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The average grains size and shape factor of solid grains were affected by melting mechanism and grain growth mechanism.
D=i=1N4AiπN (1) F=i=1N4πAiPi2N (2) where Ai and Pi are the area and the perimeter of the solid grains, respectively, and N presents the total number of solid grains.
As shown in Fig. 7(b), with the increasing of soaking time, the number of intragranular liquid droplets decreased, and large cloud-like solid grains were became into small spherical grains.
Differently, there were no intragranular liquid droplets in the microstructure and a large number of small isolated grains were formed.
Besides, it can be found that the number of recrystallized grains decreased and the size of them increased.

The results showed that Zn can refined grains of the alloy.
The grain size was determined using a linear intercept method from a large number of nonoverlapping measurements.
The grain sizes of these alloys decrease with increasing Zn content.
Fig. 5(a) shows that a great number of β＇particles which are ellipsoidal in morphology are observed in the peak-aged specimens of alloy A.
However, the average size of these particles in alloy D is bigger and lower density number than that in alloy A.

We used the same inelasticity and friction coefficients for grain−grain and grain−wall collisions including the horizontal base.
The variation of the packing fraction ρ(t) with the number of shakes t for several tapping intensities ξ is presented in Fig. 1, where more dissipative grains (disks (A)) have been used.
In this study we work with the following definition of the grain mobility: ( ) ( ) ( ) ,1 1 1∑= −+ −= N i i i d tyty N tµ (3) where N is the number of particles, yi(t) is the y−coordinate of the ith particle at time t and the angular brackets denote an average over independent runs.
When compaction goes on, the grain mobility decreases.
An example is given in Fig. 3 where we have plotted both mobility µ(t) and density ρ(t) as functions of the number of taps t.

Through orthogonal test, the paper explores such factors as roasting temperature, roasting time, hydrochloric acid concentration, reaction temperature and grain size influence on the making process, and give the best operation conditions: roasting temperature is 700℃, roasting time is 1.5～3.5h, hydrochloric acid concentration is 25%～30%, reaction temperature is 120℃ and grain size is 60 mesh.
Through researching, we elected five influencing factors, they are roasting temperature, roasting time, hydrochloric acid concentration, reaction temperature and grain size.
Table 3 L16（45）orthogonal array and test result Test Number Roasting Temperature/℃ Roasting Time/ h Hydrochloric Acid Concentration /% Reaction Temperature/℃ Grain Size /M Test Result Leaching Rate /% A B C D E 1 1 1 1 1 1 43.3 2 1 2 2 2 2 44.9 3 1 3 3 3 3 48.1 4 1 4 4 4 4 51.8 5 2 1 2 3 4 47.5 6 2 2 1 4 3 48.9 7 2 3 4 1 2 51.4 8 2 4 3 2 1 56.3 9 3 1 3 4 2 68.2 10 3 2 4 3 1 73.1 11 3 3 1 2 4 59.1 12 3 4 2 1 3 62.7 13 4 1 4 2 3 49.2 14 4 2 3 1 4 42.1 15 4 3 2 4 1 45.8 16 4 4 1 3 2 43.9 K1 188.1 208.2 195.2 199.5 218.7 836.3 52.27 K2 204.1 212.7 200.9 209.5 208.4 K3 263.2 204.4 214.7 212.6 208.9 K4 181.0 214.7 225.5 214.7 200.5 47.03 52.05 48.80 49.88 56.68 51.03 53.18 50.23 52.38 52.10 65.80 51.10 53.68 53.15 52.23 45.25 53.68 56.38 53.68 50.13 R 20.55 2.58 7.58 3.80 6.55 Through variance analysis, we found the big and small order of every factors, they are Roasting Temperature (A) > Hydrochloric Acid Concentration (C) > Grain Size (E)> Reaction Temperature (D) > Roasting Time (B)
The best experimental design is A3B4C4D4E1, that is roasting temperature is 700℃, roasting time is 3.5h, hydrochloric acid concentration is 30%, reaction temperature is 130℃ and grain size is 60 mesh.
Table 4 Three better test condition Test Number Roasting Temperature/℃ Roasting Time/ h Hydrochloric Acid Concentration /% Reaction Temperature/℃ Grain Size /M 9 700 0.5 25 130 80 10 700 1.5 30 110 60 12 700 3.5 20 70 100 According to above analysis, energy consumption, costing and so on, we selected the best test condition is roasting temperature is 700℃, roasting time is 1.5～3.5h, hydrochloric acid concentration is 25%～30%, reaction temperature is 130℃ and grain size is 60 mesh.

Very rarely has toughness been measured with a number of alternative quench paths sufficient to fit predictive equations.
For Alloy 7085 we did fractography on a limited number of the used R-curve specimens of Alloy 7085.
In a range of high hold temperature, precipitation is found only on grain boundaries.
At medium and low hold temperatures, precipitation on subgrain boundaries exceeds precipitation on grain boundaries.
This pattern was first recognized from early datasets with a limited number quench paths [14].

Since the initial positions of particles can significantly influence the simulations results, a random, isotropic distribution of grains with realistic coordination number and radial distribution function is used.
The initial density is set to 60% and the initial coordination number is 6.1.
Voigt gives an upper-bound for G/K of 0.6 that is independent from the coordination number [22].
The increase in G/K if grain rearrangements are possible is an indicator that because of an increasing coordination number the grains become more stable against shearing.
This coordination number dependence is also captured in the self-consistent estimate, which gives a G/K ratio of 0.27 for a bcc structure with a coordination number Z = 8 [22].

The SEM images indicated that in as-cast alloys, the Al2Ca intermetallic compound was located at grain boundaries with a lamellar structure, and the Al2Sm intermetallic compound was homogeneously distributed in the α-Mg matrix or near the grain boundaries with a polygonal structure, and the Al11La3 intermetallic compound was located at grain boundaries with a needlelike structure.
Moreover, the Sm addition also declined the number of the β-Mg17Al12 phase compared to that in AZ91 alloy in Fig. 3(a).
It could be found that there is the largest number of precipitated phases in AZ91-1.5Ca-0.5Sm-0.3La alloy , and all the above intermetallic compounds are generated (see Fig. 1), which precipitated in the α-Mg matrix or along the grain boundaries and will obviously restrict the movement of the adjacent grain boundaries.
However, the segregation phenomenon of Al2Sm appeared near the grain boundary.
Greer, Grain refinement of Al alloys: Mechanisms determining as-cast grain size in directional solidification, Acta.

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.

With increasing strain, the elongated subgrains transformed into elongated grains and finally into equiaxed grains with high angle grain boundaries.
The shear strain, γ at a given r can be calculated according to γ=2πNr/h, where N is the number of revolutions, h is thickness of sample and r is the distance from the center of sample (axis of rotation).
Increasing shear strain to 21.5 (Fig. 2(c)), some grain boundaries with large orientation difference appeared, and most of the elongated subgrains transformed into equiaxed grains with an average grain size of 273 nm.
It is demonstrated that the microhardness of deformed samples not only dependent upon the grain size but also upon the subgrain structure in the grain interior.
With increasing shear strain, the elongated subgrains transform into elongated grains and finally into equiaxed grains with high angle grain boundaries.

It was observed that more number of grains (~75%) lies between 40-60 µm sizes in case of LAT971C.
The high number fraction of lower grain size (<30 µm) is increased in case of LAT971R.
This confirms the presence of more number of strain free grains, which is attributed to the dynamic recrystallization (DRX) in α-phase as a result of homogenization and hot rolling at ~573K [12].
This was estimated by providing a criterion for the grain boundary (misorientation exceeding 15o) and then isolating the grains.
For a given grain, the average misorientation was calculated between all neighboring data points in the grain.