The phase field method has emerged as the tool of choice to simulate complex pattern formation processes in various domains of materials sciences. For the phase field model to faithfully reproduce the dynamics of a prescribed free-boundary problem with transport equations in the bulk and boundary conditions at the interfaces, the so-called thin-interface limit should be performed. For a phase transformation driven by diffusion, the kinetic cross-coupling between the phase field and the diffusion field has recently been introduced, allowing a control on interface boundary conditions in the general case where the diffusivity in the growing phase $D_S$ neither vanishes (one-sided model) nor equals the one of the disappearing phase $D_L$ (symmetric model). Here, we investigate the capabilities of this nondiagonal phase field model in the case of two-dimensional dendritic growth. We benchmark our model with Green's function calculations (sharp-interface model) for the symmetric and one-sided cases, and our results for arbitrary $D_S/D_L$ allow us to propose a generalization of the theory by Barbieri and Langer [ Phys. Rev. A 39, 5314 (1989)] for finite anisotropy of interface energy. We also perform simulations that evidence the necessity of introducing the kinetic cross-coupling and of eliminating surface diffusion. Our work opens up the way for quantitative phase field simulations of phase transformations with diffusion in the growing phases playing an important role in the pattern and velocity selections.

We develop a three-phase field model for the simulation of eutectic and eutectoid transformations on the basis of a nondiagonal model obeying Onsager relations for a kinetic cross coupling between diffusion and the phase fields. This model overcomes the limitations of existing phase field models concerning the fulfillment of local equilibrium boundary conditions at the transformation fronts in the case of a finite diffusional contrast between the phases. We benchmark our model in the well understood one-sided case with diffusion only in the parent phase against results from the literature. In addition to this solidification scenario, the case of solid-state transformations with diffusion in the growing phases is investigated. Our simulations validate the relevance of the theory developed by Ankit et al. [ Acta Mater. 61, 4245 (2013)], that describes in a single frame the two limiting regimes where diffusion mainly takes place whether in the mother phase or in the growing phases. In both the one-sided and two-sided cases, we verify the necessity of the kinetic cross coupling for quantitative phase field simulations.

We develop a theoretical model to predict the sublimation vapor pressure of pure substances. Moreover, we present a simple monoatomic molecule approximation, which reduces the complexity of the vapor pressure expression for polyatomic gaseous molecules at a convincing level of accuracy, with deviations of the Arrhenius prefactor for $\mathrm{NaCl}$ and $\mathrm{NaF}$ being 5.02% and 7.08%, respectively. The physical model is based on ab initio calculations, statistical mechanics, and thermodynamics. We illustrate the approach for $\mathrm{Ni}$, $\mathrm{Cr}$, Cu (metallic bond), $\mathrm{NaCl}$, $\mathrm{NaF}$, ${\mathrm{ZrO}}_2$ (ionic bond) and ${\mathrm{SiO}}_2$ (covalent bond). The results are compared against thermodynamic databases, which show high accuracy of our theoretical predictions, and the deviations of the predicted sublimation enthalpy are typically below 10%, for $\mathrm{Cu}$ even only 0.1%. Furthermore, the partial pressures caused by gas phase reactions are also explored, showing good agreement with experimental results.

The Crofer 22 APU alloy is a frequently used metallic material to manufacture interconnects in solid oxide fuel cells. However, the formation and evaporation of Cr${}_2$O${}_3$ not only increases the electrical resistance but also leads to the Cr-related degradation over the service time. In order to investigate the growth kinetics of Cr-oxide, i.e., Cr${}_2$O${}_3$, the multi-phase field model coupled with reliable CALPHAD databases is employed. The phase field simulation results are benchmarked with the predictions of Wagner’s theory. Moreover, we evidence the influence of the temperature and Cr concentration on the ferritic matrix phase and the oxygen concentration at the Cr${}_2$O${}_3$/gas interface on the growth kinetics of Cr-oxide, paving the way for further investigations of Cr-related solid oxide fuel cell degradation processes.