1991
DOI: 10.1557/proc-249-413
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Cellular Automaton Simulations of Surface Mass Transport Due to Curvature Gradients: Simulations of Sintering in 3-D.

Abstract: A cellular automaton algorithm is described that simulates the evolution of a surface driven by the reduction of chemical potential differences on the surface. When the surface tension is isotropic, the chemical potential is proportional to the curvature at the surface. This process is important in the development of microstructure during the sintering of powders. The algorithm is implemented in two and three dimensions in a digital image mode, using discrete pixels to represent continuum objects. The heart of… Show more

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Cited by 13 publications
(19 citation statements)
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“…Generally speaking the transition rules used in the literature fall into two categories, based on either cell counting or free energy. The cell counting approach has been used for modeling microstructure changes that are driven only by interface curvature (15,29,32,33), whereas the free energy based approach has been employed in modelling microstructure changes driven by other driving forces, such as stored elastic energy, stored dislocation density and crystallographic orientation mismatch (28,34,35). The advantage of the free energy based approach is that the transition rule can be made scalable to any mesh size and to any combination of interface mobility and energy (34).…”
Section: Introductionmentioning
confidence: 99%
“…Generally speaking the transition rules used in the literature fall into two categories, based on either cell counting or free energy. The cell counting approach has been used for modeling microstructure changes that are driven only by interface curvature (15,29,32,33), whereas the free energy based approach has been employed in modelling microstructure changes driven by other driving forces, such as stored elastic energy, stored dislocation density and crystallographic orientation mismatch (28,34,35). The advantage of the free energy based approach is that the transition rule can be made scalable to any mesh size and to any combination of interface mobility and energy (34).…”
Section: Introductionmentioning
confidence: 99%
“…To address this challenge, Pimienta et al [91] developed a model for simulating sintering evolution due to surface mass transport, driven by curvature differences. By estimating curvature of the surface indirectly from images, and relocating pixels (mass) based on the measured curvature differences, realistic cases of random particle collections in two dimensions were successfully simulated, and the algorithm was later extended to three dimensions [92]. In their approach, analysis begins by replacing an atomically stepped surface with a continuous depiction, represented digitally by pixels.…”
Section: Microstructure Development During Sinteringmentioning
confidence: 99%
“…By estimating curvature of the surface indirectly from digital images, and relocating pixels (mass) based on the measured curvature differences, realistic cases of random particle collections in two and three dimensions were successfully simulated in Ref. [21]. In this approach, an atomically stepped surface is replaced with a continuous depiction, represented digitally by pixels.…”
Section: Introductionmentioning
confidence: 99%
“…In this work, we employ the cellular automaton-based sintering model originally proposed in [20], and later extended to three dimensions in Ref. [21]. The model is only described briefly here, and readers are referred to Refs.…”
Section: Introductionmentioning
confidence: 99%
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