Description Of Binary System Research Articles

Phase relations in the ZrO2-Sm2O3-Y2O3-Al2O3 system: experimental investigation and thermodynamic modelling

Abstract Sub-solidus phase relations in the ZrO2-Sm2O3-Y2O3 and Sm2O3-Al2O3-Y2O3 systems were experimentally studied at 1523-1873 K and thermodynamic databases for these systems were developed. Analysis of phase equilibria in the Sm2O3-Y2O3-Al2O3 system indicated that REAM phase (Sm,Y)4Al2O9 is not stable in the Sm2O3 rich-composition. Therefore, the stability limit of the Sm4Al2O9 phase was established experimentally and thermodynamic parameters of the Sm2O3-Al2O3 system were re-optimised. The eutectic melting in the Sm2O3-Y2O3-Al2O3 system was investigated using differential thermal analysis and scanning electron microscopy. The results obtained were used to assess the mixing parameter of the liquid phase. A new description of binary system was introduced into the database of the ZrO2-Sm2O3-Al2O3 system and phase diagrams were re-calculated. The obtained thermodynamic databases were combined with literature data for the ZrO2-Y2O3-Al2O3 system and a thermodynamic database for the ZrO2-Sm2O3-Y2O3-Al2O3 system was developed.

Contribution of Thermodynamic Calculations to Metallurgical Studies of Multi-Component Zirconium Based Alloys

Abstract The Zircobase thermodynamic database for zirconium alloys coupled with Thermo-Calc software represents a powerful tool for prediction of thermodynamic and metallurgical data such as activities, formation enthalpies, phase transformation temperatures, solubility limits, existence temperature range, and chemical compositions of second phase precipitates. This database was built up with binary and ternary descriptions assessed according to the CALPHAD methodology. It is sometimes necessary to take into account new systems, but also new versions of binary descriptions as recently experienced. For example, the two binary systems Zr-Fe and Zr-Sn had to be updated in order to fit new experimental results believed to be more accurate than previously available. This paper aims at showing the improvements of the database taking into account new descriptions of binary systems, as also ternary description such as Zr-Fe-Cr, Zr-Fe-Ni, and Zr-Nb-Fe. For this last ternary system, new experimental data were necessary. New experimental study of the two ternary phases, hexagonal Zr(Nb,Fe)2 and cubic (Zr,Nb)4Fe2, allowed their crystal structures (P63/mmc and Fd3¯m, respectively) to be checked. This was useful to build up a sublattice model giving account of the existence of a composition range for these two intermetallic phases. Moreover, several specific ZrNbFe alloys were fabricated and annealed for times ranging from 1000 h to 10,000 h at 550, 700, 800, and 900°C to determine the equilibrium binary and ternary phase domains as a function of the temperature. All these data were used to obtain an improved thermodynamic modelling of this system. Finally, we illustrate some thermodynamic predictions of the different phases evolutions as a function of the temperature on multi-alloyed industrial type alloys. These examples show quite good agreement between the thermodynamic predictions and the experimental data derived from calorimetric experiments and microstructural observations.

Correlation between bulk and surface properties of ternary Ag–Sn–Zn liquid alloys and concerned binaries

A correlative study of the bulk and surface properties of the ternary Ag–Sn–Zn liquid alloys has been undertaken by extending the descriptions of concerned binaries (Ag–Sn, Sn–Zn, and Ag–Zn), obtained from statistical mechanical theory in the frame-work of quassi-lattice approximations. An improved model, in which the selection of binary compositions involves the correlation of one particular component with other components of the ternary system, has been used to compute the free energy of mixing of Ag–Sn–Zn system. The concentration dependence of the surface tension and surface composition has been explained by obtaining expression for the activity coefficients and extending the surface description of binary systems. It is worth mentioning that same set of interaction energies as those used for the bulk and surface calculations of the concerned binaries has been used to investigate the concentration dependence of free energy of mixing, surface tension (σ) and surface composition of the ternary system. The theoretical investigation of binary systems suggest the presence of short range order in Ag–Sn and Ag–Zn systems leading to the formation of intermetallic compounds (Ag3Sn in Ag–Sn and AgZn in Ag–Zn) in the melt. Sn–Zn system is characterized by the existence of diatomic tin in the melt. The concentration dependence of the free energy of mixing of Ag–Sn–Zn system for three cross section (Ag : Sn = 1 : 1, 1 : 3 and 3 : 1) has been clearly explained by our theoretical model. There is slight decrease in σ for Ag : Sn = 1 : 1 up to x Zn ≈ 0.4 whereas sharp decrease up to 50% Zn is observed in case of Ag : Sn = 3 : 1. The σ for Ag : Sn = 1 : 3 remains almost constant up to x Zn ≈ 0.25. The surfaces of Ag–Sn–Zn system for all three cross section (Ag : Sn = 1 : 1, 1 : 3 and 3 : 1) are quite enriched with Sn-atoms. The degree of segregation is lowest in Ag : Sn = 3 : 1.

Description of binary systems containing hydrocarbons and alcohols by a modified NRTL equation

The total pressure data for binary mixtures containing hydrocarbons (n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane) and n-alcohols (methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol) have been correlated by means of the NRTL equation and its modified [1] version making provisions for association. The correlation results much improve with the use of the modified equation, achieving the accuracy of representation of the excess Gibbs energy for all systems under investigation within the error limits of original experiment.

Surface tension: a simple correlation for natural gas + conensate systems

The parachor equation of Weinaug and Katz (1943) is still widely used for the prediction of surface tensions of mixtures, especially in the oil and gas industry, where data over a wide range of compositions, temperatures and pressures are needed. The method is simple, general, and never gives absurd (non-physical) results. The Weinaug-Katz method can be usefully modified by the use of a more generalised “mixing rule” for the parachor, incorporating adjustable binary parameters. This modified version leads not only to a better description of binary systems, but also to an improved prediction of ternary data.

Orthogonal coordinates for systems of many components

We show how a set of orthogonal coordinates is defined for a system having an arbitrary number of components. These coordinates, in conjunction with the limiting atom fractions of the components, define the equilateral triangle for a three component system and a regular tetrahedron for a four component system. Various manipulations of such figures in higher order space are carried out using linear algebra. Two dimensional sections are considered the most important construction. The utility of such sections is enhanced if the sections are taken parallel to important sets of tie lines. The present exercise is but one facet of the larger problem in which complex phase equilibria are calculated from thermodynamic descriptions of binary systems. We suggest that, eventually, problems involving phase equilibria for systems of many components will be addressed by calculating the required sections for the problem at hand.