Journal of Phase Equilibria and Diffusion最新文献

It is demonstrated in this work that a four parameter Debye–Einstein integral is an excellent fitting function for heat capacity values of pure elements from zero Kelvin to room temperature provided that there are no phase transformations in this temperature range. The standard errors of the four parameters of the Debye–Einstein approach are provided. As examples the temperature dependent molar heat capacities of Fe, Al, Ag and Au are calculated in the temperature range from 0 to 300 K. Standard molar entropies, enthalpies and values of a molar Gibbs energy related function are derived from the molar heat capacities and the values are compared to literature data. The next goal focuses on a seamless transition of these low temperature heat capacities to SGTE (Scientific Group Thermodata Europe) unary data. This can be achieved by penalyzing deviations in the heat capacity values and in their temperature derivatives at the transition point. Whereas the constrained heat capacities of Fe and Al mimic the experimental data, the calculated values deviate considerably in case of Ag and Au. As an alternative a smooth transition in the heat capacities and the temperature derivative is achieved by a switch function employed close to the transition region.

During his time at Royal Institute of Technology (Kungliga Tekniska högskolan) in Sweden, the present author learned nonequilibrium thermodynamics from Mats Hillert. The key concepts are the separation of internal and external variables of a system and the definitions of potentials and molar quantities. In equilibrium thermodynamics derived by Gibbs, the internal variables are not independent and can be fully evaluated from given external variables. While irreversible thermodynamics led by Onsager focuses on internal variables though often mixed with external variables. Hillert integrated them together by first emphasizing their differences and then examining their connections. His philosophy was reflected by the title of his book “Phase Equilibria, Phase Diagrams and Phase Transformations” that puts equilibrium, nonequilibrium, and internal processes on equal footing. In the present paper honoring Hillert, the present author reflects his experiences with Hillert and his work in last 40 years and expresses his gratitude for all the wisdom and support from him in terms of “Hillert nonequilibrium thermodynamics” and discusses some recent topics that the present author has been working on.

To investigate the Mg_Liq ↔ Fe_Sol (Bcc and Fcc) equilibrium up to high temperatures, a suitable protocol for the thermodynamic study of volatile elements was developed. Pure magnesium was melted between 700 and 1450 °C (973 and 1723K) in a low-carbon steel sealed crucible (C35), itself sealed in a tantalum crucible to prevent magnesium leakage. The concentration of iron was characterised by inductively coupled plasma–atomic emission spectroscopy (ICP-AES) and the distribution of iron precipitates was examined by x-Ray tomography. The liquidus composition was measured up to 1450 °C and the results obtained confirm the trend in the literature with, however, significant differences above 1000 °C where a lower Fe solubility is measured in comparison with previous thermodynamic descriptions and the scarce available experimental data in this temperature domain. The existing Calphad model of the binary system was then re-evaluated.

Thermodynamic databases are indispensable in providing phase equilibria and phase transformation for new alloys design and process optimization. The quality of calculated results is strongly dependent on the accuracy of the thermodynamic database. A thermodynamic database for multicomponent copper alloys has been developed, which contains 30 elements covering the major and minor alloying elements of most commercial copper alloys. About 330 binary and 60 ternary systems have been assessed over the entire composition range. Examples of assessments and calculations for typical binary and ternary systems were presented. A wide range of compositions from pure copper to complex commercial copper alloys can be calculated. Scheil solidification simulations were carried out using the thermodynamic database for predicting the phase formation sequence during solidification, as well as phase compositions and phase fractions. In conjunction with a compatible kinetic database, the present established thermodynamic database was used to simulate the microstructure evolution of copper alloys during the ageing process. The simulated results were verified by key experiments, which proves the accuracy of the thermodynamic database established by us.

The thermodynamic properties of chromium have been evaluated to 3000 K. Selected values include an enthalpy of sublimation of 396.8 ± 4.0 kJ/mol at 298.15 K and a boiling point at one atmospheric pressure (1.01325 bar) of 2987 K. The value for the melting point of chromium is recommended as 2135 ± 5 K on the temperature scale ITS-90.

A thermodynamic description of the intermetallic phases in the Fe-Cr-Mo-Ni system is presented based on previously unpublished experimental data in the Cr-Mo-Ni system. A review of experimental information from literature together with the new data provides a reliable base for the assessment. Together with previously published alloy systems, an open database for the Fe-Cr-Mo-Ni-N system is provided. Reliable calculations of the stability of the σ phase in the quaternary Fe-Cr-Mo-Ni system are shown, in support for predicted phase equilibria in super-duplex stainless steel.

The CALPHAD method provides an effective way to parameterize alloy free energies computed from first-principles. While the Special Quasirandom Structure (SQS) formalism offers a natural and efficient tool to generate input data for disordered solid solution phases, accounting for Short Range Order (SRO) effects in a computationally efficient way presents a challenge. In this work we introduce a Python based software pipeline which utilize the Cluster Variation Method (CVM) method in tandem with the SQS formalism to determine closed-form nonlinear expressions for temperature-dependent SRO corrections to the formation free energies. Our approach, which implements the CVM to any level of accuracy, has been integrated into the sqs2tdb software pipeline. As a proof of concept, we perform a thermodynamic assessment of the Ir-Ru binary alloy with SRO correction and show its effectiveness in accurately reproducing the known experimental phase diagram. We also perform SRO corrections to an equimolar MoNbTaVW SQS and show significant SRO effects at temperatures far above room temperature.

The phase diagram of the CaO-SiO₂-Nb₂O₅-Fe₂O₃-TiO₂ slag system has important significance for guiding the recycling and utilization processes of metallurgical slags containing niobium and titanium. In this paper, high-temperature equilibrium experiments were conducted at 1100 °C in air atmosphere to investigate the phase equilibria of the CaO-SiO₂-Nb₂O₅-Fe₂O₃-TiO₂ slag system. According to the experimental results, the liquidus surfaces of the liquid + CaTiO₃ and liquid + SiO₂ equilibrium coexistence regions in the CaO-SiO₂-Nb₂O₅-5wt.% Fe₂O₃-TiO₂ system at 1100 °C in air atmosphere were determined using interpolation and function fitting methods. Finally, the 1100 °C isothermal phase diagrams of the CaO-SiO₂-Nb₂O₅-5 wt.% Fe₂O₃-TiO₂ system were plotted. The composition range of liquid phase region was determined, and the positional relationships of the seven other equilibrium coexistence regions were illustrated.

The Redlich–Kister polynomial equation was employed to optimize the temperature-dependent interaction parameters for excess Gibbs energy of mixing of the Cd-Na binary liquid alloy, utilizing experimental data on enthalpy and excess entropy of mixing. These parameters were used to evaluate thermodynamic properties such as Gibbs energy of mixing, enthalpy of mixing, and component activity in alloys at 673 K, 773 K, and 873 K. Structural properties like concentration fluctuations in the long wavelength limit and Warren–Cowely short range order parameter were also studied using these parameters. The Butler equation with interaction energy parameters was used to study the surface tension and surface composition of the alloys at the aforementioned temperatures. Experimental results confirmed the predicted values of excess Gibbs energy of mixing, enthalpy of mixing, and activity of mixing. Additionally, the excess Gibbs energy of mixing value changed from positive to negative with increased Cd compositions in the alloy. The enthalpy of mixing of the alloys was negative for all compositions. The concentration fluctuation in the long wavelength limit shifted toward optimal values at high temperatures. The surface tension of the alloys increased non-linearly with the bulk composition of Cd.