Predictive computations of intermetallic σ phase evolution in duplex steel. I) Thermodynamic modeling of σ phase in the Fe–Cr–Mn–Mo–Ni system

Thermodynamic modeling of the σ phase was revised according to the three sublattice model developed for the Fe–Cr system (Fe,Cr)₁₀(Fe,Cr)₄(Fe,Cr)₁₆ in the view of simulating thermodynamics and kinetics for duplex stainless steels. The alloying elements Mn, Mo and Ni relevant in duplex steels were added to the σ phase model and their thermodynamic parameters were optimized. As a consequence of the change of thermodynamic model and parameters for the σ phases, alloy phases were also re-optimized. The present work include re-optimization of binaries and ternaries sub-systems in order to build a consistent bottom-up Calphad dataset for the thermokinetic simulation of duplex steels.     

Al–Cr–Fe phase diagram. Isothermal Sections in the region above 50 at% Al

The Al–Cr–Fe phase diagram was studied in the compositional range of 50–100 at% Al and partial isothermal sections were determined at 1160, 1100, 1075, 1042, 1000, 900, 800 and 700 °C. In the low-Al part of the studied compositional region the isostructural high-temperature Al–Cr and Al–Fe γ₁-phases form a continuous region of solid solutions. Both binary Al₁₃Fe₄ and Al₅Fe₂ were found to dissolve up to 6.5 at% Cr while Al₂Fe was found to extend up to 4.1 at% Cr. The solid solutions based on the Al–Cr γ₂ and μ phases were determined to reach 35.2 and 1.3 at% Fe, respectively. The dissolution of Cr in the Al–Fe binaries only slightly influences their Al concentrations, while the Al–Cr binaries exhibit decreasing Al concentration with increasing Fe concentration. The Al–Cr η-phase dissolves up to 5 at% Fe, which results in a sharp decrease of its Al concentration and increase of melting temperatures. The earlier reported existence of a ternary decagonal D₃-phase and three complex periodic phases O₁, H and ε was confirmed and their compositions at different temperatures were specified.     

Experimental investigation and thermodynamic calculation of the Mg–Mn–Ni system

Based on the critical review of the ternary Mg–Mn–Ni system, 12 alloys were prepared using a powder metallurgy method in a glove box. The isothermal section of the Mg–Mn–Ni system at 400 °C was determined. Ternary compound τ (Mg₃MnNi₂) was confirmed in the present work. In order to obtain the phase transition temperatures, differential scanning calorimetry (DSC) was applied to the selected alloys using sealed Ta crucibles. The invariant reaction temperatures for two invariant reactions in the Mg-rich corner were measured. Considering the experimental data from present work and literature, the Mg–Mn–Ni system was optimized and a set of thermodynamic parameters was obtained. Calculated results fit well with the experimental data.     

Experimental investigation of phase equilibria in the Ce-Fe-Ni system at 950 and 750 °C

The Ce-Fe-Ni system has been experimentally studied by microstructural analysis, electron microprobe analysis and X-ray diffraction over the whole concentration range. Isothermal sections at 950 and 750 °C for this system were constructed for the first time. The phase relations at 750 °C measured in this work are different from those published for 700 °C in particular because of the identification of a new binary phase Ce₅Ni₁₉. A continuous solid solution Ce(Fe,Ni)₂ (MgCu₂-type structure, cF24-Fd-3m), was found at 750 °C, with mutual substitution of Fe and Ni atoms. The liquid phase is present in the system both at 950 and 750 °C. Almost all binary-based phases at these temperatures show wide homogeneity regions and possess a constant Ce content.     

Thermodynamic assessment of the Ni–Co–Cr system and Diffusion Study of its fcc phase

In the present work, the liquidus and solidus for a series of Ni_xCo_1-2xCr_x 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.     

An evaluation of the Mn–Ga system: Phase diagram,crystal structure,magnetism, and thermodynamic properties

The Ni–Mn-Ga alloy system is attractive due to its functional properties with potentials in various applications. However, the fundamental alloy thermodynamics of the binary Mn–Ga system is still lack of investigation. Therefore, a comprehensive evaluation of the Mn–Ga is performed in this work. Different versions of Mn–Ga phase diagrams available in the literature are reviewed. A new version of the Mn–Ga phase diagram is recommended along with possible invariant reactions. The crystal structure, magnetic transition, and thermochemical properties of intermetallic compounds are reviewed by considering available experimental and modeling such as ab initio calculations. In fact, more experimental information on the Mn-rich side is required in order to perform CALPHAD thermodynamic modeling for a reliable database. Further experiments are recommended to study the high-temperature phase equilibria between liquid, (γMn), (δMn) and Mn₂Ga(h), phase reactions between Mn₈Ga₅ and Mn₇Ga₆, and invariant reactions involving the MnGa phase. Nevertheless, the summarized information on phase equilibria, phase diagram, crystallography, magnetic transition temperature, magnetic moment, heat capacity, and enthalpy of formation can support the future thermodynamic investigation of the Mn–Ga system, which is critical for the materials design and discovery of Ni–Mn-Ga alloys.     

Ordering in ternary BCC alloys applied to the Al–Fe–Mn system

TWIP (TWinning Induced Plasticity) steels are attracting a lot of attention due to their combination of strength and ductility. In a previous work [1] (B. Lindahl, M. Selleby, Calphad 43 (2013) 86–93) a thermodynamic assessment of the Al–Fe–Mn system, which forms the basis of TWIP steels, was presented. The previous assessment treated the A2/B2 order-disorder transformation in the bcc phase using a two-sublattice model. In the present work a four-sublattice model has been used in order to also be able to describe the transition into the ordered D0₃ compound that occurs at lower temperatures. pair interaction energies for the Fe–Mn system are evaluated which prove crucial to the extrapolations into the Al–Fe–Mn system. Along with this various aspects of modeling chemical ordering using the Calphad approach are discussed. Equations for determining the ternary compound energies from binary pair interactions energies are presented and equations for determining the parameter values from the ordered parameters are derived.     

Thermodynamic optimization of the Mn–P and Fe–Mn–P systems

Thermodynamic modeling of the Mn–P and Fe–Mn–P systems in the full composition was carried out using the CALculation of PHAse Diagrams (CALPHAD) method based on the critical evaluation of all available phase equilibria and thermodynamic data. The liquid and solid solutions were described using the Modified Quasichemical Model and Compound Energy Formalism, respectively. The Gibbs energies of the binary stoichiometric iron and manganese phosphides were determined based on reliable experimental data. The ternary (Fe,Mn)₃P, (Fe,Mn)₂P and (Fe,Mn)P phosphides were modeled as solid solutions with mutual substitution between Fe and Mn atoms. The Gibbs energy of the liquid solution was predicted using the Toop interpolation technique with P as an asymmetric component, without any ternary parameters. The thermodynamic properties of P in the entire composition region and the liquidus of the ternary system were well reproduced. Based on the thermodynamic models with optimized parameters, unexplored phase diagrams and thermodynamic properties of the Fe–Mn–P system were predicted.     

CONCH: A Visual Basic program for interactive processing of ion-microprobe analytical data

A Visual Basic program for flexible, interactive processing of ion-microprobe data acquired for quantitative trace element, ²⁶Al–²⁶Mg, ⁵³Mn–⁵³Cr, ⁶⁰Fe–⁶⁰Ni and U–Th–Pb geochronology applications is described. Default but editable run-tables enable software identification of secondary ion species analyzed and for characterization of the standard used. Counts obtained for each species may be displayed in plots against analysis time and edited interactively. Count outliers can be automatically identified via a set of editable count-rejection criteria and displayed for assessment. Standard analyses are distinguished from Unknowns by matching of the analysis label with a string specified in the Set-up dialog, and processed separately. A generalized routine writes background-corrected count rates, ratios and uncertainties, plus weighted means and uncertainties for Standards and Unknowns, to a spreadsheet that may be saved as a text-delimited file. Specialized routines process trace-element concentration, ²⁶Al–²⁶Mg, ⁵³Mn–⁵³Cr, ⁶⁰Fe–⁶⁰Ni, and Th–U disequilibrium analysis types, and U–Th–Pb isotopic data obtained for zircon, titanite, perovskite, monazite, xenotime and baddeleyite. Correction to measured Pb-isotopic, Pb/U and Pb/Th ratios for the presence of common Pb may be made using measured ²⁰⁴Pb counts, or the ²⁰⁷Pb or ²⁰⁸Pb counts following subtraction from these of the radiogenic component. Common-Pb corrections may be made automatically, using a (user-specified) common-Pb isotopic composition appropriate for that on the sample surface, or for that incorporated within the mineral at the time of its crystallization, depending on whether the ²⁰⁴Pb count rate determined for the Unknown is substantially higher than the average ²⁰⁴Pb count rate for all session standards. Pb/U inter-element fractionation corrections are determined using an interactive log_e–log_e plot of common-Pb corrected ²⁰⁶Pb/²³⁸U ratios against any nominated fractionation-sensitive species pair (commonly ²³⁸U¹⁶O⁺/²³⁸U⁺) for session standards. Also displayed with this plot are calculated Pb/U and Pb/Th calibration line regression slopes, y-intercepts, calibration uncertainties, standard ²⁰⁴Pb- and ²⁰⁸Pb-corrected ²⁰⁷Pb/²⁰⁶Pb dates and other parameters useful for assessment of the calibration-line data. Calibrated data for Unknowns may be automatically grouped according to calculated date and displayed in color on interactive Wetherill Concordia, Tera–Wasserburg Concordia, Linearized Gaussian (“Probability Paper”) and Gaussian-summation probability density diagrams.     

Experimental investigation of phase equilibria in the Ti-Fe-Cr ternary system

Phase equilibria in ternary Ti-Fe-Cr system at 873 and 1173 K were investigated in this work. Based on the phase constitutions and phase compositions in 32 samples prepared using the equilibrated alloys, the isothermal sections of the Ti-Fe-Cr ternary system were established. For this system, there were six three-phase regions at both 873 and 1173 K, the phase relations at the studied two temperatures are almost the same. Thereinto, two tentative three-phase regions of βCr₂Ti + β(Ti) + (Fe, Cr)₂Ti and βCr₂Ti + β(Ti) + αCr₂Ti were deduced near the Ti-Cr side at 1173 K. The (Fe, Cr)₂Ti phase has a large solubility of Cr, up to 59.1 at% at 873 K and 59.5 at% at 1173 K. Moreover, at 873 and 1173 K, the homogeneity ranges of the nearly linear ternary compounds τ₁ were measured to be 49.9–72.1 at% Fe and 52.7–77.2 at% Fe, respectively, and the solubility of Cr in (Fe, Cr)Ti were 9.0 at% and 10.6 at%.