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The distribution of grain boundary phase was not homogeneous.
The grain growth at the outside of the G40 specimen was significant.
It was clear that cracks propagated mostly through grain boundary, and number of deflection and crack branching increased with increase in Gd2O3 content, which should be the cause of increase in fracture toughness with increasing Gd2O3 content.
Grain boundary fracture was observed for specimens of all compositions.
The distribution of grain boundary phase was not homogeneous, less in outer side of sintered body, and then difference in grain size and porosity of each sintered bodies.

The microstructure of the castings indicates that the shape, size and numbers of the primary α-Al grains in different parts of the castings are highly consistent.
If the liquid alloy is poured at this temperature, the solidified primary α-Al grains in the slurry center appear like spheres and the solidified primary α-Al grains in the slurry periphery are fine dendrites or rosettes [10].
That is to say, the primary α-Al grains in the slurry center are gradually changed from spheres to dendrites and the primary α-Al grains are yet fine dendrites or rosettes in the slurry periphery, as shown in Fig.1.
The primary α-Al grains in the slurry center became more spherical and larger, and the primary α-Al grains in the slurry periphery also became generally spherical or ellipsoidal, as shown in Fig.3.
The reho-cast sample’s microstructure show that the spherical primary α-Al grains in different areas are distributed homogeneously and the grains size is perhaps equal to each other, as shown in Fig.5.

Moreover, the longer the reaction time, the bigger the acicular grains, and the stronger the electron diffrac- tion ring for the acicular grain will be.
Fig.4 The growth units for M-(OH -1)6 octahedron (M= Mg 2+, Al3+) and their grid-dot diagrams Fig.5 The dependence of the growth unit stability energy U on the number of the growth units n (one dimension).
So, these grains are very easy to gather.
And this kind of gathering is the base to produce more big grains.
Thus, it is the crystal embryo gathering that makes the interaction between the grains possible and can produce more big new grains furthermore.

The microstructure appears of a coarse grain shown in Fig. 1a for as-cast Mg-Nd-Gd-Zn-Zr and fine grain appears for Mg-Nd-Gd-Zn-Zr with 2.0 wt.% Ho in Fig. 1b.
It can be revealed that holmium acts as a grain refiner to this alloy.
They found that the addition of 0.4 wt.% Ce into the Mg-Zn-RE alloy has a smaller grain size which attributed to the grain refinement.
The cast alloy containing 2.0 wt. % Ho has the smallest grain, and size of the grain about 258.4 µm.
Acknowledgement This research is funded by Exploratory Research Grant Scheme (ERGS), vot number E023, Ministry of Higher Education, Malaysia.

The number of infinite cyclic groups Z is the q-th Betti number of K, denoted by βq or bq.
The 0-dimensional Betti number b0 is the number of connected components and the 1-dimensional Betti number b1 is the number of the surrounded areas.
C., Kida K: Image Analysis for the Structures of Grains via Homology Methods.
C., Kida K: Topological difference of grain composition in the WMZ (Weld Metal Zone) in low carbon steel Plates (JIS-SS400).
[8] Nakane K, Mizobe K, Kida K: Homology estimate of grain size measurement based on the JIS samples.

Using every welding mode, two plates were welded, and the total number of welded plates was eight.
Coarse-grained heat affected zone (CGHAZ) follows FGHAZ in this dark area, and the coarse grains are visible, especially on the macro-sections of samples WG0 and WG4.
That is, the greater the number of welding passes – the lower the measured hardness values in HAZ.
The increase of the welding gap from 0 to 8 mm is related to an increase in the required number of passes, respectively from 2 to 4.
The increase in the number of welding passes leads to a decrease in the hardness of coarse-grained heat-affected zone from 420 HV1 to 315 HV1, while the hardness of the weld metal does not depend on the number of passes. 4.

In addition, the fine and equiaxed grains were observed near the joint interface in the specimens fractured at the base metal.
A number of studies on USW technique have been carried out to characterize bonding between many different combinations of dissimilar metals since the metallic joints were achieved in 1950s [1-5].
The lower limit misorientation angle was defined 2° to prevent misreading of grain boundaries due to orientation error.
The grain size of Al alloy around the joint interface was approximately 100 – 200 nm as shown in Fig. 5 (a).
This work was supported by JSPS Grant-in-Aid for Scientific Research Number 24760590.

Introduction Equal-Channel Angular Pressing (ECAP) has been established as an effective method to achieve ultrafine-grained materials [1].
Pilot research on the ECAP-Conform process showed the capability of this approach to achieve significant grain refinement in materials such as pure Al and Ti [3-7].
By processing the Al-6061 alloy, the homogeneity develops gradually with increasing numbers of passes in the ECAP and ECAP-Conform processes.
Experimental results and discussion Previous investigations [2,14] revealed a significant grain size reduction to ultrafine grain sizes for Al-6061 samples processed by ECAP or ECAP-Conform.
At the same time, the hardness continues to slowly increase with increasing numbers of passes and reaches average values for Hv of ~95 after 4 passes.

The research results are implemented as a number of grinding techniques with controllable cutting relief of the wheels and devices which realize them.
We have found that stresses exceeding the ultimate stress limit of diamond grains and placed along the metallic phase interlayer result in the development of microcracks in a grain.
The stresses on the periphery of the grain being sintered are distributed in a way that can result in shearing grain submicroedges.
By varying the combination of diamond grain strength and grain concentration in the wheel for various bonds, one can determine combinations in which retention of diamond grain integrity was provided.
The results of calculations of temperature fields in the process of microcutting using sharp diamond grain and grain with wear site are shown in Fig. 3.

During the process of isothermal heat treatment, the γ phase at grain interface of eutectic structures (δ+γ) is dissolved at first.
At last, partial remelting and isothermal holding of the fine structures produced by NLC produces globular structures with the good thixotropic properties for SSM. 1.5 Chemical Grain Refining Method [13].
The functions of refinement or modificator in chemical grain refining method are to increase the number of nuclei, improve the microstructure and make it suitable for SSP.
Semi-solid magnesium slurry can be obtained by simply reheating chemical grain refining billet.
Due to the high Reynolds number, the flowing pattern in thixomolding is laminar, which reduces the porosity in the components, enhances the mechanical properties, makes the parts have the ability of being welded and thermal treated.