Suzana G. Fries

OpenCalphad - a free thermodynamic software

Thermodynamic data are essential for the understanding, developing, and processing of materials. The CALPHAD (Calculation of Phase Diagrams) technique has made it possible to calculate properties of multicomponent systems using databases of thermodynamic descriptions with models that were assessed from experimental data. A large variety of data, such as phase diagram and solubility data, including consistent thermodynamic values of chemical potentials, enthalpies, entropies, thermal expansions, heats of transformations, and heat capacities, can be obtained from these databases. CALPHAD calculations can be carried out as stand-alone calculations or can be carried out coupled with simulation codes using the result from these calculations as input. A number of CALPHAD software are available for the calculation of properties of multicomponent systems, and the majority are commercial products. The OpenCalphad (OC) software, discussed here, has a simple programming interface to facilitate such integration in application software. This is important for coupling validated thermodynamic as well as kinetic data in such simulations for obtaining realistic results. At present, no other high quality open source software is available for calculations of multicomponent systems using CALPHAD-type models, and it is the goal of the OC source code to fill this gap. The OC software is distributed under a GNU license. The availability of the source code can greatly benefit scientists in academia as well as in industry in the development of new models and assessment of model parameters from both experimental data and data from first principles calculations.

Upgrading CALPHAD to microstructure simulation: the phase-field method

Abstract By amending the time and space evolution of interfaces to the CALPHAD Gibbsian phase descriptions, the phase-field method now makes realistic microstructure simulations possible. This combination allows incorporating more than one century of accumulated experimental information, consistently synthesized in the thermodynamic and kinetic CALPHAD databases, into multicomponent, multiphase, 3-dimensional microstructure evolution simulations. It represents a large step in materials design and a call for creative contributions from a growing interdisciplinary community. The approach is illustrated by steel and magnesium alloy microstructure simulations.

Thermodynamic modeling of chromium: strong and weak magnetic coupling

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.

Thermodynamic modelling of the Ag–Cu–Ti ternary system

Abstract 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. Ti2Cu and Ti2Ag 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.

Microsegregation and Secondary Phase Formation During Directional Solidification of the Single-Crystal Ni-Based Superalloy LEK94

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.

Reliability evaluation of thermophysical properties from first-principles calculations.

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.

Anharmonicity, mechanical instability, and thermodynamic properties of the Cr-Re σ-phase

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 (~0.8T(m)). Finally, we show that the vibrational contribution has significant consequences on the disordering of the σ-phase at high temperature.

Analysis of phase formation in Ni-rich alloys of the Ni–Ta–W system by calorimetry, DTA, SEM, and TEM

Abstract The partial enthalpies of dissolution of pure Ni, W and Ta in liquid ternary Ni–Ta–W alloys have been determined at (17735)K using a high temperature isoperibolic calorimeter. Measurements were performed in Ni-rich alloys (from 80 to 100 at.% Ni) along sections with constant Ta:W atomic ratios 1:0, 2:1, 1:2, and 0:1. The partial enthalpies and thereby the integral enthalpy of mixing of these ternary alloys are calculated from the partial enthalpies of dissolution using SGTE Gibbs energies for pure elements as reference. The obtained thermochemical data confirm that in the investigated Ni-rich alloys the binary interactions between Ta and W as well as the ternary Ni–Ta–W interactions are negligibly small. Due to this the variation of the integral enthalpy of mixing of the ternary alloys is well described as linear combination of the constituent Ni–Ta and Ni–W binaries. Such behaviour of the ternary liquid alloys is related to a very low probability of new ternary stable phases to occur in solid state. This prediction is confirmed by differential thermal analysis, scanning electron microscopy, and transmission electron microscopy of the as-solidified and annealed samples obtained as last alloy compositions in the series of calorimetric dissolution.

Enthalpies of formation measurements and thermodynamic description of the Ag–Cu–Zn system

Abstract The enthalpies of formation of β and γ alloys of the Ag–Cu–Zn system were determined by dissolution calorimetry. The melting and solid-state transformation temperatures as well as the enthalpies of the order/disorder and β/χ transformations were measured by differential scanning calorimetry. Thermodynamic descriptions are presented for the binary Ag–Zn system and for the ternary Ag–Cu–Zn system in the entire composition ranges. The thermodynamic model parameters of the constituent binaries Ag–Cu and Cu–Zn are taken from earlier assessments. Those for Ag–Zn and the Ag–Cu–Zn system are established based on relevant experimental data available in the literature completed with experimental data obtained in the present work. Several vertical and isothermal sections as well as the liquidus surface and thermodynamic properties are calculated using the evaluated parameters and show reasonably good agreement with experimental data available.

Precipitation Kinetics Study of Al – Zr – X(Sc or Ti) Alloys by Phase Field Simulations and Atom Probe Tomography

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.