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The grains produce fine grain strengthening effect.
The number of precipitated phases in the No. 3 joint is the least.
No. 4 joint has the largest number of second phases.
According to Figure 4(g), it can be seen that there are a large number of second phases distributed in the grain boundaries and within the grains, so the No. 4 joint has poor corrosion resistance.
And because the total number of grain boundaries increases, while reducing the degree of impurity atom segregation, it can also improve the electrochemical performance of the weld.

In terms of the average number of grains through the sheet thickness, r0 had 35, r10 had 12.5, and r20 had 24.
The biaxial limit strain of r0 was lower than would be expected on the basis of a simple relationship between the number of grains through the sheet thickness, as indicated by Wilson et al
Using this definition of the limit strain, the effect of the number of elements- representing grains- through the thickness and also of the degree of orientation clustering could be evaluated.
There is a clear effect of domain thickness; limit strains in both strain states increase as the number of "grains" through thickness increases.
Predicted in-plane limit strains (ε1*) as functions of number of grain through thickness, N, for CPFEM simulations with spatially uncorrelated orientations.

Moreover, it is noted that RE addition in 316LN steel promotes to precipitate a great number of fine Laves particles within grains.
Xu et.al [5] have reported that the segregation of Ce on grain boundaries increased the grain boundaries cohesion, thus restrained the grain boundaries sliding during creep deformation and resulted in improving creep strength of P91 steel.
Under 200MPa, larger size cavities and a number of cracks are found in NRE steel, as shown in Fig. 4 (a).
While the size of cavities and the number of cracks decreased, the number of cavities also increased in 32RE steel under 200MPa, as shown in Fig. 4 (b).
(the black lines in fig. 6 represent large angle grain boundary).

The grain size level numbers (G) of alloys containing varied RE contents are shown in Table 1.
The grain size level numbers increase with the increase of the RE content.
The grain degree stage number was determined by area method.
The formula of G is shown as following [8]: 3. 2 ALogN G Log = − (1) Where G is the grain size level number, NA is the number of grains in per square millimeter.
RE content (wt%) 0.0 0.2 0.4 0.6 0.8 1.0 Grain size level number 0.19 0.30 0.47 0.51 0.77 1.09 Fig. 1 Microstructure of the as-cast alloys in low magnification case (a) Mg-16Li-5Al (b) Mg-16Li-5Al-0.2RE (c) Mg-16Li-5Al-0.6RE (d) Mg-16Li-5Al-1.0RE (b) 100w� (a) 100w� Table 1 Grain size level numbers (G) of alloys 100w� (d) (c) 100w� Fig. 2 shows the microstructure of alloys at higher magnification.

When a grain-boundary is exposed to a high, completely elastic mechanical stress σ, an embrittling species can penetrate it by grain-boundary diffusion.
On the other hand, if the crack tip iss surrounded by a high number of CSL grain boundaries, it should be possible to reduce the susceptibility to cracking by dynamic embrittlement [8,13].
As represented in the crack velocity vs. stress-intensity factor plot in Fig. 7b, crack propagation along a random high-angle grain ductile-fractured grain boundary 10µm boundary is by two orders of magnitude faster than along a special symmetrical Σ5 grain boundary.
Under the influence of a high elastic tensile stress acting normal to grain-boundary planes, an embrittling species can diffuse into the grain boundaries and lower the interfacial cohesion.
Small-angle grain boundaries or special grain boundaries with a high fraction of coincident lattice sites between the neighboring grains seem to exhibit a particularly low diffusivity of the embrittling element; i.e., they have a high resistance to dynamic embrittlement.

Cu-0.3Cr alloy: The microstructure of Cu0.3%Cr in the starting condition consisted of equiaxed grains with grain size 8-10 µm.
Fig. 3 (a) shows the GBCD as a function of the number of passes.
The components BE /BE got strengthened with number of passes.
The grain size was quite uniform with a fine distribution of equiaxed grains.
Texture weakened after ECAE in the α- phase with number of passes.

Grain refiners are widely used in the foundry.
They are considered to provide benefits in a number of ways including improved feeding during solidification, reduced and more evenly distributed porosity, and reduced hot tearing [5].
Grain refiner is added to make smaller, more uniform, equiaxed grains.
To produce cast ingots with fine grain size, grain refiners are added.
Affects the mechanical properties of the material the smaller the grain size, more are the grain boundaries.

The ASTM standard grain number is defined by the ASTM E112 [6]
The grain size of the microstructure can be estimated by grain number of per area.
Frequency Grain number [N] Deviation No.
A line is drawn for each microstructure picture to indicate where the intercept method was used to compute the grain number.
The result shows that the grain size (inverse of grain number along a line) of samples deposited with vibration is smaller than that of the samples deposited without vibration.

Introduction It is known that magnesium alloys are of great interest for medical applications since they possess a number of advantages in comparison with other materials [1-3].
The mean grain size is 42±7 µm, and the coarse grains with a size of about 200 µm are observed.
Study by TEM showed that HPT processing leads to strong grain refinement, the mean grain size is 210±15 nm (fig. 3a).
According to SEM images, the mean grain size is 1.4 µm.
The low ductility can be explained by the accumulation of a large density of lattice dislocations in the conditions of a limited number of slip planes.

Journal Title and Volume Number (to be inserted by the publisher) Fig 2.
Each lattice site is assigned a number, Si, which corresponds to the orientation of the subgrain in which it is embedded.
The number of distinct subgrain orientations is dependent on the measuring step size and area.
A grain boundary energy Ji is attached to the grain boundary sites and zero energy for sites in the grain interior, according to ( )∑δ−⋅= nn j SS i I i ji1JE
(3) Journal Title and Volume Number (to be inserted by the publisher) where ijδ is the Kronecker delta, the sum is taken over nearest neighboring(nn) sites and Ji is a positive grain boundary energy.