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At a microstructural level, a number of interactions between Zr and Mn have been noted, but not clearly related to recrystallisation resistance.
In fact, measured values of number density for these two alloys are approximately 67 and 132 µm-3 respectively.
In a 6 mm sheet the cast grain structure will be far more compressed.
A possible reason for the reduction of the Al3Zr number density is the dissolution of Zr within the Mn-containing dispersoids, reducing the Zr available for precipitation of Al3Zr dispersoids.
The predicted dispersoid distribution across a grain following homogenisation is presented in Fig. 5b; it shows that, due to the higher Mn supersaturation near the grain boundary, the nucleation rate of the Mn-dispersoids is much greater than in the grain centre, giving rise to a higher density of particles.

This was followed by a number of investigations reporting varistor action in TiO2 with low breakdown field strengths [5-8].
According to the boundary barrier model, the breakdown voltage , Eb, for a varistor is determined by the mean number of barriers n in series multiplied by vb, that is [12] : (2) where vb is the voltage barrier at a grain boundary, which is almost a constant for different samples.
Thus, the resistivity of TiO2 grains is decreased.
Most Nd3+ ions segregated at the TiO2 grain boundary to relieve elastic strain energy and thus increased grain boundary resistivity by acting as an acceptor [14].
The nonlinear electrical behavior of Nd2O3-doped TiO2-based varistor ceramics can be explained by two kinds of effect of Nd2O3 on the conduction of TiO2 grain and grain boundary.

Ogino et al. found through experimental and theoretical study that the error caused by using the thermal equilibrium assumption may become quite significant when the Reynold’s number is large and the water flow distance is long [11].
Evaluation of the thermal equilibrium assumption between water and fill grains Refer to the representative elementary volume shown in Fig. 1 for saturated water flow and heat transfer in a rock fracture with granular filling materials.
In accordance with Newton’s cooling law, the total flux of heat exchange between water and grains can be expressed as (1) where denotes the heat convection coefficient; the total surface area of the grains, for the current analysis, without loss of generality, suppose the fill is composed of spherical grains of constant diameter , then (2) For the heat exchange between water and grains, conservation of thermal energy can be formulated, for water and grains, respectively as (3a) (3b) where
denotes the porosity of the fill, density of water, specific heat of water, density of grains, specific heat of grains, and the homogenized temperatures of water and grains, and the homogenized temperature change within the time interval in water and grains, respectively.
From these analyses, it may be observed that for the heat exchange between water and fill grains, the ratio of the convection coefficient and the grain size acts as the major influencing factor, while the increases in the volumetric specific heat of the grains and the porosity of the fill may prolong the time to reach thermal equilibrium, but relatively marginally.

Figure 1 (a) shows that organize grain is relatively thick, with the increase of stress intensity, organization changes obviously by grain refinement and grain boundary clear.
The characteristics of strip exposure almost disappear, the reason is that main component of sample is ferrite + carbide, and followed creep deformation, grains are elongated.
With the increase of stress, the martensite lath characteristics gradually disperse, precipitation phases have changed in grain boundary and inside grain, and the grain boundary precipitation phases gradually refine .
Firstly, according to the calculation formula of hidden layer nodes, the scope of the number of hidden layer nodes is given generally, then, in the scope of the number of hidden layer nodes ,based on minimum mean square error (mse) between the output value and the desired output to determine the final network structure.
Figure 4 shows the mean square error (mse) value corresponding to different number of hidden layer nodes. seen from figure 4, the number of hidden layer nodes at 10 can get the minimum mean square error (mse) value 5.22 x 10-4.

It is observed that the grain size increases with increasing the oxidation temperature.
CuO has been known as a p-type semiconductor that exhibits a narrow band gap (1.2 eV) and a number of other interesting properties [1, 2].
The grain size is between 30 and 80 nm.
After 1 h oxidized in atmospheric air at 550 °C, large oxide grains are formed with big hole on the surface which is composed of several small crystal grains.
The grain size ranging from 0.5 to 1.4 mm.

In the first place, this requires that the RVE at the macro-scale consists of a sufficient number of grains, 3000 or more [2].
In the present study, the value 6 was chosen for n; the material was assumed to have no stress differential effect, and the number of strain modes used (K) was 201.
The slip rates are not estimated in the centre of a grain, as the FC Taylor model implicitly does, but rather at grain boundaries (Fig. 1a).
It is reminded that none of these grain orientations is taken at the centre of some grain: they all come from a grain boundary region.
(b) Type I or Type II: grain cluster which is supposed to be located at a grain boundary segments.

Introduction Nowadays, ultrafine grain materials with mean grain size smaller than 100nm are actively studied and present a widespread interest because they exhibit enhanced mechanical properties, such as high strength, hardness and superplasticity properties.
The initial microstructure of the as-received material is characterised by a grain size ranging between 20 and 80µm.
Because of the high vibration frequency of the system (20KHz), the shot reaches the resonance regime and peens the entire surface of the sample with a high number of impacts in a short period of time.
Transmission Electron Microscopy observations (TEM) performed near the extreme top surface of the specimens have thus shown grains in the nanometre range characterized by highly random crystallographic orientations and exhibit an average grain size of approximately 20nm.
For instance, at a depth of 3-5µm, we recorded a very high hardness around 8.5GPa which was more than 3.3 times higher than the coarse-grain hardness.

Cast magnesium alloys are resulting coarse grained structure and micro porosity.
Initial grain size of 400 µm matrix alloy is getting refined after extrusion and the grain size of ZM21 alloy is refined to 70 µm.
A number of massive intermetallic compounds with obvious cracks are observed at the Mg/Al interface.
The ZM21 Mg alloy grains are refined after rolling and average grain size of 7µm and 10µm during unidirectional and cross rolling, respectively.
· Magnesium grains were refined to 7µm.

The cracks were initiated at the grain boundaries, followed by growth along the crystallographic slip planes in the adjacent grains.
Up to now, however, there was a small number of clear evidences for crack nucleation and propagation mechanisms.
Experimental Results and Discussion Fig. 2 shows an optical micrograph of the aged alloy with bright grains and dark phases.
The matrix (bright grains) was strengthened by disc-shaped d-Ni2Si intermetallic compounds with a few nanometer diameters.
After the initiation, the crack grew with shear mode along the slip orientation of adjacent grains.

The larger number of grains of sample (a) were agglomerated together due to solvent rapid evaporation [13] or lattice mismatch between films and the glass substrates.
With the number of layer increasing from 2 to 8 layers, the surface morphologies is more and more dense, and the grain size (D) of the film was slightly increased which is confirmed with the XRD results.
With the number of layer increasing from 2 to 8, the transmittance of the prepared thin films is slightly increased.
This is because the grain of ZnO films is increased gradually, and the grain boundary density of a film is decreased [15].
With the number of layer increasing from 2 to 8 layers, the intensity of the (100), (002) and (101) diffraction peaks increased gradually, and grain size of the film was slightly increased.