On the Validation of the Monte Carlo Technique in Simulation of Grain Growth in Small, Two-Dimensional Systems

2007 ◽  
Vol 558-559 ◽  
pp. 1087-1092
Author(s):  
Ola Hunderi ◽  
Knut Marthinsen ◽  
Nils Ryum
Keyword(s):  
Monte Carlo ◽  
Grain Boundary ◽  
Grain Growth ◽  
Computer Simulations ◽  
Two Dimensions ◽  
Theoretical Treatment ◽  
Two Dimensional ◽  
Simulation Techniques ◽  
Boundary Curvature ◽  
Kinetics Of

The kinetics of grain growth in real systems is influenced by several unknown factors, making a theoretical treatment very difficult. Idealized grain growth, assuming all grain boundaries to have the same energy and mobility (mobility M = k/ρ, where k is a constant and ρ is grain boundary curvature) can be treated theoretically, but the results obtained can only be compared to numerical grain growth simulations, as ideal grain growth scarcely exists in nature. The validity of the simulation techniques thus becomes of great importance. In the present investigation computer simulations of grain growth in two dimensions using Monte Carlo simulations and the grain boundary tracking technique have been investigated and compared in small grain systems, making it possible to follow the evolution of each grain in the system.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

Estimates of critical percolation probabilities for a set of two-dimensional lattices

1972 ◽  
Vol 71 (1) ◽  
pp. 97-106 ◽  
Author(s):  
D. G. Neal
Keyword(s):  
Monte Carlo ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Critical Percolation ◽  
Site Percolation

AbstractThis paper describes new detailed Monte Carlo investigations into bond and site percolation problems on the set of eleven regular and semi-regular (Archimedean) lattices in two dimensions.

Monte-Carlo Simulation of Goss Abnormal Grain Growth in Fe-3%Si Steel by Sub-Boundary Enhanced Solid-State Wetting

2012 ◽  
Vol 715-716 ◽  
pp. 146-151
Author(s):  
K.J. Ko ◽  
A.D. Rollett ◽  
N.M. Hwang
Keyword(s):  
Monte Carlo ◽  
Solid State ◽  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Energy ◽  
Three Dimensional ◽  
Abnormal Grain Growth ◽  
Grain Boundary Energy ◽  
Simulation Based ◽  
Mc Simulation

The selective abnormal grain growth (AGG) of Goss grains in Fe-3%Si steel was investigated using a parallel Monte-Carlo (MC) simulation based on the new concept of sub-boundary enhanced solid-state wetting. Goss grains with low angle sub-boundaries will induce solid-state wetting against matrix grains with a moderate variation in grain boundary energy. Three-dimensional MC simulations of microstructure evolution with textures and grain boundary distributions matched to experimental data is using in this study.

LUTTINGER-LIQUID BEHAVIOUR IN 2D: THE VARIATIONAL APPROACH

1993 ◽  
Vol 07 (03) ◽  
pp. 119-141 ◽  
Author(s):  
CLAUDIUS GROS ◽  
ROSER VALENTÍ
Keyword(s):  
Monte Carlo ◽  
Variational Formulation ◽  
Variational Approach ◽  
Order Parameter ◽  
Luttinger Liquid ◽  
Two Dimensions ◽  
Point Of View ◽  
Two Dimensional ◽  
Liquid Type ◽  
D Wave

We study a variational formulation of the Luttinger-liquid concept in two dimensions. We show that a Luttinger-liquid wavefunction with an algebraic singularity at the Fermiedge is given by a Jastrow-Gutzwiller type wavefunction, which we evaluate by variational Monte Carlo for lattices with up to 38 × 38 = 1444 sites. We therefore find that, from a variational point of view, the concept of a Luttinger liquid is well defined even in 2D. We also find that the Luttinger liquid state is energetically favoured by the projected kinetic energy in the context of the 2D t-J model. We study and find coexistence of d-wave superconductivity and Luttinger-liquid behaviour in two-dimensional projected wavefunctions. We then argue that generally, any two-dimensional d-wave superconductor should be unstable against Luttinger-liquid type correlations along the (quasi-1D) nodes of the d-wave order parameter, at temperatures small compared to the gap.

Diffusion Mechanisms in Nanocrystalline and Nanolaminated Au-Cu

2007 ◽  
Vol 266 ◽  
pp. 13-28 ◽  
Author(s):  
Alan F. Jankowski
Keyword(s):  
Low Temperature ◽  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Diffusion ◽  
Bulk Diffusion ◽  
Grain Boundary Diffusion ◽  
Dominant Mechanism ◽  
Temperature Range ◽  
Diffusion Mechanisms ◽  
Kinetics Of

Thermal anneal treatments are used to identify the temperature range of the two dominant diffusion mechanisms – bulk and grain boundary. To assess the transition between mechanisms, the low temperature range for bulk diffusion is established utilizing the decay of static concentration waves in composition-modulated nanolaminates. These multilayered structures are synthesized using vapor deposition methods as thermal evaporation and magnetron sputtering. However, at low temperature the kinetics of grain-boundary diffusion are much faster than bulk diffusion. The synthesis of Au-Cu alloys (0-20 wt.% Cu) with grain sizes as small as 5 nm is accomplished using pulsed electro-deposition. Since the nanocrystalline grain structure is thermally unstable, these structures are ideal for measuring the kinetics of grain boundary diffusion as measured by coarsening of grain size with low temperature anneal treatments. A transition in the dominant mechanism for grain growth from grain boundary to bulk diffusion is found with an increase in temperature. The activation energy for bulk diffusion is found to be 1.8 eV·atom-1 whereas that for grain growth at low temperatures is only 0.2 eV·atom-1. The temperature for transitioning from the dominant mechanism of grain boundary to bulk diffusion is found to be 57% of the alloy melt temperature and is dependent on composition.

Modelling of Grain Boundary Stability of Materials under Severe Plastic Deformation and Experimental Verification

2010 ◽  
Vol 638-642 ◽  
pp. 2724-2729
Author(s):  
Yoshiyuki Saito ◽  
Chitoshi Masuda
Keyword(s):  
Monte Carlo ◽  
Grain Boundary ◽  
Computer Simulations ◽  
Phase Field ◽  
Field Methods ◽  
Simulation Results ◽  
Boundary Stability ◽  
Textured Materials ◽  
Phase Field Methods ◽  
Good Agreement

Thermodynamic stability of Grain boundary in materials under severe plastic deformation was simulated by the Monte Carlo and the phase field methods. Computer simulations were performed on 3-dimensional textured materials. The Monte Carlo simulation results were qualitatively in good agreement with those by the phase field model. The classification of the solution of differential equations based on the mean-field Hillert model describing temporal evolution of the scaled grain size distribution function was in good agreement with those given by the Computer simulations. The ARB experiments were performed for pure Al and Al alloys-sheets in order to validate the computer simulation results concerning the grain boundary stability of textured materials. With use of the Monte Carlo and the phase field methods. Effect of grain boundary mobilises and interface energy given by the computer simulations.

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