General method for incorporating CALPHAD free energies of mixing into phase field models: Application to the α-zirconium/δ-hydride system

Abstract

This paper presents a general method of incorporating CALPHAD-based free energies into a phase field model. While CALPHAD-based free energy descriptions provide realistic energetics of alloys, their formulations may pose numerical difficulties for phase field simulations. Specifically, the free energies of mixing for different phases may not necessarily be defined over the same concentration ranges, and their derivatives may exhibit highly nonlinear behavior. The method presented approximates the free energies of mixing using piecewise functions to eliminate the aforementioned characteristics while largely retaining the free energy values and the first and second derivative information, which affect the thermodynamic and kinetic behavior of the system. The method is verified by planar interface simulations of the α-zirconium/δ-hydride system. The phase fractions and compositions obtained from the phase field simulations are compared to the values calculated from the common tangent construction on the original free energies. The results indicate a high degree of accuracy. CALPHAD; phase field model; finite element; zirconium; zirconium hydride 1. Introduction Quantitative microstructural modeling of phase transformations such as solidification

Combining thermodynamics with tensor completion techniques to enable multicomponent microstructure prediction

“…4 gives an overview of the most common coupling approaches. [13][14][15][16][18][19][20][22][23][24][25][26] The methods using direct implementation of the CALPHAD Gibbs free energy expressions (b) or an interface with a thermodynamic software (d), give an exact and continuous representation of the composition dependence of the CALPHAD Gibbs free energies. They are considered as a reference against which the accuracy of the simulations using TTMs is evaluated.…”

“…[10][11][12] Different approaches have been proposed to include the CALPHAD thermodynamic descriptions in PFM. [13][14][15][16][17][18][19][20][21][22][23][24][25][26] A classification and discussion of the different approaches is given further in the paper. However, to date, only a few results for quaternary or higher-order systems are reported in the literature.…”

Benchmark problems for numerical implementations of phase field models

“…To provide example solutions to the benchmark problems, the MOOSE computational framework is used. MOOSE [61,62] is an open-source finite element framework and is the basis for several other phase field applications, including Marmot [33] and Hyrax [63,64]. To avoid computationally expensive fourth-order derivative operators, the Cahn-Hilliard equation is split into the two second-order equations [33,56], given by…”

Chemical modification of degenerate eutectics: A review of recent advances and current issues

“…We note that, in the phase field community, methods have been recently reported that eliminate such characteristics while largely retaining the free energy values. 80 Hecht et al have reviewed the advances in phase field modeling of multiphase solidification. 81 Other reviews 82,83 and research articles, 84,85 as well as references therein, provide additional examples of how PF modeling and other theoretical methods can be used to understand the physical mechanisms controlling the microstructural development.…”