Heat affected zone liquation cracking evaluation on FeMnAl alloys.

FeMnAl steels are currently generating a lot of interest with potential applications for structural parts in armored vehicles due to their lower density and outstanding mechanical properties. Despite the extensive mechanical performance and heat treatment exploration of this alloy class, further weldability investigation is required for future large-scale deployment. In the present study, the liquation cracking of four heats of cast FeMnAl alloys was investigated by the spot-Varestraint technique. The study focuses primarily on the effect of the major elements of the FeMnAl system: C, Mn and Al. Optical and electron microscopy were employed to investigate the microstructural features, and CALPHAD was employed to aid the discussion regarding the alloy's composition differences and their effect on the liquation cracking susceptibility. The study was able to identify that compositions with the higher Mn, C, and lower Al presented the highest liquation cracking susceptibility. Conversely, composition presenting lower Mn, C, and Al showed the most resistant behavior. Furthermore, lower Al content promoted a fully-γ microstructure at low temperatures, which encouraged the appearance of longer cracks as a γ-matrix is more susceptible to HAZ cracking than a fully ferritic (α) or duplex (α + γ) microstructure.

The present manuscript indicates that FeMnAl steels are susceptible to liquation cracking for alloys with higher Mn, C, and lower Al.

Elastic Properties of Alloyed Cementite M3X (M = Fe, Cr; X = C, B) Phases from First-Principle Calculations and CALPHAD Model.

Fe-Cr-C-B wear-resistant steels are widely used as wear-resistant alloys in harsh environments. The M3X (M = Fe, Cr; X = C, B) cementite-type material is a commonly used strengthening phase in these alloys. This study investigated the mechanical properties of cementite (Fe, Cr)3(C, B) using the first-principle density functional theory. We constructed crystal structures of (Fe, Cr)3(C, B) with different concentrations of Cr and B. The bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and hardness of the material were calculated, and a comprehensive mechanical property database based on CALPHAD modeling of the full composition was established. The optimal concentrations of the (Fe, Cr)3(C, B) phase were systematically evaluated across its entire composition range. The material exhibited the highest hardness, shear modulus, and Young's modulus at Cr and B concentrations in the range of 70-95 at% and 40 at%, respectively, rendering it difficult to compress and relatively poor in machinability. When the B content exceeded 90 at%, and the Cr content was zero, the shear modulus and hardness were low, resulting in poor resistance to deformation, reduced stiffness, and ease of plastic processing. This study provides an effective alloying strategy for balancing the brittleness and toughness of (Fe, Cr)3(C, B) phases.

Accelerated discovery of high-performance Al-Si-Mg-Sc casting alloys by integrating active learning with high-throughput CALPHAD calculations.

Scandium is the best alloying element to improve the mechanical properties of industrial Al-Si-Mg casting alloys. Most literature reports devote to exploring/designing optimal Sc additions in different commercial Al-Si-Mg casting alloys with well-defined compositions. However, no attempt to optimize the contents of Si, Mg, and Sc has been made due to the great challenge of simultaneous screening in high-dimensional composition space with limited experimental data. In this paper, a novel alloy design strategy was proposed and successfully applied to accelerate the discovery of hypoeutectic Al-Si-Mg-Sc casting alloys over high-dimensional composition space. Firstly, high-throughput CALculation of PHAse Diagrams (CALPHAD) solidification simulations of ocean of hypoeutectic Al-Si-Mg-Sc casting alloys over a wide composition range were performed to establish the quantitative relation 'composition-process-microstructure'. Secondly, the relation 'microstructure-mechanical properties' of Al-Si-Mg-Sc hypoeutectic casting alloys was acquired using the active learning technique supported by key experiments designed by CALPHAD and Bayesian optimization samplings. After a benchmark in A356-xSc alloys, such a strategy was utilized to design the high-performance hypoeutectic Al-xSi-yMg alloys with optimal Sc additions that were later experimentally validated. Finally, the present strategy was successfully extended to screen the optimal contents of Si, Mg, and Sc over high-dimensional hypoeutectic Al-xSi-yMg-zSc composition space. It is anticipated that the proposed strategy integrating active learning with high-throughput CALPHAD simulations and key experiments should be generally applicable to the efficient design of high-performance multi-component materials over high-dimensional composition space.

Thermodynamic description of metastable fcc/liquid phase equilibria and solidification kinetics in Al-Cu alloys.

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)'.

A spectroscopic hike in the U-O phase diagram.

The U-O phase diagram is of paramount interest for nuclear-related applications and has therefore been extensively studied. Experimental data have been gathered to feed the thermodynamic calculations and achieve an optimization of the U-O system modelling. Although considered as well established, a critical assessment of this large body of experimental data is necessary, especially in light of the recent development of new techniques applicable to actinide materials. Here we show how in situ X-ray absorption near-edge structure (XANES) is suitable and relevant for phase diagram determination. New experimental data points have been collected using this method and discussed in regard to the available data. Comparing our experimental data with thermodynamic calculations, we observe that the current version of the U-O phase diagram misses some experimental data in specific domains. This lack of experimental data generates inaccuracy in the model, which can be overcome using in situ XANES. Indeed, as shown in the paper, this method is suitable for collecting experimental data in non-ambient conditions and for multiphasic systems.

Computational thermodynamics and microstructure simulations to understand the role of grain boundary phase in Nd-Fe-B hard magnets.

To control the coercivity of Nd hard magnets efficiently, the thermal stability of constituent phases and the microstructure changes observed in hard magnets during thermal processes should be understood. Recently, the CALPHAD method and phase-field method have been recognized as promising approaches to realize phase stability and microstructure developments in engineering materials. Thus, we applied these methods to understand the thermodynamic feature of the grain boundary phase and the microstructural developments in Nd-Fe-B hard magnets. The results are as follows. (1) The liquid phase is a promising phase for covering the Nd2Fe14B grains uniformly. (2) The metastable phase diagram of the Fe-Nd-B ternary system suggests that the tie line end of the liquid phase changes drastically depending on the average composition of Nd. (3) The Nd concentration in the grain boundary phase can reach 100 at% if the volume fraction of the grain boundary phase is constrained. (4) The effect of Cu addition to the Nd-Fe-B system on the microstructural morphology is reasonably modeled based on the phase-field method. (5) The morphology of the liquid phase can be controlled using phase separation in the liquid phase and the grain size of the Nd2Fe14B phase.

Development of a prototype thermodynamic database for Nd-Fe-B permanent magnets.

For the Nd-Fe-B permanent magnets, a prototype thermodynamic database of the 8-element system (Nd, Fe, B, Al, Co, Cu, Dy, Ga) was constructed based on literature data and assessed parameters in the present work. The magnetic excess Gibbs energy of the Nd2Fe14B compound was reassessed using thoroughly measured heat capacity data. The Dy-Nd binary system was reassessed based on formation energies estimated from ab initio calculations. The constructed database was applied successfully for estimations of phase equilibria during the grain boundary diffusion processes (GBDP) and the reactions in the hydrogenation decomposition desorption recombination (HDDR) processes.

Stacking fault energy prediction for austenitic steels: thermodynamic modeling vs. machine learning.

Stacking fault energy (SFE) is of the most critical microstructure attribute for controlling the deformation mechanism and optimizing mechanical properties of austenitic steels, while there are no accurate and straightforward computational tools for modeling it. In this work, we applied both thermodynamic modeling and machine learning to predict the stacking fault energy (SFE) for more than 300 austenitic steels. The comparison indicates a high need of improving low-temperature CALPHAD (CALculation of PHAse Diagrams) databases and interfacial energy prediction to enhance thermodynamic model reliability. The ensembled machine learning algorithms provide a more reliable prediction compared with thermodynamic and empirical models. Based on the statistical analysis of experimental results, only Ni and Fe have a moderate monotonic influence on SFE, while many other elements exhibit a complex effect that their influence on SFE may change with the alloy composition.

A first step towards computational design of W-containing self-healing ferritic creep resistant steels.

In this work, we combine a generic alloy-by-design model with a novel concept, the nucleation barrier for the formation of Laves phase to fill the creep cavities, in order to develop multi-component creep resistant steels with kinetically tuned self-healing behaviour. In the model the high-temperature long-term strength is estimated by integrating precipitation strengthening due to M23C6 carbides and solid solution strengthening, while the optimized compositional solutions are determined by employing the coupled thermodynamic and kinetic principles. W-containing Laves phase herein is selected as the self-healing agent to autonomously fill the grain boundary cavities, so as to prolong the creep lifetime. To achieve the effective healing reaction, the nucleation time for Laves precipitates are expected to coincide simultaneously with which creep cavities start to form or reach a healable size. Using experimental data from literature, an empirical relationship to estimate the incubation time for Laves phase formation has been constructed, from which the thermodynamic driving force for onset of precipitation as a function of temperature and intended precipitate nucleation time was derived. Three sample alloys have been selected among the desirable solutions, which are predicted to have the same strength but widely different Laves phase nucleation times. The calculations are also performed for different use temperatures to explore the compatibility between high temperature strength and timely cavity filling behaviour. In its current form the model is not expected to yield the truly optimal composition but to demonstrate how the kinetics of the healing reaction can affect the predicted optimal alloy compositions.

A method for handling the extrapolation of solid crystalline phases to temperatures far above their melting point.

Thermodynamic descriptions in databases for applications in computational thermodynamics require representation of the Gibbs energy of stable as well as metastable phases of the pure elements as a basis to model multi-component systems. In the Calphad methodology these representations are usually based on physical models. Reasonable behavior of the thermodynamic properties of phases extrapolated far outside their stable ranges is necessary in order to avoid that they become stable just because these properties extrapolate badly. This paper proposes a method to prevent crystalline solid phases in multi-component systems to become stable again when extrapolated to temperatures far above their melting temperature.

Thermodynamic analysis of the topologically close packed σ phase in the Co-Cr system.

Density functional theory (DFT) calculations show that it is essential to consider the magnetic contribution to the total energy for the end-members of the σ phase. A more straightforward method to use the DFT results in a CALPHAD (Calculation of phase diagrams) description has been applied in the present work. It was found that only the results from DFT calculations considering spin-polarization are necessary to obtain a reliable description of the σ phase. The benefits of this method are: the DFT calculation work can be reduced and the CALPHAD description of the magnetic contribution is more reliable. A revised thermodynamic description of the Co-Cr system is presented which gives improved agreement with experimental phase boundary data for the σ phase.

Thermodynamic assessment of the Co-Ta system.

The Co-Ta system has been reviewed and the thermodynamic description was re-assessed in the present work. DFT (density functional theory) calculations considering spin polarization were performed to obtain the energies for all end-member configurations of the C14, C15, C36 and µ phases for the evaluation of the Gibbs energies of these phases. The phase diagram calculated with the present description agrees well with the experimental and theoretical data. Considering the DFT results was essential for giving a better description of the µ phase at lower temperatures.

Implementation of an Effective Bond Energy Formalism in the Multicomponent Calphad Approach.

Most models currently used for complex phases in the calculation of phase diagrams (Calphad) method are based on the compound energy formalism. The way this formalism is presently used, however, is prone to poor extrapolation behavior in higher-order systems, especially when treating phases with complex crystal structures. In this paper, a partition of the Gibbs energy into effective bond energies, without changing its configurational entropy expression, is proposed, thereby remarkably improving the extrapolation behavior. The proposed model allows the use of as many sublattices as there are occupied Wyckoff sites and has great potential for reducing the number of necessary parameters, thus allowing shorter computational time. Examples for face centered cubic (fcc) ordering and the σ phase are given.

About the Reliability of CALPHAD Predictions in Multicomponent Systems.

This study examines one of the limitations of CALPHAD databases when applied to high entropy alloys and complex concentrated alloys. We estimate the level of the thermodynamic description, which is still sufficient to correctly predict thermodynamic properties of quaternary alloy systems, by comparing the results of CALPHAD calculations where quaternary phase space is extrapolated from binary descriptions to those resulting from complete binary and ternary interaction descriptions. Our analysis has shown that the thermodynamic properties of a quaternary alloy can be correctly predicted by direct extrapolation from the respective fully assessed binary systems (i.e., without ternary descriptions) only when (i) the binary miscibility gaps are not present, (ii) binary intermetallic phases are not present or present in a few quantities (i.e., when the system has low density of phase boundaries), and (iii) ternary intermetallic phases are not present. Because the locations of the phase boundaries and possibility of formation of ternary phases are not known when evaluating novel composition space, a higher credibility database is still preferable, while the calculations using lower credibility databases may be questionable and require additional experimental verification. We estimate the level of the thermodynamic description which would be still sufficient to correctly predict thermodynamic properties of quaternary alloy systems. The main factors affecting the accuracy of the thermodynamic predictions in quaternary alloys are identified by comparing the results of CALPHAD calculations where quaternary phase space is extrapolated from binary descriptions to those resulting from ternary system descriptions.

Brute Force Composition Scanning with a CALPHAD Database to Find Low Temperature Body Centered Cubic High Entropy Alloys.

We used the Thermo-Calc High Entropy Alloy CALPHAD database to determine the stable phases of AlCrMnNbTiV, AlCrMoNbTiV, AlCrFeTiV and AlCrMnMoTi alloys from 800 to 2800 K. The concentrations of elements were varied from 1-49 atom%. A five- or six-dimensional grid is constructed, with stable phases calculated at each grid point. Thermo-Calc was used as a massive parallel tool and three million compositions were calculated, resulting in tens of thousands of compositions for which the alloys formed a single disordered body centered cubic (bcc) phase at 800 K. By filtering out alloy compositions for which a disordered single phase persists down to 800 K, composition 'islands' of high entropy alloys are determined in composition space. The sizes and shapes of such islands provide information about which element combinations have good high entropy alloy forming qualities as well as about the role of individual elements within an alloy. In most cases disordered single phases are formed most readily at low temperature when several elements are almost entirely excluded, resulting in essentially ternary alloys. We determined which compositions lie near the centers of the high entropy alloy islands and therefore remain high entropy islands under small composition changes. These island center compositions are predicted to be high entropy alloys with the greatest certainty and make good candidates for experimental verification. The search for high entropy islands can be conducted subject to constraints, e.g., requiring a minimum amount of Al and/or Cr to promote oxidation resistance. Imposing such constraints rapidly diminishes the number of high entropy alloy compositions, in some cases to zero. We find that AlCrMnNbTiV and AlCrMoNbTiV are relatively good high entropy alloy formers, AlCrFeTiV is a poor high entropy alloy former, while AlCrMnMoTi is a poor high entropy alloy former at 800 K but quickly becomes a better high entropy alloy former with increasing temperature.

Application of Finite Element, Phase-field, and CALPHAD-based Methods to Additive Manufacturing of Ni-based Superalloys.

Numerical simulations are used in this work to investigate aspects of microstructure and microseg-regation during rapid solidification of a Ni-based superalloy in a laser powder bed fusion additive manufacturing process. Thermal modeling by finite element analysis simulates the laser melt pool, with surface temperatures in agreement with in situ thermographic measurements on Inconel 625. Geometric and thermal features of the simulated melt pools are extracted and used in subsequent mesoscale simulations. Solidification in the melt pool is simulated on two length scales. For the multicomponent alloy Inconel 625, microsegregation between dendrite arms is calculated using the Scheil-Gulliver solidification model and DICTRA software. Phase-field simulations, using Ni-Nb as a binary analogue to Inconel 625, produced microstructures with primary cellular/dendritic arm spacings in agreement with measured spacings in experimentally observed microstructures and a lesser extent of microsegregation than predicted by DICTRA simulations. The composition profiles are used to compare thermodynamic driving forces for nucleation against experimentally observed precipitates identified by electron and X-ray diffraction analyses. Our analysis lists the precipitates that may form from FCC phase of enriched interdendritic compositions and compares these against experimentally observed phases from 1 h heat treatments at two temperatures: stress relief at 1143 K (870 °C) or homogenization at 1423 K (1150 °C).

Modeling of metastable phase formation diagrams for sputtered thin films.

A method to model the metastable phase formation in the Cu-W system based on the critical surface diffusion distance has been developed. The driver for the formation of a second phase is the critical diffusion distance which is dependent on the solubility of W in Cu and on the solubility of Cu in W. Based on comparative theoretical and experimental data, we can describe the relationship between the solubilities and the critical diffusion distances in order to model the metastable phase formation. Metastable phase formation diagrams for Cu-W and Cu-V thin films are predicted and validated by combinatorial magnetron sputtering experiments. The correlative experimental and theoretical research strategy adopted here enables us to efficiently describe the relationship between the solubilities and the critical diffusion distances in order to model the metastable phase formation during magnetron sputtering.

Towards a metadata scheme for the description of materials - the description of microstructures.

The property of any material is essentially determined by its microstructure. Numerical models are increasingly the focus of modern engineering as helpful tools for tailoring and optimization of custom-designed microstructures by suitable processing and alloy design. A huge variety of software tools is available to predict various microstructural aspects for different materials. In the general frame of an integrated computational materials engineering (ICME) approach, these microstructure models provide the link between models operating at the atomistic or electronic scales, and models operating on the macroscopic scale of the component and its processing. In view of an improved interoperability of all these different tools it is highly desirable to establish a standardized nomenclature and methodology for the exchange of microstructure data. The scope of this article is to provide a comprehensive system of metadata descriptors for the description of a 3D microstructure. The presented descriptors are limited to a mere geometric description of a static microstructure and have to be complemented by further descriptors, e.g. for properties, numerical representations, kinetic data, and others in the future. Further attributes to each descriptor, e.g. on data origin, data uncertainty, and data validity range are being defined in ongoing work. The proposed descriptors are intended to be independent of any specific numerical representation. The descriptors defined in this article may serve as a first basis for standardization and will simplify the data exchange between different numerical models, as well as promote the integration of experimental data into numerical models of microstructures. An HDF5 template data file for a simple, three phase Al-Cu microstructure being based on the defined descriptors complements this article.

The OpenCalphad thermodynamic software interface.

Thermodynamic data are needed for all kinds of simulations of materials processes. Thermodynamics determines the set of stable phases and also provides chemical potentials, compositions and driving forces for nucleation of new phases and phase transformations. Software to simulate materials properties needs accurate and consistent thermodynamic data to predict metastable states that occur during phase transformations. Due to long calculation times thermodynamic data are frequently pre-calculated into "lookup tables" to speed up calculations. This creates additional uncertainties as data must be interpolated or extrapolated and conditions may differ from those assumed for creating the lookup table. Speed and accuracy requires that thermodynamic software is fully parallelized and the Open-Calphad (OC) software is the first thermodynamic software supporting this feature. This paper gives a brief introduction to computational thermodynamics and introduces the basic features of the OC software and presents four different application examples to demonstrate its versatility.

Experimental study and thermodynamic modeling of the Al-Co-Cr-Ni system.

A thermodynamic database for the Al-Co-Cr-Ni system is built via the Calphad method by extrapolating re-assessed ternary subsystems. A minimum number of quaternary parameters are included, which are optimized using experimental phase equilibrium data obtained by electron probe micro-analysis and x-ray diffraction analysis of NiCoCrAlY alloys spanning a wide compositional range, after annealing at 900 °C, 1100 °C and 1200 °C, and water quenching. These temperatures are relevant to oxidation and corrosion resistant MCrAlY coatings, where M corresponds to some combination of nickel and cobalt. Comparisons of calculated and measured phase compositions show excellent agreement for the ß-γ equilibrium, and good agreement for three-phase ß-γ-σ and ß-γ-α equilibria. An extensive comparison with existing Ni-base databases (TCNI6, TTNI8, NIST) is presented in terms of phase compositions.