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Nanocrystalline materials with high strength have been reported in large numbers.
Additionally, nanocrystalline materials are characterized by a large volume fraction of grain boundaries and triple junctions [1].
When the grain size is reduced to the nanometer range, the dislocation density within the grain is decreased in particular for materials with average grain sizes less than 30nm [2].
This result suggests that fabricated bulk nc-Ni-W had inhomogeneous grain size.
Bulk nc-Ni with a grain size of about 60 nm exhibited an ultimate strength of 1006 MPa and good ductility of 8.8 %. 3.

The correct detection of these phases requires the high magnifications and a large number of measurements fields.
Therefore, it is important to reduce the amount of Mg17Al12 phase and introduce thermally stable precipitates at grain boundaries as well as in the grain interior by adding proper alloying elements.
In addition, globular particles inside the α-Mg grains are visible.
Needle-shaped precipitates inside the α-Mg grains in Mg-5Al-3Ca-0.7Sr-0.2Mn alloy.
Reasonable number of measurement fields was obtained until at measurement error equals SE = 30%.

The entire reaction can be expressed by Yamamoto’s equation because it contains the term of particle number.
He thought that the particle number exponentially changes in natural phenomena [5].
He introduced the particle number at time, which is expressed as follows [4]
The decreasing rate of the particle number is expressed by the following equation
The parameters, and in the term of the particle number are greater than and.

The same equation can be used for both the average grain studies and the individual grains study.
Peak locations θ were determined for all the five austenite grains' spots in the individual grain study and at a number of azimuths (fij values) in the average grain experiments.
Table 1: The Young's modulus in tensile direction for the 5 studied austenite grains Grain ID #1 #2 #3 #4 #5 Young's modulus 104 GPa 151 GPa 170 GPa 236 GPa 132 GPa 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −0.5 0 0.5 1 1.5 2 2.5 3 x 10 −3 Applied strain [%] Elastic strain in tensile direction Grain 1 Grain 2 Grain 3 Grain 4 Grain 5 1 2 3 4 5 100 110 111 b) Figure 5: a) The residual strain evolution of five individual austenite grains. b) Inverse pole figure of these five austenite grains.
The Young's modulus for the most compliant grain (grain 1) was 104 GPa, and the stiffest grain (grain 4) had a Young's modulus of 236 GPa.
Plastic anisotropy is also a factor to consider and it involves the number of operational slip systems.

However, they did not identify the effects of grain refinement and dispersoids on the oxidation of alloys with ultra-fine grains.
The Ni-20Cr-20Fe-5Nb-1Y2O3 alloys with smaller grains and larger grains, Ni-20Cr-20Fe-5Nb, commercial Inconel 718 and PM1000 alloys were oxidized at 1000℃ for up to 100 hours.
The grain size of the Ni-20Cr-20Fe-5Nb-1Y2O3 alloy after grain growth heat treatment was 490nm.
Considering that the oxidation resistance of the Ni-20Cr-20Fe-5Nb-1Y2O3 alloy with a large grain size of 490nm was far superior to that of the Ni-20Cr-20Fe-5Nb alloy with a grain size of 128nm, it is believed that the oxidation resistance depends mainly on the addition of dispersoids rather than on the grain size(Fig.3).
The large number of Cr carbide particles formed in the boundary area in the alloy prior to oxidation are believed to form CDZ(carbide denuded zone), which has a lower Cr concentration than the matrix.

Depending on number of distinct X and Y coordinates, fictitious grid lines are assumed: see figure 1.
Undeformed Grain Deformed Grain Y X Schematic showing the fictitious grid assumed in the grain structures along Y-direction.
Deformed Grain Undeformed Grain Y X (b) Figure 1.
Undeformed Grain Y X Deformed Grain Figure 2.
(a) Estimated in-grain von-Mises strain and (b) in-grain kernel average misorientation.

As can be seen, casting strip is mainly composed of columnar grain and only a small amount of fine grain is found in the middle of casing strip.
The number of enabled slip systems increases under the conditions of warm rolling.
There is large stored energy in the grains.
Numerous small grains first appear at the grain boundary during annealing.
Table 2 The annealing process and the corresponding magnetic properties of 6.5 wt. % silicon steel sheets with a thickness of 0.30 mm Number Annealing process P1.0/400 [W/kg] B50 [T] Max.

Although this method could make error in the interface of different parts of the simulation area when the grains go through the interface, but the error has less effect on the grain growth.
Although the phase field simulation of 3D grain growth has been achieved, such as equal axial grain [7], dendrites [8], columnar crystals during directional solidification [9], but these are only limited to a relatively small computational space and a simple form.
The Fig. 5 is the simulation results which the grid number is 400×400×400.The area which the grid number is 400×400×400 is calculated by using four areas that the grid number is 400×400×100 due to the grid number 400×400×100 is a extremity limitation which personal laptop can calculates.
Nikolas, Characterizing solute segregation and grain boundary energy in binary alloy phase field crystal models, Comput.
Simulation of the structure and motion of grain boundary in pure substances by phase field crystal model, J.

Each particle is assigned an independent orientation number q for distinguishing the individual state.
The neighbor interaction energies in the system given by (1) Here N is the total number of sites is the space; δ is the Kronecker delta; qi is the state of the grain or pore at the site i, and qj is the state of the nearest neighbor at site j.
First, a random grain site is chosen.
With annihilation of vacancies, the mass center of the adjoining grain moves to the grain boundary, thus giving densification.
Time in this model is measured in units of Monte Carlo step: 1MCS corresponds to N attempted changes where N is the total number of sites in the system [19].

At present, there is a limited number of superplastic aluminum alloys feasible for application in aerospace industry [3].
The mean linear intercept method was used to measure the average grain size of more than ~500 grains.
Most of grains are bounded by HABs (Fig. 2b).
The main reason of grain growth is coarsening of Al2Cu particles, which become unable to inhibit grain growth [7].
At T≥525oC, dynamic grain growth takes place resulting in increase of average grain size by a factor of ~2 (Table 1).