Phase-field simulation of solid state sintering

Hötzer, Johannes; Seiz, Marco; Kellner, Michael; Rheinheimer, Wolfgang; Nestler, Britta

doi:10.1016/j.actamat.2018.10.021

Cited by 77 publications

(35 citation statements)

References 41 publications

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“…The local phase fractions of the phases are represented by the N order parameters /â, which are stored in the vector /. Similar to the works [20,31,32], the phases a; b; . .…”

Section: Phase-field Modelmentioning

confidence: 99%

Data workflow to incorporate thermodynamic energies from Calphad databases into grand-potential-based phase-field models

et al. 2021

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In order to approximate Gibbs energy functions, a semi-automated framework is introduced for binary and ternary material systems, using Calphad databases. To generate Gibbs energy formulations by means of second-order polynomials, the framework includes a precise approach. Furthermore, an optional extensional step enables the modeling of systems in which a direct generation leads to the unsatisfactory results in the representation of the thermodynamics. Furthermore, an optional extensional step enables the modeling of systems, in which a direct generation leads to the unsatisfactory results, when representing the thermodynamics. Within this extension, the commonly generated functions are modified to satisfy the equilibrium conditions in the observed material systems, leading to a better correlation with thermodynamic databases. The generated Gibbs energy formulations are verified by recalculating the equilibrium concentrations of the phases and rebuilding the phase diagrams in the considered concentration and temperature ranges, prior to the simulation studies. For all comparisons, a close match is achieved between the results and the Calphad databases. As practical examples of the method, phase-field simulation studies for the directional solidification of the binary – and the ternary – eutectic systems are performed. Good agreements between the simulation results and the reported theoretical and experimental studies from literature are found, which indicates the applicability of the presented approaches. Graphical Abstract

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“…The local phase fractions of the phases are represented by the N order parameters /â, which are stored in the vector /. Similar to the works [20,31,32], the phases a; b; . .…”

Section: Phase-field Modelmentioning

confidence: 99%

Data workflow to incorporate thermodynamic energies from Calphad databases into grand-potential-based phase-field models

et al. 2021

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“…Chakraborty et al [74] studied the phenomenon of surface diffusion and electromigration-induced grain boundary grooving in the grand-potential framework and used an obstacle-type potential. Within a similar approach, Hötzer et al [75] studied the sintering of particles with surface diffusion as one of the primary mass transport mechanisms, as well as concurrent grain growth. To restrict diffusion along the interfaces, all aforementioned works have considered a scalar mobility function.…”

Section: Coupled Second-order Conservative and Nonconservative Equationsmentioning

confidence: 99%

“…Moreover, it should be mentioned that the ability to recover the sharp interface solution is not discussed in works where surface and grain-boundary diffusion are introduced [74,75,96]. This is the starting point for the extension presented in the following section.…”

Section: A Grand-potential Modelmentioning

confidence: 99%

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

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Grand-potential based multiphase-field model is extended to include surface diffusion. Diffusion is elevated in the interface through a scalar degenerate term. In contrast to the classical Cahn-Hilliard-based formulations, the present model circumvents the related difficulties in restricting diffusion solely to the interface by combining two second-order equations, an Allen-Cahn-type equation for the phase field supplemented with an obstacletype potential and a conservative diffusion equation for the chemical potential or composition evolution. The sharp interface limiting behavior of the model is deduced by means of asymptotic analysis. A combination of surface diffusion and finite attachment kinetics is retrieved as the governing law. Infinite attachment kinetics can be achieved through a minor modification of the model, and with a slight change in the interpretation, the same model handles the cases of pure substances and alloys. Relations between model parameters and physical properties are obtained which allow one to quantitatively interpret simulation results. An extensive study of thermal grooving is conducted to validate the model based on existing theories. The results show good agreement with the theoretical sharp-interface solutions. The obviation of fourth-order derivatives and the usage of the obstacle potential make the model computationally cost-effective.

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“…The simulation framework is based on the phase-field method [15] and contains multi-physical coupling to fields such as temperature, concentration or stresses to include their effect on microstructure evolution. The solver contains modules for diffuse interface approaches (Allen-Cahn, Cahn-Hilliard) [15], grain growth [16][17][18], grain coarsening [19,20], sintering [21,22], solidification [23,24], mass and heat transport, fluid flow (Lattice-Boltzmann, Navier-Stokes) [25], mechanical deformation (elasticity, plasticity) [26][27][28], magnetism [29], electrochemistry [30] and wetting [31,32]. The equations are discretized in space with a finite difference scheme and in time with different time integration methods such as explicit Euler schemes and implicit Euler via conjugated gradient methods [22,33].…”

Section: The Pace3d Frameworkmentioning

confidence: 99%

Lustre I/O performance investigations on Hazel Hen: experiments and heuristics

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With ever-increasing computational power, larger computational domains are employed and thus the data output grows as well. Writing this data to disk can become a significant part of runtime if done serially. Even if the output is done in parallel, e.g., via MPI I/O, there are many user-space parameters for tuning the performance. This paper focuses on the available parameters for the Lustre file system and the Cray MPICH implementation of MPI I/O. Experiments on the Cray XC40 Hazel Hen using a Cray Sonexion 2000 Lustre file system were conducted. In the experiments, the core count, the block size and the striping configuration were varied. Based on these parameters, heuristics for striping configuration in terms of core count and block size were determined, yielding up to a 32-fold improvement in write rate compared to the default. This corresponds to 85 GB/s of the peak bandwidth of 202.5 GB/s. The heuristics are shown to be applicable to a small test program as well as a complex application.

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Phase-field simulation of solid state sintering

Cited by 77 publications

References 41 publications

Data workflow to incorporate thermodynamic energies from Calphad databases into grand-potential-based phase-field models

Data workflow to incorporate thermodynamic energies from Calphad databases into grand-potential-based phase-field models

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

Lustre I/O performance investigations on Hazel Hen: experiments and heuristics

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