Multiscale modeling based on phase-field approaches: consistency analysis regarding growth and melting kinetics in metals
Final Report Abstract
The need for multiscale modeling is motivated by the fact that important phenomena in materials sciences and engineering often involve interactions between microscopic and macroscopic length and time scales. Considering the solidification process, for instance, solid-liquid interfaces are on the order of a few angstroms, whereas microstructural features are on the length of tens of micrometers. Time scales of solidification span from picoseconds for the typical atomic dynamics processes to seconds needed for transport of heat and matter away from the interface. Understanding the physics of solidification over such disparate length and time scales, about ten orders of magnitude, represents one of the challenges of materials sciences, for which new mathematical models and numerical simulations algorithms have to be developed. In our project, we focused on one of the central challenges in multiscale modeling, namely how to bridge the gap among atomistic and macroscopic approaches in order to ensure that the descriptions at all levels are quantitatively consistent with each other. This task were achieved for one of the promising multiscale methods, namely the hierarchical coupling approach that combines molecular dynamics (MD) with phase-field (PF) simulations. The consistency analysis were carried out by detailed comparisons of quantitative predictions of the considered modeling methods for the growth and melting kinetics in metals. The MD simulations provide the physical quantities needed for the construction of the multiscale models. Of central importance are the bulk free energy and the solid-liquid interfacial free energy whose calculation requires the use of special methods. Our way of proceeding consists of two steps: (1) Analyzing how the phenomenological PF model can be properly designed in order to reproduce quantitatively the solidification kinetics observed by MD. The latter atomistic approach, considered as the reference, provides all the physical parameters needed to construct the former continuous one. (2) Once a consistent MD/PF hybrid model is constructed, we use it for a better understanding of the growth kinetics, going further than would one single approach. The consistency analysis is aimed at continuously improving the design of the PF model and, consequently, enhancing the predictive accuracy of the MD/PF coupling. We applied this MD/PF coupling approach for an understanding of the thermodynamics and kinetics during growth of bcc Zr from an undercooled NiZr melt under chemical nonequilibrium. We showed that the PF approach describes the same aspects of physics as MD, when the key parameters (like free energy, diffusivity and interface properties) are transferred from MD to PF. Moreover, the effective thermodynamic enhancement of the diffusivity through the strong negative enthalpy of mixing in the NiZr solution was quantified. In another study, we applied the same coupling approach to capture, quantitatively, the correlation between the short-range order in the melt, the in-plane ordering at the crystal-liquid interface and the stability of the liquid against crystallization. In a further study, we linked MD simulations to PF and phase-field crystal (PFC) modeling for a better understanding of the collision-controlled growth kinetics from the melt of pure Fe, going –thereby– further than would one single approach. The MD/PF comparison shows, on the one hand, that the PF model can be properly designed to reproduce quantitatively different aspects of the growth kinetics and anisotropy of planar and curved solidliquid interfaces. On the other hand, it demonstrates the ability of classical MD simulations to predict interface morphology and dynamics in accordance with the underlying anisotropies up to a length scale of about 0.15 µm. After mapping the MD model to the PF one, this latter permits to analyze the separate contribution of different anisotropies to the interface morphology.
Publications
- Local atomic order in the melt and solid-liquid interface effect on the growth kinetics in a metallic alloy model, Phys. Rev. Lett. 110, 086105 (2013)
M. Guerdane, H. Teichler, B. Nestler
(See online at https://doi.org/10.1103/PhysRevLett.110.086105) - Free energy of melts and intermetallic compounds of binary alloys determined by a molecular dynamics approach, Phys. Rev. E 89, 023308 (2014)
M. Guerdane
(See online at https://doi.org/10.1103/PhysRevE.89.023308) - Self-diffusion in intermetallic AlAu4 : Molecular dynamics study down to temperatures relevant to wire bonding, Computational Materials Science 129, 13 (2017)
M. Guerdane
(See online at https://doi.org/10.1016/j.commatsci.2016.11.012) - Crystal-melt interface mobility in bcc Fe: Linking molecular dynamics to phase-field and phase-field crystal modeling, Phys. Rev. B 97, 144105 (2018)
M. Guerdane and M. Berghoff
(See online at https://doi.org/10.1103/PhysRevB.97.144105)
