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Grain boundaries which separate such grains are the CSL-boundaries.
Grain tolerance angle was 5°, minimum grain size was 5 points.
A home made software was developed to count the number of good and undesired junctions.
IQ means the "goodness" of the Kikuchi-images formed during EBSDmeasurement, and is given by a number.
The better the Kikuchi image, the higher this number will be.

The influence of the grain size distribution on the grain growth process has been studied.
The growth of a single grain in a system of grains was postulated by Hillert in 1965, [1].
Simultaneous GBM and GRC, a linear combination of both case 1 and case 2, may be given as )(),,(),( 2211 tdNtrGadttrfadr θ+ = (1) where the aiis are the "compensation coefficients" that indicate the proportion in which the two growth mechanisms combine, f(r,t)=f(r,θ,t) is a curvature driven mechanism, ),,( trG θ grain misorientation angle driven mechanism and dN(t) is the increment of the number coalescence mechanisms during an infinitesimal time interval.
Considering the fact many other mechanisms bring about the variations in the size of the grain, the grain size in the system at any time, t, is independent of the number of coalescence mechanisms (stochastic counting processes) up to that time instant.
The number of coalescence between the a grain and its neighbour is given 1 1 12)( i i i ii i tN θ θΔ θ θθ = − = (6) where 1iθ is the misorientation angle at the initial time, t=0, and 2iθ is the misorientation angle after time, t.

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.

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.

This method is useful, because previously it was difficult to identify a limited number of very small grains which existed in a huge number of matrix grains and grew to enormous grains.
Therefore, in case that there are a huge number of very small grains, the calculation accuracy is not necessarily adequate.
However, because the grain boundaries are approximated by not curve lines but polygonal lines, the small number of vertices on the grain boundaries makes errors.
The shrinking velocity by the proposed model is the same as that by the curvature model when the number of virtual vertices is equal to or more than three.
We consider grain boundary energy and mobility depending on grain misorientation.

With increase in number of passes, the grain size is reduced to 13 μm in the third pass (Fig. 1(f)).
After subjecting the billet to six number of passes, the elongated strips of grains are arranged into a distinct lamellar structure (Fig. 1(g)).
The trend reversed again for the higher number of passes.
In case of nine and ten pass samples the number fraction of LABs reduces further and stabilizes at 15%.
In as-cast material between two high angle (>15°) boundaries of a grain, a number of low angle (<15°) boundaries exist and point-to-point misorientation angle of these boundaries are in the range of 5-10o.

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.

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].

However, depending on the diffusion time and grain size a given tracer atom can be expected to cross a number of grain boundaries in its diffusion time.
It is clear that a tracer atom need not sample a large number of grains and grain boundaries in order for its effective diffusivity in the structure to be fully developed.
In a diffusion experiment in a polycrystalline material, it can be expected that tracer atoms will traverse a number of grains in the diffusion time.
To simulate a thin-film (instantaneous) tracer source, 10 6 particles are created and released from the surface and allowed to diffuse for a time t (proportional to the number of jump attempts per particle).
These concentration profiles are built up simply by determining the number of particles that have reached a given distance from the tracer source plane after a diffusion time t [10].

The high number of total lattice points with 250250250 ×× MCUs keeps the number of grains adequately for statistical analysis.
Figure 2: Temporal development of the: a - number of grains vs. grain radius and b - relative number of grains vs. relative grain size.
Fig.3b) so that the number of still existing grains during coarsening is always large enough for statistical data analysis.
Figure 5: a - Number of neighbouring grains vs. relative grain size; b - Volumetric rate of change vs. number of neighbouring grains divided into classes after 500 time steps (the three grey crosses are data that are ignored because the associated grains disappear during the considered time steps).
Acknowledgments The authors would like to thank the Deutsche Forschungsgemeinschaft for financial support under grand number GKMM 828.