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Detecting an inadequate number of diffracting grains also contributes to the random uncertainty and this is rarely considered.
Estimating the number of detected diffracting grains NDG.
However measuring 5 times has increased the effective number of grains detected on the detector.
The next section is concerned with deriving actual number of grains needed to reduce the value of u(2θgrain).
The number of grains however depends on the gauge volume size chosen and the average size of the grains (and hence diffracting grains) within the gauge volume and this should be taken into account.

Introduction China is a major grain producer as well as a major grain consumer.
As an industry engaged in grain purchasing and storage, the operation in grain depot has its timeliness and periodicity.
Moreover, the forecasting of the grain depot’s electric power guarantees the safety of our state’s grain, which is macro-controlled by the state itself.
Is the number of hidden layer node present, and stands for threshold value.
If we want to increase the accuracy and improve the efficiency, we could integrate a number of other environmental factors in the power prediction, which is also our objective of the study in the future.

To clarify this notion, the grain’s shape is characterized using the fractal dimension (Df), which is a number measuring the degree of irregularity or the fragmentation of a grain.
These numbers constituted the size of the object.
The method is based on a theory that the number of grains smaller than the predetermined size can be made exponentially: NX>x=KxDf (4) Such that x is a predetermined particle size; X is the linear dimension of the grains bigger than x’s dimension, N is the number of grains (fragments), K is a proportionality constant; and Df is the fractal dimension of fragmentation [5, 6].
In dealing with a graph showing the size of the boxes representing the grain’s fragment size according to the number of the boxes (number of grain fragment), the fractal dimension is obtained by the slope given by the equation (Df =-m).
The differences are quite close to the grain of 5 mm and 4 mm as they are important for grains of 3.14 mm.

Each element of simulation box is a number zi called spin or orientation which value lies between 1 and Q.
Q represents the number of possible crystallographic orientations of a grain (in this simulation Q=4).
Two adjacent numbers whith different spins constitute the grain boundary.
Moreover the number of spins has to be considered.
Thus we used a 5 mm grain diameter.

The influence of the number of roughing passes on the grain size and volume fraction of induced ferrite was determined.
It was observed that a higher number of roughing pass decreases the grain size and the critical strains for dynamic transformation.
A decrease in grain size was observed when the the number of passes (or accumulated strain) is increased.
The dependence of prior-austenite grain size on the number of passes and the amount of ferrite formed and retained on the number of passes and cumulative strain (at 1100 °C).
The DRX grain size decreases with the amount of strain and/or number of roughing passes.

Magnesiums have only three separate slip systems at room temperature and poor ductility, therefore,a large number of practical applications are cast magnesium alloys.But wrought magnesium alloys have better strength, toughness and processability than cast magnesium alloys.
After rolling the sheet D through the same process, only a small part of the twinning existed in the individual grains and a large number of fine grains could be found in the initial grain structure surrounding.
Near the grain boundary a number of recrystallized grains appear and there is almost no twinning happening.
Such grains are likely to the bow of the grain boundary nucleation or subgrain rotation nucleation.
It can be seen in Fig. 2d that a large number of new fine recrystallized grains tend to accumulate and round the coarse initial grain boundary, which have different orientation distribution and formate large deformation zones or ductile shear zones.This dynamic recrystallization mechanism is the typicaliy rotating dynamic recrystallization.

The a-N curve showed that crack length list is MG>LG >SG under a same cycle number.
In terms of SG alloy, grains with a size smaller than 20μm possess the majority and only a small number of grains exceed the upper size.
The FCP curves (crack length versus cycle numbers, a-N) of the alloys are shown in Fig. 6(a).
On the meantime, the curves have clear disparity of cycle numbers at same crack lengths due to different grain sizes.
Apparently, to reach a same crack length, SG alloy needs larger cycle numbers.

GRAIN REFINEMENT OF PURE COPPER BY ECAP N.
Heavy deformation was introduced in the samples after a considerable number of ECAP passes, namely 1, 4, 8, 12 and 16.
In the ECAP process, samples with cross section of a square or circular shape can be deformed without undergoing significant changes in the dimensions, enabling significant deformations through an unlimited number of passes within a die.
Theses increments are in accordance with the grain size.
Grain size for the ECAP sample.

Furthermore, it was found that Δρ of grains unrelated to crack initiation increased continuously with the number of cycles, whereas that around the crack initiation site decreased with crack initiation.
In both materials, the number of grains with small β (shown in blue) decreases and the number of grains with large β (shown in red) increases as the number of cycles increases, except (j), indicating that the number of grains reconstructed immediately before fracture is significantly reduced.
In the homogeneous and harmonic materials, the filling ratio decreased with increasing number of cycles, reaching about 25% immediately before fracture.
The intensity of diffraction spots decreased and eventually disappeared as misorientation increased, which was found to be the cause of the decrease in the number of reconstructable grains and the decrease in filling ratio with increasing number of cycles.
Δρ in the homogeneous material shown in (a) is almost constant after 1.00×103 cycles for grains larger than 20 μm, whereas it increases with the number of cycles for grains smaller than 20 μm.

Current issues concerning the characterization of grain boundary networks via five-dimensional (5D) grain boundary distributions are considered.
It is clear that the number of boundary data needed for evaluating the distribution depends on the number of distinct boundary types (number of bins), the acceptable error level and the distribution itself.
With ng denoting the number of grains, the corresponding number of complete boundaries is roughly 13ng/2.
Approximate number of grains (ng»2N/13) which need to be investigated to reach the given error level D for c=1 and f0=1 versus the number of equi-volume bins (1/v).
The integration can be done in a number of ways.