Magnesium silicide stannide solid solutions, Mg2(Si,Sn), are prominent materials in the development of devices for thermoelectric energy conversion for intermediate operating temperatures, owing to the high values of their thermoelectric figure of meritzT, elemental abundance, and non-toxicity. The manufacturing of thermoelectric generators, however, relies also upon long-term stable contacts with low thermal and electrical resistivity and good bonding of the metallic contact bridge (electrode) to the thermoelectric legs of Mg2(Si,Sn) with a similar thermal expansion coefficient. In the assembly of thermoelectric generators, the thermoelectric legs have to be bonded to metallic electrodes to establish an electrical circuit. In this work, contacts between Mg2(Si0.3Sn0.7) and Cu were made at 600 °C and investigated using thermodynamic equilibrium calculations to gain understanding on the phase transformations occurring in the bonding process. Cu is selected as a metallic electrode as it is a highly conductive element with a thermal expansion coefficient similar to that of the thermoelectric material. Contacting methods usually deviate from equilibrium conditions; nevertheless, we use this contact couple to illustrate that equilibrium thermodynamic considerations are an efficient support to anticipate and identify the reaction products forming the final microstructure of the bonded region, and ultimately, for improving the contact design. A thermodynamic database of Gibbs energies for quaternary Cu-Mg-Si-Sn was built up and made available in this work. With this database, thermodynamic calculations were done in order to complement the experimental observations on the microstructure and thermochemistry of the Mg2(Si0.3Sn0.7)/Cu interconnections. The approach developed in this work is general and therefore applicable to the investigations of different thermoelectric materials and/or metallic electrodes, by enlarging the thermodynamic description, providing an effective guide to the experimental settings of the contacting process. © The Royal Society of Chemistry 2021.

The γ′ volume fraction is a key parameter in precipitation-strengthened Co- and Ni-base superalloys and mainly determines the alloys’ properties. However, systematic studies with varying γ′ volume fractions are rare and the influence on thermal expansion has not been studied in detail. Therefore, a series of six Ta-containing Co-based alloys was designed with compositions on a γ–γ′ tie-line, where the γ′ volume fraction changes systematically. During solidification, Laves (C14-type) and µ (D85-type) phases formed in alloys with high levels of W and Ta. Single-phase γ or two-phase γ/γ′ microstructures were obtained in four experimental alloys after heat treatment as designed, whereas secondary precipitates, such as χ (D019-type), Laves, and μ, existed in alloys containing high levels of γ′-forming elements. However, long-term heat treatments for 1000 hours revealed the formation of the χ phase also in the former χ-free alloys. The investigation of the thermal expansion behavior revealed a significant anomaly related to the dissolution of γ′, which can be used to determine the γ′ solvus temperature with high accuracy. Compared to thermodynamic calculations, differential scanning calorimetry (DSC) and thermal expansion analysis revealed a larger increase of the γ′ solvus temperatures and a lesser decline of the solidus temperatures when the alloy composition approached the composition of the pure γ′ phase. © 2021, The Author(s).

The Al–Ni system has been intensively studied both experimentally and theoretically. Previous first-principles calculations based on density-functional theory (DFT) typically investigate the stable phases of this system in their experimental stoichiometry. In this work, we present DFT calculations for the Al–Ni system that cover stable and metastable phases across the whole composition range for each phase. The considered metastable phases are relevant for applications as they are observed in engineering alloys based on Al–Ni. To model the Gibbs energies of solid phases of the Al–Ni system, we combine our DFT calculations with the compound energy formalism (CEF) that takes the Bragg–Williams–Gorsky approximation for the configurational entropy. Our results indicate that the majority of the investigated configurations have negative energy of formation with respect to Al fcc and Ni fcc. The calculated molar volumes for all investigated phases show negative deviations from Zen’s law. The thermodynamic properties at finite temperatures of individual phases allow one to predict the configurational contributions to the Gibbs energy. By applying a fully predictive approach without excess parameters, an acceptable topology of the DFT-based equilibrium phase diagram is obtained at low and intermediate temperatures. Further contributions can be added to improve the predictability of the method, such as phonons or going beyond the Bragg–Williams–Gorsky approximation that overestimates the stability range of the ordered phases. This is clearly demonstrated in the fcc order/disorder predicted metastable phase diagram. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.

In this work, we report the thermodynamic modelling of the Ni–Zr system using the Calphad method combined with ab initio calculations. Density functional theory (DFT) is employed to calculate the enthalpy of formation of the intermediate phases. The calculated enthalpies of formation are in close agreement with the experimental data. An approach based on special quasirandom structures (SQS) was used for calculating the enthalpy of mixing of the fcc solid solution. The vibrational contribution to the heat capacities of NiZr, NiZr2, Ni3Zr and Ni7Zr2 phases were calculated using the quasiharmonic approximation (QHA) and the corresponding electronic contribution was obtained using an approach based on Mermin statistics. The total heat capacities for these phases were fitted to appropriate expressions and integrated to obtain the Gibbs energy functions valid down to 0 K. The calculated thermochemical properties along with critically selected experimental constitutional and thermochemical data served as input for the thermodynamic optimisation of the system. The calculated phase equilibria and the thermodynamic properties using the optimised Gibbs energy functions are in good agreement with the input data. The calculated congruent melting points of NiZr and NiZr2 phases are close to the recent experimental data. The Ni10Z7 phase forms by a peritectic reaction, which is also in agreement with the experimental data. © 2019 Elsevier Ltd

Thermomechanical processing has been used to control the grain size/shape of the equiatomic CrCoNi medium-entropy alloy (MEA) and obtain excellent strength and ductility. However, in the cast state, the alloy has coarse columnar grains with average widths and lengths of approximately 120 and 1000 μm, respectively, resulting in inferior mechanical properties. To overcome this deficiency, here we microalloyed with Ti and C and successfully changed the grain shape (from columnar to equiaxed) and refined the grain size. The degree to which the microstructure changes depends on the amount of Ti and C added, with the best results obtained at 0.4 at.% each. In the optimal alloy [(CrCoNi)99.2Ti0.4C0.4], the as-cast grains were nearly equiaxed with a uniform size of ∼75 μm. Associated with this change in grain shape/size was a significant improvement of yield strength, ultimate tensile strength and elongation to fracture at both 293 and 77 K. The columnar to equiaxed transition is attributed to the strong mutual affinity of C and Ti, which leads to their build-up ahead of the solid-liquid interface and, in turn, to enhanced constitutional undercooling. © 2018 Elsevier B.V.

The microalloying of low-alloyed steels with Nb can improve the strength-to-toughness balance. Such an effect of Nb is usually ascribed to the refinement of the grain structure occurring in the austenite regime during hot forming. In the present work, we report that Nb enhances the impact toughness of a low-alloyed Cr–Mo steel by a mechanism which has not been appreciated so far. The lower impact toughness in the Nb-free Cr–Mo steel is due to segregation of Mo to boundaries, which facilitates the formation of fine Mo-rich ξ-phase carbides lining up along the boundaries. This further promotes the nucleation and propagation of microcracks. The addition of Nb leads to the formation of Mo-enriched NbC particles. The interfaces between these particles and the matrix supply new preferential sites for precipitation of Mo-rich ξ-phase carbides upon subsequent tempering. In this way, Nb additions result in a decrease of Mo segregation to boundaries, significantly reducing the precipitation of ξ-phase carbides on grain boundaries, thus leading to improved impact toughness. In addition to the classical microstructural explanation (grain size effect), this chemical role of Nb sheds new light on the design strategies of advanced low-alloyed steels with optimized strength-to-toughness ratios. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

The structural and chemical changes at ω/β interfaces and the evolution of the morphology of ω in a near-β alloy during isothermal ageing at 573 K were investigated by atom probe tomography and aberration-corrected high-resolution transmission electron microscopy. Ledges and local O enrichment at semi-coherent isothermal ω interfaces are proposed to provide the key driving force for nucleation of ω-assisted α. Following nucleation of α, the morphology of ω evolves from ellipsoidal to rod-like, induced by rapid consumption of ω by α. © 2018 Acta Materialia Inc.

A set of advanced single crystalline γ′ strengthened Co-base superalloys with at least nine alloying elements (Co, Ni, Al, W, Ti, Ta, Cr, Si, Hf, Re) has been developed and investigated. The objective was to generate multinary Co-base superalloys with significantly improved properties compared to the original Co-Al-W-based alloys. All alloys show the typical γ/γ′ two-phase microstructure. A γ′ solvus temperature up to 1174 °C and γ′ volume fractions between 40 and 60 pct at 1050 °C could be achieved, which is significantly higher compared to most other Co-Al-W-based superalloys. However, higher contents of Ti, Ta, and the addition of Re decrease the long-term stability. Atom probe tomography revealed that Re does not partition to the γ phase as strongly as in Ni-base superalloys. Compression creep properties were investigated at 1050 °C and 125 MPa in 〈001〉 direction. The creep resistance is close to that of first generation Ni-base superalloys. The creep mechanisms of the Re-containing alloy was further investigated and it was found that the deformation is located preferentially in the γ channels although some precipitates are sheared during early stages of creep. The addition of Re did not improve the mechanical properties and is therefore not considered as a crucial element in the design of future Co-base superalloys for high temperature applications. Thermodynamic calculations describe well how the alloying elements influence the transformation temperatures although there is still an offset in the actual values. Furthermore, a full set of elastic constants of one of the multinary alloys is presented, showing increased elastic stiffness leading to a higher Young’s modulus for the investigated alloy, compared to conventional Ni-base superalloys. The oxidation resistance is significantly improved compared to the ternary Co-Al-W compound. A complete thermal barrier coating system was applied successfully. © 2018, The Minerals, Metals & Materials Society and ASM International.

The formation of a ternary μ-phase is documented for the system Co-Ti-W. The relevant compositional stability range is identified by high-throughput energy dispersive X-ray spectroscopy, electrical resistance and X-ray diffraction maps from a thin-film materials library (1 μm thickness). Bulk samples of the identified compositions were fabricated to allow for correlative film and bulk studies. Using analytical scanning and transmission electron microscopy, we demonstrate that in both, thin film and bulk samples, the D85 phase (μ-phase) coexists with the C36-phase and the A2-phase at comparable average chemical compositions. Young's moduli and hardness values of the μ-phase and the C36-phase were determined by nanoindentation. The trends of experimentally obtained elastic moduli are consistent with density functional theory (DFT) calculations. DFT analysis also supports the experimental findings, that the μ-phase can solve up to 18 at.% Ti. Based on the experimental and DFT results it is shown that CALPHAD modeling can be modified to account for the new findings. © 2017 Acta Materialia Inc.

Cu-In-Sn alloys are among the suggested materials to replace Pb-Sn alloys traditionally used in joining processes by the electronic industry. Thorough thermodynamic understanding is required for the selection/design of adequate and efficient alloys for specific applications. Understanding the effects that high cost elements such as In have on microstructure and phase stability is imperative for industrial use. In this work ternary alloys were prepared by melting high purity elements (5N) for selected compositions of the 17 at.% Cu isopleth, and cooling down to reproduce process conditions. Chemical composition was determined using scanning electron microscopy equipped with electron probe microanalysis. Measurements of transition temperatures were done by heat-flux differential scanning calorimetry. We present a comprehensive comparison between our experimental results and phase diagram calculations using Liu et al. (J Electron Mater 30:1093, 2001) thermodynamic description based in the CALPHAD method, available in the literature. © 2017 ASM International

We apply the exact-muffin-tin-orbitals (EMTO) method to investigate structural properties, formation enthalpies, mechanical stability and polycrystalline moduli in Ni-Re, Ni-Cr and Cr-Re disordered fcc, bcc and hcp phases. Substitutional disorder is treated by using the coherent potential approximation (CPA). We predict the alloy lattice parameters in good agreement with the experiment. We find a continuous softening, as a function of Cr composition, of the tetragonal shear modulus C′ in fcc Ni-Cr phase indicating mechanical instability in Cr-rich Ni-Cr alloys. On the other hand, we show that the mechanical stability of fcc Ni-Re alloys persists through the whole composition range. We observe an intriguing behaviour of the Young's modulus vs. the intrinsic ductility curve in Ni-rich Ni-Re fcc phase. © 2016 Elsevier B.V. All rights reserved.

We perform density functional theory based first-principles calculations to identify promising alloying elements (X) capable of enhancing the compressive uniaxial theoretical (ideal) strength of the fcc Ni-matrix along the 001 direction. The alloying element belongs to a wide range of 3d,4d, and 5d series with nominal composition of 6.25 at. %. Additionally, a full elastic study is carried to investigate the ideal strength of fcc Ni and fcc Co. Our results indicate that the most desirable alloying elements are those with half d-band filling, namely, Os, Ir, Re, and Ru. © 2016 American Physical Society.

The mechanical properties of γ′-strengthened Co-Ni-Al-W-Cr model superalloys extending from pure Ni-base to pure Co-base superalloys have been assessed. Differential scanning calorimetry measurements and thermodynamic calculations match well and show that the γ′ solvus temperature decreases with increasing Co-content. The γ/γ′ lattice misfit is negative on the Ni- and positive on the Co-rich side. High Ni-contents decelerate the oxidation kinetics up to a factor of 15. The creep strength of the Ni-base alloy increases by an order of magnitude with additions of Co before it deteriorates strongly upon higher additions despite an increasing γ′ volume fraction. © 2015 Elsevier Ltd. All rights reserved.

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 OpenCalphad (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. © 2016 Elsevier B.V.

Using density-functional theory in combination with the direct force method and molecular dynamics we investigate the vibrational properties of a binary Cr-Re σ-phase. In the harmonic approximation, we have computed phonon dispersion curves and density of states, evidencing structural and chemical effects. We found that the σ-phase is mechanically unstable in some configurations, for example, when all crystallographic sites are occupied by Re atoms. By using a molecular-dynamics-based method, we have analysed the anharmonicity in the system and found negligible effects (∼0.5 kJ/mol) on the Helmholtz energy of the binary Cr-Re σ-phase up to 2000 K (∼0.8Tm). Finally, we show that the vibrational contribution has significant consequences on the disordering of the σ-phase at high temperature. © 2014 AIP Publishing LLC.

In the present work, thermodynamic modelling of the high temperature oxidation behaviour of a γ'-strengthened Co-base superalloy is presented. The ternary Co-9Al-9W alloy (values in at%) was isothermally oxidised for 500h at 800 and 900°C in air. Results reveal that the calculated oxide layer sequence (Thermo-Calc, TCNI6) is in good agreement with the formed oxide scales on the alloy surface. Furthermore, prediction of the influence of oxygen partial pressure on Al2O3 formation is presented. The modelling results indicate pathways for alloy development or possible pre-oxidation surface treatments for improved oxidation resistance of the material. © 2014 Elsevier Ltd.

The structural stability of topologically close-packed phases in binary transition metal alloys is investigated with a combination of first-principles calculations based on density-functional theory and the Bragg-Williams-Gorsky approximation for the description of the configurational entropy. For a variety of different (i) exchange-correlation functionals, (ii) pseudopotentials, and (iii) relaxation schemes, for the relevant phases in Re-X (X = Ta, V, W) binary systems, we compare the energy of formation at T = 0 K, as well as the phase diagrams and site occupancies at finite temperatures. We confirm previous findings that the configurational entropy plays a stabilising role for complex phases in these systems at elevated temperatures. Small differences in the calculated energy of formation for different exchange-correlation functionals, pseudopotentials and relaxation schemes are expected, but give rise to qualitatively different phase diagrams. We employ these differences in order to estimate the order of magnitude of the standard deviation necessary in the qualitatively-reliable calculation of phase diagrams and site occupancies. In an attempt to determine the accuracy that is required to assure a qualitatively correct prediction of phase diagrams, we modify our first-principles results numerically by random variations with the determined standard deviation as maximum amplitude. Taking the order of site occupancies and the set of stable phases as simple criteria for a qualitatively correct prediction, we find that the accuracy required for the energy of formation of the individual configurations in these systems is approximately 5 meV/atom (≈0.5 kJ/mol at). © 2013 Elsevier B.V. All rights reserved.

Most applications of thermodynamic databases to materials design are limited to ambient pressure. The consideration of elastic contributions to thermodynamic stability is highly desirable but not straight-forward to realise. We present examples of existing physical models for pressure-dependent thermodynamic functions and discuss the requirements for future implementations given the existing results of experiments and first-principles calculations. We briefly summarize the calculation of elastic constants and point out examples of nonlinear variation with pressure, temperature and chemical composition that would need to be accounted for in thermodynamic databases. This is particularly the case if a system melts from different phases at different pressures. Similar relations exist between pressure and magnetism and hence set the need to also include magnetic effects in thermodynamic databases for finite pressure. We present examples to illustrate that the effect of magnetism on stability is strongly coupled to pressure, temperature, and external fields. As a further complication we discuss dynamical instabilities that may appear at finite pressure. While imaginary phonon frequencies may render a structure unstable and destroy a crystal lattice, the anharmonic effects may stabilize it again at finite temperature. Finally, we also outline a possible implementation scheme for strain effects in thermodynamic databases. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Thermophysical properties, such as heat capacity, bulk modulus and thermal expansion, are of great importance for many technological applications and are traditionally determined experimentally. With the rapid development of computational methods, however, first-principles computed temperature-dependent data are nowadays accessible. We evaluate various computational realizations of such data in comparison to the experimental scatter. The work is focussed on the impact of different first-principles codes (quantum espresso and vasp), pseudopotentials (ultrasoft and projector augmented wave) as well as phonon determination methods (linear response and direct force constant method) on these properties. Based on the analysis of data for two pure elements, Cr and Ni, consequences for the reliability of temperature-dependent first-principles data in computational thermodynamics are discussed. © 2014 IOP Publishing Ltd.

The Au-In-Ga ternary phase diagram is of importance for understanding the involved thermodynamic processes during the growth of Au-seeded III-V heterostructure nanowires containing In and Ga (e.g. Au-seeded InAs/GaAs nanowires). In this work the Au-In-Ga system has been thermodynamically modeled using the CALPHAD technique based on a recent experimental investigation of the phase equilibria in the system. As a result, a set of self-consistent interaction parameters have been optimized that can reproduce most of the experimental results. © 2014 Elsevier B.V. All rights reserved.

As chromium is a decisive ingredient for stainless steels, a reliable understanding of its thermodynamic properties is indispensable. Parameter-free first-principles methods have nowadays evolved to a state allowing such thermodynamic predictions. For materials such as Cr, however, the inclusion of magnetic entropy and higher order contributions such as anharmonic entropy is still a formidable task. Employing state-of-the-art ab initio molecular dynamics simulations and statistical concepts, we compute a set of thermodynamic properties based on quasiharmonic, anharmonic, electronic and magnetic free energy contributions from first principles. The magnetic contribution is modeled by an effective nearest-neighbor Heisenberg model, which itself is solved numerically exactly by means of a quantum Monte Carlo method. We investigate two different scenarios: a weak magnetic coupling scenario for Cr, as usually presumed in empirical thermodynamic models, turns out to be in clear disagreement with experimental observations. We show that instead a mixed Hamiltonian including weak and strong magnetic coupling provides a consistent picture with good agreement to experimental thermodynamic data. © 2013 IOP Publishing Ltd.

A multicomponent phase-field method coupled to thermodynamic calculations according to the CALPHAD method was used to simulate microstructural evolution during directional solidification of the LEK94 commercial single-crystal Ni-based superalloy using a two-dimensional unit cell approximation. We demonstrate quantitative agreement of calculated microsegregation profiles and profiles determined from casting experiments as well as calculated fraction solid curves with those determined in differential thermal analysis (DTA) measurements. Finally, the role of solidification rate on dendrite morphology and precipitation of the secondary phases is investigated and a new measure of the dendrite morphology is presented to quantify the effect of back diffusion on the amount of secondary phases. © 2012 The Minerals, Metals & Materials Society and ASM International.

First-principles calculations of formation energies for 243 different configurations of the Cr-Ni-Re σ phase were used to calculate a ternary phase diagram in the Bragg-Williams-Gorsky approximation (BWG) and to model finite-temperature thermodynamic properties. The binary and ternary phase diagrams were then calculated at different temperatures. Correct topology of the experimental ternary isothermal section of the phase diagram has been obtained with a relatively small difference in temperature between calculations and experiments. © 2011 American Physical society.

Phase field modeling of precipitation kinetics in Al - Zr - Sc and Al - Zr - Ti ternary alloys has been performed. The free energy was evaluated using the Thermo-calc data. Our simulations showed that L12 precipitates in Al - Zr - Sc alloy consists of Sc rich zone of in core and Zirconium rich zone at the precipitate / matrix interface. In Al - Zr - Ti system, Al3 (Zr-Ti) precipitates are homogeneous and no segregation is observed. Phase-field simulation results are compared with 3D APT data. © (2011) Trans Tech Publications.

The phase field method has been applied to simulate the microstructural evolution of a commercial single crystal Ni-based superalloy during both, HIP and annealing treatments. The effects of applying high isostatic pressure on the microstructural evolution, which mainly retards the diffusion of the alloying elements causing the loss of the orientational coherency between the phases is demonstrated by the simulation and experimental results. © (2011) Trans Tech Publications, Switzerland.

The Ag-Cu-Ti system is important for brazing applications, particularly for ceramic joining. This system is characterized by numerous intermetallics in the Cu-Ti binary and the existence of a miscibility gap in the liquid phase. For applications, knowledge of the phase equilibria, invariant reactions in the temperature range of interest and thermodynamic activity values (mainly of Ti) are important. Thermodynamic model parameters for all the stable phases in the Ag-Cu, Cu-Ti and Ag-Ti systems, previously obtained using the Calphad method and available in the literature are used. A new thermodynamic description for the ternary interaction parameter of the liquid is obtained from experimental informations. Ti 2Cu and Ti 2Ag which have the same crystallographic structure were modelled as a single phase. The same was done for TiCu and TiAg. Finally, solid solubility of Ag in the Ti-Cu intermetallics is taken into account. The parameters obtained in this assessment are later used for the calculation of selected sections that can be useful for research and applications in the field of joining with Ti-activated Ag-Cu braze. © Carl Hanser Verlag GmbH & Co. KG.