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The preferred ratio is defined as the number of cells in the preferred direction to the number of cells in the other (in two dimensions the preferred ratio is 2).
For each cell, a randomly allocated orientation number, q, was assigned to each grain.
The orientation number indicates primarily the orientation of a cell and maximum number of q was 936, which represents 936 texture components, which were equally distributed in orientation space.
The misorientation is obtained from the q numbers of the neighbouring grain where ∆q is the difference between orientation numbers of two adjacent grains and 10 < ∆ ≤ q q (12) In the present study, an adjustment of the nucleation criterion used in Raabe's study [28] was adopted.
The recrystallised grain grows continually until it impacts on the other growing grains.

The results indicated that Al microparticles slowly dissolved into nickel grain to form an ultrafine-grained Ni3Al/NiAl composite with micro-sized pores dispersion due to volume shrinkage.
After 3h annealing, both the number and size of black Al microparticles significantly decreased, but gray areas with micro-sized voids dispersion around Al microparticles appeared, as seen in Fig.2c.
From Fig.2d, it can be found that the grain size increased to the averaged ~220 nm.
Thus, the number of alumina nuclei formed on the A-EMC Ni-Al increased with the increasing of annealing times.
In another word, the number and size of voids gradually decreased with the increasing of annealing time, as seen in Fig.2.

At a low value of Z abnormally large grains formed during annealing.
Although a number of studies have been undertaken on the static recrystallization of cold rolled interstitial free steel [e.g. 2-5], there is only minor reference in the literature to the recrystallization behaviour following warm working.
The average linear intercept ferrite grain size thus achieved was 25µm [10].
After 30 s a few new strain free grains can be observed.
In Figure 4c a number of the large apparently recrystallized grains contain, in their interior, a few low angle boundaries.

However, the elongation under shear manifested a reduction when the number of ARB passes increased.
A reduction in individual layer thickness was detected with increasing the number of ARB passes.
Furthermore, the number of layers and interface lines are related to the number of cycles and can be calculated with the relationships of 2n and 2n–1 , respectively [14,15].
Notwithstanding that the microstructural evolution in 2024 indicates elongated grains with high aspect ratio, Creation of fine structures was not detected for 6061 with an average grain size of 5 microns.
Both reasons contribute to achieving finer grain size in Al 2024 [16,17].

The Schulz back reflection method is used to measure three incomplete pole figures numbered {111}, {200} and {220}.
Figure 3 indicate that the shape of the recrystallized grains is irregular.
With increase the holding time, the grains grows up gradually.
In the initial stage of the annealing, the grains have a faster growth rate while there are no significant changes in the grain size with the time passing.
Therefore, the sample display a weaker recrysatlllization texture and finer recrystallized grains.

The loading chips are mechanically removed with abrasive grains and bonding materials from the wheel surface by dressing, and abrasive grains under the previous wheel surface show up.
They are increase with increasing the number of treatment � till the four or five times.
Even if just once wheel treatment is carried out, the abrasive grains can project about one third of grain size.
The number of grinding, in which grinding current is higher than the steady current, increases with increasing the number of treatment �.
The surface roughness decreases with increasing the number of wheel treatment at steady grinding process.

Effect of grain statistics In a simple situation we could assume that the orientation of different grains are stochastically independent and thus cor(X(gi), X(gj)) = 0 for gi and gj measured on different grains, while the orientation within the grain is approximately constant and thus cor(X(gi), X(gj)) ≈ 1 for gi, gj measured on the same grain.
Consequently for N grains with mk, k = 1, . . . , N measurements on grain number k we get n = NX k=1 mk4 andccor = 1 n nX i=1 nX j=1 cor(X(gi), X(gj)) = 1 n NX k=1 m2k = 1 m PN k=1 m2k 1 m PN k=1 mk = m2 ¯m = ¯m + (mk − ¯m)2 ¯m where ¯m denotes the arithmetic mean of mk.
Thus with equisized grains the statistical error behaves like having one measurement on each grain.
• Misorientation across grain boundaries, called grain misorientation in the following
Depending on grain size, number of actual measurements, calculated quantity and band width of the kernel estimator the precision can vary several orders of magnitude.

This process, grain growth, requires short-range transfer of atoms across the grain boundary.
(2) Here Nα and Nβ are the number of crystallographic orientations in the α- and β phase respectively, and the dependence of ϕα and ϕβ on space and time is suppressed as shorthand.
Four were with 500 α- and 500 β grains, and one was with 150 α and 150 β grains.
The white arrow on figure 3 points to an α grain surrounded by β grains.
The α grain pins the grain boundaries it contacts, while it diffuses through its neighbors.

It has been shown that grain refinement and grain growth occurred simultaneously during the MAC process.
Fig. 3b shows that the fine grains are surrounded by coarse grains with the size of about 20~40 μm.
Hence, the grain size variation during MAC is determined by two factors: grain refinement and grain growth.
When the grain refinement and grain growth reach a balance, the average grain size remains a steady state.
Ai et al. [23] have proved that a large number of the contraction twins emerge and lead to an increased strain-hardening rate after the extension twins completely consume the matrix.

The grain size of the sulfides is generally 0.01-0.03 mm.
In the overwhelming number of cases, bornite, as set Shneyderhёn [2] has a variable, but generally weak anisotropy.
Covellite is grain size of 0.005 to 0.03 mm, small clusters of up to 0.05 mm (Fig. 7).
The grain size of the sulfides is mainly 0.01-0.03 mm.
All sulphides are located within the host rock grains.