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Introduction Severe plastic deformation (SPD) is regularly applied to achieve ultrafine-grained (UFG) metals and alloys that have grain sizes in the submicrometer and nanometer ranges [1,2].
Fig. 3: The volume fraction of texture components versus number of turns.
Then, the texture is fairly isotropic after processing by HPT through a total number of 20 turns.
Superplastic flow is observed in the samples processed by HPT through total numbers of more than 5 turns.
Langdon, Twenty-five years of ultrafine-grained materials: Achieving exceptional properties through grain refinement, Acta Mater. 61 (2013) 7035-7059

The grain size of the 1% Mn steel is coarse.
By contrast, the grain size of 2% Mn is quite small.
Also the number of the transformation nuclei is changed.
Rex. 3) Number of transformation nuclei The progress of the transformation is slightly faster with increasing the number, and the transformed grain size decreases (Fig.4(c), Fig.6).
In the experiments, when the transformation initiates at an early stage of the recrystallization, the number of the transformed nuclei increases; this can result in a refined microstructure because the nucleation of the transformation can occur not only at the grain boundaries but also within the deformed grains, which have larger dislocation densities.

However, the number of simulated subgrains may still be too small to give reliable results.
In order to detect these grains a large number of grains has to be measured.
One important result is shown in figure 6a which displays the number of grains of a particular number of corners over there orientation distance to the Goss orientation.
According to the von-Neumann Mullins theory ([35]) grains which have a geometrical growth potential should have a significantly higher number of corners than others.
In brief it assumes that Σ9 grain boundaries have lower energy than others and that Goss grains meet a particularly high number of Σ9 grain boundaries in the primary recrystallised matrix.

The average grain size is close to 30µm (Figure 1).
Figure 4 : SMT–induced microstructure in the ultrafine grain region.
Grains are equiaxed with an average size of 300-500 nm.
The wear volume is plotted as a function of the number of sliding cycle on figure 6.
Right – wear volume as a function of the number of sliding cycles.

We apply the method to hydrogen diffusion in Si grain boundary.
Hydrogen Diffusion in Si Grain Boundary.
Fig. 2: Atomic positions of (001)Σ5 twist grain boundary of Si with a H atom.
where n is the number of particles, and the two boundary points, Ri (0) and Ri (T), are fixed.
In the discrete representation of the time integration in Eq. (3), the action is redefined as , 1 1 2 ,∑∑== = N k n i kiS ε (4) where tTN ∆≡ / is the total number of time steps.

Another approach is to produce ultrafine-grained alloys as it has been long known from Hall-Petch relation [1, 2] by metallurgist that smaller grain size gives higher strength.
A high level of misorientation occurs and finally sub-grain boundaries and high-angle grain boundaries can be formed that gives rise to ultrafine grains.
In this study, 6061 aluminium alloy was ECAPed using route Bc with different number of passes.
The sample was subjected to an equivalent strain of 0.89 (calculated from Eq. 1 [5]) for 1 pass and increasing with number of passes i.e. 1.43, 2.14, and 2.85 for 2, 3, and 4 passes respectively
The distribution of different grain sizes in the 4-pass sample was demonstrated in Figure 6 and that the average grain size was at 2.23 µm and this was in fine-grain regime.

Materials A1 and B1 (Fig. 1(a)-(b)) have similar coarse grain size and elongated grain morphology, although, on average, the grains in the latter are coarser than in the former (97 μm vs. 83 μm from linear intercepts).
While material C1 (Fig. 1(c)) contains a number of coarse grains that are sometimes elongated, they are heavily outnumbered by small ones.
Fig. 4 shows a simplistic, schematic depiction of how post-cold-rolling grain sizes vary with the initial (grain) size and shape.
Fig. 4(e)-(g) represents circular grains.
Acknowledgements This research was carried out under the project number MC4.05238 in the framework of the Research Program of the Materials innovation institute M2i (www.m2i.nl), the former Netherlands Institute for Metals Research.

When temperature is relatively low (the thickness of liquid is relatively thin), grains contacted with each other, which produced irregular-shaped grains.
In contrast to the traditional die casting and forging processes, thixoforming has a number of advantages, such as less energy consumption; less solidification shrinkage (low shrinkage porosity); no handling of liquid metal; and prolonged die life due to decreased thermal shock [3].
A large number of liquid droplets formed intracrystalline and grain boundary of two grains during partial remelting (Fig. 6 (a)).
Therefore, recrystallised grain gradually becomes rounded.
When recrystallised grains were not completely surrounded by liquid film, two grains contacted with each other and therefore merged into a new grain with larger size, which resulted in occurrence of irregular-shaped grains, as shown in Fig.2 (c), Fig.3 (c) and Fig.4 (c).

The random number generator is based on the Box-Muller transformation [11], a pseudo-random sampling method for generating standard normally distributed random numbers.
The cellular automata space is a grid of finite number of cells described by several internal variables and it can be represented by the array of integers.
Particular gains grow until the whole space is covered with grains.
Difference between circles/spheres and grains distributions.
After growth procedure (Fig. 5) grains increase their size in comparison to initial circle/sphere size and translate the grain size distribution to the right, towards higher mean average grain sizes.

The goal of this research was to create a surface topography that would promote cell attachment onto Ultrafine-grained Grade 2 Titanium.
Viewed as a process that can be optimised, definitive results are difficult to find without exhausting a large number of processes and parameters.
Reduced grain size enables pure UFG-Ti to mimic titanium alloys with aluminium and vanadium in strength and lightness, but without toxicity concerns.
Meanwhile, reduced grain size of UFG-Ti also creates denser arrays of 3-point surface grain boundaries – shown to give habitats that encourage denser cell colonisation [9].
Törköly, Microstructure and Mechanical Behavior of Ultrafine-Grained Titanium, Mater.