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As will be seen in more detail below, the number of γ-fibre grains nucleated at grain boundaries and in-grain interiors was higher in the finer grained steel.
The effect of initial grain size on the number of in-grain shear bands in the present samples warm rolled at selected temperatures is illustrated in Fig. 1.
There are also a number of references that relate the amount of in-grain shear bands to the final formability [15-17].
As mentioned above, the finer HBGS sample yielded a higher number of γ grains nucleated at grain boundaries, as expected; it also had the higher number of SBN belonging to the same fibre.
Finer HBGS's yield higher numbers of γ-grain boundary nuclei.

The legend indicates the number of grains in the RVE.
Total number of grains distributed over the mesh Average number of grains within each RVE Number of time steps Computing time 25000 5 400 3 h 100000 20 280 5 h 200000 40 290 9 h 500000 100 280 20 h Table 1 Description of deep-drawing simulations performed with reduced grain samplings.
Every element has 8 integration points and the average number of grains in each RVE is given in the legend.
The average number of grains within every one of the 40 RVE is indicated in the legend.
The average number of grains within every one of the 40 RVE is indicated in the legend.

Two components in the Mössbauer spectra of nanocrystalline materials were also observed in a number of other publications (see, e.g., [11-14]), where it was assumed that one of them was formed by atoms in the crystallite lattice whereas another one by those in inter-crystallite areas.
This method was successfully applied for the investigation of grain boundaries in a number of coarse-grained materials [17,23-29].
Specified Model of Grain-Boundary Diffusion According to the emission Mössbauer investigations of grain boundaries in a number of coarse-grained metals [17,21-29], there are two lines in the grain-boundary spectra.
NGR Spectroscopy of Grain Boundaries in Coarse-Grained Materials Let us consider what information can be extracted from the Mössbauer studies of grain boundaries in coarse-grained materials.
Nevertheless, in spite of these limitations, the emission NGR spectroscopy is one of the most effective methods of investigation of the state of grain boundaries in UFG materials processed by SPD, and it was used in a number of publications [5,6,49-54].

The CSL theory consists in assigning a natural number, called Σ, to a given two crystal interface (i.e.
When the number of deformation steps was varied, the strain per step varied too.
Cycle number is the number of cycles subsequent to prestraining to ε=0.5 Fig. 5: Grain size and Σ3 fraction in torsion test samples.
At a strain rate of e0, the Σ3 fraction increases with the number of cycles.
Since the total amount of strain is constant, the deformation per step decreases when the number of steps increases, leading to a higher fraction of Σ3

And the insulation process after high temperature hot rolling can make a large number of the Cu2S diffusion precipitation, There was no significant effect on the precipitation of Cu2S after low temperature hot rolling, still remain in the precipitate state after hot rolling. 1 Introduction Grain-oriented electrical steel has high performance of high magnetic sensitivity and low iron loss.
Hot rolling temperature and thermal maintain time of the experimental steel plate number Hot rolling temperature(℃) thermal maintain time (seconds) number Hot rolling temperature(℃) thermal maintain time (seconds) 1-1 1050.2 30 2-1 966.9 30 1-2 1103.6 300 2-2 978 300 1-3 1083 600 2-3 975.8 600 2.2 Experimental Method.
During the hot rolling process, the ferrite grain were dynamically recrystallized, after hot rolling, during the postrolling maintain process, the ferrite grain did not grow up significantly with the extension of the insulation time, This is because if there are diffusion-distributed second-phase particles in the ferrite matrix, these particles can hinder crystal boundary moving and grain growth, It makes the grain difficult to grow up normally in the thermal maintain process [5].
The high temperature hot rolled grain of about 1100℃ is larger than the size of about 950℃, in the rolling surface normal longitudinal section from the surface to the center grain size is getting smaller and smaller; this is due to the deformation shear pressure of the surface layer, making the surface grain size larger than the central layer
Developments in the production of grain-oriented electrical steel.

For face-centered cubic (FCC) metals, a considerable number of experimental studies have demonstrated that the efficiency of grain refinement varies with not only the processing route and also the die angle.
Statistic data in terms of the average number of active slip systems per grain was then computed for each increment, i, by comparing the simulation results at that increment and those of the previous one, (i − 1).
It is therefore reasonable to infer the relative efficiencies 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number a Average number of slip systems Nall Nnew Nrev 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number b Average number of slip systems 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number c Average number of slip systems Figure 2.
(3) 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number a Average number of slip systems Nall Nnew Nrev 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number b Average number of slip systems 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number c Average number of slip systems Figure 3.
A higher number of newly activated slip systems is found for the experimentally identified optimum route for grain refinement in FCC metals.

The structure of particles in the sol changes along with time from tetrahedral [TiO4] to octahedral [TiO6], with the coordination number changing from 3.14 to 5.18, accordingly.
Therefore, the structure becomes closer to an anatase, which is octahedral [TiO6] with a coordination number of 6.0.
It seems the structure of the 390-day sol very close to that of anatase powders that have the lattice structure of octahedral [TiO6], whose coordination number is 6.0.
There are nano crystalline grains in the sol, whose lattice structure and coordination number change from tetrahedral [TiO4] to octahedral [TiO6], and from 3.14 to 5.18, respectively, and finally turns into an anatase structure.
Some of the crystalline grains can be grown up to about 200 nm.

Measure the equivalent circles of each grain by measuring the area of each grain, and calculate the average number value of diameter (similar to the linear intercept method).”
Table 3 Grain size distribution statistics of collocation ratio experiment of coarse and fine WC grains Code 1# 2# 3# 4# 5# 0～1µm 94 / 9.0% 71 / 6.7% 116 / 9.0% 112 / 10.0% 2400 / 66.5% 1～2µm 492 / 47.2% 558 / 52.8% 745 / 57.5% 630 / 56.3% 980 / 27.2% 2～3µm 280 / 26.8% 243 / 23.0% 265 / 20.4% 216 / 19.3% 176 / 4.9% 3～4µm 87 / 8.3% 96 / 9.1% 104 / 8.0% 73 / 6.5% 34 / 0.9% 4～5µm 48 / 4.6% 54 / 5.1% 43 / 3.3% 52 / 4.6% 11 / 0.3% 5～6µm 29 / 2.8% 15 / 1.4% 10 / 0.8% 20 / 1.8% 4 / 0.1% 6～7µm 5 / 0.5% 9 / 0.9% 6 / 0.6% 5 / 0.4% 4 / 0.1% 7～8µm 6 / 0.6% 5 / 0.5% 7 / 0.5% 2 / 0.2% -------------- 8～9µm 2 / 0.2% 3 / 0.3% -------------- 3 / 0.3% -------------- 9～10µm ------------- --------------- -------------- 3 / 0.3% -------------- Above 10µm ------------- 2 / 0.2% -------------- 3 / 0.3% -------------- Total number of WC grain 1043 1056 1296 1119 3609 ≤peak (2µm) number of WC grain >peak(2μm) number of WC grain 586 457 629 427 861 435 742 377 3380 229 ≤2μm
But in sample 4 # with additives of fine WC increasing to 30%, the ratio of total number of WC grain to fine grain begin to decrease.
It can be conjectured from the above data that during the growing up of a number of WC grains adjacent to each other by grain boundaries fusion, external boundaries fuse first, whereas liquid cobalt surrounded in the center which is too late to be exhausted to the external from the channel and has to be retained in the internal grain after boundaries fusion to form free Co aggregation point in the internal grain after cooling solidification.
It can be known from Table 3 that when the fine WC powder content reaches 30% in Sample 4, the percentage of fine WC grain drops to 66.2%, and the total amount of WC grain goes down to 1119; and it can be observed from the SEM images of Fig.7 and Fig.8 that when the proportion of fine WC grain continue to increase, the number of WC grain per unit area that undergoes grain boundary fusion increase considerably, and then the contiguity of WC grain decrease, then the stacking density of WC grain go down.

A particle changes its own shape through interaction with neighbor particles, then, the coordination number affects particle motion.
The state of a grain f is classified according to its number of faces.
The initial sintering force increases with increasing number of grain boundaries on a particle, or, the coordination number: it is F3 for the ring ( N = 3), and F6 for the tetrahedron ( N = 4) from the geometry, where F is the force for the particle pair ( N = 2).
However, the values for various clusters are almost the same at a given sintering force, and are independent of the number of neighbor particles.
The shrinkage rate increases with increasing coordination number of a particle, because the sintering force increases with the number of necks 1−N .

Simulation procedure and results At first the grain structure is mapped onto a two-dimensional random numbered hexagonal lattice.
Here the random numbers should assume numbers between 1 and 64.
A grain was defined as a collection of points that have the same orientation number.
In other words, two adjacent grid points having the same orientation number are considered to be a part of the same grain.
The simulation time was defined by a dimensionless number known as MCS, which was related to the number of re-orientation attempts.