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The grain is defined as the group of dendrites, which grew in the same direction.
Following this definition, it is found that the crack propagated along the grain boundary, also the segregation line was observed on the grain boundary.
Thus, the number of sharp peaks (�v) and the length of hot tear or segregation line as a function of copper content have been analyzed.
On the other hand, in the case of high solute content, such as Al-10 mass%Cu in this study, the number of crack formation is high but the length of propagation may be short.
Thus, hot hear indicates open crack. 3) In the case of Al-10 mass%Cu alloy, the number of crack formation is high and the crack may be healed by residual liquid.

Three different casting process parameters were specifically designed The number (Table 1.) is poured into test bar with residual size, and the main chemical composition measured by direct reading spectrometer is shown in Table 2.
Serial number Alloy Shell temperature (℃) Pouring temperature (℃) 1 K4169 950 1410 2 950 1460 3 1050 1500 Table 2.
It can be seen from the figure that the alloy structure has a typical dendrite morphology, and there are a large number of island-like Laves phases between the dendrites, which are continuously distributed, as shown in Fig. 2(c).
It can be seen from Fig. 3(b) that after heat treatment of group B, the Laves phase and the needle like δ phase around the dendrite and at the grain boundary are basically eliminated, and only a small amount of Laves phase and MC type carbide are left.
After heat treatment in Group F, a large number of Laves hard and brittle phases formed by segregation of Nb elements remained between the dendrites.

Results Grains will grow up gradually and be well spheroidized during the resting process after stirring, but long time resting may make the grains coarsening.
Concave parts of the grains were filled up due to atom diffusion.
The reason is tiny grains with low melting point melted and disappeared, and large grains survived and grew.
Fig. 3 Micrographs of semi-solid slurry with different resting time (a) 0s (b) 30s (c) 60s (d) 90 s Discussion Large numbers of well-ordered clusters will be formed in the melt because of structure and energy fluctuation existing in molten metal.
At last, spherical grains were formed.

Four of the packets exist along the prior austenite grain boundaries and one packet grows from the boundary edge into the prior austenite grain.
White broken lines indicate the austenite grain boundaries.
Figure 3 shows 3D images of incipient-formed lath martensite regions in a prior austenite grain, corresponding to the prior austenite grain in Fig. 1.
The prior austenite grain shown in Fig. 3 has five packets in the prior austenite grain.
The number of incipient blocks with rule 1, which is the same as rule i+ii in Ref. 2, was consistent at a ratio of three over seven.

In addition, the final texture in the microstructure depends strongly on the number of template particles [4].
Randomly-oriented polycrystalline KSN ceramics show inferior electrical properties compared to KSN single crystals due to abnormal grain growth that inhibits densification [9], limited number of polarization directions [8] and averaging of electrical properties.
There are limited number of results on textured KSN ceramics.
A duplex microstructure consisting of mm-sized grains together with smaller grains develops in the N1-T0 (Fig. 5a).
Template particles controlled matrix grain growth and, therefore, no cracking or abnormal grain growth were observed in the samples textured by TGG.

The grain morphologies reveal that irregular-type and cubic-type grains coexist, and pores are observable on the surface.
Because vaporization of Bi2O3 (or Bi+3) is unavoidable, the number of vacancies in the stoichiometric NBT-BT3 ceramic increases considerably, causing distortion of the unit cell.
The number of pores and the amount of excess Bi2O3 are believed to be the two most important factors.
From the morphology revealed by the SEM image in Fig. 1, a decrease in the number of pores appears to be the primary cause of this increase.
The excess Bi2O3 segregates at the grain boundary of NBT-BT3 and inhibits grain growth by filling the space between the grains.

Decreasing grain size usually results in the mechanical properties improvement.
Final product properties are strongly dependent on the ECAP process parameters, such a temperature, type and number of passes and pressing rate, and also on the structure of the initial material.
In the case of AZ91 magnesium alloy the ultra-fine grained microstructure remains stable bellow 300 °C while increased temperatures (350 °C and 400 °C) leads to gradual grain coarsening [8,9].
Enhanced corrosion resistance of ultra-fine grained magnesium alloys prepared by SPD techniques was studied, however still only limited number of works describing the corrosion mechanism is available [4, 11, 12, 14, 15].
There are areas with small grains with the average grain size of 3.3 ± 0.5 µm with large amount of small Mg17Al12 particles, and areas with larger grains, with the average grain size of 9.9 ± 4.5 µm where the density of small Mg17Al12 particles is low.

Among the methods capable of producing such structures a certain number (e.g. inert gas condensation, ball milling, rapid solidification techniques) result in production of powders and thin ribbons which must be subsequently consolidated.
Some of these samples were subjected to severe plastic deformation (SPD) by high pressure torsion described in [4] under pressure 6GPa and number of rotations N=5 for additional structure refinement.
Average grain size in these samples varies from 0.5 to 0.7 μm.
Domain walls do not limit separate grains, but encircle a lot of disoriented grains and form “exchange” domains.
Superposition of DS with image mode shows that in smaller grains domain walls are pinned at grain boundaries.

The number of “effective” crystallization contacts is determined from the correlation of approached particles sizes and a number of particles of different size in a dispersive system.
The optimal structure providing maximum of contacts is formed under the condition of one grain of small size being placed between grains with greater sizes.
Small sized grains fill in porous space like liquids since they easily pass through big-sized.
The optimal granularity ensures the most compact packing in a unit space with maximum of contacts of varying-sized grains(see Fig. 8 a).
The equations for the coordination number in disordered systems.

As shown in Fig. 3a, b, c, columnar grains and the proeutectoid ferrite precipitates mainly distribute in the weld center along the grain boundary.
The microstructure of the grain interior is composed of tiny ferrite and pearlite, and.
So the tensile samples were taken from near surface, 1/4 thickness and 1/2 thickness of the start welding position and they were numbered A1, B1, C1.
The same sampling method was used to take tensile samples from the end welding position, and they were numbered A2, B2 and C2.
Moreover, the size of the ferrite grain in these two locations is about 20~35 µm.