Numerical Prediction of the Thermodynamic Properties of Ternary Al-Ni-Pd Alloys

2016 ◽  
Vol 35 (1) ◽  
pp. 37-45
Author(s):  
Maryana Zagula-Yavorska ◽  
Jolanta Romanowska ◽  
Sławomir Kotowski ◽  
Jan Sieniawski
Keyword(s):  
Thermodynamic Properties ◽  
Ternary System ◽  
Boundary Conditions ◽  
Mole Fraction ◽  
Thermodynamic Functions ◽  
Binary Systems ◽  
Interaction Parameters ◽  
Ternary Interaction ◽  
The Third ◽  
Gibbs Triangle

AbstractThermodynamic properties of ternary Al-Ni-Pd system, such as exGAlNPd, µAl(AlNiPd),µNi(AlNiPd) and µPd(AlNiPd) at 1,373 K, were predicted on the basis of thermodynamic properties of binary systems included in the investigated ternary system. The idea of predicting exGAlNiPd values was regarded as calculation of values of the exG function inside a certain area (a Gibbs triangle) unless all boundary conditions, that is values of exG on all legs of the triangle are known (exGAlNi, exGAlPd, exGNiPd). This approach is contrary to finding a function value outside a certain area, if the function value inside this area is known. exG and LAl,Ni,Pd ternary interaction parameters in the Muggianu extension of the Redlich–Kister formalism were calculated numerically using the Excel program and Solver. The accepted values of the third component xx differed from 0.01 to 0.1 mole fraction. Values of LAlNiPd parameters in the Redlich–Kister formula are different for different xx values, but values of thermodynamic functions: exGAlNiPd, µAl(AlNiPd), µNi(AlNiPd) and µPd(AlNiPd) do not differ significantly for different xx values. The choice of xx value does not influence the accuracy of calculations.

scholarly journals Calculation of the thermodynamic properties of liquid Ag-In-Sb alloys

2006 ◽  
Vol 71 (3) ◽  
pp. 203-211 ◽  
Author(s):  
Dragana Zivkovic ◽  
Dragan Manasijevic ◽  
Ivan Mihajlovic ◽  
Zivan Zivkovic
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Thermodynamic Properties ◽  
Ternary System ◽  
Interaction Parameter ◽  
Thermodynamic Data ◽  
Binary Systems ◽  
Ternary Interaction Parameter ◽  
Ternary Interaction ◽  
Mutual Agreement

The results of calculations of the thermodynamic properties of liquid Ag-In-Sb alloys are presented in this paper. The Redlich-Kister-Muggianu model was used for the calculations. Based on known thermodynamic data for constitutive binary systems and available experimental data for the investigated ternary system, the ternary interaction parameter for the liquid phase in the temperature range 1000-1200 K was determined. Comparison between experimental and calculated results showed their good mutual agreement.

scholarly journals Cu-Al-Zn system: Calculation of thermodynamic properties in liquid phase

2013 ◽  
Vol 67 (1) ◽  
pp. 157-164 ◽  
Author(s):  
Lidija Gomidzelovic ◽  
Ivan Mihajlovic ◽  
Ana Kostov ◽  
Dragana Zivkovic
Keyword(s):  
Mathematical Modeling ◽  
Liquid Phase ◽  
General Solution ◽  
Thermodynamic Properties ◽  
Ternary System ◽  
Shape Memory ◽  
Ternary Interaction ◽  
General Solution Model ◽  
Shape Memory Materials ◽  
System Calculation

In the paper are presented the results of thermodynamic analysis of Cu-Al-Zn ternary system, which belongs to a group of copper-based shape memory materials. General solution model was used for calculation of thermodynamic properties in the temperature interval from 1373 to 2173 K, in sections from Cu, Al and Zn corner, respectively, with following ratios of 1:3, 1:1 and 3:1. Also, on the basis of the obtained results, ternary interaction parameters were determined using Mathematical Modeling System (MLAB).

scholarly journals Thermodynamic analysis of ternary system Ga-In-Sb

2008 ◽  
Vol 62 (3) ◽  
pp. 153-159 ◽  
Author(s):  
Lidija Gomidzelovic ◽  
Dragana Zivkovic ◽  
Ivan Mihajlovic
Keyword(s):  
General Solution ◽  
Ternary System ◽  
Temperature Interval ◽  
Thermodynamic Analysis ◽  
Interaction Parameters ◽  
Ternary Interaction ◽  
Gibbs Energies

The results of thermodynamic analysis of ternary system Ga-In-Sb are presented in these work. Thermodynamic analysis was carried out by applying general solution predicting method in sections from Ga, In and Sb corner, respectively, with following ratios 1:3, 1:1, 3:1 in the temperature interval 873 to 1673 K. Based on this, excess molar Gibbs energies and activity of all components in specified temperature interval were calculated. Also, using the obtained data and MLAB software, ternary interaction parameters for Ga-In-Sb system were determined.

Thermodynamic properties of binary liquid mixtures

1976 ◽  
Vol 54 (14) ◽  
pp. 2280-2282 ◽  
Author(s):  
Murari Venkata Prabhakara Rao ◽  
Puligundla Ramachandra Naidu
Keyword(s):  
Statistical Theory ◽  
Thermodynamic Properties ◽  
Binary Mixtures ◽  
Binary Systems ◽  
Liquid Mixtures ◽  
Excess Volumes ◽  
Diethyl Ketone ◽  
Binary Liquid ◽  
The Third ◽  
Heats Of Mixing

Excess volumes of the three binary mixtures: (1) cyclohexane – diethyl ketone, (2) cyclohexane–benzonitrile, and (3) toluene–benzonitrile have been measured at 303.15 K using a dilatometer. Excess volumes of the first two systems are positive over the whole range of composition and are negative for the third system. The measured excess volumes and the excess heats of mixing reported in the literature for the three binary systems have been analysed in the light of the statistical theory of liquid mixtures developed by Flory. The analysis has shown that the theory in its modified form is approximately applicable to the mixtures cyclohexane–diethylketone and cyclohexane–benzonitrile.

scholarly journals Thermodynamic properties of 1-ethyl-3-methylimidazolium ethyl sulphate with nitrogen and sulphur compounds at T = (298.15 - 318.15) K and P = 1 bar

2016 ◽  
Author(s):  
◽  
Siyanda Brian Chule
Keyword(s):  
Refractive Index ◽  
Thermodynamic Properties ◽  
Binary Mixture ◽  
Binary Mixtures ◽  
Mole Fraction ◽  
Ethyl Acetoacetate ◽  
Binary Systems ◽  
Composition Range ◽  
Molar Refraction ◽  
The Ideal

In this work, the thermodynamic properties for the binary mixtures containing the ionic liquid (IL): 1-ethyl-3-methylimidazolium ethyl sulphate ([EMIM] [EtSO4]) were calculated. The binary systems studied were {pyridine (Py) or ethyl acetoacetate (EAA) or thiophene (TS) + [EMIM] [EtSO4]}. The results were interpreted in terms of the intermolecular interactions between the (pyridine + IL), (ethyl acetoacetate + IL), and (thiophene + IL) molecules. The physical properties: density, speed of sound, and refractive index were measured for the binary mixtures over the complete mole fraction range using an Anton Paar DSA 5000 M vibrating U- tube densimeter and an Anton Paar RXA 156 refractometer, respectively. The measurements were done at T = (298.15, 303.15, 308.15, 313.15, and 318.15) K and at p = 0.1 MPa. The experimental data was used to calculate the derived properties for the binary mixtures namely:- excess molar volume (V E ), isentropic compressibility (ks), molar refractions (R) and deviation in refractive index (Δn). For the binary mixtures, (Py or EAA or TS + IL), V E was negative throughout the whole composition range which indicates the existence of attractive intermolecular interaction between (pyridine + IL) and (ethyl acetoacetate + IL) for (thiophene + IL), V E was negative at low mole fraction of thiophene and became positive at high mole fraction of thiophene. For the binary mixtures (pyridine + IL), (ethyl acetoacetate + IL), ks was positive indicating that the binary mixtures were more compressible than the ideal mixture. For the binary mixture (thiophene + IL) ks was negative at low thiophene composition and positive at high composition indicating that the binary mixture was less compressible than the ideal mixture at low thiophene composition and more compressible at high composition of thiophene. The molar refraction, R, is positive for the (Py or EAA or TS + IL) binary systems at T = (298.15 – 318.15) K, molar refraction decreases as the organic solvent composition increases. For the binary mixture (pyridine + [EMIM] [EtSO4]), Δn is negative at mole fractions < 0.75 of pyridine and positive at mole fractions >0.75 at all temperatures and decreases with an increase in temperature. For the binary system (ethyl acetoacetate + [EMIM] [EtSO4]), Δn values are positive over the entire composition range and at all temperatures and increases with an increase in temperature. Δn values for the (thiophene + IL) system are negative for mole fractions of thiophene < 0.62 and becomes positive for mole fractions of thiophene > 0.62 and Δn increases with an increase in temperature. The Redlich-Kister smoothing equation was used successfully for the correlation of V E and Δn data. The Lorentz- Lorenz equation gave a poor prediction of V E , but a good prediction of density or refractive index.

scholarly journals MODELING OF THERMODYNAMIC PROPERTIES OF THE MELTS OF TERNARY Ge-Mn-Gd SYSTEM

2019 ◽  
pp. 18-22
Author(s):  
N. Golovata ◽  
N. Kotova ◽  
N. Usenko
Keyword(s):  
Thermodynamic Properties ◽  
Gibbs Energy ◽  
Ternary System ◽  
Binary Systems ◽  
Thermodynamic Characteristics ◽  
Published Data ◽  
Liquid Alloys ◽  
Model Calculations ◽  
Enthalpies Of Mixing ◽  
Gibbs Energies

In the present work, the Gibbs energies of mixing of liquid alloys of the Ge-Mn-Gd ternary system were determined, which was made on the basis of an analysis of published data on the thermodynamic properties of liquid alloys of boundary binary systems that form the ternary Ge-Mn-Gd, as well as on the basis of the model calculations in these binary systems. To determine the activities of the components, the Gibbs energies of mixing, and the enthalpies of mixing of liquid alloys of the Ge-Mn(Gd) systems, for which alloying process is accompanied by significant heat release, an ideal associated solution model was applied. For the melts of the Mn-Gd system, which are characterized by rather insignificant exothermic effects, a model of regular solutions was used. The surface of the Gibbs energy of mixing for the alloys of the Ge-Mn-Gd ternary system has been determined on the basis of the concentration dependences of the Gibbs energies of mixing obtained for constituent binary systems under the assumption of additivity of pair interactions using the Redlich-Kister-Muggianu method. The obtained topology of the Gibbs energy isolines projections is compared with the thermochemical properties of liquid alloys of this system that we have determined earlier. A comparative analysis of the topology of these surfaces in the Ge-Mn-Gd system led to the conclusion that the surfaces of ΔG and ΔmH monotonically decrease from the manganese-rich angle of the diagram towards the Ge-Gd side of the concentration triangle. The minimum value of the thermodynamic characteristics of mixing of the ternary liquid alloys corresponds to the composition, which coincides with the composition of the most stable intermetallic compound in the Ge-Gd system. From the course of isolines of free energies and integral enthalpies of mixing, one can also conclude about the influence of a short-range order, existed in the Ge-Mn system near the composition with a mole fraction of mangan greater than 0.7, on the properties of ternary alloys in the vicinity of this composition. Thus, the topology of isolines and the large exothermic values of the obtained thermodynamic properties allow us to make a reasonable conclusion that the strong interaction between unlike components inherent in the Ge-Gd system in the solid state is also maintained for liquid alloys of the Ge-Mn-Gd system.

Phase equilibria of the Ag–Sn–Cu ternary system

2004 ◽  
Vol 19 (8) ◽  
pp. 2298-2305 ◽  
Author(s):  
Yee-wen Yen ◽  
Sinn-wen Chen
Keyword(s):  
Ternary System ◽  
Phase Equilibria ◽  
Binary Systems ◽  
Stable Phase ◽  
Thermodynamic Models ◽  
Ternary Interaction ◽  
Isothermal Sections ◽  
Stability Diagrams ◽  
Binary Compounds ◽  
Good Agreement

Phase equilibria of the Ag–Sn–Cu ternary system have been determined experimentally as well as using the calculation of phase diagram (CALPHAD) method. Various Ag–Sn–Cu alloys were prepared to study the isothermal sections of the Ag–Sn–Cu ternary system at 240 and 450 °C. No ternary compounds were found and all the binary compounds had only limited ternary solubility. The ∈1–Cu3Sn phase is a very stable phase. It is in equilibrium with the Ag, ζ–Ag4Sn, ∈2–Ag3Sn, η–Cu6Sn5, and Cu phases at 240 °C, and is in equilibrium with the Ag, ζ, ∈2, L, and δ–Cu4Sn phases at 450 °C. Thermodynamic models of the Ag–Sn–Cu ternary system were developed based on available thermodynamic models of the constituent binary systems without introducing ternary interaction parameters. The isothermal sections at 240 and 450 °C were calculated, and the results were in good agreement with those determined experimentally. In addition to the isothermal sections, stability diagrams of Sn and Cu were calculated as well.

Density and viscosity of the system Ca(NO3)2-H2O-dimethyl sulphoxide

1983 ◽  
Vol 48 (7) ◽  
pp. 1810-1819 ◽  
Author(s):  
Zdeněk Kodejš ◽  
Jindřich Novák ◽  
Ivo Sláma
Keyword(s):  
Ternary System ◽  
Mole Fraction ◽  
Binary Systems ◽  
Mixed Solvent ◽  
Dimethyl Sulphoxide ◽  
Viscosity Data ◽  
Empirical Equations ◽  
Temperature Range ◽  
Concentration Dependences ◽  
The Ideal

The density and viscosity of the ternary system Ca(NO3)2-H2O-dimethyl sulphoxide were measured over the temperature range 0 < t < 60 °C, with the mole fraction of the salt in the system varied in the range 0.05 < x < 0.16. The temperature and concentration dependences of density and viscosity have been described by empirical equations. The viscosity data show a pronounced dependence on the solvent composition. Maximum deviations of viscosity from the ideal additive behaviour of the two salt-solvent binary systems occur at a mole fraction of DMSO in the mixed solvent of 0.3. The observed dependence is discussed in relation to the structure of the solution.

The Representation of Thermodynamic Properties in Multicomponent Alloys

1982 ◽  
Vol 19 ◽  
Author(s):  
I. Ansara
Keyword(s):  
Thermodynamic Properties ◽  
Binary Systems ◽  
Theoretical Models ◽  
Higher Order ◽  
Interaction Parameters ◽  
Experimental Measurements ◽  
Multicomponent Systems ◽  
Multicomponent Alloys ◽  
Summation Methods ◽  
Different Types

ABSTRACTIn addition to theoretical models which have been developped to interpret the interactions in metallic systems, polynomials of different types have been used to represent the thermodynamic properties of solution phases. Ternary and higher order systems have been described by adding the properties of the limiting binary systems, using various summation methods ; interaction parameters specific to the multicomponent systems can be derived from sufficiently precise experimental measurements.

Columnar to Equiaxed Transition in Al-Cu-Ag

2010 ◽  
Vol 649 ◽  
pp. 379-384 ◽  
Author(s):  
Els Nagels ◽  
Ludo Froyen
Keyword(s):  
Temperature Gradient ◽  
Ternary System ◽  
Cooling Rate ◽  
Binary Systems ◽  
Temperature Gradients ◽  
Alloying Element ◽  
The Third ◽  
Columnar To Equiaxed Transition ◽  
Lower Temperature

In this work the transition from columnar to equiaxed growth is studied during the solidification of the univariant eutectic L=> α(Al) + θ-Al2Cu in the ternary Al-Cu-Ag system. The columnar to equiaxed transition (CET) in a ternary system behaves very similar to the CET observed in binary systems [1]. It is observed that the CET occurs at lower temperature gradients when the amount of the third alloying element, in this case Ag, is increased. Another important solidification parameter is the cooling rate of the furnace. When the cooling rate is increased, the CET will occur at lower positions in the sample where the temperature gradient is lower.

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