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But in polycrystalline metals, the grains are randomly oriented and the dislocation motions in individual grains must be restricted by their neighboring grains.
The propagation of initial fatigue cracks formed in individual grains also must be arrested by their neighboring grains.
According to their considerations, the yielding strength of a polycrystalline metal is a stress to "spread out" the dislocation motion from some weak grains to their neighbouring grains and the variation of σ y with grain diameter, d, can be expressed asσ y＝σ 0+ ky d -1/2，where σ 0 is the stress resisting the movement of dislocations along the slip plane within weak grains, while the ky is a coefficient reflecting the resistance to unpin dislocations from their source in the neighbouring grains.
Actually, the ky , as well as theσ y should be higher for a weak grain located in the interior than that for a weak grain at or near the surface.
It is because that the dislocation motion in the internal grain is restricted by the neighboring grains from different sides, while that in the grain at the surface is only restricted from the internal side and is free from its surface side.

It is shown that the basic mechanisms of initiation are very similar from a physical point of view: PSB and Grain boundary cracking.
In this case, the cyclic plastic deformation is related to the stress concentration around a defect: inclusion, porosity, super grain, etc...
At low deformation, the plasticity can appear only if the grain orientation and the grain size are in agreement with the dislocations sliding.
However, the number of PSB increases with the number of cycles and no experiment exists to prove that some PSB cannot form at 1010 cycles or more.
These slip bands are multiplied or grown in the same grain due to following cycles.

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.

Grain size distribution, hardness and temperature profiles in the welded zones were determined in order to obtain the relationship between the grain structure and the hardness profile in these regions.
In each alloy, the average grain size in the weld nuggets was identical.
The Vickers hardness numbers of the welded zones in all specimens were measured on a cross-section perpendicular to the welding direction using a Vickers indenter using a 100 gf load applied for 15 seconds.
In all specimens, the average grain size in the weld nuggets was the same.
Microhardness numbers of joints across the mid-sections; (a) 2024, and (b) 5083 alloys.

Multiple scattering theory for acoustic waves, proposed by Foldy [5], was represented following heuristic integral equation by Lax [6], , (1) where is conditional number density of scatterers at if a scatterer is known to be at , and is a T-matrix.
Grain size distribution of each sample of S3 and S5 Table 1.
For the bimodal grains, however, dispersions are slightly different.
And the attenuation of larger size grains increase more steeply.
For, grains can be considered as scatterers.

Thus, it is expected that a magnetic field will control the orientation of nc-grains.
On the other hand, there were two peaks in the grain size distribution of the specimen crystallized with a 6T magnetic field, and the peak in the grain size distribution at larger grain sizes was composed of {110} grains.
The TEM micrographs reveal that the number density of nucleated grains in the sample seems to be higher with the magnetic field than without the magnetic field.
rate, the number density of nuclei per unit volume was measured on the TEM micrographs as a function of annealing time, as shown in Fig.3.
There was a good linear correlation between the natural logarithm of the number density and annealing time, and therefore the nucleation rate of grains nN& could be expressed as: ( )btaN expn=&

Introduction During the fabrication processes of integrated circuits, the interconnect materials are subject to a number of thermal cycles.
To date, there have been many studies of the various factors affecting hillock formation, such as the grain size [1], grain orientation [2] and grain-boundary characteristics [2].
Thus, the most plausible site for hillock nucleation might be the grain-boundary triple points.
The number of these points is proportional to one over the square of the grain size (d -2) [1].
The hillock density decreases with increasing film thickness, because the number of plausible nucleation sites for hillock formation, such as grain-boundary triple points, decreases.

Hence, virtually all positrons thermalized inside grains diffuse to grain interfaces and are trapped at open volume defects there.
Because of smaller size of Cr atoms, the lifetime of trapped positron increases with increasing number of Cr neighbors surrounding the trap.
Hence, Cr cations scavenging electrons should be located at grain boundaries.
This appears due to Cr cations segregated at grain boundaries.
Bečvář: Application of Maximum-Likelihood Method to Decomposition of Positron-Lifetime Spectra to Finite Number of Components, Mater.

Prior austenite grain size.
It can be seen that the grain is anisometric and fine.
The results are shown in Table 3 and Fig. 2c.The grain size is mainly concentrated below 18μm.When the quenching temperature increases by 10℃,the number of grain with size between 6μm and 12μmdecreases from 3928 to 3325,and the number of grain with size between 12μm and 18μmincreases from 1277 to 1459, but the average grain size is almost unchanged.
Fig.1Mechanical properties after different heat treatment: (a) rockwell hardness; (b) tensile strength and yield strength; (c) impact toughness Table 3 Results for prior austenite grain size measurement Quenching temperature minimum grain diameter maximum grain diameter Average grain diameter 910 1.09 39.05 8.01 920 1.18 47.06 8.31 Fig.2(a) OM image of prior austenite grain size quenching at 910℃；(b) OM image of prior austenite grain size quenching at 920℃；(c)Statistical results for grain size quenching at 910℃ and 920℃;(d) OM image of microstructure for process2-3.
Fig.3(a) TEM image of martensite lath for process number 1;(b) TEM image of martensite lath for process number 2-1;(c) TEM image of martensite lath for process number 2-2;(c) TEM image of martensite lath for process number 2-3 Analysis of carbides.

- the Miller Test based on ASTM test [6] allows to determine of SAR (Slurry Abrasion Response) number during the wear in slurry.
The comparative results of Miller Test and values of SAR number for investigated materials.
The wear proceeded not only by alumina grain crushing, but also by weakening of grains boundaries and whole grains removing, as a result.
As an effect whole grains or grains agglomerates could be removed.
This counteracts too fast grain boundary erosion.