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1. A non-isothermal phase-field crystal model with lattice expansion: analysis and benchmarks

   https://doi.org/10.1088/1361-651X/ada784  

   Punke, Maik; Salvalaglio, Marco; Voigt, Axel; Wise, Steven M (January 2025, Modelling and Simulation in Materials Science and Engineering)

   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. 

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2. A Phase-Field Model for In-Space Manufacturing of Binary Alloys

   https://doi.org/10.3390/ma16010383  

   Ghosh, Manoj; Hendy, Muhannad; Raush, Jonathan; Momeni, Kasra (January 2023, Materials)

   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. 

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3. Nearest-neighbor Gaussian Process Emulation for Multi-dimensional Array Responses in Freeze Nano 3D Printing of Energy Devices

   https://doi.org/10.1115/1.4045795  

   Segura, Luis Javier; Zhao, Guanglei; Zhou, Chi; Sun, Hongyue (December 2019, Journal of Computing and Information Science in Engineering)

   Abstract Energy 3D printing processes have enabled energy storage devices with complex structures, high energy density, and high power density. Among these processes, Freeze Nano Printing (FNP) has risen as a promising process. However, quality problems are among the biggest barriers for FNP. Particularly, the droplet solidification time in FNP governs thermal distribution, and subsequently determines product solidification, formation, and quality. To describe the solidification time, physical-based heat transfer model is built. But it is computationally intensive. The objective of this work is to build an efficient emulator for the physical model. There are several challenges unaddressed: 1) the solidification time at various locations, which is a multi-dimensional array response, needs to be modeled; 2) the construction and evaluation of the emulator at new process settings need to be quick and accurate. We integrate joint tensor decomposition and Nearest Neighbor Gaussian Process (NNGP) to construct an efficient multi-dimensional array response emulator with process settings as inputs. Specifically, structured joint tensor decomposition decomposes the multi-dimensional array responses at various process settings into the setting-specific core tensors and shared low dimensional factorization matrices. Then, each independent entry of the core tensor is modeled with an NNGP, which addresses the computationally intensive model estimation problem by sampling the nearest neighborhood samples. Finally, tensor reconstruction is performed to make predictions of solidification time for new process settings. The proposed framework is demonstrated by emulating the physical model of FNP, and compared with alternative tensor (multi-dimensional array) regression models. 

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4. The Effects of Inoculation on the Weldability of 6061 Aluminum Processed with GMA-DED

   https://doi.org/10.29391/2025.104.017  

   KLEINDIENST, JOSEPH; KLEMM-TOOLE, JONAH; BAGSHAW, NICK; ITEN, JEREMY (March 2025, Welding Journal)

   The weldability of plain and inoculated 6061 aluminum processed with gas metal arc directed energy deposition (GMA-DED) was evaluated and compared to wrought 6061. Autogenous gas tungsten arc welds of varying heat inputs were made, and the degree of solidification cracking was evaluated. The degree of cracking in the inoculated 6061 material was lower than that of plain GMA-DED and wrought 6061. Microstructure characterization revealed that the welds on the inoculated 6061 produced fine, equiaxed grains, whereas the plain 6061 showed coarse, columnar grains. A combination of heat transfer and solidification models were employed to predict the solidification morphology of the 6061 welds, which closely matched the experimental results in all cases. A model was developed to understand the effect of grain morphology on solidification cracking, and it was found that equiaxed grains shifted the critical liquid film range for cracking to lower solid fractions where thermal stresses are the lowest. However, cracking can be caused if sufficient external stresses are applied when the critical liquid film thickness is present during solidification of the equiaxed grain structure. This work provides insight into the role grain size and morphology control can have in suppressing solidification cracking of other aluminum alloys. 

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5. Improved time integration for phase‐field crystal models of solidification

   https://doi.org/10.1002/pamm.202200112  

   Punke, Maik; Wise, Steven M.; Voigt, Axel; Salvalaglio, Marco (May 2023, PAMM)

   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. 

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