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Alternately, quasi-equiaxed ultrafine-grained structure can be generated after ultrasonic treatment only in the surface layer of Armco-iron specimens characterized by a large number of defects.
Beside that, EBSD – images indicate that in the modified surface layer of CP-Ti specimens a large number of deformation twins intersecting in different crystallographic orientations is generated.
The twin length is limited by a grain size.
It should be noted that the fraction of LAB in fine-grained specimens is less than in coarse-grained specimens.
EBSD – maps of the lateral side microstructure (a) and grain-boundary misorientation distribution (b) of fine-grained titanium subjected to UIT.

The second area of study is the inhibition of grain growth due to second phase particles pinning the grain boundaries so as to stagnate the grain size from growing any further.
A square matrix of size ‘N’ is then generated, which contains all its elements as random numbers ranging from 1 to Q, where Q stands for the number of grain orientations. 3.
If ΔE ≤ = 0, the change is accepted else if ΔE > 0, compute probability, p = exp(-ΔE/kT) (4) where k = Boltzmann constant, and, T = temperature if r < p where r is a random number generated and uniformly distributed between 0 & 1, the change is still accepted, else, rejected.
No Author(s) Year Equation for Limiting Grain Size 1.
The number of nearest neighbors considered was 26 and the size of second phase particles was kept at one voxel, or one cube, when studying the effects of static particles on grain growth parameters.

Detecting an inadequate number of diffracting grains also contributes to the random uncertainty and this is rarely considered.
Estimating the number of detected diffracting grains NDG.
However measuring 5 times has increased the effective number of grains detected on the detector.
The next section is concerned with deriving actual number of grains needed to reduce the value of u(2θgrain).
The number of grains however depends on the gauge volume size chosen and the average size of the grains (and hence diffracting grains) within the gauge volume and this should be taken into account.

Y X O O‘ x y particle scale (sub-coordinate system) pore network dryer scale (macro-coordinate system) hot wind outlet wire mesh container wall corn hot wind inlet (a) (b) constructed enlarged (c) throat corn particle pore (node) Fig.1 Drying container (a), pore network physical model (b) and enlarged pore network (c) Pore Network Physical Model Generally, the parameters for describing the structure characteristics of grain materials included the porosity, area density of pore and grain number, particle size distribution and the pore size distribution.
A two-dimension pore network physical model could be described by the parameters of pore and particle size distribution, distance between two nodes, the number of model scale, and coordination number [3-4].
As said above, the grain materials included two kinds of different scale pore system at least.
Then, the mass and heat transfer equation at the particle scale can be obtained: (4) (5) where D is the moisture diffusion coefficient in the skeleton grain (m2/s), r is the spherical coordinate variable (m), M is the local moisture content at certain moment and place inside the grain(d. b.), is the heat consumed by vaporizing the grain water during unit time (J/s), is the heat received from heat convection between the vapor-phase and grain surface during unit time (J/s), R is the grain radius (m), is the grain density (kg/m3), and Cg is the specific heat capacity of the grain (J/(kg·K)).
Table 1 Main parameters for pore network model node number corn grain density [kg/m3] mean grain diameter [mm] pore number density [unit/m2] grain number density [unit/m2] pore coordination number 1801 1004 8.8 17504 17289 4 Results and Discussion Drying and Temperature Curves Compared Experiment with Simulation.

Firstly, the formula for estimating the bed load transport rate in the bed of sand waves of prototype by model experiment was derived based on the similarity of grain Froude number; Secondly, several model experiments that the bed forms is similar with the prototype were carried, and the formula was verified.
The similarity based on grain Froude number proposed in reference [4], is the method for estimating the bed load transport rate in the bed of sand waves of prototype by model experiment, wherein the Froude number is defined as: where τ* is the dimensionless tractive force including grain resistance and form drag; u* is the shear velocity; s is the effective gravity constant; g is the gravity acceleration; d is the mean size.
The flow condition of ripple or dune bed form that was discussed mainly in this paper is the lower flow regime, and Froude number of flow was less than 0.8.
It could be judged that the bed form was ripple because the grain Froude number of this experiment was less than 20.
The number of large data of τ*e obtained from our experiment was not enough, so it was necessary to bring into the data of experiment done by Shinohara et al.

After five and ten turns, as shown in Fig. 2(b) and (c), the distributions of the number fractions of the misorientation angles have a similar tendency.
Detailed inspection shows the number fractions of high-angle grain boundaries increase at the center and the peak of low-angle boundaries is reduced significantly by comparison with those of a quarter turn.
Fig. 2 Distributions of the number fractions of the grain boundary misorientations at the centers and edges of the disks processed by HPT through (a) 1/4 turn, (b) 5 turns and (c) 10 turns.
Moreover, the gradual evolution towards homogeneity with increasing numbers of turns was visible in this Cu-0.1% Zr alloy in which the results were presented in the form of the microhardness evolution [7].
These low-angle miorientations are formed because large numbers of dislocations begin to arrange into low-energy configurations in the form of low-angle grain boundaries.

Magnesiums have only three separate slip systems at room temperature and poor ductility, therefore,a large number of practical applications are cast magnesium alloys.But wrought magnesium alloys have better strength, toughness and processability than cast magnesium alloys.
After rolling the sheet D through the same process, only a small part of the twinning existed in the individual grains and a large number of fine grains could be found in the initial grain structure surrounding.
Near the grain boundary a number of recrystallized grains appear and there is almost no twinning happening.
Such grains are likely to the bow of the grain boundary nucleation or subgrain rotation nucleation.
It can be seen in Fig. 2d that a large number of new fine recrystallized grains tend to accumulate and round the coarse initial grain boundary, which have different orientation distribution and formate large deformation zones or ductile shear zones.This dynamic recrystallization mechanism is the typicaliy rotating dynamic recrystallization.

The number of angular extrusion pass executed on specimen ranged from 1 to 8, and expressed as C1, C2, up to C8.
However, further refining is not achieved even when the number of extrusions are increased up to eight passes (Fig. 5).
As such, doubling the number of passes through the 120o die angle will accumulate more shear strain than passes through 90 o, yet the resulting grain structure was not fine.
The above data and associated argument indicate that fine or extremely fine grain by ECAE is not solely dependent on extrusion angle or number of passes.
Extrusion Temperature Number of Extrusion Pass Average grain size (μm) As-received (C0) 10 C1 8.5 C1 3.9 C2 3.7 C3 2.6 C4 2.6 C5 2.8 C6 3.0 C7 2.7 200℃ C8 2.6 C1 C3 C5 C7 Fig. 4 Optical metallographic microstructures of AZ31 processed by ECAE (channel angel=90°, one initial pass at 250℃, followed by C1、C3、C5、C7 at 200℃). 2 C0 C1 C2 C3 C4 C5 C6 C7 C8 0 2 4 6 8 10 12 Average Grain Size(μ m) Number of Extrusion Pass Φ= 120 o Φ=90 o Fig. 5 Average grain size of the AZ31 after ECAE processing at 200℃ with two different channel angels.

Emission Nuclear Gamma-Resonance Spectroscopy of Grain Boundaries in Coarse-Grained and Ultrafine-Grained Polycrystalline Mo V.V.
Introduction A method based on the emission nuclear gamma-resonance (NGR) spectroscopy on radioisotope nuclei inserted in grain boundaries (GBs) has been recently successfully applied for the study of structural and physical properties of high-angle grain boundaries in a number of metals.
Recently the state of grain boundaries in coarse-grained materials has been investigated by emission NGR spectroscopy in a number of studies [3-7].
As demonstrated in a number of recent publications including [8-9], grain boundaries in ultrafine-grained (UFG) metals processed by severe plastic deformation (SPD) differ from the grain boundaries of recrystallization origin in conventional polycrystals, though most of the available studies allow to judge on these differences only qualitatively.
Summary The state of grain boundaries in coarse-grained and ultrafine-grained Mo has been studied by the emission Mössbauer spectroscopy.

The total number of order parameters is , and .
The area fraction of the particles is fixed at 1.5%, while the number of particles varies from 2 to 8.
When the number of particles increases, the reduction speed of the grain 2 area fraction is lowered.
Fig. 7 Effect of particle size on pinning effect: (a) area variations of grain 2 with different number of particles; (b) 8 particles, = 50.
Yang, Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain-growth kinetics, Phys.