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(1) In the formula: g for the test number (1 ~ 9), Wk is the weight of a performance index, (yg)k for a round of testing of a performance index, (ymin)k is the minimum value of a performance index, Rk is the extreme differential value of a performance index, k take 1 to evaluate the tensile strength, k take 2 to evaluate the elongation rate, k take 3 to evaluate the hardness.
This could be regarded as the reference volume for grain refining and modification.
(b) Fig. 3 Optical micrographs of as-cast alloys:(a) master alloy; (b) grain refining and modification alloy Grain refining and modification had satisfied results (Fig.4).
Then they were distributed in the grain boundaries of plastic α-phase.
Further, porosity was significantly reduced after grain refining and modification.

A commercially available hydroxyapatite (HA) was sintered for a number of sintering temperatures and times between 1150°C to 1350°C and 0 to 12 hours respectively.
However, sintering at 1350°C shows a large increase in the grain growth with grain sizes in the region of 20 µm after 12 hours.
As full density is reached after sintering at 1250°C for 1.5 hours, the driving force for sintering is transferred to the grain growth process shown by a slight increase in the grain growth rate and therefore the overall grain size.
Using the relationship (D-D0) = ktn, where D is the measured grain size after time t, D0 the average grain size after time t = 0 and n is the grain growth exponent, k, the rate constant, was calculated for each of the sintering temperatures as seen in Fig. 4.
The grain growth exponent (n) of 0.44 was used as the best fit value of the error.

It is well known that Ca addition is effective to obtain homogeneous microstructure of fine grains and highly resistive grain boundaries.
When the sintering temperature was lower than the critical temperature, Ca content greatly affected the grain boundary mobility and dominated the grain growth.
G=π×L/n, where L is the length of the diagonal line of the image to be analyzed, n is the grain boundary intersection count (the number of times the diagonal line cuts across).
It is noticed that the changing trend in number and size of the porosity at different temperature ranges was almost the same as shown in Fig. 5.
Thus, Ca segregated at grain boundary plays a dominate role for the grain growth when temperature is lower than the critical temperature.

Extensive grain refinement provided the formation of fully recrystallized structure with an average grain size of ~0.6 μm.
Extensive grain refinement affects mechanical behavior significantly.
In the material with UFG structure at room temperature, a number of dimples with deep conical shape are observed (Fig. 3a’).
First, intergranular brittle fracture takes place occasionally along limited number of planar boundaries of unrecrystallized grains (Fig.4b’).
As a result, a large number of small dimples are observed and crack propagation requires considerable plastic deformation (Fig. 4b’) [12].

Domestic researches are mostly about the effect of grain grading on properties of concrete [6-7].
In conclusion, researches about the effect of different grain grading of sands on properties of mortar is limited.
Thus, according to a large number of water consumption test in the lab and the requirement of construction site, we determined the water consumption of mortar is m(water): m(dry powder)=1: 4.
Fig 1 Influence of grain grading on consistency Fig. 2 Influence of grain grading on strength of mortar of mortar Influence of grain grading on compressive strength and flexural strength of mortar.
Influence of grain grading on bonding strength of mortar.

Applying electromagnetic field during the solidification of Cu-Fe alloys can further refine grain of hepoperitectic alloys, but has no obvious effect on the grain size of heperperitectic alloys.
The first effect will result in grain refinement via grain multiplication, whereas the second will reduce the number of heterogeneous nucleation sites.
It is believed that in the hepoperitectic region, the grain multiplication has augmented the effect of iron in promoting grain refinement, resulting in further grain refinement, as shown in Fig. 3(b-d).
In the heperperitectic region, however, the grain multiplication has been just balanced by the reduction of the number of heterogeneous nucleation sites, resulting in grain size remaining unchangeable, as shown in Fig. 5(b-d).
(2) Applying electromagnetic field during the solidification of Cu-Fe alloys can further refine grain of hepoperitectic alloys, but has no obvious effect on the grain size of heperperitectic alloys

Therefore, after two TC the microstructure was composed of fine grained reverted austenite and RA of large grain size.
IPF map depicting the progress of recrystallisation with increasing number of TC is shown in Figure 2.
Table I: Change in the % volume fraction of DIM with increasing number of TC.
Interestingly, no significant increase in the grain size and reduction in the fraction of low angle boundaries (LAB) were found by increasing the number of TC.
The persistence of LABs even after eight numbers of TC indicates incomplete or longer duration of recrystallisation.

Impurity segregation at grain boundaries in polycrystalline alloys is known to have a tremendous impact on the material properties such as grain boundary mobility, cohesion...
Impurity segregation depends on the misorientation of the grain boundary [1] but unfortunately, there are no direct techniques that allow to conveniently measure both segregation level and misorientation on a large number of GBs.
In spite off the relatively low number of boundaries, the population is reasonably close to a random one.
The samples were quenched before completion of recrystallization in order to observe the interfaces between recrystallized grains and non-recrystallized grains.
Because of the high dislocation density in deformed grains it is not possible to get the misorientation information between new grains and deformed ones using EBSD.

As PWHT temperature increased, a normal grain growth of as-welded equaxied grains ceased and abnormally grown grains with elongated shape coarsened.
Huge elongated grains changed into smaller equaxied grains at 500℃.
As a result, the FSW is now established as a credible method for joining Al alloys. 7055Al-T6 alloys are precipitation hardening Al-Zn-Mg-(Cu) alloys, with a large number of applications in the aerospace and transportation industry. 7055 Al alloy containing Sc (0.1 wt%) have a high strength because the thermal stable dispersoids pin the movement of the dislocation and grain boundary at high temperature, which resulted in the retardation of recrystallization.
The unaffected base metal (BM, a) has the elongated grain structure with high aspect ratio and sub-grain structures are also observed inside the grains.
The smaller particles were still arranged in the grain or sub-grain boundaries and pinned the movement of grain boundaries in the BM.

A number of examples are presented, including grain boundary segregation, precipitation of second-phase particles in a polycrystal, and interaction between segregation at a grain boundary and coherent precipitates inside grains.
For example, the left-hand side grain (Grain I) is ascribed a misorientation angle = with respect to a fixed reference, while an angle = q () is ascribed for the right-hand side grain (Grain II) in Fig. 1 (a).
Coherent precipitates inside grains and grain boundary segregation.
One was embedded in Grain I, while the other was embedded in Grain II.
Fig. 2 Coherent precipitates inside grains in different crystallographic orientations in the case of (a) bi-crystal (60o grain II), (b) bi-crystal (45o grain II), and (c) 4 grains system.