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GRAIN BOUNDARY PINNING BY PARTICLES Paulo R.
The free energy decrease driving grain growth is equal the decrease in grain boundary area per unit of volume, SV , times the grain boundary energy per unit of area, γ, or , γ∆SV .
No grain growth can take place if this extra free energy required to move the grain boundaries is equal or higher than the free energy change driving the grain growth.
The limiting grain radius is sometimes called the critical grain radius.
In order to see if the model expression is being used correctly one can calculate the number of particles that touch the boundary of a grain that possesses a radius equal to the limiting grain radius[3], RL Np (RL) = 1 6f . (9) Eq. 9 was derived assuming that RL = r 6f .

However, the number of the precipitates at the grain boundary in the Cu-added and Ge-added alloys is smaller than that in the binary alloy.
These dislocations increase in number as the number of repeated loading cycles increases.
The number of the precipitates on the grain boundary in the Cu-added alloy or Ge-added alloy is smaller than that of the binary alloy.
Therefore, the increase of the fatigue strength in Cu-added alloy or Ge-added alloy is mainly attributed to the number of the precipitates on the grain boundary in Cu-added or Ge-added alloy decreased than that of the binary alloy.
The number of the precipitates at the grain boundary in the Cu-added or Ge-added alloys is smaller than that in the binary alloy.

If the sample contains large gains, either large average grain size compared to the beam size or some extreme large grains mixed with fine grains, the measured diffraction profile will not produce an accurate 2q peak position.
With some extreme large grains, even the average grain size is fine, the high diffraction intensity from a few large grain may shift the peak position significantly.
In the weighted linear least squares method, the weight of a data point on the diffraction ring is proportional to the diffraction intensity, which is directly related to the number of participating grains.
First, this will increase the number of available data points for stress calculation so as to improve the sampling statistics.
By using multiple diffraction rings, it is also possible to reduce the number of sample tilt angles without reducing the angular coverage.

b) FIB notch in front of a grain boundary with a crack emitted from the notch tip passing the grain boundary.
For example the overall crack length in respect to the number of load cycles is shown in figure 4a.
Fig.4 a) Crack length as function of the number of cycles as measured and as calculated for a specimen without grain boundary.
It has to be pointed out that for the notch positioned closer to the grain boundary the crack arrested over a period of 7,500 cycles at the grain boundary until the crack overcame the grain boundary.
The crack length in respect to the number of load cycles for both cracks was used to calculate the crack growth velocity by a 5-point polynominal fit.

Thus, the grain growth under the specimen sputtering process may also be another reason that cause the elongation of grains.
Based on the calculation of stereology, the calculated average number of 14 is in a fine accordance with the average number of grains within one island, which is computed to be (26/10.6)3=14.8.
(c) Plot of the number of grains inside islands versus the ESD of individual islands.
The average number of grains within individual islands is 14.
The radius of the smallest segmented grain is 1.7 nm

Introduction Huge grains are formed during secondary recrystallization of grain oriented silicon steel.
As the magnetic properties of grain oriented silicon steel are dominated by the resulting texture of the secondary recrystallized grains, a large number of investigations have been conducted on the control of texture [1].
Besides macroscopic curvature of each grain boundary facet, microscopic curvature near the inhibitors was found on grain boundaries.
enriched on the grain boundary.
Therefore, the grain boundary motion in secondary recrystallization of Fe-3 mass% Si alloys is directly or indirectly controlled by a number of factors such as the size and distribution of inhibitors and grain boundary segregation.

(1) (2) Where, D — the equivalent diameter of primary silicon grains; FS — the shape factor of primary silicon grains; A — the area of a primary silicon grain; N — the total number of primary silicon grains; P — the perimeter of a primary silicon grain.
As a result, a large number of primary silicon nuclei can be formed and a part of them may grow up along the inner wall surface.
Therefore, a large number of small primary silicon crystal nuclei or grains can survive in the slurry.
If a large number of primary silicon grains appear in the Al-25%Si aluminum silicon alloy slurry, the distance among the grains may be very much small and the mutual interference in the solute field and the temperature field can inhibit the excessive growth of the primary silicon grains, which makes the primary silicon grains significantly fine.
Apart from the pouring temperature, the curve number of the used serpentine channels also affects the equivalent diameter of the primary silicon grains in Al-25%Si aluminum silicon alloy slurry.

Theoretical and Practical Considerations of Grain Refinement of Mg-Al Alloys L.
This is followed by considerations of the theoretical and practical aspects of grain refinement of Mg-Al alloys by carbon-based grain refiners.
While Zr is very effective in grain refining a number of Mg alloys, it does not work in Mg-Al alloys.
Zr reacts with the dissolved Al to form a number of intermetallics.
The grain refining effect is obvious, although it is not as strong as expected.

RESULTS AND DISCUSSION Fig. 1 shows the relation between stress (σ) and the number of cycles to fracture N for samples exposed to various aging times (tA).
At tA= 6ks, precipitates of average size 78 nm form at the grain boundary.
These dislocations increase in number as the number of repeated loading cycles increases.
Therefore, at aging times that cause the formation of many grain boundary precipitates, repeated loading results in a dramatic accumulation of dislocations in the grain boundary and grain boundary precipitates.
As tA increases to above 6ks, large scale grain boundary precipitates of around 100nm in size are formed along the grain boundary, together with a PFZ of width approximately 0.4 (µm).

Then, grain distribution was observed using a microscope, grain size was determined by the Jeffries and the Heyn methods, and strengthening was investigated by micro-Vickers hardness test.
The number of measurement points was more than 400. 3.
Table. 1 Average value of grain size [µm] Initial Without torsion With torsion Number of grains 81 (41) 85 (46) 126 (45) Jeffries method 59.6 57.7 49.2 Heyn method 47.3 43.3 38.3 3-2.
Table. 1 shows the average grain sizes of the specimens, which were measured by the Jeffries method and the Heyn method, and the number of grains measured was more than 100.
Here, the values in ( ) show the number of grains which are located at the boundary of the measurement area.