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It is well known that, the quality of castings can be improved by grain refinement which reduces the size of α–Mg grains in the casting [5].
Normally, uniform fine grains are achieved in castings by addition of grain refiners to the melt prior to solidification [10].
It can be seen clearly from Fig. 3a that the pure Mg has coarse columnar grain structure and its grain size is about 1300 μm.
Addition of 0.5 wt% Al–4B has shown a strong grain refinement in pure Mg and the grain size is reduced to 720 μm (Fig. 3b).
When Q is large the rate of growth is small, thus allowing a large number of substrates to act as nucleation sites.

grain boundary phenomena.
On the other hand, the effect of grain boundaries on bulk properties has been studied and utilized so far by mainly focusing on the grain size, i.e. the density of grain boundaries.
The fully computerized SEM-EBSD/OIM technique has been widely being used for rapid/precise orientation determination or miscroscale texture analysis, and the characterization of a huge number of grain boundaries (say a few tens of thousands) in a polycrystalline sample.
There are a number of promising structural materials expected as future high temperature materials, but hindered from their development because of their intrinsic brittleness due to a high propensity to intergranular fracture.
Relationship between Texture and Grain Boundary Microstructure Since a grain boundary is geometrically characterized by the relative orientation relationship of adjoining grains, it is feasible that any local change of the orientation distribution of grains (local texture) must directly affect the grain boundary character distribution (GBCD) and the heterogeneity of grain boundary microstructure.

The number of grains in a model of a 10 µm square area was changed from 23 to 1200.
Average grain size, number of nodes and number of elements of each FEM model are shown in Table 2.
Figure 6 shows the Young's modulus as a function of number of grains obtained by FEM analysis.
C11 C12 C44 165.7 GPa 63.9 GPa 79.6 GPa Table 2 Average grain size, number of nodes and number of elements of FEM models.
Soboyejo: ASTM STP 1413(2001), p.1411 10 1 10 2 103 160 170 180 Young's Modulus GPa Number of Grains n n=23 n=52 n=101 n=300 n=1200 Mean Value Fig. 6 Scatter of Young's modulus as a function of number of grains

The discussion leads to the following guide: simultaneously controlling the initial grain size, diffusivity, dynamic grain growth, homogeneity of microstructure and the number of residual defects is essential to attain high-strain-rate superplasticity.
For suppressing damage accumulation by the void growth, it is necessary to reduce the number of residual defects in the sintered body and to suppress cavity nucleation during deformation.
Such a microstructure should appear when a small number of residual defects grew with plastic flow under strongly suppressed cavity nucleation.
If cavity nucleation is active as observed in conventional materials (Fig. 2), a large number of micrometer-sized voids must grow from cavity nuclei during superplastic deformation.
For this attainment, the knowledge about superplastic deformation, cavitation and dynamic grain growth emphasizes the importance of simultaneously controlling the following factors: the initial grain size, the number of residual defects, diffusivity, dynamic grain growth and the homogeneity of microstructure.

These are if some grains with many more facets than the other grains, or if only some grains with a pin up force caused by precipitates at grain boundaries just the half value of the pin up force to stop grain growth or if the mobility of large grains is significantly high than that of small grains.
A huge number of simulation experiments have demonstrated that there are only three ways to achieve the goal as followings.
The special orientated grains with low grain boundary could be the grains with twin grain boundary or coincident lattice site grain boundary.
The local high restored strain energy will give extra driving force to cause partial abnormal grain growth to introduce a number of separate big gains in the matrix of nano-size grains if the plastic pre-strain is carefully controlled to form different local strains.
The special orientated grains could be the grains with twin grain boundaries or coincident lattice site grain boundaries. 3.

In this simulation, a series long-range orientation field variables η are chosen to describe the microstructure and spatial orientation of grains: η1(r, t), η2(r, t), η3(r, t)...ηp(r, t), p is the possible number of the grain orientations in the system, and it is taken as 32 as suggested in ref. [16].
When the grain is marked as η1, η1=1 in the grain, and ηi(i≠1)=0; η1 is continuously changed from 1 to 0, when it passes through the grain boundaries between η1 grain and the adjacent grain.
It is shown from Fig. 3 that the grains grow up from 20min to 80 min, and the number of grain boundaries is decreased.
The grain size is largest when there is no particles when the annealing time is the same, which means the particles will hinder the grain growth, because they have the pinning effect on the grain boundary moving.
Particles (small dark spots) are located at grain boundaries in the grains.

Importance of grain boundary atomic structure in superplastic ceramics In fine-grained ceramic materials, the combination of grain boundary sliding, grain switching and grain rearrangement accommodated by diffusion can be regarded as the main mechanism of superplastic deformation [22].
Dispersion of second phase particles is highly effective to suppress initial grain size and dynamic grain growth.
When initial grain size and the number of fine pores in the sintered body is at similar levels, the failure process, and hence the tensile ductility, are mainly controlled by the cavity nucleation [22].
Nanocrystallization should improve the tensile ductility in superplastic ceramics, because the flow stress can be lowered owing to nanocrystallization, and because cavity nucleation is suppressed owing to increased number of grain boundaries,.
The combination of the decreased grain size, increased grain boundary diffusivity and decreased grain boundary energy is likely to be responsible for the improved ductility of PX172-G.

In usual cases, coarse crystal grains are included in aluminum casting alloy.
The two problems arise because of the existence of the coarse crystal grains.
For an accurate estimation of the stress measurement by neutron diffraction, a sufficient number of crystal grains must exist in the gage volume.
However the casting materials usually include coarse crystal grains.
The total number of measurement points was 616.

The original matrix microstructure of as-cast ZL205A alloy consists mainly of α (Al) phases and a large number of θ (Al2Cu) phases on grain boundaries, and the grain orientation is random distribution before extrusion (Fig. 4(a)).
The original matrix microstructure of as-heat treatment ZL205A alloy consists mainly of α (Al) phases and a large number of θ (Al2Cu) phases on grain boundaries, and the θ (Al2Cu) phases along the grain boundaries tended to random distribution (Fig. 5(a)).
After 2 passes, the number of dimples increased, and the depth was almost the same(Fig. 6(c), 6(d)), it’s due to microstructure of cast alloy is refined, and the micro crack growth is affected by the small grains around it, resulting in the resistance of its diffusion bonding increases, and expands to the boundaries of large grains.
After 1 pass, the number of micro voids and pits of fracture decreased than cast alloy, and the number of dimples increased in comparison to cast alloy after 1 pass.
(2) The original matrix microstructure of ZL205A alloy consists mainly of α (Al) phases and a large number of θ (Al2Cu) phases on grain boundaries.

After 2 passes, the number of recrystallized grains had increased the distribution of recrystallized grains and the precipitated phase was coincident.
The yield strength then decreased with further increase in the number of passes.
As to the yield strength, above 4 passes, the grain size of matrix did not change with the increasing number of passes, while, the size and amount of the second phase increased.
Summary During the first 4 passes, the grains of the GW103K alloys were refined gradually with the increasing number of passes.
The second phase particles precipitated preferentially near the grain boundaries and grew gradually with the increasing number of passes.