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Therefore the grain orientation spread is not independent on the grain size.
The minimal number of points, which are required to decide whether a given group of points should be considered as "grain" (the Minimum Grain Size), can be specified by the user along with the Grain Tolerance Angle.
Fig. 3 shows the grain misorientation and the grain orientation spread as a function of creep time.
This is the stage of the process when the strains within the grains have the maximum value, as the grain orientation spread and the grain average misorientation values show it.
In this period the average subgrain size is the smallest, i.e. there is the maximum number of small angle boundaries, therefore the strength of the material is the highest.

There are number of twins found in 870-Q Fig. 8-(c).
Grains annex and grow up.
Grain boundaries get thin and straight.
The TEM results show there are a great number of needle-like twins.
Temper at this moment, the ductility and corrosion resistance of alloy increase due to β-Zr which precipitates along the grain boundaries. 7 Quench at a higher temperature above Tcq, the microstructure gets fine and a large number of twins form.

Introduction The grinding process is composed of the instant and high-speed motion, which is done by a large number of tiny abrasive grain edges, and the process has the character of complexity, randomicity and unemersion.
When the abrasive grain size is definite, the grain radius is within a certain range.
A specific grain radius is in the following range: )fk(1dd did 0i += (1) Where di is the radius of grain i(mm); d0 is the average radius of a certain grain size (mm); kd is the change coefficient of the grain radius and fdi is a random number equably distributed in [-0.5, 0.5] engendered by the computer.
Supposing that the grain is a rough geometry object which approximates a sphere, the grain contour line height in the section which is the cross-sphere center and vertical to the grain movement direction [4] is given by： ( ) (x)]fk(x)f[kd)x(x/2)(dzxz rir sisi 2 i 2 i i + +−−+= (2) where xi, zi are the grain sphere center position coordinates (mm); ks, kr are the grain geometric shape coefficient and grain roughness coefficient, respectively and fsi(x), fri(x) are the grain geometric shape function and grain roughness function, respectively, their value being different on the each point of contour line, and a random number equably distributed in [-0.5, 0.5].
The surface roughness has relationship with the grain number of the identity area, the grain distribution, the cutting trail and so on.

The grain sizes were determined using a lineal intercept method average over 200 grains.
The length of the dendrites is defined as half the grain size that it means as grain radius.
The result determined by the growth rate V and the nucleation number.
Fig. 9 Effect of grain size on coherency point: (a) big grain with low fraction of solid at coherency and (b) small grain with high fraction of solid at coherency.
Dendrite coherency depends on the dendrite growth rate, dendrite morphology and the number of the nucleation.

Crystallite and grain sizes are obtained through XRD and SEM.
By increasing the number of coating cycles grain coarsening takes place and the grain size increases from 54nm for 3 coating cycles to 92 nm for 10 coating cycles, which is in agreement with the crystallite size calculated from XRD analysis.
Fig 2 shows the mass percent and the visual grain size of films as a function of the number of coating cycles.
As Grain size increases with the thickness which results in lower resistivity due to higher number of carrier concentration present.
Crystallite size and grain size determined by XRD and SEM.

On a macro-level, the model material can be considered as aggregate grains dispersed in a cement matrix.
In contrast, a finer aggregate system contains larger number of small grains, which subdivide the open space into smaller and less accessible spaces [12].
Gap grading activates the mechanism of 'migration capacity' of fine sand particles into the network structure of coarse aggregate grains; or, analogously, of the fine particles of the mineral admixture into the network structure of the coarser grained Portland cement.
Fig. 2 reveals clearly the effects of the PSD of coarse aggregate grains on the migration capacity of the fine sand particles.
It should be noted that computing time restrictions impose significant limitations to the number as well as the size range of coarse aggregate grains in the simulation study (due to the significantly larger number of fine sand particles that have to be generated in proportion to the mass of coarse aggregate).

Boron-doped diamond (BDD) films were grown with different grain sizes.
The constant interruption of the crystal evolution means there is a fundamental limit on the maximum grain size, and thus thick films can be grown with a small distribution of grain sizes [18,19].
The acceptor number can be calculated from the slope of the linear region of the Mott-Schottky plots (MSP) analysis [20,21] and the results of acceptor concentrations are presented in Table 1.
All films were grown with similar boron doping (30,000 ppm), thus, the grain size changed from micro to nanocrystalline further an increase in the number of diamond grains and consequently increases the doping.
This increased presence of boron in the grain boundary is not measured by MSP and thus decreasing the number of carriers for the films with 80 and 85% argon [20].

The grains of thixoextruded tube were homogeneously distributed and equiaxed grains were observed.
Material in the container flows through the porthole with multi-hole, and this material is divided through the number of portholes and is gathered and welded by high pressure in the welding chamber.
The grains of thixoextruded tube were homogeneously distributed and equiaxed grains were observed.
As shown in Fig. 3, the equiaxed grain structures were observed at the each position.
The grains of thixoextruded tube were homogeneously distributed and equiaxed grains were observed.

The goal is to generate finer grain size through recrystallization process leading to nucleation of new grain during the thermal cycling process thus increasing their strength.
The cold rolling at 52% of thickness reduction reveals angular grain of medium sphericity not the elongated grain such as mostly detected in cold rolling of steel in Fig 3b.
By limiting the exposure time to 35 seconds, there were not enough energy available to allow grain growth thus keeping the grains in finer size.
The number of cycles was meant to allow the nucleation of the new grain in each cycle process until all the deformed grain was fully converted.
Fig. 6 shows the comparison of calculated grain size of thermally cycled samples at different temperatures exposures with investment casting and cold-rolled samples grain size.

Macroscopic work hardening description needs to account the hardening process at the grains scale.
This model allows each grain to deform differently, depending on the strength of the interaction between the grain and its surroundings.
Analyzing the τ-γ behavior for individual orientations, Cases I and II show interesting differences: − The number of deformation systems activated in case I is lower than in case II.
− Performing statistics on the ensemble of grains, the greater deformation systems activity reported for the case II is also evidenced by the evolution of the mean value of this activity in grains.
Fig. 2: Evolution of the average number of active deformation systems with deformation.