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Table 1 Table of experimental burden Number addition of powder of rare earth, g/100g metal Average grain size ,μm Number addition of powder of rare earth, g/100g metal Average grain size , μm 1 0 — 5 2.5 1.47 2 0.5 0.46 6 0.5 3.41 3 2.5 0.46 7 2.5 3.41 4 0.5 1.47 Result and analysis of experiment Effect on content of inclusion adding Sm2O3 particle The adding particle must not make content of inclusion in steel increase obviously because it is not advantage to the performance of steel.
It can be seen that there is rare earth element Sm in inclusions and there is a lot of S and Mn in the inclusion number 1 that is sulphide inclusion and there is a lot of Mn and Si in the inclusion number 2 that is product of deoxidate.
Table 4 Effect on crystal grain degree of cast structure adding rare earth oxide Number addition of powder of rare earth, g/100g metal Average grain size ,μm grain degree Number addition of powder of rare earth, g/100g metal Average grain size ,μm grain degree 1 0 — 2.0 5 2.5 1.47 4.5 2 0.5 0.46 4 6 0.5 3.41 4 3 2.5 0.46 45 7 2.5 3.41 4.5 4 0.5 1.47 4 Effect on crystal grain size of rolled structure adding Sm2O3 particle The rolled structure without and with adding Sm2O3 particle are shown as Fig 4.
So size of crystal grain is refined.
a b c d e f g Fig. 4 Microstructures of hot-rolling 20# before and after adding Sm2O3 powders a Free-Sm2O3 particle; b Added 0.5% and 0.46μm Sm2O3; c Added 2.5% and 0.46μm Sm2O3;d Added 0.5% and 1.47μm Sm2O3;e Added 2.5% and 1.47μm Sm2O3;f Added 0.5% and 3.41μm Sm2O3; g Added 2.5% and 3.41μm Sm2O3 Table 5 Effect on crystal grain degree of rolled structure adding rare earth oxide Number addition of powder of rare earth, g/100g metal Average grain size ,μm grain degree Number addition of powder of rare earth, g/100g metal Average grain size ,μm grain degree 1 0 — 6.5 5 0.375 1.47 10.5 2 0.075 0.46 7.5 6 0.075 3.41 10 3 0.375 0.46 8.5 7 0.375 3.41 11 4 0.075 1.47 9.5 In short, considering Sm2O3 particle effecting on content of inclusion and size of crystal grain of cast structure and rolled structure, it can be seen that when size of the adding Sm2O3 particle is lower than 1.47 μm, the content of inclusion will not increase and the size of crystal grain

And then, N(δ) is the minimum number that covers the three-dimensional profile with mesh size δ (δ﹥0).
If there is a fractal nature in this three-dimensional profile, the relationship between N(δ), δ and fractal dimension Ds is given by (1) where c is a constant number.
The topography of PcBN grain after grinding test Based on the above method, the whole topography of PcBN grain selected by microscope is extracted and as shown in Fig.2.
When mesh size is δ=5, from Fig.6, only broad profile of the grain can be observed, and it is difficult to grasp detailed fractures on top surface of the grain.
The reconstruction model clearly expresses the wear topography of the grain

Because only SRXed grains appeared and grew, NGed Cu-Zn alloy shows abnormal grain coarsening.
The grains evolved in the samples MDFed at 77 K contain a larger number and plural variants of annealing twins, while those MDFed at 300 K include lower number of a single variant of twins.
The number of annealing twin increases with increasing strain and/or decreasing MDF temperature.
accelerated grain growth to cause rather coarser grains.
The number and the size of the new grain are larger in the samples with higher density of mechanical twins and grain boundaries.

The raw video results allow a number of qualitative statements to be made about grain growth behaviour in these systems and some simplistic quantitative statements.
Grain Tracing.
Data Analysis - Grains.
Journal Title and Volume Number (to be inserted by the publisher) 3 (especially the most active) grow beyond the field of view, or the specimen drifts to give that result.
This generated a stream of Journal Title and Volume Number (to be inserted by the publisher) 5 Fig10.

When there is an additional driving force for grains to grow beyond the limit of normal grain growth or when the normal grain growth process is inhibited, an abnormal grain growth will take place.
As a result, abnormal grain growth induces a bimodal grain size distribution.
The number of large grains is very small, as clearly shown in Fig. 5d.
As the annealing time and temperature are increased, the regions with small grains decrease in size and number.
Clusters of small grains coexist with large grains.

In general, CA-model could be defined for any number of dimensions.
The number of neighbours is equal to six.
When we divide eight by six we get, not surprisingly, the number equal to 1.3 where three is the periodic number.
Simply said, the algorithm used in this study count the number of unlike neighbours of a cell belonging to the other grain/grains.
After counting the continuous number of neighbours belonging to the other grain, it is decided whether a reorientation of the given boundary cell is performed or not.

When uses the running mean method carries on the data smoothing, an important question is how determines the smooth time number (n).
If the sequence is quite smooth, and has the autocorrelation, by now used the small smooth time number to be able to obtain the good smooth effect; If the sequence fluctuation is big, and does not have the autocorrelation, by must use the big smooth time number to be able to obtain the good smooth effect.
This research acts according to these two commonly used principles, and unifies the massive case study, had determined following three suit the food production potential forecast the smooth time number definite method.
The entire province grain total output data origin was 1983 to 2010 altogether 27 year grain total output data.
Note: Heilongjiang Province education department science and technology financing projects,Project number：11531259 References: [1] Tanksley,S.D.

There have low angle grain boundaries along the cross-section of the grain microstructures.
For the multi-pass pressing, although the pressing pass numbers are same, the processing routes were of important significance on the grain sizes and grain distribution and grain boundaries (GBs) orientations of workpieces.
For the multi-pass pressing, although the pressing pass numbers are same, the processing routes were of important significance on the grain sizes and grain distribution and grain boundaries orientations of workpieces.
Most of the grain boundaries of the materials exhibit an equiaxed grain structure and the grain distribution is uniform in the view field.
The grain distribution and grain boundary grain orientations were conducted.

An alternative technique, the stereological method, has been developed to obtain statistical GB orientation distributions in a sample using great number of 2D EBSD mappings containing millions of grains [5].
For a selected host grain and a neighbouring grain, the voxels that belong to the host grain with at least one adjacent voxel that belongs to the neighbouring grain are identified as host boundary voxels.
Therefore the numbers of facets that bisect host-neighbour vectors along X, -X, Y, -Y, Z and -Z are counted separately, and these numbers are denoted as Nx, N-x, Ny, N-y, Nz, and N-z.
We start the analysis by choosing a host grain (grain 105) and one of its neighbouring grains (grain 155) in the dataset.
Crystal orientations (namely {001}, {011}, and {111}) of grains 105 and 155 are represented by red (grain 105) and blue (grain 155) symbols laid to the same stereographic projection.

The ferrite grains were almost equiaxed and surrounded by high angle boundaries.
This grain refinement is likely to be caused by an increased number of nucleation sites for the transformation from austenite to ferrite due to the ultra-fast cooling.
The α grains were almost equiaxed with a low internal dislocation density.
Perhaps, a large amount of strain imparted in the deformed prior-γ is kept remained by the ultra-fast cooling until the temperature of samples decreases to the range in which α transformation becomes active, then the increased number of nucleation sites caused by the strain may result in the observed ultra-fine grain structure.
It is also thought that an internal nucleation of α in γ grains should play an important role in the grain refinement in this experiment.