ S E ) ijk values by Graph theory compare well with their corresponding experimental values.

Excess molar volumes and excess isentropic compressibilities of tetrahydropyran + benzene + cyclo or n-alkanes ternary mixtures at 308.15 K

Excess molar volumes, V i j k E , speeds of sound, u ijk , of tetrahydropyran ( i) + benzene ( j) + cyclohexane or n-hexane or n-heptane ( k) ternary mixtures have been measured as a function of composition at 308.15 K and atmospheric pressure. The observed speeds of sound data of the investigated ternary mixtures have been utilized to calculate their excess isentropic compressibilities, ( κ S E ) i j k . The V i j k E and ( κ S E ) i j k have been fitted to the Redlich–Kister equation to calculate ternary adjustable parameters and standard deviations. Connectivity parameters of third degree of the constituents of mixtures (which in turn depends on the topology of a molecule) have been employed to determine excess molar volumes, V i j k E , and excess isentropic compressibilities, ( κ S E ) i j k . It has been observed that V i j k E and ( κ S E ) i j k values calculated by the Graph theory (which involves connectivity parameter of third degree of a molecule) compare well with their corresponding experimental values.

Thermodynamic Properties of Ternary Liquid Mixtures of 2-Pyrrolidinone with Aromatic Hydrocarbons

Molar excess volumes, \({V^{\rm E}_{ijk}}\), and speeds of sound, uijk, of 2-pyrrolidinone (2-Py) (i) + toluene (j) + o-xylene or p-xylene (k) ternary mixtures have been determined by using a dilatometer and interferometer as a function of composition at 308.15 K. The speeds of sound of ternary mixtures have been utilized to predict their excess isentropic compressibilities. The Redlich-Kister equation has been fitted to the molar excess volumes, \({V^{\rm E}_{ijk}}\), and excess isentropic compressibilities, \({\left( {\kappa _S^{\rm E}}\right)_{ijk}}\), to predict ternary adjustable parameters and standard deviations. The observed data have been analyzed in terms of the Flory theory and the Sanchez and Lacombe theory.

Experimental investigation and thermodynamic modelling in the ZrO2–La2O3–Y2O3 system

Abstract Phase equilibria in the La 2 Zr 2 O 7 –Y 2 O 3 join were studied in the temperature interval between 1250 and 1600 °C using the X-ray diffraction and thermal analysis. It was demonstrated that the maximal solubility of Y 2 O 3 in the La 2 Zr 2 O 7 (pyrochlore structure) was approximately 20 mol% of Y 2 O 3 . In mixtures containing more than 20 mol% Y 2 O 3 the La 2 Zr 2 O 7 reacted with Y 2 O 3 forming the fluorite structure at increasing temperature. The compound energy formalism was applied to describe solubility of Y 2 O 3 in pyrochlore structure assuming that Y 3+ can occupy both La 3+ and Zr 4+ enriched sites in the crystal structure. The Gibbs energies of compounds with pyrochlore structure were assessed. Ternary mixing parameters were included in thermodynamic description of the fluorite phase to reproduce in calculations its wide homogeneity range extending from ZrO 2 –Y 2 O 3 binary in the direction of LaYO 3 . Calculated phase diagrams reproduce general character of experimental data.

Thermodynamic modeling of the Al–Bi, Al–Sb, Mg–Al–Bi and Mg–Al–Sb systems

All available thermodynamic and phase diagram data of the binary Al–Bi and Al–Sb systems and ternary Mg–Al–Bi and Mg–Al–Sb systems were critically evaluated, and all reliable data were used simultaneously to obtain the best set of the model parameters for each ternary system. The Modified Quasichemical Model used for the liquid solution shows a high predictive capacity for the ternary systems. The ternary liquid miscibility gaps in the Mg–Al–Bi and Mg–Al–Sb systems resulting from the ordering behaviour of the liquid solutions can be well reproduced with one additional ternary parameter. Using the optimized model parameters, the experimentally unexplored portions of the Mg–Al–Bi and Mg–Al–Sb ternary phase diagrams were more reasonably predicted. All calculations were performed using the FactSage thermochemical software package.

Thermodynamic assessment of the Pd–H–D–T system

The three binary systems H–Pd, D–Pd and Pd–T have been modelled in the frame of the Calphad approach. A complete literature search has been undertaken and the most significant experimental data have been selected for a thermodynamic assessment of these systems. To complement the available data, pressure–composition curves have been measured for the three systems in the present work. The three systems are characterized by a strong isotope effect which is well taken into account in the modelling. They have been combined to perform calculations in the quaternary H–D–Pd–T system. It is shown that a reasonable extrapolation can be made without the use of ternary parameters if it is calculated with the so-called Toop model.

Excess molar volumes and excess isentropic compressibilities of 2-pyrrolidinone at 308.15 K

Molar excess volumes V ijk E and speeds of sound, u ijk of 2-pyrrolidinone (i) + benzene (j) + toluene or o- or p-xylene (k) ternary mixtures have been measured as a function of composition at 308.15 K. The observed speeds of sound data have been utilized to calculate their excess isentropic compressibilities. The observed data have been fitted to Redlich–Kister equation to calculate ternary adjustable parameters and standard deviations. Molar excess volumes, V ijk E and excess isentropic compressibilities, ( κ S E ) ijk data for the investigated mixtures have been analyzed in terms of Graph theory and Flory theory. It has been observed that V ijk E and ( κ S E ) ijk values calculated by Graph theory compare well with their corresponding experimental values.

Modified embedded-atom method interatomic potentials for the Fe–Ti–C and Fe–Ti–N ternary systems

Modified embedded-atom method (MEAM) interatomic potentials for the Fe–Ti–C and Fe–Ti–N ternary systems have been developed based on the previously developed MEAM potentials for sub-unary and binary systems. An attempt was made to find a way to determine ternary potential parameters using the corresponding binary parameters. The calculated coherent interface properties, interfacial energy, work of separation and misfit strain energy between body-centered cubic Fe and NaCl-type TiC or TiN were reasonable when compared with relevant first-principles calculations under the same condition. The applicability of the present potentials for atomistic simulations to investigate nucleation kinetics of TiC or TiN precipitates and their effects on mechanical properties in steels is also demonstrated.

Thermodynamic Assessment of the Al-Mn and Mg-Al-Mn Systems

The binary Al-Mn system has been critically evaluated based upon available phase equilibrium and thermodynamic data, and optimized model parameters have been obtained giving the Gibbs energies of all phases as functions of temperature and composition. The liquid solution has been modeled with the modified quasichemical model to account for short-range ordering. The results have been combined with those of our previous optimizations of the Al-Mg and Mg-Mn systems to evaluate and optimize the Mg-Al-Mn system. All available data for the ternary system are reproduced with only one small ternary model parameter for the liquid phase.