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This statistical cut off was set to be one plus the average number of different slip systems active in all grains.
The matrix grains with the highest stored energy are associated with the highest number of nuclei.
We assumed the total number of nuclei Ntot as tot rand GB stab trans N N N N N = + + +
Then the ratio of Fstab to Ftrans was related to the absolute numbers of stable grains nstab and grains with transition bands ntrans, which were derived with the nucleation spectra models described above.
For a use in a space resolved growth model like a cellular automaton absolute numbers have to be predicted.

Fatigue-Crack-Growth Behavior of Ultrafine-Grained Al-Mg-Sc alloy Produced by ECAP E.
After extrusion and annealing, the alloy was composed of a non-uniform partially recrystallized microstructure with a bimodal distribution of the grain size, namely, coarse elongated grains lying parallel to the extrusion axis, and fine equiaxed grains in their mantle regions (Fig. 1(a)).
Besides, some remnant parts of original grains were present in this structure.
Data for coarse-grained Al-6%Mg-0.3%Sc alloy are plotted for comparison.
The size of facets is gradually increased with increasing ∆K, so that every facet "covers" a number of UFG grains.

The influence of grain size on the lattice constant in some nanocrystallites of perovskite structure was studied in experiment.
It was found that their lattice constants all decreased with the decreasing grain sizes.
It was found that the lattice constant increased with the decreasing grain size of some nanocrystallites[5], while some changed inversely[6].
The perovskite structure was a simple cubic lattice, the coordination number of A was 12, B was 8, and forms altogether the apex’s BO6 octahedron.
From Table 1, one could conclude that the lattice constant decreased with the reduction of the grain size for CaMnO3 nanocrystallites.

Grain Boundary Diffusion.
Last 60 years special attention in material science is paid to grain boundaries.
Certainly, the main effect is connected with GB structure, determined by orientation of one grain to another.
The typical distribution of ln P value is presented at Fig. 3 b (N is number of GB with given value of P, step is equal to 0.5).
For chemical reaction at grain boundary: nAb+mBb=AnBmb the equilibrium constant can be written as : or for dilute solution.

There the basic mechanisms on recrystallization in aluminum have been already understood quiet well [1] and have been sophisticated by a considerable number of studies for many years [2-4].
Grain growth and grain boundary movement.
Figure 3 shows the grain growth behaviors of a grain nucleated on a grain boundary (X1, Y1 in Fig.2) and a grain nucleated in a deformed band (X2, Y2 in Fig.2).
As shown in the Fig.3, the grain growth of the grain in the deformed band is larger than that on the grain boundary in each specimen.
The grain boundary of Y2-grain neighboring the deformed matrix moved more rapidly than that of Y1-grain.

The Study on used Properties of Mine Tailings Sand Gang Li1, a, YingJie Chen2,b and Hao Di3,c 1State Key Laboratory of Ministry of Education of China for High Efficient Mining and Safety of Metal Mine , University of Science and Technology Beijing, Beijing 100083, China 1Shenkan Qinhuangdao Engineering & Technical Corporation MCC, Qinhuangdao 066001, China 2,3Department of Civil Engineering and Mechanics,yanshan University,Qinhuangdao aemail:ligang0504@126.com, bemail:cyjysu@126.com, cemail:dihaohaodi@126.com Keywords: mine tailings;gradation of grain;compressive strength;loss on ignition Abstract: Nowadays,there are a large number of mining tailings in China,ore tailings not only pollute the environment,but also consume plenty of land resources,even threat the safety of people's life.In this article ,researches have been done to gradation of grain of tailings in QinHuangdao by the test,and compressive strength and loss on ignition with different volume of tailing concrete.
Messive discharge of tailings accumulation not only occupy the land ,causing environmental pollution, and poorly designed tailings dam collapse will result in casualties, at the same time, tailings transportation emissions requires a large number of mechanical equipment and power facilities.
In the early eighteen sixties,the Soviet Union began studying and producing building materials using tailings , such as the Krivoy Rog iron ore in tailings proper graded as aggregate , with fine grained tailings production silicate building products.
Table l Tailing grain-size composition analysis table of Miaogou Iron ore Mesh Particle size (mm) Yield（%） Cumulative yield（%） 80 +2 4.07 4.07 100 -2～+1.5 5.98 10.05 140 -1.5～+0.10 5.80 15.85 200 -0.10～+0.076 10.20 26.05 280 -0.076～+0.055 16.22 42.27 350 -0.055～+0.042 4.19 46.46 400 -0.042～+0.03 10.80 57.26 — -0.03～+0.02 9.15 66.41 — -0.02～+0.01 6.22 72.63 — -0.01 27.37 100.00 Particle density of Miaogou tailings is 2.85 t/m3, pulp density is 40% of tailings, tailings average particle size is 0.056mm,out of which -200 mesh accounted for 74% of, -400 mesh 50%.
Table 2 Tailing grain-size analysis table of Cherry blossoms Iron ore Grain（mm） +0.074 -0.074～+0.056 -0.056～+0.037 -0.037～+0.019 -0.019 Yield（%） 31.04 19.47 17.04 14.60 17.85 The average particle size of Luan County cherry tailings is 0.0978mm, tailings median particle size is 0.028mm.

Simulation of oxygen contaminated silicon grain boundaries in cluster approximation A.L.
Skaryna av. 4, Minsk, 220050 Belarus, fedotov@bsu.by Keywords: silicon, grain boundaries, oxygen, gettering Abstract.
Introduction Grain boundaries (GBs) in silicon attract cosiderable interest because of their gret technological value.
The majority of silicon polycrystals contain a number of oxygen atoms (~ 10 17-1018 cm-3) as a common impurity.
Cluster models of the grain boundary structure Cluster models of GBs have been constructed as follows.

With the increasing of annealing temperature, semi-solid primary α-Mg grain boundary become obscure gradually, grain growth is indistinct and β-Mg17Al12 phase is precipitated from the inner α-Mg grain.
Fig.2 shows that the grain of primary-Mg grain is round and the boundary is distinct, the Fig.6 shows that the roundness of primary-Mg grain had greatly changed and the boundary of some grain is obscure.
Contrast Fig.2 with Fig.3-6, it was found that the biggest change happen in the number and shape of the aberrated eutectic around primary-Mg grain, as the temperature increase, the number of -Mg phase in eutectic structure increases, and their continuous state become half-continuous and then blocky.
In a word, as the temperature rises, the growth of primary -Mg grain is obscure, but the boundary become obscure gradually; The α-Mg grain number and size increases continuously in the eutectic structure, and becomes blocky, separates gradually from β-Mg17Al12 phase, approaching the equilibrium solidification structure(-Mg in primary +-Mg eutectic structure and β- Mg17Al12 at the grain boundary), β-Mg17Al12 phase precipitates from the inner α-Mg grain; β-Mg17Al12 phase in the eutectic structure increase continuously and mesh together, distributing on the boundary of -Mg grain.
The reason is that though there are a large number of α-Mg grains in the eutectic structure, they are smaller than those in the primary α-Mg and their boundary are bigger, and β phase also exists in the eutectic structure, all these make the hardness of liquid region higher than the α-Mg phase, but as the temperature increases, α-Mg grain in the liquid region grows up, and also the β-Mg17Al12 phase, but the α-Mg grain grows up in a lager scale, then the hardness decreases, when the temperature exceeds 400℃, β-Mg17Al12 precipitates from the inner α-Mg grain, this makes the β-Mg17Al12 grow in a lager scale, and cause strengthening process, so the hardness increases.

The press rolling time is set by the wheel feed rate and the number of rolling coverage.
Abrasive grains hardly appear and project on the wheel surface.
SPa has a direct correlation with the projecting height of grain approximately.
The SPa of loading wheel surface with no projecting height of grain is about 0.8mm, and SPa is about 1mm larger than the projecting height of grain.
(1) The projecting state of abrasive grain on acting wheel surface can be investigated by analyzing SPa of wheel surface, SPa has a direct correlation with the projecting height of grain approximately

Coarse grain (CG) Titanium with original grain size of 150 μm had been pressed by ECAP at 425oC by 4, 8 and 12 passes, respectively.
There is uniformity in the arrangement of grains in sample and the signal of elongation of grains on rolling direction.
It can be inferred from the results that the hardness of Ti increase proportionally to the number of processing pass, from 228 of 4 passes to 311 of 12 passes.
This indicates the uniformity in the grain arrangement and the significant increase of grain density of Ti during ECAP.
Acknowledgements This work was financially supported by the Vietnam National Foundation for Science and Technology Development (Nafosted), Grant Number 107.02-2010.10.