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The calculated results compare well with the limited number of experimental observations and theoretical conclusions.
Firstly, the initial microstructure with prescribed grain size and equiaxed grain structure was generated.
The mean radius of primary grain,, is defined as (1) where is the distance between two neighbouring cell, is the number of CA cells andis the number of primary grains.
Initial grain sizes affect the kinetics of DRX because of the change of grain boundary surface fractions for the nucleation of new grains.
In contrast, Initial grain sizes have no effect on the stable grain sizes.

The number of twin crystals, of which two c-axes are perpendicular to the twin plane, increased and the number of twin crystals, of which c-axes are parallel to the twin plane, decreased with increasing amount of Sb2O3 doped.
Average grain size was estimated from the average area calculated for approximately 160 grains.
The twin crystals of ZnO were formed by doping with Sb2O3 shown in Figure 1 and the ratio of the number of twins to that of ZnO grains was approximately 60~70%.
The number of twin crystals of which the two c-axes are intersecting is very large.
Relationship between values of α before/α 30min after and ratio of number N1 of twin crystals to what, of which two c-axes are parallel to twin plane.

Early in sintering this is approximated as follows: ΔEG= c NC γSSρ G XG2 (2) where X is the neck diameter, G is the grain size, NC is the coordination number or number of bonds per grain, ρ is the theoretical density of the material, and c equals 0.75.
There are slight variations in the coefficient with different grain shapes and coordination numbers, but 1.6 is a representative average.
Depending on the grain coordination number and dihedral angle, the relative solid-vapor surface area is a function of the fractional density.
As the grain coordination number increases during sintering, the grain shape and pore character follow a standard trajectory.
Prior efforts to capture grain boundary area trajectories during sintering assumed constant coordination number and 60° dihedral angle [46].

The number of ultrafine grains increased with straining, leading to development of submicrocrystalline structure.
The number of high-angle boundaries increases by subsequent deformation.
The numbers in schematic drawings indicate the boundary misorientations in degrees.
At small to moderate strains of about 2, the new grains evolve by means of gradual increase of number and misorientation of deformation subboundaries.
Upon further straining the number of ultrafine grains increases; the layers composed of the ultrafine grains spread out towards the central portions of original grains.

Results show that alloying elements Nb and Al have a strong pining effect on the grain boundaries, Al/N ratio between 2.0-2.5 can promote the grain not to grow up for a long time, and refine grains significantly with furnace heating and after carburizing-quenching once, and can inhibit the abnormal growth of individual grains.
Table3 The level of grain size and the maximum grain size Heat number Code name Grain size/level Maximum grain/level Maximum grain size/ German material A1 B1 A2 B2 A3 B3 7 6 7.5 7 8 8 4 4 7 2 8 8 16 15 8 23 4 5 22180 A1 B1 A2 B2 A3 B3 8 8 8 7.5 9 8 6 5.5 7 7 9 8 9 10 8 8 3 5 13141 A1 B1 A2 B2 A3 B3 6 7 6 7 8 8 4 1 5 1 8 7 15 35 11 30 6 7 10105 A1 B1 A2 B2 A3 B3 8 7 7 7 8.5 8.5 5 6 4 6 8 8 13 9 17 9 4 4 Fig.1 The relationship between the overall grain size and the methods of heating and cooling Fig.2 The relationship between the maximum grain and the methods of heating and cooling Fig.3 The relationship between the maximum grain size and the methods of heating and cooling From Fig.1 to Fig.3 we know that the overall grain size in heat number 22180 is the best, and maximum grain size is the smallest.
The overall grain size in heat number 13141 is coarser than others’, individual grain grows seriously and austenite grain size is inconsistent(coarse grain is bigger 5-6 times than small ones).
The coarse grains will tend to eat up small grains and coarser at a high coarsening rate[5], the maximum grain is 3.5.
The level of grain size of German and heat number 10105 material is also good, but individual grain growth phenomenon happened, the reasons may be German material without Nb and lack of grain refining elements, and Al/N ration in both material is higher or lower.

Citation & Copyright (to be inserted by the publisher ) Grain surface relaxation and grain interaction in powder diffraction M.
Keywords: XRD, Grain interaction, Grain surface relaxation, Nanocrystals, Residual stress.
A possible residual stress/strain state for a PVD thin film is shown in (c). �� �� �� �� �� Journal Title and Volume Number (to be inserted by the publisher) 3 Figure 2.
Journal Title and Volume Number (to be inserted by the publisher) 5 Figure 4.
Journal Title and Volume Number (to be inserted by the publisher) 7 quantity and quality of information extracted from a single diffraction pattern.

Introduction The geometry of grain boundaries is described both by the crystallographic misorientation between the neighbouring grains and the crystallographic orientation of the grain boundary plane, i.e. the grain boundary texture, with respect to both grains.
Results and Discussion The proportion of Σ3, Σ9 and Σ27 boundaries, as a fraction of total number of grain boundaries, is recorded on figure 1.
The increase in Σ9 numbers is directly attributed to the joining of two Σ3s according to Σ3+Σ3→Σ9.
Following MSGBE, the peak MRD value recovered to 914, accompanied by an increase in Σ3 number fraction to 44%.
Proportions of Σ3n boundaries for the AR, single-step (SSGBE) and multi-step (MSGBE) specimens as fractions of total grain boundary numbers.

Both an increase in the number of low angle boundaries, and an increase in the number of low-index planes in boundaries was reported.
For numerical efficiency in grain growth simulations, which are effectively coarse domain structures, the number of field variables evaluated at any given point is restricted to the locally active set [30].
Plot of number of grains in the simulation (right axis) and the voxel difference signal (left axis) between the simulated microstructures and the measured microstructure [39].
The dotted horizontal line indicates the number of grains, 340, present in the measured microstructure.
The earlier time, (a), shows a large number of grains, whereas the later time, (b), shows that some large grains have grown into the measured volume that were not initially present; one such invading grain is labeled "I".

Figure 1 shows the variation of grain size of different mc-Si ingots. [1-3] Since the grain boundaries (GBs) may act as the carrier recombination centers, the mc-Si ingots with large grains have been regarded as superior to those with small grains.
After h > 8mm, the number fractions have not changed so much.
Number fraction of GB characters with growth height.
Number fraction of GB annihilation according to the GB character.
Number fraction of GB genrtation according to the GB character.

Grain Boundary Structure and Boundary Migration Behaviour For a rough grain boundary, there are an unlimited number of sites on the two grain surfaces at which atoms can attach or detach.
Grain boundary migration takes place by diffusion across the grain boundary.
If the grain boundary is faceted, then the number of sites at which atoms can attach to the surface of the growing grain are limited.
If DGC « DGmax, then a large number of grains have DG > DGC, many grains can grow and pseudo-normal grain growth results.
A small number of grains will have DG > DGC; these grains will grow rapidly to form abnormal grains.