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The results show that there exist second phase Er2TiO3 on the surface of TiO2 grains.
The grain size was found to decrease with increasing Er2O3 content.
The decrease of grain size is attributed to the precipitation of secondary phase in the grain boundaries.
Fig. 6 shows the grain boundary defect model for (Er, Ta)-doped TiO2 varistors.
In order to illustrate the grain boundary barriers formation in (Ta, Er)-doped TiO2 varistors, a grain bounary defect barrier model was introduced.

A large number of black lumps disperse in the austenite matrix.
The analysis of the morphology of grain boundary carbide.
From Fig.2 a) and Fig.2 b) it can be seen that a large number of carbides disperse on the grain boundary of the original high-manganese steel, but only a small amount of carbide exist on the grain boundaries of high-manganese steel reinforced by nano-SiC Master Alloy .
The toughness of high manganese steel improves because that there is a large number of second phase presence in the matrix to pin dislocations and hinder the movement of grain boundaries.
The microstructure of ZGMn13Cr2 improve significantly when added the nano-SiC master alloy, additional the grain boundary carbides reduce significantly, and a large number of hard second phase grains disperse on the matrix. 2.

It has been shown that grain refinement and grain growth occurred simultaneously during the MAC process.
Fig. 3b shows that the fine grains are surrounded by coarse grains with the size of about 20~40 μm.
Hence, the grain size variation during MAC is determined by two factors: grain refinement and grain growth.
When the grain refinement and grain growth reach a balance, the average grain size remains a steady state.
Ai et al. [23] have proved that a large number of the contraction twins emerge and lead to an increased strain-hardening rate after the extension twins completely consume the matrix.

There are crack deflection and grain bridging toughening mechanisms owing to the rodlike grains of TiB2 in the products, which makes their fracture toughness is as high as 7.3MPa·m1/2.
The less the pores are, the less the 'head-water' of crack growth and numbers of crack are, thus fracture toughness of the materials is higher.
Effectiveness of grain bridge toughening is due to grain size, and the big the size of grain is, the more obvious the toughening effectiveness is.
Conditions of Grain b and c are different.
When the crack encounters grain TiB2 (b and c shown in Fig.4), it keeps away from the grains and grows along phase boundary of the grains, which is intercrystalline crack deflection.

Fig. 12. and 13. show the inverse pole figure maps (IPF) of the selected areas and optical microscopic images of numbered color etched microstructure.
Color etched image the area of interest (Original magnification: 500x, Klemm I-Beraha 10/3 reagent) [3] The individual grains are numbered on both the color etched image and on the IPF map.
Table 1 shows the orientations of grains in the area of interest.
Table 1 The orientations of individual grains in Fig. 12.
Grain No.

These grains are initially formed on the pre-existing grain boundaries and gradually consume the deformed matrix as the deformation proceeds [1-3].
The disparity of substructure characteristics between the deformed matrix and DRX grains can partly be related to the grain size difference.
The organized band substructure observed within the coarse-grained deformed matrix is known to form through a restricted number of active slip systems largely concentrated on a particular {111} slip plane [11].
In contrast, the triple point and grain boundary regions in the fine-grained DRX structure will rapidly spread throughout the grain interiors with increasing strain.
Moreover, in contrast to the original matrix grains, the boundaries of DRX grains are moving while the grains are being deformed until the equilibrium grain size is reached.

After adding modifying elements B, Ti in ZA303：the microstructure of the alloy is from gross dendrites to uniform equiaxed grains , the quantity, morphology and distribution of the (α + η) have greatly change: the quantity of (α + η) is less, from a continuous network to intermittent block, and its end become blunt, or even cylindrical horn and dispersed distribution; on the grain boundary, the size of ε phase become smaller and dispersed distribution, the number of mesh ε phase reduced but intermittent strips increased; adding B, Ti have a good effect of restraining Al element segregation，so the foundry defects decreased obviously.
For this reason, modifying elements B, Ti can prompt the grains fine[1-3] (Fig. 2 a)).
For this reason: the microstructure of ZA303 is from gross dendrites to uniform equiaxed grains, the a) 11sample modification b) 12sample without modification Fig. 3 Tensile fracture surfaces of ZA303 quantity of (α + η) eutectoid is effectively reduced and the homogenization of the dendriticcrystal of aluminium-rich phase.The increase of dimples due to the equiaxial grain, play an important role in tensile strength and elongation increase(Fig. 3 a) ).
Modifying elements B, Ti in ZA303 can prompt the grains fine, the homogenization of the dendriticcrystal of aluminium-rich phase and the increase of tensile strength and elongation. 2.

It can be concluded that because the grain size of the sample with solid solution (T4) is coarser than that of the sample without heat treatment，the elongation and the strength of the specimen treated with solid solution are lower.
It also has some advantageous properties that make it an excellent choice for a number of applications.
These properties make it valuable in a number of applications including automobile and computer parts, aerospace components, mobile phones, sporting goods, handheld tools and household equipment [1-5].
While, because of the grain size of the sample with solid solution is coarser than that of the sample without heat treatment，the elongation and the strength of the specimen treated with solid solution are lower.
Conclusion The reason for the elongation and the strength of the specimen treated with solid solution are lowest is that the grain size of the sample with T4 treatment is coarser than that of the sample without heat treatment.

Grain boundaries and interfaces are mesocrystalline characterized by lower density and presence of defects such as grain boundary dislocation, vacancies and interstitials.
In Table 2, we have listed results in a large number of polycrystalline materials.
After prolonged annealing, the interface between the Pb and Sn grains behave more or less like a high grain boundary as shown in Fig. 6(B).
SUMMARIZI#G REMARKS We have examined a large number of diverse materials to establish that the absolute interface/grain boundary free energy is the difference between the free energies for self- diffusion in the lattice and the interfaces.
McLean, Grain Boundaries in Metals, Oxford Uni.

This process, grain growth, requires short-range transfer of atoms across the grain boundary.
(2) Here Nα and Nβ are the number of crystallographic orientations in the α- and β phase respectively, and the dependence of ϕα and ϕβ on space and time is suppressed as shorthand.
Four were with 500 α- and 500 β grains, and one was with 150 α and 150 β grains.
The white arrow on figure 3 points to an α grain surrounded by β grains.
The α grain pins the grain boundaries it contacts, while it diffuses through its neighbors.