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The observed grain boundary diffusion phenomena can be classified as C-type diffusion.
The need for a simpler, more straightforward evaluation method is also dictated by the increasing number of different diffusion experiments carried out in thin film systems, by measuring composition profiles e.g. with SIMS, AES [8,9,10] or SNMS [1,2,3] techniques.
Thus the effective GB diffusion coefficient of intermixing decreases with increasing time (as was indeed observed in [2] at 593 K) and all of them are smaller than the value belonging to the number calculated from the first appearance.
The volume fractions of the grain boundaries and the Ta-penetrated layer of grains (the volume penetration depth, in the lack of Ta bulk diffusion data in Cu, was estimated from the Cu self diffusion data [18] and about 0.5 nm was obtained [2]) are approximately 5%, supposing a grain size of 10 nm in Cu.
Supposing 40 nm grain size and C-type kinetic regime the average Si concentration in the grain boundaries are estimated to be about 83 %.

We prepared three groups of specimens which were quenched a different number of times.
The length of grains was calculated by using the following equation: l=LnL (Eq. 1) where the L is the length of the line (mm), l is the average size of the grains (mm), nL is the total number of the number of interceptions and 0.5 which is a modification number for broken grains on the periphery.
The average carbide particle size increased with the number of quenchings.
The roundness values in each group of the number of quenching times were similar.
Acknowledgment This research work was supported by JSPS KAKENHI grant numbers 19K14875.

However, because the overall grain size is so fine and all grains are almost equiaxed in shape, also the dotted grains must be recrystallised, not only recovered.
In the Nb steel (0.15%C, 0.033%Nb) distinctly a higher number of cementite particles were found.
Here, it seemed that two grain growth modes, normal and abnormal, can occur in the UFF grained microstructures.
Anyhow, the present results demonstrate that the UFF microstructure in steels can be thermally stable up to temperatures about 0.5Tm, obviously due to the dispersion of carbide particles present, but in very reasonable numbers and sizes, hardly affecting detrimentally the mechanical properties.
Refining the prior austenite grain size enhances the ferrite grain size refinement.

The grain growth and grain size distribution during recrystallization are discussed.
The Bright lines of network denote the grain boundary, and the dark region denotes the region inside grains.
It can be seen in Fig 1d that the grain structure is close to the equiaxial grain with a small size, the large grain structure in primary deformed alloy disappears after recrystallization.
Fig.4 The grain structure and distribution of grain diameter at T=473K, evolution times are t=50s, 250s, respectively.
For example, at T=673K, the grain size of range from 1 to 15 become that of range from 1to 30, and the greatest grain number are from 180 down to 70; while at T=473K, the size of range from 1 to 10 become that of range from 1 to 15, and the amount of grain at peak is from 650 down to 200; This means the grain number decrease after grain growth, and the peak site of the amount of grain moves to site of large size.

It is an answer to the question of how far the particle will be from an arbitrary starting point after some very large number of random jumps, given the number of jumps per second and the mean jump distance.
Over the period of hours or days, the number of jumps becomes astronomical.
In this diffusion model, the computer specimen is decomposed into certain number of cells.
A cell is characterized by its label (0-n), its position (X, Y ) and the number of atoms in it A cell representing the bulk of a grain Cells representing grain boundaries Examples A random computer specimen is generated and shown in Fig. 2a.
There are a large number of diffusion coefficients available in the software database.

To achieve ferrite grain refinement in steel, there are two potential routes, the transformation route and the recrystallization route.
In the former case, the limit of refinement is about 2 µm, and, in the latter case, ferrite grains with a size in the hundreds of nanometer are obtained.
In severe plastic deformation processes, caliber rolling is an effectual process for producing ultrafine-grained steels efficiently [1-3].
The number of passes was determined according to the strain predicted from the FEA.
At sites s7.9-coy and s7.9-coz where large εeq of over 5.7 is introduced, a significant number of fine equiaxed grains below 1µm were formed with the fraction of HAGB [3], and, at this time, the average grain sizes at sites s7.9-coy and s7.9-coz were approximately 680nm and 650nm, respectively.

This study developed new algorithms to simulate the grain pattern and orientation of radiata pine boards based on the geometrical and growth features of radiata pine trees.
Wood grain has been an interesting topic for sawmills, as severe grain deviation decreases wood strength [4], and is the most serious single defect resulting in drying deformation associated with variation of moisture content [5].
Sawmills have been looking for feasible log breakdown strategies to maximize timber value [6], and it is desirable to know the grain pattern and orientation prior to log cutting.
Conclusion and Discussion Severe grain deviation is one of the key factors significantly affecting timber quality.
Adjusting factors should be applied when a tree has severe spiral grain, which will be reported in other paper.

Such a behavior is conditioned by a hexagonal-close packed lattice of magnesium with an axial ratio c/a=1.624, being close to the ideal value and resulting in the lack of adequate number of slip systems to accommodate overall strain.
Total number of cycles was 18 with corresponding true strain of a billet e=10.2 (i.e., 4.2 at 400, 3.0 at 300 and 3.0 at 2000C).
Namely, the areas of the fine equiaxed grains acquired the volume fraction of ~75-80% and so, the fine grains became the main structural component.
One can, therefore, conclude that the main structural changes on the second step of MIF were related to further decrease in the fraction of the coarse fragments of original grains, as well as to the refinement of more coarse grains that were present in fine-grained matrix.
Final MIF step at 200oC results, in turn, in grain refinement down to the nearly submicron grain size level, promoting, however, rather non-uniform on both the meso- and microscopic levels the alloy ultrafine grain structure.

For the final extrusion the opposite punch was removed, the cumulated true strain is calculated by the equation[2]: d n D ln)12(2 −=ε , where n is the number of extrusion passes.
Although many grains are already significantly refined after only 1 pass, the grain structure is inhomogeneous with fine grains of 1-2µm as well as coarse grains of greater than 8µm.
Equiaxed grains are formed in both samples with an average grain size of 1.2µm and 0.8µm, respectively.
It is evident from the curve that there is a significant increase in hardness with the number of extrusion passes.
Further investigation is required to underpin this point. 60 65 70 75 80 85 90 HV (Kg/mm2 ) 15P 7P 1P ex-extruded Number of Extrusion Passes 100 150 200 250 300 350 400 Compressibility (%) Stress (MPa) Number of Extrusion Passes AZ61: CEC at 573K Yield Stress Compressive Stress 15 20 25 30 35 40 15P 7P 1P ex-extruded Compressibility Conclusions (1) CEC process can refine the grains of AZ61 Mg alloy effectively.

The important properties studied are moisture content, total clay content, grain fineness number, and grain shape.
Results obtained revealed that the river sand has average moisture content of 7.78 %, clay content of 3.20%, and grain fineness number (GFN) of 46.
Most mold sands should fall within 50-60 grain fineness number (GFN) or 220-250 microns average grain.
The grain distribution for each samples were obtained and the Grain Fineness Number (GFN) was calculated using the equation: GFN=Wn x SnWn (3) Where Wn is the weight of sand collected on each sieve and Sn is grain fineness coefficient.
This number classifies it under coarse grain size, which is still within the acceptable range of mold sand and suitable for metal casting application [7, 10, 14,15].