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These fine grains are produced by dynamic recrystallization at the grain boundaries of original grains.
Smaller grains a few microns in size are mainly distributed surrounding original large grains in the form of either necklace or colony.
However, the number (or the volume fraction) of the recrystallized grains increases significantly with strain.
Microstructures in the fractured samples consisted of small recrystallized grains and non-recrystallized large grains.
The recrystallized grains were grouped in a necklace structure around large grains.

Doping leads to a further hardening due to the occurrence of Mn atoms and Zr in solid solution; grain refinement; increase heat resistance due to the establishment of the grain boundaries of inclusions of thermally stable compounds [1 – 2].
Reduced structural stability was mainly caused by particle stimulated nucleation of recrystallized grains in the deformation zones around coarse Mn-bearing phases that developed during the homogenization, and also by a reduced number density of Al3Zr dispersoids.
In the grain boundaries detected Mg2Si particles and Al6(Mn,Fe).
The number of phase L12 sample 4 more.
The number of Mg2Si particles 4 is less than the sample.

In a twinning-layer film, a number of new grains also can be formed.
There are a number of new fine grains, when static recrystallization occurs.
Therefore, the number of the nucleation of recrystallization decreases and reduces the grains to becoming coarse and asymmetry.
Therefore, the number of nucleation of recrystallization increases with a long time to complete the re-crystallization process, and fine and uniform grains are received finally at low annealing temperature [3].
In addition, the existence of a large number of twinning grains lead to the increase of strength of magnesium alloy sheets.

Due to the high vibration frequency of the system, the sample surface was struck repetitively by a large number of balls, resulting in a progressive refinement of coarse grains into the nanometer scale.
It can be seen that the plastic deformation degree decreases with increase of the depth and the original coarse grains in the surface layer are severely refined into ultrafine grains, in which grain boundaries could not be identified.
The microstructures in the treated layer change gradually from ultrafine-grained structures in the topmost layer to the undeformed grains in the matrix.
Firstly, high number density of grain boundaries and triple junctions in nanocrystalline materials can provide rapid mass transport paths [16,17], which is believed to be the primary diffusion mode of Fe and Cr elements.
Grain growth is mostly attributed to the grain boundary migration and grain boundary is the primary channels for accommodating solute atoms.

Furthermore, small addition of MgO caused the second crystalline phase in the ceramic structure and higher concentration of MgO produce an increased number of second crystalline phases (spinel) [7,8].
Apart from that, the addition of MgO led to an increase in densification and decrease in porosity that occurs in ceramic samples, the increase in densification occurs because of magnesia at grain boundaries which reduces the mobility of the grain boundaries, magnesia can also increase the grain boundary energy and consequently increase the surface diffusion mobility Al2O3 pore trapped in the grain increases and can be moved [9].
Graph between Vickers hardness numbers with compaction pressure.
Solid-state sintering can happen by coarsening and grain growth.
(a) Ceramic grain growth and (b) Structure micro of ceramic composite.

At the same time, the redundant Zn bonds with Ca and Mg to form Ca2Mg6Zn3, which distributes in the grain interior and grain boundary.
However, for the MZC0.7Zr alloy specimens, some of the superfluous Zr particles congregate at grain boundary as impurities to disrupt the continuity of the secondary phases, which can speed up corrosion spreading from one grain to another grain.
The addition of Zr refined the grains and did not form new phase.
With the increment of Zr content, the number of Zr particle distributed along the the grain boundary was increased. 2.
The result was attributed to the best combination of the refinement in the grain sizes, continuous distributions of the secondary phases and less number of Zr particles.

During the meshing process the space was discretised and described with a 3D digital image composed of voxels (pixels in 3D) that can be labelled with the number of grains they belong to.
The grain sizes of workpiece were assumed to be 6, 45, 120, and 248 μm with two kinds of grain size distribution.
According to the grain hardness, grained heterogeneity can be figured out.
Generally, the grain-boundary volume within a metal polycrystalline increases when the grain size decreases.
These active dislocations intertwine in the grain boundaries during plastic deformation, so there will be a large number of mutually repelling dislocations intertwined if the grain size is small.

Each lattice site is assigned to a number, n which corresponds to the orientation of the grain in which it is embedded.
In present study, Monte Carlo simulation was performed on a triangular lattice of size 200×200 sites with periodic boundary conditions and the number of distinct grain orientations, Q was 2,000.
The initial grain orientations (Q=2,000 numbers) were defined as the Euler angles (g) after separating from the ODF for the cold rolled 5182 aluminum sheets without annealing to the individual grains and these were used to generate a set of 2,000 initial grain orientations for Monte Carlo simulation.
In this simulation, when one lattice site is selected in order to try the orientation change, if the lattice sites were the interior of grains, the orientation change was not tried, however, it was included in the number of trial, N.
As time passes, the recrystallized grains are growing and the deformed grains are shrinking.

Conductivity is measured using the QJ36-type bridge arms, sample size is 200mm × 3mm × 1mm, an accuracy of ± 0.05%; hardness number is tested in the HVS-1000 micro hardness tester at 100g load for 20s; Tensile strength tested by using CSS-44100 universal tensile machine.
The addition of rare earth compound with some low melting point impurities in copper and these compounds act of crystals core dispersed in the melt, those significantly increased the number of grains and the grain thus be refined. 2) clean the grain boundary Because the metallurgy atmosphere present oxidizability and the hydrogen content is high during non-vacuum melting process of Cu-Cr-Zr alloy, the metal components form oxide and hydride easily.
The compound that didn’t come-up during solidification distributes in grain boundaries.
Therefore, it is necessary to add certain content of La and Ce to clear grain boundary.
Because the rare earth is provided with the effect of degassing, dedusting, fining grain and clearing grain boundaries and so on, the change of optical microstructure should have some effect on alloy properties.

Grain orientation has a great influence on the formation of twins.
Zhao[10] states that the increased densities of twins make great contributions to finer grain size and higher microhardness besides for large number of dislocations when CP Ti sample is processed by ECAP with the angle of 120° between channels at room temperature.
The average grain size of annealed Ti is 90μm (see fig.1a).
It may relate with grain orientations.
At even small strain, there are a large number of twins in samples processed by DPD.