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.

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.

The thermodynamic description of the C-Cr-Ti ternary system has been reassessed. The main reason was to adjust the solubility limit of Cr in MC (M = Cr, Ti), but also to take the solubility of Ti in M3C2 and M7C3 into account. Another reason was that the thermodynamic descriptions of all the three constituent binary systems (C-Cr, C-Ti and Cr-Ti) had been revised after the previously published description of the C-Cr-Ti system. Important metastable end-members and interaction parameters were calculated using Density Functional Theory (DFT). For fcc-CrC and Ti3C2, DFT was used together with a recently published method to calculate the molar Gibbs energy as a function of temperature (Gm(T)). For fcc-CrC also the magnetic contribution and the magnetic transition temperature, i.e. the Curie temperature (TC), were included. DFT was also used to calculate Gibbs energy of formation at 0 K for Ti7C3 and to calculate the molar excess Gibbs energy contribution, and TC, as a function of Ti composition in MC. DFT calculated parameters were compared with experiments or previous assessments. Selected experimental information from literature was then used to optimize parameters that are difficult to calculate with DFT, e.g. interaction parameters for the liquid phase and temperature dependence for interaction parameters in the solid phases. The resulting thermodynamic description, which is based on critically reviewed binary descriptions, reproduces the experimental solidification sequence, found in literature, equally well as the previous description of the C-Cr-Ti system. Furthermore, in contrast to the previous description, the new description also reproduces the most recent experimentally determined solubility of Cr in MC and takes the solubility of Ti in M3C2 and M7C3 into account. Finally the new description uses DFT calculated metastable end-members and interaction parameters, which gives more reliable predictions, especially at low temperatures.

A method for calculation of finite temperature thermodynamic properties for magnetic allotropes has been developed. The developed method is based on quasi-harmonic approximations using the Debye-Gruneisen model. Electronic contributions are included and magnetic disordering contributions are added with the empiric model often used in CALPHAD (CALculation of PHAse Diagrams) databases. The developed method also includes two new ways to estimate the Debye temperature (theta(D)(V-0)) which enables calculation of finite temperature thermodynamic properties also for allotropes that are dynamically unstable at 0 K. Also a new CALPHAD approach for estimation of Curie- (T-C) or Neel- (T-N) temperatures is presented. The developed method was used to calculate Gibbs energy as a function of temperature (G(T)) and isobaric heat capacity as a function of temperature (C-P(T)) for the body-centred-cubic (bcc), the face-centred-cubic (fcc) and the hexagonal-closed-packed (hcp) allotropes of Fe, Co and Ni. The results were compared with the SGTE Unary database. By using the developed method the phase transitions in Fe and Co were predicted. The calculations of the metastable allotropes fcc-Fe, hcp-Fe and bcc-Ni in this work indicates that the descriptions of these allotropes in the SGTE Unary database need to be updated, especially regarding the magnetic parameters. Furthermore, contradictory to previously reported results in literature, the calculations in this work show that the magnetic ground state structure of fcc-Fe is the double layer antiferromagnetic structure (AFM-D) and not a spin-spiral. The final conclusion is that by using the developed method it is possible to calculate finite temperature thermodynamic properties, not only, for stable and metastable magnetic allotropes, but also for magnetic allotropes that are dynamically unstable at 0 K, which is very important for the development of thermodynamic databases.