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However, only less than 1% of the added TiB2 particles are active for nucleation of α-Al grains [6].
Experimental Properties requirement of aluminium sheet for automotive application are met largely by a number of Al-Mg alloys (5xxx series) .
The line intercept method was used to measure the grain size along the transverse section.
Enough numbers of the potent oxide particles as nucleation substrates can enhance the heterogeneous nucleation throughout the whole melt volume, resulting in grain refinement as seen in Fig. 2.
Greer, Control of grain size in solidification, in: B.

The larger, elliptoid M23C6 particles mainly precipitate on prior austenite grain boundaries and sub-grain boundaries, while the finer spherical MX particles are precipitated on the dislocations within martensite laths.
The M23C6 particles precipitated on the grain boundaries are elongated along the grain boundaries direction, in which diffusion coefficient relatively high.
Therefore, with the temperature increasing, M23C6 and MX particles which begin to coarsen and dissolve in matrix, can not cause an effective pinning on the grain or sub-grain boundaries and dislocations.
Moreover, in this two-step tempered sample, the size of laths width and precipitates is lower than that of sample S2, while the dislocations density and precipitates number is higher than the latter.
These particles precipitated at early stage can pin the grain or sub-grain boundaries and dislocations, retarding recovery of which at a higher temperature.

In specimens were examined the sizes and number density of carbides, the prior austenite grain size and the fineness of the resulting hardening-type microstructure.
Size and Number Density of Carbides.
The smaller was the size of carbides in the microstructure, the greater was their number density.
The prior austenite grain size is related to the number density of carbides in the matrix.
Prior austenite grains were polyhedral in all specimens.

n is a dimensionless number and defined as the number of grains which could be always founded in a volume wherever as large as n times the specific volume per grain, which means that the grains are uniformly distributed at the scale of n times the specific volume per grain, within that volume, however, n number of grains are randomly distributed.
However, the actual number of abrasive grains remaining on the working surface is much less because the over-exposed grains would pull out during conditioning operation.
One is the areal density of grains number Nm ( T > t ) with the protrusion height T larger than the specified t , as shown in Fig. 6, which represents the cutting edge distribution Nm ( T > t ) in depth-wise, and also is one of the most important factors influencing on grinding process.
Bt=i=0Nmπ(rgi2-(t-Zi)2)　　 (1) In this Eq. (1), Nm represents the number of the protruding grains at the specified height t , and rgi and Zi stand for the grain radius and the center position of abrasive grains in z-axis, respectively.
From the information of these results, the areal density of grains number Na ( T > t ) of protruding abrasive grains with the protrusion height T larger than the specified t can be counted.

Behavior of Basal Plane Dislocations and Low Angle Grain Boundary Formation in Hexagonal Silicon Carbide Yi Chen1,a, Govindhan Dhanaraj 1,b , William Vetter 1,c , Ronghui Ma2,d and Michael Dudley 1,e 1 Department of Materials Science and Engineering, Stony Brook University, Stony Brook, NY, USA 11794 2 Department of Mechanical Engineering, University of Maryland Baltimore County, Baltimore, MD, USA 21250 a yichen1@ic.sunysb.edu, bgdhanaraj@ms.cc.sunysb.edu, cwvetter@ms.cc.sunysb.edu, d roma@umbc.edu, emdudley@notes.cc.sunysb.edu Keywords: Low angle grain boundary, Basal plane dislocation, Dislocation dipole Abstract.
The three-dimensional (3D) distribution of BPDs can lead to aggregation of opposite sign edge segments leading to the creation of low angle grain boundaries (LAGBs) characterized by pure basal plane tilt of magnitude determined by the net difference in densities of the opposite sign dislocations.
It is also believed that the influence of low angle grain boundaries (LAGBs) on device performance is related to the presence of BPDs which in part comprise them.
The three-dimensional distribution of BPDs in the crystal caused by the thermal gradient will lead to the formation of low angle grain boundaries in SiC.
Colin Wood) and by Dow Corning Corporation under contract numbers N0001405C0324 and DAAD1701C0081.

A large amount of strengthening phases such as Mg3Zn6Y(I-Phase), Mg12ZnY(X-Phase) and MgZn2, which were massive, grainy and clavate, dispersedly precipitated from the matrix along grain boundary during ageing treatment at 225℃ after extrusion, and made the sliding of grain boundaries restrained, which resulted in an enhancement for mechanical properties to a great extent.
As can be seen, the average grain size of the as-cast is 50-60μm.
As can be seen from the graph, a large amount of strengthening phases which are block-like, grain-like and rod-like precipitate in the grain and along the boundary after being ageing treated.
While the grains grow obviously and the amount of precipitated strengthening phases decrease when the ageing time is as long as 28h.
Acknowledgements Thanks for “The General Program of Liaoning Province Committee of Education (program number: L2012035) and the 12th Five-Year” National Science and Technology Support Program (program number: 2011BAE22B01) for funding supporting the experiment.

An addition of BLT generally decreased grain size of the ceramics.
High purity PZT - BLT ceramics with systematic microstructural changes from equiaxed PZT-rich grains to plate-like BLT-rich grains were observed.
BLT ceramic contained plate-like grains while PZT had more equiaxed grains [3].
This was a reason the ceramic with smallest grain size (0.97PZT - 0.03BLT) showed the highest hardness value compared to those with larger grains.
Not only the number of grain boundary played an important role on hardness changes, but also the density of ceramics, i.e. 0.97PZT - 0.03BLT ceramic had the highest density.

The grain size decreased with increasing strain rates at 750k. 1.
The microstructure consists of elongated grains with serrations developed in the grain boundaries and newly formed equiaxed grains of different sizes, indicating dynamic recrystallizatioin (DRC) occurred during hot compression deformation at strain rate of 0.01s-1 (Fig3(a)).
The coarsening of precipitation phases at grain boundary could pin the grain boundary, and prevent it from fast migration, so both the newly formed recrystallized grain and old grain would not grow very fast.
That is why the grain size decreased with increasing temperature at 750k.
Acknowledgement It is a project supported by natural science foundation of shanxi province China (project number: 2009011028-1; 2011011021-1).

It is noteworthy that the number density of the dispersoids significantly increases with strain.
Figs. 2(a) through (d) represent transmission electron micrographs showing the evolution of recrystallized grain structure during SPD.
During the early stages of SPD, large, highly misoriented subgrains developed by local migration of boundaries [marked by arrows in Fig. 2(a)] and merger of suitably oriented subgrains leading to recrystallized grains [one such grain is labeled at the centre of Fig.2(b)].
Such processes, however, became increasingly restricted because of the formation of an increasing number density of dispersoids with strain.
With increasing strain, both the number density of the dispersoids and the percentage recrystallization increased.

The model of abrasive grain’s wear.
Abrasive grains move at a constant speed.
Fig.3 The relationship between grinding force and surface roughness The reduction of surface roughness is directly related to the number of active grains Ng and the shape of the grains.
Under these conditions, abrasive grains are worn quickly or can be extracted from the bonding phase which may decrease the number of real active grains Ng.
New grains are involved in grinding.