An official website of the United States government
Abstract We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The fundamental thermodynamic relation between internal energy and entropy, as well as entropy production, is derived analytically and further verified by numerical benchmark simulations. Furthermore, we examine how the different model parameters control density and temperature evolution during dendritic solidification through extensive parameter studies. Finally, we extend our framework to the modeling of open systems considering external mass and heat fluxes. This work sets the ground for a comprehensive mesoscale model of non-isothermal solidification including thermal expansion within an entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification.
more »
« less
Explicit temperature coupling in phase-field crystal models of solidification
Abstract We present a phase-field crystal model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the microscopic density field. We showcase the model capabilities via selected numerical investigations which focus on the prototypical growth of two-dimensional crystals from the melt, resulting in faceted shapes and dendrites. This work sets the grounds for a comprehensive mesoscale model of solidification including thermal expansion.
more »
« less
- Award ID(s):
- 2012634
- PAR ID:
- 10370950
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Modelling and Simulation in Materials Science and Engineering
- Volume:
- 30
- Issue:
- 7
- ISSN:
- 0965-0393
- Page Range / eLocation ID:
- Article No. 074004
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract We optimize a numerical time‐stabilization routine for a class of phase‐field crystal (PFC) models of solidification. By numerical experiments, we demonstrate that our simple approach can improve the accuracy of underlying time integration schemes by a few orders of magnitude. We investigate different time integration schemes. Moreover, as a prototypical example for applications, we extend our numerical approach to a PFC model of solidification with an explicit temperature coupling.more » « less
-
The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.more » « less
-
Abstract The solidification of a putative magma ocean sets the stage for subsequent subsolidus mantle convection. Whereas it may have resulted in a compositionally stratified mantle, the efficiency of relevant processes to cause chemical differentiation, such as crystal accumulation and matrix compaction, remains uncertain. The purpose of this study is to present the thermochemical structure of end‐member cases where potential differentiation mechanisms are taking full effect. We employ a self‐consistent thermodynamic model to make our model consistent in both thermal and chemical aspects. The accumulation of crystals at the base of magma ocean can enrich the upper mantle with iron, but such a global‐scale compositional stratification is likely to be quickly eliminated by gravitational instability, leaving small‐scale heterogeneities only. On the other hand, the compaction of solid matrix in the deep mantle creates a long‐lasting molten layer above the core‐mantle boundary. Our results suggest that the efficiency of compaction is the key factor to generate compositional stratification during solidification.more » « less
-
Abstract Dynamic solidification behavior during metal additive manufacturing directly influences the as-built microstructure, defects, and mechanical properties of printed parts. How the formation of these features is driven by temperature variation (e.g., thermal gradient magnitude and solidification front velocity) has been studied extensively in metal additive manufacturing, with synchrotron x-ray imaging becoming a critical tool to monitor these processes. Here, we extend these efforts to monitoring full thermomechanical deformation during solidification through the use of operando x-ray diffraction during laser melting. With operando diffraction, we analyze thermomechanical deformation modes such as torsion, bending, fragmentation, assimilation, oscillation, and interdendritic growth. Understanding such phenomena can aid the optimization of printing strategies to obtain specific microstructural features, including localized misorientations, dislocation substructure, and grain boundary character. The interpretation of operando diffraction results is supported by post-mortem electron backscatter diffraction analyses.more » « less
