Journal of Phase Equilibria and Diffusion最新文献

In 1970, Hillert and Staffansson published a paper entitled “The Regular Solution Model for Stoichiometric Phases and Ionic Melts”. It was the beginning of the sublattice model that has been a key component in the development of Computational Thermodynamics. This formalism, now often called the Compound Energy Formalism (CEF), has been used to describe a great variety of phases driven by the need for accurate descriptions of thermodynamic phase stability in a wide range of materials involving many elements. The purpose of this paper is to describe the formalism, the physical meaning of its various parameters and the way they can be assessed using experimental and theoretical data. Furthermore, new developments derived from the CEF, such as the Effective Bond Energy Formalism, and other ideas for further development are presented.

The theoretical assessment of the Al-Cu-Si was carried out in this work based on recent experimental studies (Riani et al. in Intermetallics, 17:154-164, 2009; He et al. in CALPHAD, 33:200-210, 2009. http://dx.doi.org/10.1016/j.calphad.2008.07.015; Ponweiser N and Richter KW in J. of Alloys and Compd, 512:252-263, 2012; Hallstedt et al. in CALPHAD, 53:25-38, 2016; Zobac et al in J Mater Sci, 55:5322-15333, 2020). The reassessment of the Cu-Si system was also carried out in the scope of this work, as experimental data indicates reasonable solubility of Al in all intermetallic phases in the Cu-Si binary system, and the stoichiometric models used in previous assessments of the Cu-Si binary system are not fully suitable for the extension into the ternary system. Excellent agreement was reached for the reassessment of the Cu-Si system with previous works, and new original results were obtained during the assessment of the ternary system. The high solubility of Si in the β(bcc) phase at high temperatures was modelled to explain experimental inconsistencies in the Cu-rich corner between 600 and 800 °C, and this assumption was confirmed experimentally. All main features of the experimental Al-Cu-Si phase diagram were reproduced well by theoretical modelling.

Accurate thermodynamic prediction at low temperatures presents a significant challenge in solid state physics and materials science. To address this, the third generation Calphad (CALculation of PHAse Diagrams) models are being developed, which enable a physics-based prediction of thermodynamic properties down to zero kelvin. Furthermore, the Inden-Hillert-Xiong (IHX) model, an improved Calphad magnetic model, has been proposed to enhance the modeling accuracy of magnetic transition temperatures and magnetic moments across the entire composition range. The previous assessments of the Mn-Ni system based on the second generation Calphad encountered limitations in reproducing the magnetic properties for the (γMn,Ni) phase, particularly due to the contrasting ferromagnetic behavior on the Ni-rich side and the antiferromagnetic behavior on the Mn-rich side. In this work, the Mn-Ni system was reoptimized on the basis of third generation unary descriptions and Calphad models. To represent the structural characteristics, both the ordered fcc and bcc phases were described by the four-sublattice model for the first time. The obtained thermodynamic parameters result in satisfactory predictions of the phase diagram and thermochemical properties for the Mn-Ni system.

This paper presents an overview of the models we used so far for the 3rd generation Calphad descriptions of the elements. It covers both stable and metastable solid phases, as well as the liquid phase. The “evolution" of thermodynamic descriptions of the key elements Al, C, Cr, Co, Fe, Ga, Ni, and W is discussed in detail and new assessments are conducted when deemed necessary. To support future work, we provide practical guidelines, including suggested starting values for optimising various parameters. Comprehensive thermodynamic descriptions of the elements are also included to facilitate further modelling efforts.

Despite the importance of Al and Ta as alloying elements for Co- and Ni-base alloys, there has been limited research on the phase equilibria in the Al-Co-Ta and Al-Ni-Ta systems. Additionally, the available data are sparse and sometimes inconsistent due to the peculiar experimental challenges of these systems. Based on that, a comprehensive and critical evaluation of their phase equilibria is useful in view of further experimental and computational studies. Within this framework, the Al-Co-Ta and Al-Ni-Ta ternary systems and the respective binary subsystems are here critically assessed. All available literature investigations are analyzed and as a result, a set of self-consistent diagrams and tables are presented, reporting crystal structure data, liquidus projections, isothermal sections, etc.

A model has been developed to simulate the precipitation kinetics of cementite during the tempering of martensitic steels, with a particular focus on the spontaneous transition of the solute partitioning behavior at the cementite/martensite growth interface from initial para-equilibrium (PE) to ortho-equilibrium (OE) conditions. The effect of this transition on the growth kinetics has been discussed and compared with experimental data.

Thermodynamic analysis of the Fe-B-C ternary system was performed using the CALPAHD approach coupled with first principles calculations, and then based on the evaluated thermodynamic parameters, the amounts of segregated B and C in the grain boundary were calculated. The calculated phase diagrams and thermodynamic properties agreed with the experimental data as well as the results of the first principles calculations, and thus highly accurate parameters for this ternary system were evaluated. In using the obtained thermodynamic parameters, the grain boundary segregation behavior of B and C was analyzed by means of the parallel tangent scheme. The Gibbs free energy of the liquid phase obtained in the present work was adopted for that of the grain boundary phase. According to the model, it was confirmed that the amount of segregated B content in the grain boundary of γ -iron decreased the addition of C. Thus, B and C atoms show tendencies to compete for a finite number of segregation sites. When equilibrium precipitates are formed in a matrix phase, the amount of B segregation further decreases due to a solution of B in the borocarbide phases, such as Fe₂₃(B,C)_6, Fe₃(B,C) Fe₂(B,C), and Fe(B,C) phases. Therefore, irrespective of the presence or absence of precipitates, the effect of hardenability decreases with the presence of C in steel due to the decreasing segregated B content in the grain boundary.

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.