In the following article the authors want to express a caveat on the use of complex equilibrium software, especially with respect to the incorporation of ideal solutions as a user defined “on the fly” option into such calculations. The background is the analysis of the phase behavior of the overall composition Fe2O3 + x H2 in the Fe–H–O system as a function of temperature. The different phase respectively species distributions resulting from variation of x, the molar amount of H2 relative to one mole of hematite, are investigated. Thermodynamically clearly inconsistent results in recent publications are discussed and consistent results are given to fully understand the reduction paths of Fe2O3 for different temperatures and hydrogen amounts. For a series of x values the paths are integrated into the T vs xO (Type 2) phase diagram of the Fe–O system, i.e. navigation in the phase diagram is provided (see the Graphical Abstract).

Co-producing clinker and steel during electric arc furnace (EAF) steelmaking is an emerging pathway to reduce carbon emissions in cement production. However, several elements in steel may compromise EAF clinker performance. This study investigated the distribution of Mn in EAF clinker produced from normal steel scrap. The results reveal that these EAF clinkers contained 7-8 wt% Mn oxide and Mn in divalent and trivalent forms. The average Mn fractions substituting for Ca, Si, and Al in calcium silicate and aluminate phases were below 3.4 wt%, but up to 7.2 wt% in brownmillerite, Ca-4(Al1-x-yFexMny)(4)O-10, generally with y < 0.25. Most (44-58 wt%) of the Mn was distributed in the RO phase (i.e. divalent metal oxide solid solution), consistent with the thermodynamic modelling results. These findings demonstrate that Mn can be incorporated into several EAF clinker phases, which is an important initial step to understanding and controlling the effects of Mn on EAF clinker properties such as reactivity.

The thermodynamic description of the Al-Cu system is reassessed considering metastable states of Al based alloys in rapid solidification. In previous work, only an improved thermodynamic description of the FCC phase was presented based on experimental results from electromagnetic levitation and simulation results for free dendritic growth to be in accordance with existing thermodynamic descriptions of the liquid phase. The phase diagram thus obtained enabled the correction of the artificial miscibility gap when calculating metastable extensions of the FCC/liquid phase equilibria, the unphysical change of the slope of the solidus line on the Al-rich side and the artificial maximum on the Cu-rich side. However, the description did not well align with the most recent experimental results on the Cu-rich side. The new description reassessing FCC, liquid and the α′-phase demonstrates high consistency with these recent experimental results, reproducing all invariant reactions (temperatures) with an accuracy of ± 4 K and the experimental liquidus line with an accuracy of ± 10 K, all well within the experimental error. The results provide a robust framework for predicting phase behavior under metastable conditions, as confirmed by our experimental data.

Extractive metallurgists unmix complex mixtures arising either from ores and minerals or designed products and their functional materials to create high quality metals, compounds and alloys. To fully understand economic aspects of this endeavor, a deep understanding of solution chemistry is required be it solid solutions, high temperature liquid or aqueous solutions. Especially the configurational and excess entropies of a solid and liquid solution are important in this regard. For this reason, the simplified definition for calculating the exergy of non-ideal solutions as defined by Szargut is shown in this paper to be problematic. We reinterpret the equation Ex = (H–H°)-T°(S–S°), which is generally applied for the calculation of chemical and physical exergies of pure substances in the framework of solution phase thermodynamics. Here we demonstrate that it is more rigorous to use full solution chemistry for deriving the enthalpies (H and H°) and entropies (S and S°) for a particular system of given composition. The suggested approach links H, H°, S and S° rigorously, which is not necessarily the case in the Szargut methodology. Various examples show and compare different approaches using the Szargut approach in comparison with the general Ex -equation. We show with various examples, ranging from metal alloys to oxide slag systems, the discrepancies between the standard Szargut approach and the method of including non-ideal solution phase chemistry as suggested here. From the results presented here, it is evident that exergetic efficiencies may not have been correctly calculated in the literature so far, especially if systems show highly non-ideal behavior of the solution phases and exhibit non-stoichiometric intermetallic as well as other compound phases. The examples clarify the significant errors that can result if solution chemistry is not included. The ultimate objective is to formulate a rigorous pairing of H, H°, S and S° for each industrial and societal process and/or material stream to correctly calculate Ex to evaluate exergetic efficiency of processes and supply chains. Therefore, we suggest that all published exergies (e.g. by software, in publications, etc.) should be revisited to fully describe exergy flows in industrial systems, which the authors as engineers have found to be deficient. Graphical Abstract

This chapter discusses the thermochemical conditions for the production of low-carbon stainless steels. Austenitic stainless steels classically contain the elements iron, chromium, and nickel; chromium to give corrosion resistance and nickel to improve the ductility of the Fe–Cr alloys. However, during the production of these alloys, the presence of carbon can never be avoided. Higher carbon contents lead to the formation of M23C6 mainly containing chromium, thereby reducing the corrosion resistance. It is therefore necessary to establish a production process that yields Fe–Cr–Ni–C alloys with low carbon and high chromium contents. In the converter, oxygen is blown through the liquid Fe bath, thus removing carbon as CO gas. However, chromium also has a high affinity for oxygen and oxidation of chromium from the melt is quite probable, especially if the activity of chromium oxide is reduced because it is dissolved in the slag.

This chapter presets a schematic summary in the form of a tree showing which mathematical tools relate the Gibbs energy of a system to the various other items. From single-equilibrium calculations, the method of phase mapping based on the Gibbs–Duhem equation leads to the phase diagrams of three different but interrelated kinds. To obtain quantitative relationships in multi-component systems, two-dimensional sections can be generated using appropriate computer programs. Some models, such as the cell model or the quasi-chemical model for ionic liquids, require a phase internal minimization with respect to composition and subsequent numerical differentiation, with all the inherent disadvantages.

The method of constrained equilibria has already found extensive use for a good number of years in conjunction with the programmers library ChemApp and freely adaptable ASCII based thermodynamic datafiles. In the present paper a method is demonstrated which permits the application of this method in the framework of the Integrated Thermodynamic Databank System (ITDS) FactSage. Both, modules which interact with the databases and modules which carry out thermodynamic calculations are used, thus emphasizing the aspect of integration in the ITDS. In the paper a link will be established between original thoughts by J.W. Gibbs concerning the definition of the components of a system and kinetic inhibitions in the system and the method of constrained equilibria as such. Furthermore, reference is made to Mats Hillerts use of driving forces in complex (non-)equilibrium cases. A number of application cases with different degrees of complexity will be demonstrated. These range from partially or fully constrained complex equilibrium calculations to phase diagrams with new types of axis variables.

Through the judicious use of “virtual elements” that have zero atomic mass but that are included in the materials balances, it is possible to apply a variety of constraints to chemical equilibrium calculations without the necessity of writing dedicated software for each individual application. Several examples are presented, including the suppression of decomposition of metastable molecules and ions or redox reactions in aqueous solutions, the suppression of internal equilibria in molten salts and ceramics, the calculation of the surface tension of solutions, following the course of reactions with time, paraequilibrium calculations and limiting the extent of a reaction.

The relation between the experimentally observed metal dusting attack and parameters calculated from the test conditions is analysed. Commercial alloys were exposed for nearly 1000 h at elevated pressure in four gas mixtures. The gases had a constant carbon activity regarding the synthesis gas and the Boudouard reaction. However, these parameters did not correlate properly with the observed aggressivity. Alternative descriptions by the CO/H2 ratio, the carbon activity after water gas shift reaction and at metastable equilibrium are discussed. The results show that the whole set of reactions between gas and solid needs to be considered to describe the complex system.

The thermodynamic description of the fcc phase in the Al-Cu system has been revised, allowing for the prediction of metastable fcc/liquid phase equilibria to undercoolings of ΔT = 421 K below the eutectic temperature. Hypoeutectic Al-Cu alloys that are prone to pronounced microsegregation were solidified containerlessly in electromagnetic levitation. Solidus and liquidus concentrations were experimentally determined from highly undercooled samples employing energy-dispersive X-ray analysis. Solid concentrations at a rapidly propagating solid/liquid interface were additionally calculated using a sharp interface model that considers all undercoolings and is based on solvability theory. Modelling results (front velocity versus undercooling) were also corroborated by in situ observation with a high-speed camera. A newly established thermodynamic description of the fcc phase in Al-Cu is compatible with existing CALPHAD-type databases. Inconsistencies of previous descriptions such as a miscibility gap between Al-fcc and Cu-fcc on the Al-rich side, an unrealistic curvature of the solidus line in the same composition range or an azeotropic point near the melting point of Cu, are amended in the new description. The procedure to establish the description of phase equilibria at high undercoolings can be transferred to other alloy systems and is of a general nature. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Vanadium oxides were added to the existing GTOx database because of its important role in the ferro-titanium metallurgy as well as in petroleum coke gasification. The CaO–FeO–Fe 2 O 3 –MgO–SiO 2 system is a part of GTOx database and is chosen because of the existence of experimentally determined vanadium distributions between vanadium ferroalloys and metallurgical slags. The CaO–FeO–Fe 2 O 3 –MgO–SiO 2 –V 2 O 3 –V 2 O 5 system including all binary and ternary sub-systems was thermodynamically assessed using all available experimental data. Vanadium was introduced into the thermodynamic description of solid solution phases such as MeO, Spinel, Corundum and Ca 2 SiO 4 -α using available experimental information. Particular attention was given to the phase Spinel which forms the wide completely miscible solid solution Fe 3 O 4 –FeV 2 O 4 –MgV 2 O 4 –MgFe 2 O 4 . The thermodynamic description of the metallic vanadium containing systems was taken from the SGTE alloy database. With the knowledge about the complex behavior of vanadium in slags as well as in liquid metal alloys it is possible to calculate the vanadium distribution ratios (V)/[V] between iron melts and slags in a wide range of temperatures and compositions, corroborating the validity of the model under reducing conditions. The additionally developed viscosity model shows good agreement between the calculated and experimental values in vanadium-containing slags.

The ternary subsystems of the quaternary sulphate system Na2SO4-K2SO4-MgSO4-CaSO4 were thermodynamically assessed using the available experimental information on phase equilibria. The dataset containing all binary sub-systems, published earlier, was extended to describe phase equilibria of the four sub-ternary systems. Furthermore, a first dataset covering the entire quaternary system has been generated. In the absence of the experimental information on the high order systems the proposed dataset can be used for interpolative and predictive thermodynamic calculations. Ternary interaction parameters were embedded in the framework of the modified associate species model for the description of the liquid phase. The solubility between langbeinite compounds (K2Me2(SO4)(3) with Me = Ca, Mg) was treated with a multi-sublattice model. The resulting new databank being compatible with the general oxide database is used for the representation of phase equilibria in the ternary subsystems. To validate the thermodynamic dataset, the calculated values of phase transition temperatures are compared with the experimental results of the selected compositions of the ternary systems obtained by differential thermal analysis (DTA).

The binary subsystems of the quaternary system Na2SO4–K2SO4–MgSO4–CaSO4 were thermodynamically assessed using the available experimental information including own thermochemical and structure measurements. Phase equilibria and thermodynamic properties of all six binary systems were properly considered. The modified associate species model was successfully applied for the description of the liquid phase while the mutual solubility between various sulphates in the solid state was treated with appropriate multi-sublattice models. The resulting new databank being compatible with the general oxide database was used for the representation of the thermodynamic properties in the binary systems including phase equilibria, activity and mixing data. The calculations are in good agreement with the experimental data.