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The model can predict the final microstructure both grain size and grain morphology.
The model is also applied to a commercial alloy to predict the final grain size and grain morphology.
In the CA model, each meshed unit is characterized with several variables, including temperature, solute concentration, curvature, phase number, preferential growth direction and growth velocity.
The present model is computational efficient and can simulate both grain size and microstructure morphology.
The model can also predict the final grain size and microstructure morphology.

The grain sizes are below 1µm and decrease with increasing current density.
The number of coarser grains in Fig.8a is obviously less than in Fig.8b, while most of the grains in Fig.8c is finer.
It is shown in the dark-field micrograph of Fig.8a and Fig.8b that the defects of grain growth, such as twins and dislocation, appear on the coarser grains.
It can be explained by the increase of Mn content and the grain refinement.
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The grain size was decreased with increasing Zr content.
The compositions of BZT films were controlled by number of Ba and Zr metal pieces [16].
The addition of Zr to the BaTiO3 decreased the grain size of crystallized films.
In other words, the decrease in grain size with increasing Zr content seems to be associated with the lower grain-growth rate caused by the slow diffusion of the Zr4+ ion, which has a larger ionic radius than Ti4+.
A good correlation between the crystallinity, the grain size and the dielectric properties has been found.

Therefore, the article prepared the samples of coarse-grained soil with the different initial fabric of grain using the cellular automata (CA) that had had the features of space-time discreteness and complex system's dynamic modeling.
Num_1 is representative of the total number of neighbor cellular whose state is 1, Num_2 is representative of the total number of neighbor cellular whose state is 2.
It is only when the two cellulars are quite close in the evolution that the Num_1 and Num_2 can not be equal to zero at the same time; 3) To compare Num_1 with Num_2, the central center has the evolution trend to the cellular of big number, its probability of evolution is Max (Num_1, Num_2) × 0.125.
Status quo and tendency of studies on scale effects of coarse-grained materials[J].
Fabric analysis of two-dimensional tests for coarse-grained soils[J].

The zinc additions increase the number of particles during the annealing process.
Grain sizes of the annealed alloys at 450°C at different times are shown in Table 2.
Grain sizes of A and D alloys are smaller than that of B and C alloys.
Thus, alloying Mg-Ce with zinc has an influence on grain refinement.
Thus, the cerium addition refines the grain size during the annealing process.

Slip bands, disorientation zones, and carbide inclusions in austenite grains.
Due to the inhomogeneity of the material, grains, grain boundaries, inclusions, already-formed cracks, and disoriented areas hinder the movement of dislocations.
Discussion Based on the analysis of the obtained experimental results, it can be concluded that the value of the average propagation distance reaches “saturation” and ceases to change when the number of dislocations in the cluster is equal to a certain threshold value.
Grain boundaries, interfaces, and inclusions are obstacles to lattice dislocation motion.
As the grain size decreases to 30–20 µm, the volume fraction of grain boundaries increases.

First case is that the grain cuts an infinite plane, and the other is that grain cuts a peak of the surface die.
Because the surfaces of grains are so rough that the workpiece material is stuck around the grains surface during polishing, establish full frictional boundary condition between the workpiece and grain surfaces.
The cutting part shape of grain is different, but every grain is regarded as cone with 150˚ cone angle [4].
Using a vidicon with 20 times magnification, and the photographs are uploaded into a computer, and count the number of grains at any 5 regions, then the even grain density is obtained.
Since all acting grains are not on the same plane of the polishing head, when the force is small, the total number of acting grains is less, and the polishing depth is more, therefore, the forecase of Mn is more.

By this way, the propagation of grain occurs.
The heterogeneous nucleation nucleus is the survival separating grain at last.
In this study, superheat is the unique variable, hence we assume that the number of the original separating grain is the same at different superheats.
In this situation, the number of the survival separating grain which can become the heterogeneous nucleation nucleus finally is greater.
As a result , the equiaxed grain ratio will be raised greatly.

Grinding quantity experimental analysis The belt linear speed on the material grinding quantity has a great influence, as shown in figure 2 shows: in a certain range, abrasive belt grinding quantity Z increase with the increase of the belt linear speed v, but v increase to certain limit, Z began to decrease .With the increasing of the v, the number of abrasive grain that per unit time through the grinding zone is increase, namely increase the number of cutting edge.
When feeding speed is small, the number of abrasive grain that per unit time through the grinding zone is increase, namely increase the number of cutting edge, so the grinding amount is very large.
After 3 Δ t, the abrasive belt wear remain constant, because there are always new grain, replacing the old grain participate in grinding process.
Figure 5 The relationship between the clogging degree of belt and grinding time The causes of this phenomenon are as follows: in the initial of grinding, a large number of grain top broken or whole happened broken, attached to the abrasive surface of the titanium alloy with abrasive grain broken down, therefore not in the belt surface to form a stable jams layer.
When the belt working after a certain period of time, only the last layer of abrasive grain, no new abrasive grains exposed, adhesion complexes are rapidly into the belt chip space to constitute the entire jam of abrasive belt.

Hence, the normal grinding force of single grinding grain decreased.
Because the total number of grinding grains that acting in grinding at one time increased, the total grinding force would increase [3].
Meanwhile, the total number of grinding grains in the grinding area is not changed, so the macroscopical normal grinding force would decrease [4, 5].
The increase of spindle speed increased the number of grinding grain in grinding area, and decreased the maximum grinding depth of single grinding grain.
The micro pulse engaging and retracting caused by ultrasonic vibration made the grinding grain cutting in a pulse mode.