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La2O3 doping promotes crystal grain growth, CeO2 doping makes grain crystal size uniform, changes tetragonal into granular structure and restrains crystal grain growth.
The doping of La2O3 can promote grain growth.
Compared to samples doped with 0.5 wt.% CeO2, the number of large size grains reduced, the size of grain tends to mean in samples when without CeO2 doping.
From the view of grain shape, the number of square shaped grain decreased, while granular grain increased, therefore the growth of grain was restricted when CeO2 doped.
The growth of the grain is promoted when La2O3 doped; the crystal grain size tends to average and the view of grain turns to granular from square shaped when CeO2 doped.

Because the initial inelastic scattering generates electrons with a continuous range of directions, a number of planes fulfill the Bragg condition.
The orientation and grain size of each grain were determined by EBSD measuring system.
The grain size was defined by a diameter of the circle that has the same area of a particular grain.
EBSD pattern was generally measured at the center part of grains.
All SEBSD are evaluated at the center of grains.

It could absorb crack propagation along grain boundary.
And it played fine grain role on this ceramic.
Increased crack propagation path, grain refinement and more grain boundary of AlON were all caused by SiC pined on AlON grain boundary.
The sample grain was smaller with more SiC added.
Acknowledgements This work was supported by the National Nature Science Foundation of China (grant number 50672060) and the Shenyang Science Fund (grant number 1081237-1-00).

Metals of nano-grain sizes deform by grains sliding pass each other, with little distortion occurring in the grain cores.
Accommodation mechanisms such as grain boundary diffusion, grain sliding and grain rotation control the kinetics of the process.
Nano-grain metals of such small grain sizes deform mainly by neighboring grains sliding pass each other with insignificant distortion in the grain shape.
There are about 3N number pairs ( α αα Xx −= td/d α α θ= α θ td/d α α x= ω ),βα belonging to this set.
The cell contains 9 regular hexagon grains and is termed the 9-grain cluster model.

Little coarsening of grains were observed below 1060℃ during annealing treatment, whereas grains coarsened obviously over 1080℃.
Nomenclature ultimate grain size (μm); recrystallized grain size, or initial grain size before annealing (μm); annealing holding time (s); annealing temperature (K)； grain growth activation energy (J/mol)； , , and are constants.
For instance, the increase in the number of dislocations is a quantification of work hardening; yield strength is increased in a cold-worked 690 alloy.
Sellars includes the effect of initial grain size.
Initial grain size,, is defined by the average value that grains grow to for 3mins exposure.

A large number of voids are observed close to internal and external surface, Fig. 1 b.
Grain I is characterized by high density of microtwins with the average distance between them of ~ 0.8 μm and a vast number of related large voids.
In grain II without profound mesostructural elements the number of voids is close to the value fixed in grain I, but their average size was significantly smaller, Table 1.
In grain III high density of low-angle grains (misorientations) is observed, thus leading to the absence of a single grain orientation, i.e. to grain fragmentation.
Quantitative characteristics of radiation porosity in three adjacent grains in the region close to the internal cladding surface Region Grain I Grain II Grain III Number of voids, pcs 1247 1022 218 Maximum void size, nm 340 100 116 Average void size, nm 55 44 46 Calculated swelling value, % 2.9 1.0 0.3 Thus the connection between radiation porosity and local material structure was revealed.

These define limits for grain size and shape, grain boundary location and the misorientation between grains RD, Reference Direction RP, Reference Plane Figure 1.
Main grain (primary) orientation.
Grain boundary misorientation R-values.
The R-value, a number in units of angle (°), is used to assess grain ‘misorientation’ or, more correctly, ‘disorientation’, as it is the minimum angular displacement between adjacent grains.
If grains on either side of a boundary are designated A and B, the R-value represents a summary of the rotations required to align grain A with grain B.

Finite element modelling can be used to enable the manufacturing of complex-shaped parts economically as the number of experimental trials can be reduced.
The finite element calculations take into account also grain size evolution.
This included two aspects as follows: Grain Growth.
(1) The static grain growth ̇dstatic in Eq. 2 captures the grain growth by atomic diffusion due to the high temperatures in the absence of deformation conditions.
Fig. 1 also shows that the grain size values of Ti64 alloy are higher than those of Ti54M alloy as the rate of grain growth of Ti64 alloy was higher than that of Ti54M alloy and the initial grain size of Ti64 alloy was greater than that of Ti54M alloy.

The grain size number was determined from the microphotograph taken at 100X magnification and analysis using the comparison method as per ASTM E112-10.
The grain size corresponds to ASTM grain size No; as per ASTM E-112.
The grains of pearlite show no elongated grains.
The grain size corresponds to ASTM grain size No; as per ASTM E-112.
The grains of pearlite show no elongated grain.

The number of biomedical applications of hydroxyapatite (HA) ceramics can be increased if the bioactivity is improved.
The number density of dislocations was observed to be low (0-8 per grain) in both materials.
d(31-4-1)=2.147 Å Continuous grain boundary 2 nm d(30-30) = 2.147 Å Fig. 5: HRTEM image showing a continuous grain boundary in 0.4wt%Si-HA.
This study was founded on the assumption that the incorporation of silicon into phase pure HA would increase the number of dislocations in this material.
In particular there appeared to be a higher number of triple-junctions in the Si-HA samples.