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Materials Data on KHS by Materials Project

SKH1 crystallizes in the trigonal R3m space group. The structure is three-dimensional. K1+ is bonded in a 6-coordinate geometry to three equivalent H1+ and six equivalent S2- atoms. All K–H bond lengths are 2.91 Å. There are three shorter (3.30 Å) and three longer (3.35 Å) K–S bond lengths. H1+ is bonded in a distorted single-bond geometry to three equivalent K1+ and one S2- atom. The H–S bond length is 1.35 Å. S2- is bonded in a single-bond geometry to six equivalent K1+ and one H1+ atom.

36 MATERIALS SCIENCE↗

Materials Data on KHS by Materials Project

SKH1 crystallizes in the monoclinic P2_1/m space group. The structure is three-dimensional. K1+ is bonded in a 9-coordinate geometry to three equivalent H1+ and six equivalent S2- atoms. There are two shorter (2.99 Å) and one longer (3.00 Å) K–H bond lengths. There are a spread of K–S bond distances ranging from 3.28–3.40 Å. H1+ is bonded in a single-bond geometry to three equivalent K1+ and one S2- atom. The H–S bond length is 1.35 Å. S2- is bonded in a distorted single-bond geometry to six equivalent K1+ and one H1+ atom.

36 MATERIALS SCIENCE↗

The effects of introducing elasticity using different interpolation schemes to the grand potential phase field model

Introducing elastic energy in the phase field method has been shown to influence interfacial energy, depending on the elastic interpolation scheme. This study investigates the impact of the elastic energy when using a grand potential-based phase field method, comparing the result of Khachaturyan’s strain interpolation scheme (KHS) and Voight-Taylor’s elastic energy interpolation scheme (VTS). The KHS model leads to a decrease in the interfacial energy, while the VTS model leads to an increase. The change in interfacial energy is greater with the VTS model than the KHS model, which suggests that the KHS model is more appropriate to limit the artificial impact of the elastic energy on the interfacial energy. When the contribution at the interface is not negligible, it is shown that both the microstructure evolution kinetics and the equilibrium microstructure can be influenced by the choice of the elastic scheme being used. In addition, this paper shows that the grand potential model might not be appropriate when the system requires the introduction of a composition-dependent term in the elastic energy contribution. This limitation is due to the need for an explicit and invertible relation between the total potential and the composition.

36 MATERIALS SCIENCE↗

Comparison of excess free energy at an interface according to the applied interpolation scheme for elasticity: A phase-field method

Phase-field modeling is an effective simulation technique for modeling microstructure evolution of elastically anisotropic systems. To introduce the elastic energy contribution in a phase field model, an interpolation scheme is used to define the mechanical properties within the phases and across the continuous interface. Several existing interpolation schemes introduce a potential excess elastic energy at the interface, which undesirable effect on microstructure evolution needs to be evaluated. In this study, we focused on three interpolation schemes including Khachaturyan’ scheme (KHS), Voigt–Taylor’s scheme (VTS), and Steinbach–Apel’s scheme (SAS). Comparisons of these schemes’ performances were performed in three configuration types using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework: bi-crystal, isotropic particle-matrix and anisotropic particle-matrix. The contribution of excess elastic energy on the interface energy as a function of interface width and the computational time to steady-state were evaluated in these three configurations. SAS introduces the lowest excess elastic energy contribution and the VTS has the biggest contribution amongst the considered schemes. Moreover, when modeling precipitation in an anisotropic elastic material, the SAS approach seems to predict more physical convex shapes during growth, making it preferable to KHS and VTS. Finally, as currently implemented, SAS requires the largest computational time and KHS requires the smallest time to reach steady-state amongst the considered schemes.

36 MATERIALS SCIENCE↗