Kinetic simulations of σ phase precipitation in duplex and hyper duplex stainless steels were carried out by employing mean field approach. For duplex and hyper duplex steels, time-temperature-precipitation (TTP) curves were calculated and compared with experimental results. Thermokinetic predictions confirm that segregation of Cr and especially Mo at grain boundaries of ferrite plays an important role for the nucleation of σ phase in ferrite. This is also reflected by the concentration change of dissolved Mo in σ phase from early nucleation stage to precipitation after long-term isothermal aging of several hours. From the present results, predictive simulations of modified alloy compositions are presented and discussed.

An essential step in CALPHAD is assigning relative weights to different datasets, but there is no consensus as to the best approach regarding this issue. Currently, such an assignment of weights for experimental or first-principles data is performed manually based on the knowledge and experience of the modeler. Since the existing manual treatment is subjective and time consuming, manipulation of such data is rapidly advancing toward automated procedures through statistical and data mining tools. In the present study, we propose an automated approach to determine the weight of datasets based on the K-Fold Cross-Validation method, modified under the conditions that each fold is selected non-randomly and contains an unequal number of observations. This approach can be considered for researchers as a support tool to evaluate the reliability of each dataset involved in the CALPHAD modeling and quantify the impact of weighting by statistical analysis of the corresponding model. We demonstrate the efficacy of this method through the evaluation of heat capacity data of fcc nickel, hcp magnesium, and bcc iron.

In the present work, the Al–Co–Mn ternary system is thermodynamically modelled using the Calphad approach. In the modelling, experimental data such as liquidus, solidus, tie lines, and phase boundaries are included. An order–disorder model is used to describe the bcc and B2 phases. The bcc/B2 description was modified in the binary Al–Co system to improve the fit of bcc/B2 equilibria in the ternary system. The thermodynamic models of Al5Co2, M-Al13Co4, γ 1 , and γ 2 intermetallic phases were modified to include the third element to reflect the solubility of this element in the ternary system. The ternary phase T-AlCoMn is described as a stoichimetric compound. Ternary interaction parameters for liquid, bcc, β-Mn, and hcp were optimized, using all the relevant experimental data in the literature. Calculated isothermal and isoplethal sections are compared with experimental data. A comparison between modelling and experimental measurements showed a good agreement between the present results and experiments.

Assisted by the first-principles calculations, the molar volumes of γ and γ′ phases in the binary Ni–Al system were modeled within the framework of the CALPHAD method. A CALPHAD database integrating thermodynamic and molar volume descriptions was established. The present Ni–Al binary database was validated to make good predictions of molar volumes/lattice parameters and thermal expansivities for both γ and γ′ phases. The predicted γ/γ′ lattice misfits from low to high temperatures turn out to be reasonable.

For a binary ordered solid solution, the configurational microscopic state of the system is described in terms of the correlation functions (CFs). In CE – CVM, these are functions of point CF (u0, which is related to the composition), the Bragg-Williams long range order parameter (ξ), temperature (T) and cluster expansion coefficients (CECs). In this communication, a detailed procedure for obtaining the limiting values of the CFs (defined in the orthogonal basis) and their derivatives with respect to u0 and ξ at the stoichiometric composition in the limit of perfect ordering is presented for several frequently occurring binary ordered phases based on bcc, fcc and cph structures. This is achieved by defining new bases called sublattice solvent bases. The results are given for the cases of the B2, B32 and D03 ordered phases based on the bcc structure using (irregular) tetrahedron (T) approximation of CE – CVM, the L10 and L12 ordered phases based on the fcc structure using (regular) tetrahedron (T) and tetrahedron-octahedron (TO) approximations as well as the L11 phase using TO approximation and the B19 and D019 ordered phases based on the cph structure using triangle-tetrahedron (TT) and TO approximations. In all these cases, limiting values of the CFs and their first derivatives with respect to u0 and ξ are independent of CECs and T, while the higher order derivatives are dependent on the ratios of CECs and T. It is shown that the equilibrium values of CFs in the sublattice solvent bases can be calculated to much lower temperatures than those possible with CFs in orthogonal basis.

In the present work, the liquidus and solidus for a series of NixCo1-2xCrx alloys were measured by means of differential scanning calorimetry, and the first-principles calculations were performed to obtain total energies for all solid solutions and end-members of the intermediate phases in the Ni–Co–Cr ternary system. Various types of data from the present work and the literature were used in the assessments of the Ni–Co–Cr ternary system and sub-binary systems by the CALPHAD method, and were well reproduced by the present thermodynamic database. In addition, diffusion couples of fcc Co–Cr and Ni–Co–Cr alloys were assembled and annealed at different temperatures to extract interdiffusion coefficients. Experimental diffusion data from the present work and the literature, in conjunction with thermodynamic parameters, were adopted to assess the atomic mobilities of the fcc phase in the Ni–Co–Cr system. The calculated and experimental diffusion coefficients reach a satisfactory agreement. The diffusional kinetic database developed was further validated by appropriate predictions of composition profiles and diffusion paths.

The density of Al2O3–CaO–MgO–SiO2 system is calculated using a model for molar volume. The model is similar to the one used for enthalpy of a multicomponent solution in the CALPHAD approach. The expression for molar volume consists of two terms: one representing the volume contribution from pure components and the other the volume of mixing. The molar volume of mixing takes into account of the binary and the ternary interactions. A total of 565 experimental density data for the constituent unary, binary and ternary systems were collected from the literature. These were used as input to simultaneously optimise the model parameters describing the molar volume, after ensuring that the data belong to a fully molten state. During the optimisation 48 data points that showed significant deviation from the average trend were excluded. The optimised model parameters for the unary, binary and ternary subsystems were used to calculate the density of the quaternary system. The calculated results were compared with experimental data. Finally, it is shown that the volume of mixing of binary systems correlates well with the corresponding enthalpy of mixing.

Sodium and potassium carbonates and their mixtures are important for different applications, e.g. for latent thermal energy storage, die-casting processes and molten carbonate fuel cells. In this work the phase diagram and thermodynamic properties of Na2CO3–K2CO3 system were studied by differential thermal analysis, differential scanning calorimetry and high temperature X-ray diffraction. Three carbonate mixtures (56, 25 and 75 mol% of Na2CO3) have solid-solid transition in a wide temperature range between 648 K and 823 K. The high temperature XRD analysis has shown that this transition is a continuous process of changing of the unit cell volume without structural changing of the hexagonal lattice. This phenomenon has also been observed on the measured heat capacity curves. The obtained experimental results were compared with calculations performed using the previous thermodynamic datasets. The comparison of these results shows that further thermochemical assessment of this system needs to be performed to achieve better agreement with the available experimental data.

Using a combination of first-principles calculations, special quasi-random structures and quasi-harmonic Debye model methods, we investigated the structural properties, magnetic moments, phase stability, electronic structure, mechanical properties and thermodynamic properties of fcc and bcc FeNi1-xCrx disordered alloys. The results show that the volume per atom and lattice constant of fcc and bcc FeNi1-xCrx alloys exhibit different nonlinear decreasing trends with increasing Cr content, which can be understood by the coupling effect of the composition-dependent antiferromagnetic interaction and atomic volume. Only fcc FeNi1-xCrx alloys with x less than 0.25 are relatively easy to synthesize, while FeNi1-xCrx alloys with other compositions all have a strong tendency to phase separation. The DOS of fcc and bcc FeNi1-xCrx alloys gradually moves to the shallower energy level with the increase of Cr content, which makes TDOS narrow. As the Cr content increases, the hardness and rigidity of fcc FeNi1-xCrx (x = 0, 0.125, and 0.25) alloys gradually increase, while the toughness, ductility and compression resistance gradually weaken. Increasing Cr content is beneficial to reduce the volumetric thermal expansion coefficient of fcc FeNi1-xCrx (x = 0, 0.125, and 0.25) alloys, which also can decrease Debye temperature and weaken interaction between atoms.