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This is the natural boundary conditon for equilibrium of the Journal Title and Volume Number (to be inserted by the publisher) 2 Mullins Equation, a fact that may not be well known.
Journal Title and Volume Number (to be inserted by the publisher) 4 We conclude this section with a description of the critical events.
Loss of grain: some neighboring grain GN will absorb a small target grain GT.
Journal Title and Volume Number (to be inserted by the publisher) 5 Figure 1.
Depiction of a 3 D grain from an ensemble of about 500 grains.

Unfavourable influence of coarse-grain microstructure and favourable influence of its refinement on a number of mechanical properties place the problem of finding solutions for the effective grain refinement in the circle of fundamental issues for this group of alloys [9÷11].
The number of cycles was changed from 1 to 20.
Further increasing the number of cycles has slight effect on changes in size (Fig. 9a) and shape (Fig. 9b) of grain and relative surface area of its boundaries (Fig. 9c).
During the next cycles, a unique state of equilibrium between the number of undissolved lamellar precipitations of g phase and the number of grains is established.
Too low heating rate causes that the number of these precipitations is small, which affects lower grain refinement.

Grain growth will take place if the grain boundary curvature of the matrix, H, is larger than HL.
The grain growth anneals were carried out in the temperature range of 500 oC to 620 oC in 20 oC Journal Title and Volume Number (to be inserted by the publisher) 3 steps.
TA, the number of points of tangency between a sweeping test line and a curved grain boundary trace on a section per unit test area was measured.
Below 540 oC, the measured grain boundary area is lower than the limiting grain boundary area and grain growth, that is, a decrease in grain boundary area, cannot take place.
Journal Title and Volume Number (to be inserted by the publisher) 5 Figure 4 - Grain boundary curvature, H, as a function of annealing temperature in an Al1mass%Mn alloy.

For example, every town has its own grain purchasing station before mergence, but after mergence, because of simplifying structure, it is no double that the former grain purchasing locations will be decreased.
The research on grain purchasing is limited.
The cost in the process of food transportation is related to the transport distance, expenses, and the total public grain which is handed in by every village and the quantity of grain purchasing locations.
Therefore, the objective function can be expressed: (1) (1)N=｛1, 2, …, n｝represents sequence number set; Mij is the assembling place whose distance is less than d between the village and the grain purchasing location; kij represents the distance between villages (i) to gain purchasing (j); Hj represents the operation cost of gain purchasing location (j); Sj represents variable from 0 to 1.
Major Parameters The names of parameter Value Statement populationsize 13 population size memorycapacity 8 memory capacity iterativetimes 20 iteration number crossoverprobability 0.5 crossover probability mutationprobability 0.4 mutation probability evaluationparameter 0.95 evaluation parameter Grainnumber 2-13 purchasing location number punishnumber 3000 threshold carryprice 4 transportation price （kg/km） managerprice 20000 Acquisition cost/every place In order to meet the minimum cost during the process of grain transportation in objective function F (i, j), solution is produced by adopting immune algorithm.

The results indicated that irrigated 60 mm each at jointing and heading stages during the winter wheat growing seasons, grain yield was the highest, which could be attributed to significantly (LSD, P<0.05) increase the spike numbers.
Spike number per m2, kernel numbers per spike, and thousand kernel weights were determined.
T3 resulted in the highest grain yield, which contributed to the spike numbers were significantly increased.
Kernel numbers were not significantly different among any treatments.
The result showed that irrigated 60 mm each at jointing and heading stages of winter wheat significantly increase spike number, hence, the grain yield significantly enhanced.

The microstructure of the material is observed with increasing number of passes using optical microscopy (OM), laser microscope and scanning electron microscopy (SEM) electron backscattered diffraction (EBSD).
Moreover, the hardness of material also increasing up to 41Hv for the first pass and constantly increased with the increasing number of pressing.
The influence of NTE pass number on grain size and hardness properties of material was studied at first.
Grains are equiaxial after subjected to 4 passes of NTE.
Following that the grain size was measured by using linear intercept method.

Lineal intercept procedure is:（1）Estimate the average grain size by counting(on the ground-glass screen, on a photomicrograph of a representative field of the specimen)the number of grains intercepted by one or more straight lines sufficiently long to yield at least 50 intercepts.
An intersection apparently coinciding with junction of three grains should be scored as;（3）Calculation： Mean lineal intercept length： (1) 一Length of a test line, unit for mm； —Mean lineal intercept length； — Magnification used； 一 Number of intercepts with a test line； 一 Number of intercepts per unit length of test line。
All specimens grain-size number is in Table 3 and Fig. 4 HAZ Heat input（KJ/cm） Average grain-size number Mother material —— 11.0 ICHAZ 5 9.5 10 9.5 15 10.5 CGHAZ 5 5.5 10 5.0 15 6.0 ICCGHAZ 5 6.0 10 6.5 15 6.0 SCCGHAZ 5 5.5 10 6.0 15 5.5 Table 3 Grain-size number of HAZ Fig. 4 Average grain-size number of HAZ It is obvious from the ferrite grain size of mother material in the Table 3 that SMA490BW corrosion resistance steel has ultrafine grain size, while the size of the grain has decisive impact on metal's machinery properties such as tensile strength, toughness, plastic and so on.
As is shown in Table 3 and Fig.4：the grain-size number of ICHAZ is the highest, according to GB/T 6394-2002, the higher grain-size number is, then smaller grain size is, so grain size of ICHAZ is the smallest.
The reason is that the peak temperature of the ICHAZ is the highest and after high temperature heating, austenitic grain has significant trend to grow up , so after cooling , austenitic grain becomes bulky; in ICHAZ and CGHAZ, the grain size increases with the heat input increasing as is shown that when E=15KJ/cm the grain-size number is the lowest, this is because more welding heat input is in grain growth’s favour; grain size of ICCGHAZ and SCCGHAZ is smaller than CGHAZ is because that second thermal cycle have good role in fine grains.

The condition for the microstructural instability of a single grain of given size and grain boundary properties reads where and are the grain boundary mobility and energy of the isolated grain,and are the grain boundary mobility and energy of the surrounding matrix and and are the radius of the selected grain and the average grain radius of the matrix [7] (figure 1).
Figure 3 shows the ratios of a set of 9 selected grains versus the total number of remaining grains in the studied structure, which reflects the time evolution.
(a) (b) (c) Figure 3: Radius of potentially abnormal grains divided by average grain radius plotted against the remaining total number of grains for different relative grain boundary energies (a)-(c).
Grains with 14 faces only showed abnormal grain growth, when the grain received an adequate energy and mobility advantage.
The evolving grain morphology of an abnormally growing grain is shown in figure 4.

Journal Title and Volume Number (to be inserted by the publisher) Consideration of crystallographic neighbourhood in magnetic sheets of Fe3%Si.
Behaviour prediction of grain growth from the texture function.
In this modified Monte-Carlo approach [13]: - A site is not characterized by an orientation number, but by a triplet (φ1, φ, φ2) corresponding to its orientation in Euler space
Table 2 Characteristics of considered Goss grains.
Fig.3 Goss grain growth kinetics in global matrix without (-a-) and with (-b-) texture consideration Goss grain growth in oriented matrixes The two components of texture have a different behaviour with regard to Goss grains.

Grain Boundary Surface Tension, Segregation and Diffusion in Cu-Sn System Gershman Evgeny 1,a and Zhevnenko Sergey 1,b 1 Moscow State institute of steel and alloys (Technological University), 4, Leninsky pr., Moscow, 119049, Russia a av14746@comtv.ru b sergeyng@mail.ru Keywords: Grain boundary tension; Grain boundary adsorption; Free surface tension; Zero creep method; Grain boundary diffusion Abstract.
Today is a lack of such data due to the limited number of the measuring methods.
The average grain size was 115 µm.
It is possible to evaluate the number of sites in surface monolayer A A m N N V n 3 2 max −       = (3) where Vm is the tin molar volume and NA is the Avogadro number.
Isotherms of surface tension and adsorption in Cu-Sn system: a,b - for free surface; c,d - for grain boundaries From the data obtained it is possible to evaluate the Cu selfdiffusion coefficient in Cu and Cu-Sn alloys using the relation of Borisov et. al. [9]: (6) where DGB is the grain boundary diffusion coefficient; D is the bulk diffusion coefficient; a is the mean distance between the atoms in the GB (approximately equal to the lattice parameter); γGB is the grain boundary surface tension; NA is the Avogadro's number; Т is the absolute temperature; R is the gas constant.