Three-dimensional normal grain growth: Monte Carlo Potts model simulation and analytical mean field theory

2006 ◽  
Vol 54 (9) ◽  
pp. 1697-1702 ◽  
Author(s):  
Dana Zöllner ◽  
Peter Streitenberger
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Grain Growth ◽  
Potts Model ◽  
Model Simulation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional

Monte Carlo Potts Model Simulation and Statistical Theory of 3D Grain Growth

2007 ◽  
Vol 558-559 ◽  
pp. 1219-1224 ◽  
Author(s):  
Dana Zöllner ◽  
Peter Streitenberger
Keyword(s):  
Grain Size ◽  
Monte Carlo ◽  
Grain Growth ◽  
Potts Model ◽  
Model Simulation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Rate Of Change ◽  
Volumetric Rate

An improved Monte Carlo (MC) Potts model algorithm has been implemented allowing an extensive simulation of three-dimensional (3D) normal grain growth. It is shown that the simulated microstructure reaches a quasi-stationary state, where the growth of grains can be described by an average self-similar volumetric rate of change, which depends only on the relative grain size. Based on a quadratic approximation of the volumetric rate of change a generalized analytic mean-field theory yields a scaled grain size distribution function that is in excellent agreement with the simulation results.

Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory

2007 ◽  
Vol 550 ◽  
pp. 589-594 ◽  
Author(s):  
Dana Zöllner ◽  
Peter Streitenberger
Keyword(s):  
Field Theory ◽  
Grain Size ◽  
Monte Carlo ◽  
Distribution Function ◽  
Grain Growth ◽  
Mean Field Theory ◽  
Mean Field ◽  
Size Distribution Function ◽  
Three Dimensions ◽  
Self Similar

A modified Monte Carlo Potts model algorithm for single-phase normal grain growth in three dimensions in presented, which enables an extensive statistical analysis of the growth kinetics and topological properties of the microstructure within the quasi-stationary self-similar coarsening regime. From the mean-field theory an analytical grain size distribution function is derived, which is based on a quadratic approximation of the average self-similar volumetric rate of change as a function of the relative grain size as it has been determined from the simulation. The analytical size distribution function is found to be in excellent agreement with the simulation results.

Potts Model Simulation of Grain Boundary Junction Limited Grain Growth

2012 ◽  
Vol 715-716 ◽  
pp. 623-628 ◽  
Author(s):  
Dana Zöllner ◽  
Peter Streitenberger
Keyword(s):  
Grain Growth ◽  
Potts Model ◽  
Model Simulation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Simulation Studies ◽  
Average Growth ◽  
Growth Regime ◽  
Self Similar ◽  
Small Grains

The standard Monte Carlo (MC) Potts model is modified regarding the mobility of grain boundaries and their junctions allowing the simulation of a size effect observed in nanocrystalline grain growth. In large simulation studies different properties are measured. For initially very small grains the early growth regime corresponds to a separate coarsening state, which is characterised by an average growth law and a self-similar grain size distribution that both show strong deviations from the parabolic normal grain growth behaviour. The simulation results can be described by a theoretical model based on a statistical mean-field theory for nanocrystalline grain growth.

Electronic and magnetic properties of honeycomb transition metal monolayers: first-principles insights

2014 ◽  
Vol 16 (26) ◽  
pp. 13383-13389 ◽  
Author(s):  
Xinru Li ◽  
Ying Dai ◽  
Yandong Ma ◽  
Baibiao Huang
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Magnetic Properties ◽  
Transition Metal ◽  
First Principles ◽  
Mean Field Theory ◽  
Mean Field ◽  
Electronic And Magnetic Properties ◽  
Dirac Systems

The electronic and magnetic properties of d-electron-based Dirac systems are studied by combining first-principles with mean field theory and Monte Carlo approaches.

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