Melting properties are critical for designing novel materials, especially for discovering high-performance, high-melting refractory materials. Experimental measurements of these properties are extremely challenging due to their high melting temperatures. Complementary theoretical predictions are, therefore, indispensable. One of the most accurate approaches for this purpose is the ab initio free-energy approach based on density functional theory (DFT). However, it generally involves expensive thermodynamic integration using ab initio molecular dynamic simulations. The high computational cost makes high-throughput calculations infeasible. Here, we propose a highly efficient DFT-based method aided by a specially designed machine learning potential. As the machine learning potential can closely reproduce the ab initio phase-space distribution, even for multi-component alloys, the costly thermodynamic integration can be fully substituted with more efficient free energy perturbation calculations. The method achieves overall savings of computational resources by 80% compared to current alternatives. We apply the method to the high-entropy alloy TaVCrW and calculate its melting properties, including the melting temperature, entropy and enthalpy of fusion, and volume change at the melting point. Additionally, the heat capacities of solid and liquid TaVCrW are calculated. The results agree reasonably with the CALPHAD extrapolated values.

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.

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.

The CALPHAD XLIX conference took place in Stockholm, Sweden, from May 22 to 27, 2022. 112 participants from 18 countries attended the conference. The scientific program included 69 oral presentations divided into 16 thematic topics and 27 posters.

Application of the Neumann-Kopp rule to aluminum containing compounds produces a kink in the specific heat caused by the description of pure aluminum in the SGTE Unary database. Two ways to get rid of this problem are investigated. In a first step, we tried to redefine the description of aluminum above its melting point using a reverse Neumann-Kopp approach. After a systematic review of the experimental Cp data for all the aluminum based compounds, we could evaluate the accuracy of the Neumann-Kopp rule. We could find a nearly systematic overestimation of the Cp of the order of 15%. This makes the use of the reverse Neumann-Kopp approach inapplicable. In a second step, based on this analysis of the available data, we propose another approach consisting in defining the Cp of a compound by a composition average of the Cp of the pure elements, not at the same temperature as in the Neumann-Kopp rule, but rather at a temperature normalized to the melting point of each pure element and the compound. Not only are the results in much better agreement with the experimental data than the conventional Neumann-Kopp rule, but also, there is no longer a need to define the Cp of aluminum above its melting point.

A third generation Calphad description is provided for pure W. In addition, a comprehensive review of the thermodynamic models suggested for the third generation unary systems is given. The thermodynamic properties of the phases (bcc, fcc, hcp and liquid) for pure W are described using these new suggestions. The model parameters are evaluated taking into account the available experimental and DFT information. A good agreement to the selected data is achieved.

More physically-based models are used when developing the third generation Calphad descriptions, which en -able to calculate and predict the thermodynamic properties with higher reliability in an extended temperature range. In order to examine the unary descriptions and verify the models for developing binary descriptions, the W-C binary system was selected as test vehicle. The description of liquid C was first re-assessed adopting the most recent suggestion on modelling the liquid phase. The Einstein/Neumann-Kopp model (the hybrid model) was applied to model all the end-members of the solid solution phases. This work further verifies the hybrid model and the method used to extrapolate the solid data of pure W.

Thermodynamic calculations with Thermo-Calc software and the steel database TCFE3 was applied to investigate the precipitation behavior of industrial grades of duplex stainless steels with high copper content, 1.6 and 2.3 wt.%, Duplok 27 and DUP 27, respectively. Well-documented super duplex stainless grade SAF 2507 with copper content of 0.20 wt.% was used as the reference steel. The results of the calculations are compared with the experimental results obtained previously for these steels. It is shown that copper decreases the high-temperature limit of precipitation of sigma and chi phases and reduces the equilibrium amount of precipitated chi phase. Copper addition to a duplex stainless steel facilitates precipitation of chromium nitride phase and stabilizes it at elevated temperatures. The ferrite-austenite balance at high temperatures is also affected in these steels by the copper addition.