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The grain sizes were expressed the grain size number G, standardized by ASTM.
As-received AZ31 sheet 1.0mm thick showed fine and uniform equiaxed structure and the average grain number was approximately 9, while specimens 1.6mm and 2.0mm thick showed the abnormal grain irregularly.
Grain size increased with annealing temperature.
The grain size numbers of as-received and annealed AZ31 sheets are shown in Fig. 6.
Fig. 6 Grain size number of AZ31 sheets Fig. 7 Vickers hardness of AZ31 sheets Fig. 8 shows the mechanical properties of AZ31 sheets annealed at different temperatures during 1 hour.

The values of Vx =0.34 (<111> fiber) and Vx Journal Title and Volume Number (to be inserted by the publisher) 3 =0.171 (<100> fiber) are obtained (the relative error has been estimated and reaches ±0.04).
The first one is related to more or less spherical and stable grains with a relatively important grain size (30 µm in diameter) and are mainly connected to the two main orientations.
The intragranular misorientation for all this category of grains has been calculated and is more or less similar for all grains (not higher than 5°).
The advantage of nucleation and growth related to the <100> orientation is rapidly lost at the beginning of the process and gives the opportunity to a large number of orientations to nucleate and grow inside the deformed matrix.
During recrystallization, the <100> oriented grains develops first from the highly deformed areas at grain boundaries, in the intermediate regions of the wire.

There are also a number of other limitations.
It was used to verify the model for static grain growth (GG).
This temperature is close to the solvus temperature of the η-phase [2] that decorates grain boundaries and impedes grain growth.
The average grain size of new RX grains DRX was calculated based on the accumulated plastic work of deformation according to Eq. 5 [[] O.I. 
According to the results of experimental grain size measurement, the initial average grain size of about 10 µm has increased to an average grain size of about 70 µm during the heating operation.

Crystalline grain level could be a transition zone between macro and micro level material.
The reasons for enhancement of carrying capacity are: the grain boundaries become irregular or grain boundaries become more twists and turns.
The elements in affine transformation matrix [S] can be determined by the complexity of the grain boundaries which means the number and the twist of grain boundary interfaces
[ε0] is initial strain vector, which is caused by tension or compression of the grains.
After strengthening, grain boundary of the material is pulled pressure and distorted.

Addition of grain refiner and modifier is an alternative for this problem, through the control of solidification process that results in grain refining and microstructure modification.
The Ti grain refiner was varied 0.063, 0.083 and 0.108 wt. % Ti and added at the holding furnace prior to LPDC process.
One of the alternative to overcome this problem is by addition of modifier and grain refiner.
The solute elements restrict the grain growth by segregating to the newly formed solid surface.
The total number of cylinder heads produced during the trial was 764 pieces for each of the standard and the modified alloy.

The crack on the nozzle’s vanes was studied and a kind of grain refiner was used to solve crack issues by improving shell strength.
Moreover, the number of the turbine nozzle’s vanes is 31 with only 0.7mm thickness, so the cracks usually grow in the vane trailing edge.
Repeated experiments were made to determine the shape and size of the part A and the No.1’ sprue with no changing of the number of the elder sprues.
The cobalt particle generated through the casting process refined the grain of the vane’s surface.
During the crystallization nucleus increases, the grain size of the vanes refined [9].

On all EBSD maps shown in the following figures Cube grains are marked blue, S grains – green, Cu grains – red and Brass grains – yellow.
To compare the nucleus density from different nucleation sites, the number of nuclei developed from large Cube bands was also counted.
The results revealed 42 recrystallized Cube grains from 24 large Cube bands on the same sample area, i.e. on average 2 Cube grains per large Cube band.
In general, it is well known that the Cube orientation has a highly mobile high angle grain boundary with S-grains due to a special 40°<111> orientation relationship.
Hence, Cube nuclei with highly mobile grain boundaries to S-grains were preferred and showed the highest growth rate compared to nuclei having grains of other orientation as next neighbors.

After conventional melt-treatment, there were still a number of oxide inclusions, still distributed non-uniformly and gathered together; but their size decreased to about 10-20μm.
After high-efficient melt-treatment the number of inclusions was decreased obviously, and distributed along grain boundary or within the grain very uniformly (about or less than 4μm), and no congregation of inclusions was found in this material.
From Fig.1 it can be seen that the high-efficient melt-treatment can decrease effectively the number of inclusions and improve their existing morphologies.
The inclusions congregated in a large lump form and distributed non-uniformly along grain boundary.
After high-efficient melt-treatment, the number and content of inclusions in molten Al have decreased remarkably, and their size was very small [2-4].

Impedance/modulus analyses indicate that a third resistance-capacitance (RC) response is present in the sample, in addition to the grain and grain-boundary RC elements above 573K.
Variation of bulk ac conductivity as a function of temperature shows that Ba(Ti0.8Sn0.2)O3 follows the classical Arrhenius relation.The results show that the activation energy of grains and grain boundaries are 0.61 and ~1.08 eV, respectively.
The impedance spectra (IS) are widely used to study microstructure such as grain, grain-boundary, and interface in materials for their different electric responds in frequency domain.
The number of Z'' peaks increases with temperature, which means more components are detected at higher temperature.
At 773 K, three different contributions are observed, which should corresponding to grain, grain boundaries and layer effects[11] respectively as frequency decreasing.

The average grain diameter of TiN particles was ~33 nm, while Ni grains measured approximately 53 nm. 1.
When the ultrasonic power was further increased, TiN particles in the composite coating were small in number and exhibited slight aggregation (Fig. 1c).
The reason for this is that nanoparticles that enter and homogeneously disperse in the composite coating lead to an increase in the number of nuclei for nucleation of nickel grains and inhibition of grain growth.
Furthermore, the mechanical force produced by acoustic streams during ultrasonication may break the normal growth of grains and disrupt larger grains to produce smaller nuclei.
Ni grains were also nano-sized, measured as approximately 53 nm.