Thermodynamics Of Liquid Alloys Research Articles

Thermodynamics of Liquid Alloys and Vapor–Liquid Equilibrium in the Antimony–Tellurium System

The partial and integral thermodynamic functions of formation and evaporation of antimony-tellurium melts were calculated based on the vapor pressure values of the components in the Sb–Sb2Te3 and Sb2Te3–Te systems. It is shown that integral functions of evaporation enthalpy and entropy insignificantly change in value from the alloy corresponding to the Sb2Te3 composition and slightly decrease in the direction of antimony and tellurium on the state diagram. However, they can be described by a linear dependence in the entire concentration interval of solutions existence within the experiment error. The boundaries of liquid and vapor coexistence fields at atmospheric pressure (101.3 kPa) and in vacuum (0.9 kPa) were calculated based on the partial pressure values of melt components. It is shown that the separation of antimony alloys with tellurium by distillation into elements at atmospheric pressure is difficult because of high boiling temperatures of antimony-based alloys. It would require a significant number of condensate re-evaporation cycles in a vacuum. The results aim at creating the fundamental physical and chemical foundations of the distillation technologies for processing melted chalcogenide systems. The second aim is to issue effective practical recommendations necessary for developing and improving the process of extracting rare metals from polymetallic mattes by vacuum-thermal method.Graphical

Thermodynamics of liquid alloys

The experimental methods (calorimetric measurements, measurements of vapor pressure and electromotive forces) to obtain reliable thermodynamic data of liquid alloys at constant pressure as a function of composition and temperature are briefly reviewed. The main objective of the experimental work is the direct and most accurate determination of the partial or integral values of the enthalpy and Gibbs energy of formation as well as the measurement of the heat capacity. A consistent set of macroscopic thermodynamic data is important, e.g. to test the potential of a thermodynamic model of liquid alloys to describe quantitatively the experimentally determined composition and temperature dependencies, to test the extrapolation of thermodynamic properties into regions of temperature and composition where direct experimental measurements do not exist and to examine the microscopic assumptions of a thermodynamic model. A semi-empirical approach to calculate thermodynamic properties of liquid alloys could be used if experimental data are not accessible.

Thermodynamics of Liquid Alloys and Metastable Phase Transformations in the Copper - Titanium System

We have used solution calorimetry at temperatures of 1573 K and 1873 K over broad concentration ranges to study the mixing enthalpy of Cu - Ti liquid alloys. The molar mixing enthalpies of the system are significant negative values. We have established the temperature dependence of the molar mixing enthalpies of the system: there is an increase in their exothermicity as the temperature is lowered. The significant negative mixing enthalpies of the system allow us to conclude that the chemical bonds are localized in the studied melts and consequently associates form. We tested this conclusion within ideal associated solution theory, which describes well the results obtained with a set of CuTi and CuTi2 associates. Using the model obtained, we have calculated the excess thermodynamic functions of mixing (enthalpy, Gibbs free energy, heat capacity) for the liquid alloys. We estimated the Gibbs energies of fcc, bcc, and hcp solutions in the system by the CALPHAD method, using data from the initial sections of the phase diagrams and from the corresponding thermodynamic data. We have calculated the metastable phase equilibria between the limiting solid solutions and the liquid or supercooled liquid phase. It was shown that for the supercooled liquid and the amorphous phase, a broad concentration range of relative thermodynamic stability can be obtained. The concentration range of amorphization of Cu - Ti melts corresponds to the position of the metastable liquidus line and the T0 line at temperatures close to the temperature range of amorphous solidification.

Thermodynamics of Liquid Alloys, and Stable and Metastable Phase Equilibria in the Copper ― Iron System

Enthalpies of formation of liquid Cu ― Fe alloys are studied using high-temperature calorimetry. Measurements are performed at 1673 K in the composition range x Fe = 0-0.12. The temperature dependence of the enthalpy of mixing is established by comparing the results with those obtained previously at 1873 K. There is an increase of alloy heat of formation with decreasing temperature. Thermodynamic models of phases of the system are constructed using the experimental results, published data about the activities of components in the liquid and solid solutions, and also data about stable and metastable phase transformations. Thermodynamic evaluation of the system is performed using the CALPHAD-method. Calculated values are in good agreement with the majority of data for thermodynamic properties and phase transitions. A model of the liquid phase is constructed taking into account the temperature dependence of the enthalpies of mixing. Parameters of stable (L + δ ⇔ γ, L + γ ⇔ e, γ ⇔ e + α) and metastable (L 1 ⇔ L 2, L 1 + L 2 ⇔ e) phase equilibria are calculated by means of the thermodynamic models obtained. The occurrence of a metastable monotectic transformation L 2 ⇔ L 1 + δ with participation of δ-phase in the region of its metastable solidification is suggested. The thermodynamic description of the system obtained is used successfully for theoretical interpretation of the limits of forming supersaturated BCC- and FCC-solutions by quenching from the liquid. A connection between the thermodynamic properties of phases of the system and the limits of forming of supersaturated solutions within it during highly nonequilibrium alloy synthesis is demonstrated.

Thermodynamics of liquid alloys

An adiabatic calorimeter was used to measure the dependence on temperature and composition of the heat capacity C p l(x, T) of liquid magnesium-rich La-Mg-Ni, lanthanum-rich Al-La-Ni alloys and of Al 7.5Cu 17.5Ni 10Zr 65. The C p l(x, T) of these alloys exhibit large values near to the liquidus temperature. C p l(x, T) values of the glass-forming alloys exceed their values of the undercooled liquid state above the glass transition temperature. The C p l dependence on temperature reveals therefore a maximum in the undercooled liquid state. This specific behaviour of liquid alloys is described using an association model.

Simple model for the structure and thermodynamics of liquid alloys with strong chemical interactions. III: phase separation

For pt.I see Hafner et al., ibid., vol.14, p.1139, (1984). A simple model used by Hafner et al. to describe the structure and thermodynamics of liquid alloys with chemical short-range ordering is extended to describe liquid Li-Na. The model is based on simple approximations for the electron-gas and pseudoatom self-energy contributions to the heat of mixing and model-pair interactions of a hard-core Yukawa form. It achieves a reasonably consistent description of the energetic conditions for phase separation and of the critical divergence of the long-wavelength concentration fluctuations.

Thermodynamics of liquid alloys and glass formation

Abstract The ease of glass formation in metallic systems is considered as a function of the difference in the specific heats of the liquid and solid phases and of the excess specific heat of the liquid derived from mixing properties. Data have been collected for various glass-forming alloys and are compared with those, newly obtained, for a non-glass-forming eutectic (Al88Si12). Approximate formulae for computing the thermodynamic quantities of undercooled metallic melts are reviewed, and a correlation of the glass-transition temperature with the thermodynamic properties of the liquid is discussed. The possible relationship between high specific heat in the liquid phase and glass formation by solid-state amorphization is outlined.

Viscosities of aluminum-rich Al−Cu liquid alloys

Viscosity data for Al−Cu liquid alloys in the ranges of 0≤C L≤33.1 wt pct Cu and 1173≤T ≤973 K are reviewed. It was found that Andrade's equation can be used to represent the variation of viscosity with temperature for a given composition, but that each of the two parameters in Andrade's equation shows no systematic variation with composition of the liquid-alloys. Consequently, arithmetic averages of the parameters were used and assumed to apply to all compositions in the range 0≤C L ≤33.1 wt pct Cu. Such a procedure implies that the viscosity happens to vary with composition solely because the specific volume varies with composition. In order to establish the predictability of extrapolating such simple behavior, a more complex model was considered. The latter model was recently presented by Kucharski and relates viscosity to the structure and thermodynamics of liquid alloys. Viscosities obtained by interpolating Andrade's equation and Kucharski's model compare closely; furthermore, values obtained by extrapolations to lower temperatures also compare favorably. Finally the simpler model was used to calculate the viscosity of the interdendritic liquid during solidification.

Simple model for the structure and thermodynamics of liquid alloys with strong chemical interactions. II. Chemical order and packing constraints

A model presented recently by the authors for the structure and thermodynamics of liquid alloys with strong chemical interactions is applied to Na-Pb and Na-Sn. They show that the thermodynamic 'anomalies' observed in these systems arise from the interplay of ordering effects induced by a preferred interaction between unlike atoms and packing effects. They demonstrate that the structural implications of the model are supported by a diffraction experiment.

Simple model for the structure and thermodynamics of liquid alloys with strong chemical interactions. I. Chemical short-range order

The authors present a simple model for the structure and thermodynamics of liquid alloys with strong chemical interactions. Starting from the fact that these systems are characterised by the existence of a non-vanishing ordering potential phi CC=c1c2( phi 11+ phi 22-2 phi 12), the authors model the interatomic potentials by a hard-sphere potential for the mean pair interaction phi NN=c12 phi 11+c22 phi 22+2c1c2 phi 12 and a hard-sphere potential of the same diameter plus a Yukawa tail for phi CC. The volume forces are calculated in an electron-gas model. Based on the solution of this model in the mean spherical approximation, the authors find analytic expressions for the thermodynamic excess functions and the partial structure factors. They have applied their model to liquid Li-Pb, Li-Ag and Li-Mg alloys and find very good results for the heat and the entropy of formation and good agreement between their structure data and neutron scattering experiments.

Mass spectrometry measurements of activities in liquid Ag-Ge alloys: Critical assessment of the thermodynamics of the AgGe system and short distance order

In the system AgGe, the tendency to cluster formation or the setting up of a local order effect can be explained by the thermodynamics of liquid alloys. For a precise and reliable knowledge of their activities, we measured them by multiple Knudsen cell mass spectrometry. The assumptions used to evaluate this local order from neutron diffraction measurements agree with our calculations from thermodynamics and the mixing volume.

Thermodynamic study of (magnesium + bismuth) by vapour-pressure measurement by transpiration

A detailed study on the thermodynamics of liquid alloys { xMg + (1 − x)Bi} has been carried out by measuring the partial pressures of magnesium over them, using a transpiration technique in the range x = 0.202 to 0.888 and in the temperature range 1023 to 1223 K. The results are compared with data from the literature. A detailed analysis of the vapour pressures is given for the complete composition range.