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The Effect of Grain Boundary Junctions on Grain Microstructure Evolution: 3D Vertex Simulation L.A.
However, a polycrystal is formed not only by grain boundaries (GBs) and grains but also by triple lines (TLs) (line where three grains meet) and quadruple points (QPs) (point where four grains meet).
In such approach only the grain boundary is discretized whereas the grain interior is not.
The sum of the forces over all facets surrounding the vertex leads to the net force ( ).∑= × ×× ⋅= n 1i i0i1 i0i1i0 sum ss sss 2 F rr rrr r γ (2) where n is the total number of facets adjoining at P0.
In our case the grain size is represented by the term x0, which scales with the grain size.

Characteristics of sexual reproduction of two L. chinensis ecotypes under saline-alkali soil and sandy soil habitats on Songnen plain were studied, such as number of florets, number of grains, seed-setting percentage and the weight of thousand grains.
The results showed that number of florets, number of grains, seed-setting percentage and the weight of thousand grains of two L. chinensis ecotypes fluctuated at some range.
Variation coefficients of number of florets, number of grains and seed-setting percentage were 34.63%, 79.37% and 87.2% higher, but variation coefficient of the weight of thousand grains was lower.
The number of florets, seed setting rate and the weight of thousand grains of both two L. chinensis ecotypes fluctuated within a certain range, and the number of changes was ecological plasticity.
Meanwhile, the coefficient of variation of the number of florets, the number of grains per panicle and seed setting rate were up to 34.63%, 79.37% and 87.2%, but the coefficient of variation of the weight of thousand grains was smaller, this change was in response to plant habitat adaptation.

Particle - grain boundary pinning configuration is well studied [1-2].
Simulation procedure MC simulation of grain growth is well introduced [4].
N is the number of sites in the microstructure.
Journal Title and Volume Number (to be inserted by the publisher) 3 0 2000 4000 6000 8000 10000 12000 14000 16000 0 100 200 300 400 500 600 700 Time (MCS) Grain area (sites) particules : elongated circle square 200x200 fraction 5% random spread (a) 0 2000 4000 6000 8000 10000 12000 14000 16000 0 200 400 600 800 1000 1200 1400 1600 1800 particules : elongated circle square 200x200 fraction 1% random spread Time (MCS) Grain area (sites) (b) Fig. 3.
Kinetic of grain growth corresponding to particle conditions of Fig. 4.

Mössbauer investigations of grain-boundary diffusion and segregation V.V.
In particular, Mössbauer investigations make it possible to evaluate directly the grain-boundary segregation factor, to determine the grain-boundary diffusion mechanism, to estimate the rate of the diffusant pumping from a grain boundary core into the bulk, etc.
In particular, Mössbauer investigations can give information on the grain-boundary diffusion mechanism and enable to determine the grain-boundary segregation factor, to evaluate the rate of the diffusant pumping from a grain boundary into the bulk, and to obtain some data on composition of a grain-boundary core and near-boundary areas.
Let's consider this model of grain-boundary diffusion (Fig. 4).
Number 1 denotes component 1, and number 2 - component 2.

The grain adjacent to the abnormal grain is a kind of incompletely recrystallized grain (Fig. 1).
However, grain boundary between abnormal grain and its adjacent grains is a high-angle boundary.
RD TD ND a)IPF RD TD ND a)IPF b)PF b-PF Fig.5 PF and IPF of the abnormal grain and its surroundings a) Inverse pole figure b) Pole figure The {100} <001> texture is cubic, indicating that a large number of grains are arranged in this direction.
b) Fig.11 CSL grain boundary near the abnormal grain a) Map of the orientation b) CSL number The growth of the abnormal grain depends on its coalescence with its adjacent normal grains by rotation.
Grains grow by grain-boundary rotation or bugling.

If the neighboring grain is smaller, a random number rs is generated; if rs > ps no state change is made 4.
Then a random number r is generated.
Nevertheless the evolution is slower than expected, and the number of grains remaining in the microstructure soon becomes insufficient for a statistically valid determination of quantitative texture.
For avoiding the problem of statistics associated with the decrease in grain number, sequential modeling was used to enable longer simulation times to be achieved in the grain growth evolution.
First, even if the number of grains is statistically sufficient with regards to the initial texture determination, it may be not sufficient to take into account subpopulation effects and also decrease rapidly during the simulation.

The traditional methods of getting the grain size depend on artificiality.
When the grain size was measured through intercept method, the relationship between average diameters (L) and grain size (G) just as the Eq.5
Fig.7 The average diameters Table.1 Grain sizes A B C Manual 12.951585 12.64429 12.299873 Computer 12.833637 12.725512 12.372498 Table.2 shows the average time consumed in the process of scanning an image at different number of sampling.
Table.2 Consumed Time Number of sampling in an image 1600 2000 Time（ms） 22 37 Form the data Table.2, we can see that the consumption of time in level of ms.
Metal-methods for Estimating the Average Grain Size.

We determine a smaller number of selected GB plane orientations with all the 5 needed parameters for each of them.
First the orientation matrices (with i=1,2) of the two grains at the opposite sides of a grain boundary plane is determined from their respective CBED patterns.
Although these numbers are modest from a statistical point of view, their distinct distributions uncover important differences between them.
Orientation distribution for the S3 grain boundaries.
Although the number of observations did not allow for detailed statistical analysis, some general trends can be assumed from the measurements.

Keywords: Hubei Province，Water Disaster，Grain Production，Grey Correlation Analysis Abstract: The grain fluctuation situation of Hubei was analyzed by calculating the grain fluctuation coefficient from 1990s.
Flood and drought, especially serious flood and drought will be bound to result in a significant reduction in grain-based agricultural products, with a large number of reduction in agricultural productions, and the reproduction of the agricultural disaster areas coming to a standstill[1] Xie Yonggang.
Hubei is a major grain production base, with grain planting area accounting for 55% of the total crops planting area, and the grain yield accounting for about 4.5% of the total output of the whole country.
Comparative sequence： m is the sequence number ，m=1，2，3……8 Reference sequence：；n is the years，n＝1，2 ……7 The second step: Normalize the raw data, namely divide each value of sequence by the initial value of sequence to generate initialization sequence.
Planting structure is a most decisive factor for grain productivity, defined by the percentage of grain area of total crop area, a indicator to reflect planting grain area.

Using an approach of grain boundary interfacial area (Sv) calculation, which attempts to account the number of sites for potential nucleation of ferrite in thermomechanically processed austenite, an essential correlation of the correspond measured grains was developed.
Although partially recrystallized, the austenite grain boundaries still account the number of sites for potential nucleation of ferrite.
In general, because the ferrite grain size is related to the number of sites for ferrite nucleation, and because this number is related to the austenite grain boundary area per unit volume, the ferrite grain size will decrease as this boundary area increases.
In addition, presumably because the smaller grains have a large number of grain boundaries per unit volume greater than the large grains, so that nucleation can occur in many sites.
Nucleation rate is proportional to the square of the number of grains per unit surface area of ferrite grains austenite.