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Effects of the geometrical alignment of an idealized deformation microstructure on the migration of recrystallization boundaries are studied using a phase-field model. A deformation field consisting of two sets of regularly arranged bands is used as an example to mimic typical deformed microstructures, while the migration of both initially flat and circular recrystallization boundaries are considered. The results show that for both cases the local variations in the deformation field affect not only the local shape of the migrating boundary but also the overall distances traveled. It is revealed that boundary migration into heterogeneously distributed energy fields are not uniform neither in space nor time, and can therefore not be expressed by the classic migration model with a uniform migration assumption, even when averaged over the whole boundary and long time. [ABSTRACT FROM AUTHOR]

The phase-field method has already proven its usefulness to simulate microstructural evolution for several applications, e.g., during solidification, solid-state phase transformations, fracture, etc. This wide variety of applications follows from its diffuse-interface approach. Moreover, it is straightforward to take different driving forces into account. The purpose of this paper is to give an introduction to the phase-field modelling technique with particular attention for models describing phenomena important in extractive metallurgy. The concept of diffuse interfaces, the phase-field variables, the thermodynamic driving force for microstructure evolution and the phase-field equations are discussed. Some of the possibilities to solve the equations describing microstructural evolution are also described, followed by possibilities to make the phase-field models quantitative and the phase-field modelling of the microstructural phenomena important in extractive metallurgy, i.e., multiphase field models. Finally, this paper illustrates how the phase-field method can be applied to simulate several processes taking place in extractive metallurgy and how the models can contribute to the further development or improvement of these processes. [ABSTRACT FROM AUTHOR]

Microstructure evolution in non-conserved and volume-conserved isotropic two-phase grain structures, with equal interfacial energy for all interfaces and equal volume fractions of the two-phases, is compared based on large-scale phase-field simulations. Two important observations are as follows: (1) the growth mechanism has a larger effect on the grain size distributions of the two alloys than on their grain topology distributions; (2) the growth rate and normalized grain size relation of the grains per topological class are much more scattered for the conserved system than the non-conserved system. [ABSTRACT FROM AUTHOR]

• A multi-component multi-phase field model is coupled with inhomogeneous elastic effects. • The elastic properties of the BCC and FCC phases of AlCrFeNi alloy are calculated using DFT calculations based on quasirandom crystal structures with the equilibrium compositions of the phases. • The CALPHAD composition dependence of the Gibbs energy and diffusion mobilities of the BCC and FCC phase are taken from the Thermo-Calc TCHEA2 and MOBHEA2 databases and accurately introduced into the phase field model for studying the AlCrFeNi multicomponent alloy. • The presence of elastic stress affects the BCC precipitate shape, size and the equilibrium concentrations in the two phases. We introduce a new approach to include for high and medium entropy alloys, stress effects in a Phase-field model (PFM). The approach is applied to simulate the evolution of two-phase BCC/FCC microstructures of AlCrFeNi alloys, combining phase-field method with CALPHAD data and DFT (Density Functional Theory) calculations. The composition dependent Gibbs energies and diffusion mobilities of the BCC and FCC phase as a vital input for simulating real alloys into the PFM are calculated from the Thermo-Calc TCHEA2 and MOBHEA2 databases. The special quasirandom structures (SQS) method was used to obtain the complex multicomponent lattice structures and compute with DFT the elastic properties of the BCC and FCC phases. It is found that elastic stresses emerging due to a difference in eigenstrain between the BCC and FCC phases during a phase transformation have a significant effect on the precipitate formation. The effect of the eigenstrain induced elastic stress on the BCC precipitate shape, size and the equilibrium concentrations in the two phases are quantitatively studied. The PFM presented is one of the first attempts to simulate elastic effects on high entropy alloys(HEAs) microstructures. This work contributes to the understanding of the mechanisms of phase transformation and microstructure evolution in HEAs. [Display omitted] [ABSTRACT FROM AUTHOR]

Several pyrometallurgical industries encounter production losses due to the attachment of metallic droplets to solid particles in slags. Although scarce, due to experimental challenges, the available results indicate the importance of interfacial energies. Simulations based on a phase field model potentially circumvent this lack of experimental data and allow a more systematic insight into the observed phenomenon. In the present work, a phase field model for solid–liquid binary systems with spinodal decomposition in the liquid is implemented to simulate the metal droplet formation and growth in slags with non-reacting solid particles. The simulations allowed evaluating the influence of the interfacial energies and initial slag composition on the attachment of metallic droplets to solid particles as a function of time for four different regimes, namely no wettability of the metal on the particle, low wettability, high wettability and full wettability. [ABSTRACT FROM AUTHOR]

A detailed investigation was carried out to study the effect of volume fraction on microstructure evolution in segregation-free isotropic volume-conserved two-phase alloys. Large scale two-dimensional (2D) and three-dimensional (3D) simulations were performed for 10/90, 30/70 and 50/50 alloys with a modified quantitative phase-field model. The grain growth in the two-phase alloys was consistent with volume-diffusion controlled growth with growth exponent m ∼ 3 . The kinetic coefficient, mean grain size, mean number of faces, grain size distribution (GSD), grain topology distribution (GTD) and grain size/topological class relation were all influenced by the volume fraction of the minor phase ( α ) in the two-phase alloys. In the 10/90 alloy, a bimodal distribution in the GSD and GTD for the 2D total grain structure was found. The timelines of evolution of major-phase grains in 3D simulations for all alloys were examined. ‘Particle-like’ grain migration of isolated α -phase grains was observed in the 2D simulations. The formation and evolution of non-constant curvatures on interphase boundaries in the isotropic volume-conserved two-phase alloys is discussed. The microstructure evolution in the volume-conserved two-phase alloys was compared with that in non-conserved two-phase alloys ( m ∼ 2 ). Simulation results are found to be in good agreement with a wide range of previous experimental and computer simulation results. [ABSTRACT FROM AUTHOR]

Pyrometallurgical industries encounter production losses due to the attachment of metallic droplets to solid particles in liquid slags. Experimental work on this topic remains very challenging. Simulations based on a phase field model can circumvent this lack of experimental data and allow a more systematic insight into the role of the different parameters on the observed phenomenon. In the present work, a recently developed phase-field model to simulate the attachment of liquid metal droplets to solid particles in slags is extended to consider real microstructures of solid particles in liquid slags. Furthermore, it is investigated which initialization method for the liquid metal droplets corresponds best to the experimental conditions. One of the initialization methods used spinodal decomposition of a supersaturated slag to introduce the metallic droplets, whereas the other initialization consists of positioning metallic droplets in the slag in a random way. The simulations showed that both initialization methods result in microstructures that correspond with experimental observations, which points to the existence of several origins for the attachment of metal droplets to solid particles in slags. [ABSTRACT FROM AUTHOR]

Metallic droplets can be attached to solids in slags, resulting in insufficient decantation and eventually production losses in several metal producing industries. Experiments and previous simulations indicate that interfacial energies play an important role in this interaction. In the present work, a recently developed phase field model is used to evaluate the influence of the morphology and fraction of the solid particles on the attachment behaviour of metallic droplets to solid particles. When the metallic droplets wet the solid particle partly or fully, the size, shape and proximity of the solid particles influence the size and number of attached droplets. The perimeter per area only influences the amount of attached metal at high wettability. Moreover, the space available around the particle, determined by the shape and proximity of other particles, can restrict the amount of attached metal. The simulations reveal that, in practice, fewer but larger solid particles close to each other would give rise to less attached metal and thus the chance for metal losses by mechanical entrainment decreases. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we present a phase field model to simulate the crystallization of Fe3O4 in FeO x –SiO2 melts under oxidizing conditions. The diffusion of FeO and Fe2O3 is considered, because the FeO/Fe2O3 ratio in the melt can be related to the local oxygen potential of the melt. A boundary condition is developed to ensure conservation of Fe while the ratio of FeO/Fe2O3 is in equilibrium with the oxygen fugacity of the atmosphere. Two-dimensional simulations are performed with different nucleation densities of Fe3O4 and varying oxygen fugacity in the atmosphere. The results show that, for the considered nucleation densities, the crystallization of the melt has a larger effect on the oxidation state than the oxygen fugacity of the atmosphere. Furthermore, for the considered composition range, the growth velocities of the spinel crystals increase with decreasing oxygen fugacity. [Copyright &y& Elsevier]

High temperature oxidic systems are encountered in nature (magma chambers) and pyrometallurgical processes. In these systems, the solidification of the oxidic liquids influences the flow, the cooling after tapping, the viscosity and rheological behaviour within the reactor and also the freeze lining behaviour. On the mesoscale, the phase field concept has proved to be a very powerful tool for modeling crystallizing microstructures. However, application of the method to slag solidification is still challenging. In this work, we present a phase field model to simulate the faceted crystallization of Fe 3 O 4 in a quaternary FeO–Fe 2 O 3 –Cu 2 O–SiO 2 melt under different partial pressures of oxygen to solve certain problems encountered related to more realistic simulations in oxidic systems. The ratio of FeO/Fe 2 O 3 at the upper boundary is in equilibrium with the oxygen fugacity of the atmosphere, while conserving Fe. Two-dimensional simulations are performed with different varying oxygen fugacity in the atmosphere. For the considered composition range, the growth velocities of the spinel crystals increase with decreasing oxygen fugacity. One of the focus points in creating more realistic phase field models is the incorporation of the thermodynamic driving forces in multicomponent multiphase-field models by coupling to thermodynamic databases. The first part of this work used a tabular method. However, as the number of components in the system increases, the number of thermodynamic data points also increases exponentially, and so do the computational and memory requirements. A possible solution for this might be the use of a canonical polyadic decomposition of the tensors containing the thermodynamic data. In this way, the huge tensors are approximated well by compact multilinear models or decompositions. This promising solution has been applied in the second part of this work on the same oxidic liquid-solid system. [ABSTRACT FROM AUTHOR]