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When changing a position of the sample, different numbers of grains with the same orientation prove to be in the reflecting position, so that the measured intensity of Xray reflection shows significant fluctuations.
ΔA y1 y2 y2 y1 Ω  φ θ A0 number of grains n at the irradiated surface ΔA, whereas the value of intensity I, averaged by all positions of the sample, is proportional to the mean number of grains n, giving an input into the obtained reflection:   sin 0 c zzi a A nI (1)         sin4 4 0 c z zz a AJ nJ nI , where z - the coefficient, taking into account absorption of X-rays depending on the depth of their penetration z; J - the multiplicity factor of the given reflection; Ω =  - the solid angle, depending on the geometry of X-ray measurement and containing normals to planes, giving input into intensity of the diffraction line [2-3]; А0 - the cross-section area of the initial beam; ca - the area of one grain at the surface of sample.
For different positions and orientations of sample the number of grains n within the area ΔA oscillates near the main value n.
As a result of each rotation new grains prove in the reflecting position, so that changes in their orientation and their number result in fluctuations of the registered intensity.
Hence the PF section {111} with  = 55-60° characterizes grains of component <100>, and PF section {200} with  = 55-60° grains of component <111>.

Atomic Mechanisms of Grain Boundary Motion A.
asuzuki@gmu.edu, ymishin@gmu.edu Keywords: grain boundary migration; grain boundary dislocations; molecular dynamics simulation Abstract.
Introduction Grain boundary (GB) migration in materials plays an important role in many processes such as grain growth and recrystallization.
(b) Displacements of the grains and of the GB plane as functions of time. relative velocity of the grains parallel to the GB plane.
Suppose the GB moves up by a distance L, so that the lower grain 1 grows at the expense of the upper grain 2.

This result is more consistent with the occurrence of a transient stage of abnormal grain growth than with a grain-size-dependent change in the rate-limiting mechanism for grain-boundary migration.
Introduction Unlike in coarse-grained polycrystalline materials, which manifest grain-boundary-controlled—i.e. parabolic—growth kinetics, nanocrystalline specimens are presumed to exhibit a coarsening behavior that is affected by their high number density of triple junctions and quadruple points [1].
If the kinetics of grain growth undergo a transition as a function of grain size, then this ought to be reflected in a qualitative change in the shape of isothermal grain growth curves.
the constant of proportionality depending on the average grain shape.
For example, in a sample consisting of spherical grains, area = (2/3)area and vol = (3/4)vol, where D denotes grain diameter [3].

The mechanism of grain boundary diffusion of Co in Mo and temperature dependences of segregation factor and grain boundary diffusivity have been determined.
At the same time a number of experimental studies by the emission Mössbauer spectroscopy showed that their results cannot be interpreted in the framework of this model [4-6].
Numbers 1 and 2 indicate spectrum components The temperature below which the volume diffusion is suppressed can be estimated based on temperature dependence of volume diffusivity.
We made such estimation based on the grain-boundary diffusion studies of Co in W and obtained quite reasonable value of grain-boundary diffusion width [13-14].
In particular, one can quite accurately determine all parameters of grain-boundary diffusion, such as the grain boundary diffusivity, segregation factor, grain boundary diffusion width, and make certain conclusions on possible mechanism of grain boundary diffusion.

It was found that grain refinement decreased the grain size and made the grain morphology more globular.
Both of these affect the grain size and grain morphology.
It has been observed that grain size is reduced by increasing the growth restriction factor, Q, the nucleant potency, which is the inverse of the nucleation undercooling ΔTn, the number of nucleant particles and the cooling rate [7].
This leads to the grain morphology changing from large dendritic equiaxed (or columnar) grains, to grains which are cellular with the grains showing obvious dendrite arms but not extensive dendrite networks.
As well as reducing the grain size, grain refinement makes the grain morphology more globular.

Beijing Aeronautical Manufacturing Technology Research Institute and Central South University have carried out large numbers of investigations against the preparation of superplastic fine-grained sheets and the superplasticity of fine-grained 1420 Al-Li alloy together.
But the grain size has been grown slightly compared to as-received material.
A large number of dislocations were existed in deformed material and these dislocations came from the second phase and grain boundary especially triple point (Fig.7).
Dislocation would glide and climb near grain boundary during deformation, which contributed to grain boundary slipping.
(a) δ′ phase in grain (b) δ′ phase in grain boundary Fig.6 The second-phase of fine-grained 1420 after superplastic deformation (a) Dislocation near grain boundary (b) Dislocation around the second phase Fig.7 Dislocation morphology after superplastic deformation Conclusions Fine-grained 1420 Al-Li alloy which prepared by two-stage aging and turning rolling process exhibited good superplasticity.

The grain boundary slipping is understood as the displacement of one grain relatively the other grain over the whole surface of the boundary.
The shear is developed in one grain, reaches the boundary, and causes the slipping in the other grain.
The paper [3] shows that a grain boundary slipping is realized due to the movement of grain boundary dislocations.
G1 and G2 - grains, CC - calculation cell, GB - grain boundary, θ r - vector of grain disorientations, n r - unit vector of a GB normal.
The number of atoms in three-dimensional calculated blocks ranged from 20000 to 50000.

Introduction The importance of understanding three-dimensional (3D) grain growth for controlling materials properties is well-recognized, and a large number of experimental and theoretical studies have investigated fundamental microstructural mechanisms associated with thermal processing.
Since the incident beam irradiates a large number of grains with different orientations as it penetrates the sample, many Laue patterns are superimposed in a single raw image (e.g.
During the data analysis, distinctive reconstructed Laue images containing rows of a large number of sharp Bragg peaks were observed at a few isolated locations superimposed on the fcc Al patterns.
The initial hot-rolled microstructure consists of many grains ~5-10 µm in size, and a large number of low-angle boundaries are observed in this (001)-textured sample.
After annealing at 355ºC, many small grains have been consumed, and only a few of the original grains are unchanged.

The substructure of a single grain in an electron backscatter diffraction (EBSD) data map is studied, focusing on the influence of the grain boundary configuration on the misorientation to the average grain orientation of data points close to the grain boundary.
These orientation variations were attributed to grain-grain interactions.
and a small number of misorientation boundaries (low mean θptp) or to fragment boundaries having higher misorientations (high mean θptp).
Depending on the orientation of the boundary plane (which can not be characterised by 2D EBSD measurements of plane sections) and the misorientation axis between the crystallites a number of misorientation angles that minimise the surface energy of the boundary can be found.
Sutton and Vitek [6] suggest that the boundary will split up in a number of shorter sections having misorientation angles that are alternately higher and lower than the average misorientation angle.

In case of the <100>-tilt grain boundaries two different configurations were examined: (1) grain boundaries with <100>-tilt axis and a grain boundary normal direction close to (010) and (2) grain boundaries with a <100>-tilt axis and a grain boundary normal direction close to (110).
The average grain size was determined for each sample by measuring the grain sizes of at least 300 grains (for large grain sizes) and 800 grains (for small grain sizes).
This system delivers information of the average grain size and grain size distribution
The number of measured orientations was in the range of 5 5 2 10 to 7 10⋅ ⋅ .
In contrast, if the grain boundary forms a continuous interfacial slab as in high angle grain boundaries, vacancies can reach the dislocations easily through the grain boundary plane by grain boundary diffusion.