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At first the grain structure is mapped onto a two-dimensional random number lattice.
Here the random numbers should assume numbers between 1 and 64.
A grain was defined as a collection of points that have the same orientation number.
In other words, two adjacent grid points having the same orientation number are considered to be a part of the same grain.
The simulation time was defined by a dimensionless number known as Monte Carlo Step (MCS), which was related to the number of re-orientation attempts.

(a) Small-grain-size (118 µm) sample (b) Large-grain-size (219 µm) sample Figure 1.
Given the calculation time, we selected two areas with relatively smaller grain sizes and a sufficient number of grain boundaries for simulation.
(a) Small-grain-size (3.02 µm) sample (b) Large-grain-size (5.45 µm) sample Figure 5.
Oxygen concentration distributions in (a) small-grain-size and (b) large-grain-size samples.
These results may be attributable to the smaller number of grain boundaries within the large-grain-size sample, which plays a role as a fast diffusion path for oxygen, compared with the small-grain-size sample.

It is proposed a parallel Monte Carlo algorithm to simulate templated grain growth in sintering ceramics materials.
The algorithm applies the general Potts model to treat the matrix as the discrete lattices for simulating the grain growth and there will be a number of lattices to be computed synchronously.
Introduction Grain growth of ceramic crystalline materials sintering has been studied for many years.
It is called an attempt to change the orientation value, and the attempt will be repeated N times while N is the total number of lattices.
Experimental Firstly it is shown the results of the former serial simulations for the templated grain growth.

It was found that the microstructures of Cu samples with a small number of ECAP passes (4-8) were not inhomogeneous and the fraction of high-angle grain boundary (HAGB) was low (25~43%).
While for the samples with many number of ECAP passes (12-24), the grains became more equiaxed-like and the GB misorientations exhibited double-peak distribution with high fraction (51~64%) of HAGB.
Fig.3 Average grain size and the fraction of HAGB vs.
By contrast, the numbers are increased up to 57.9% and 62.4% when the number of ECAP passes is 16 and 24, respectively.
The increase in the fraction of HAGB in the many-pass samples and the decrease in the average grain size imply that more cells have transformed into real grains after many passes.

(a)Volume fraction of dispersoids and β’-Mg2Si across the grain, calculated using Thermo-Calc (b) SEM image showing size and number area fraction variation across a grain in LF condition.
It is also observed that the volume fraction of dispersoids is not affected as severely as those of β’-Mg2Si, hence the number of nucleation sites or number density of dispersoids would be affected more prominently compared to the volume fraction across the grains.
The grain boundaries have the highest supersaturation for Mg and Si atoms which can translate into higher number and volume fraction of nucleation sites and consequently higher number density and higher fraction of dispersoids.
PF is the highest heating rate in this study and hence the retention of concentration gradient would be highest for this case, also implying higher fraction of regions (grain centre) with lower number density of dispersoids and a greater number of such grains (Fig.2,a).
It is observed that the number density of dispersoids reduce whereas the size of dispersoids increase from grain boundary to grain centre. 2.

Grain boundary sliding.
Shear traction acting on a plane boundary with a normal vector can be calculated as follows: (2) The superscript β indicates the number of assumed boundary plane.
It is worth mentioning that assuming a higher number of slide directions than 12 had no significant change in the results, therefore, only 12 slide directions were enough in the present modeling.
The numbers of grains P with various diameters in nano-crystalline materials can usually be well represented by a log-normal distribution function: (46) where d is the grain diameter and Do and are constant parameters describing the median and shape parameters of the distribution, respectively [22].
In the model, grain interior plasticity, grain-boundary diffusion and grain-boundary sliding are considered.

Besides, a great number of dispersed MnS particles with the size of 20-30nm were observed in the hot rolled strips.
The average grain size is 378μm.
Thus, the coarse columnar grain was developed.
After hot rolling with 20% and 50% reduction respectively, a large number of fine MnS precipitates were observed in both strips with the average size of 20~30nm.
A great number of fine and widely distributed MnS particles in the size of 20~30nm were formed in the hot rolled strip.

Temporal Evolution of Grain Size Distributions in Two- Dimensional Pinned Cells C.
Elapsed time: 703 h Cell Number area (a.u.)
Initially, the distribution is dominated by a large number of "small" sized (quasi ordered) cells but, as time is going on, the cell scattering appears evolving to a bimodal pattern.
As shown, the best fit is obtained with two bell shaped Gaussian curves. 0 1000 2000 3000 4000 5000 6000 0 2 4 6 8 10 12 14 16 18 Cell Number Area (a.u.)
Herrera, p. 379 in Recrystallization and Grain Growth (Springer Verlag, 2001) [10] C.

A number of authors, including one of the present writers, have suggested that this effect is due to the influence of grain size on mechanical twinning (e.g. [4]).
Grain size control through recrystallization A number of workers have pointed out that the static recrystallization of magnesium and its alloys is enhanced by the presence of deformation twins [5, 6].
An example of the rate at which the grain size evolves with annealing time for a number of different alloys is shown in Figure 5.
It is assumed here that this evolution is reflective of the kinetics of a recrystallization reaction. 1 10 1000.1 1 10 100 1000 10000 Annealing Time (s) Grain Size ( m) AZ11 AZ21 AZ31 AZ61 (a) Grain Size (µm) 1 10 1000.1 1 10 100 1000 10000 Annealing Time (s) Grain Size ( m) AZ11 AZ21 AZ31 AZ61 (a) Grain Size (µm) 1 10 1000.1 1 10 100 1000 10000 Annealing Time (s) Grain Size ( m) Mg-0.3Zr Mg-0.5Zr Mg-1Zr Mg-1Zn-0.5Zr Mg-6Zn-0.5Zr (b) Grain Size (µm) 1 10 1000.1 1 10 100 1000 10000 Annealing Time (s) Grain Size ( m) Mg-0.3Zr Mg-0.5Zr Mg-1Zr Mg-1Zn-0.5Zr Mg-6Zn-0.5Zr (b) Grain Size (µm) Figure 5.
The more solute rich alloys display the finer grain sizes.

Journal Title and Volume Number (to be inserted by the publisher) a b Fig. 1.
The curved boundary in configuration Fig. 1a can be represented by a number of differently inclined "pure tilt" elements, the boundary in configuration Fig. 1b - by a number of mixed tilt-twist elements with increasing twist component along the boundary.
The driving force was provided by the surface tension of a curved grain boundary: bpa =γ , where bγ is the grain boundary surface tension and a is the width of the shrinking grain.
grain I grain II I I I directions of motion ϕ I ψ Fig. 3.
Journal Title and Volume Number (to be inserted by the publisher) 100 µm 0200 400 600 800 1000 0 100 200 300 400 500 600 Y [µm] X [µm] a b Fig. 6.