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WQ at 785°C WQ at 830°C WQ at 765°C WQ at 960°C WQ at 890°C WQ at 926°C WQ at 977°C WQ at 1000°C WQ at 1040°C Journal Title and Volume Number (to be inserted by the publisher) 3 occurred among the grains that had already recrystallized, cf.
This is confirmed by quantitative grain size data, which are represented in Table I.
The data suggest that this grain refining has saturated beyond heating rates of 1000°C/s.
This mechanism will have a refining effect on the grain size.
In the end, the final grain size will be the result of a compromise Journal Title and Volume Number (to be inserted by the publisher) 5 between these two opposing tendencies.

This paper presents a simple and novel model for low-frequency noise generation in polycrystalline-Si resistors within the number fluctuation model.
Recently, assuming a thin amorphous layer at the grain boundary [5], a number fluctuation model [1] was proposed that considers thermal activation [6], tunneling [7] across the thin amorphous layer {Fig. 1(b)}, and a combination of these two mechanisms.
uniform barrier height and grain size.
Quadratic current dependence has always been observed in poly-Si resistors, which can be explained by the number fluctuation model.
However, three number fluctuation mechanisms have quite different temperature dependences.

The initial material has a uniform coarse-grained microstructure with a mean grain size of ~42 μm.
Moreover, cracks were developed for numbers of turns larger than three.
The initial material exhibits a coarse-grained γ-austenite with a mean grain size of ~42 μm.
Table 1 lists the grain size values obtained by TEM at the disk periphery for different numbers of turns.
A further reduction in grain size was observed with increasing numbers of HPT revolutions and after 20 turns the mean grain size was refined to ~48 nm.

However, as the grain size was reduced, fewer of these aligned microstructural features were formed, and at the smallest grain sizes, there was little evidence of significant substructure within the deformed grains.
Different grain sizes then were obtained by annealing the extruded bars, to coarsen the microstructures by grain growth.
In the 3µm grained material, micrographs showed no evidence of aligned substructures within the grains.
The low angle boundaries are considered in two misorientation groups, 0-3 o and 5-10 o and figure 3 presents data from samples of 60µm and 3µm grain size, where the number of boundaries analysed in each histogram is typically 5000-10000.
Low angle boundary alignment to the rolling plane in samples deformed to a strain of 0.7. a) 60µm grained material, 0-3o boundaries b) 60µm grained material, 5-10o boundaries, c) 3µm grained material, 0-3o boundaries and d) 3µm grained material, 5-10o boundaries.

To achieve ferrite grain refinement in steel, there are two potential routes, the transformation route and the recrystallization route.
In the former case, the limit of refinement is about 2 µm, and, in the latter case, ferrite grains with a size in the hundreds of nanometer are obtained.
In severe plastic deformation processes, caliber rolling is an effectual process for producing ultrafine-grained steels efficiently [1-3].
The number of passes was determined according to the strain predicted from the FEA.
At sites s7.9-coy and s7.9-coz where large εeq of over 5.7 is introduced, a significant number of fine equiaxed grains below 1µm were formed with the fraction of HAGB [3], and, at this time, the average grain sizes at sites s7.9-coy and s7.9-coz were approximately 680nm and 650nm, respectively.

The microstructure evolution during the ARB process was explained by grain subdivision.
Introduction High strengh of ultra fine grained metallic materials has attracted a number of researchers both in scientific and industrial fields.
In the previous studies about aluminium alloys and ferritic steels, it has been clarified that the mechanism for forming the ultra fine grain structure is grain subdivision [5-6].
(a) (b) (c) 0 1 2 3 4 5 6 0 5 10 15 Spacing of HAB Number of ARB cycles 0 1 2 3 4 5 6 0 20 40 60 80 100 LAB HAB Boundary fraction (%) Number of ARB cycles 0 10 20 30 40 50 60 0 10 20 30 40 Number frection (%) Misorientation angle (deg.) 0 10 20 30 40 50 60 0 10 20 30 40 Number fraction (%) Misorientation angle (deg.) 0 10 20 30 40 50 60 0 10 20 30 40 Number fraction (%) Misorientation angle (deg.)ARB processed OFHC copper at quarter thickness position.
It was demonstrated obviously that the grain subdivision progresses with increasing the number of the ARB cycle.

Conventional wire drawing with a sufficiently high degree of deformation, a high number of passes and relatively low annealing temperatures also yields UFG NiTi alloys with fine microstructures, Fig. 1f.
With increasing number of cycles, a two-step transformation (B2→R, first peak on cooling, followed by R→B19', second peak on cooling) evolves.
In large grains there are only a few grain boundaries which act as obstacles for elementary lattice shear processes.
Although our study only provides a small number of data points, our results indicate that the required undercooling strongly increases with decreasing grain size, once the grain diameters fall below a threshold value of about 100nm.
This indicates that the material only partly transforms into B19' on cooling because a high number of grain boundaries acts as obstacles for the lattice shear processes which govern the martensitic transformation [4, 5].

It shows a lot of grains whose sizes lie in the range φ5~15 µm, and the grain boundaries between them.
In this process, it is necessary to repeatedly alternate the abrasive size from large to small to prevent the AlN grains from detaching as a result of grain boundary fracture.
As a result the number of effective cutting edges increases, and the Figure 2 Ultra-precision plane honing machine Grinding wheel with radial pattern Workpiece head Truing head Table 1 Main specifications of plane honing machine Workpiece head High stiffness double hydrostatic bearing Maximum workpiece diameter φ120mm Maximum rotation number 900rpm Constant feed rate and pressure feed back effective stroke 150mm Feed resolution 0.1µm Maximum machining force 200N Truing head Maximum rotation number 900rpm Servomotor control effective stroke 150mm Feed resolution 0.1µm Grinding wheel spindle High stiffness hydrostatic bearing Wheel diameter φ375mm Maximum rotation number 900rpm Table 2 Experimental conditions Workpiece AlN, 1-inch square, 6pieces Grinding wheel Radial pattern wheel Rough processing SD400B, SD1500B Feed rate: 3µm/min Finishing processing SD3000B, SD3000V, SD8000V Feed rate: 1µm/min Machining force Maximum 120N Grinding fluid
Fig. 7 shows the machining force and the number of effective cutting edges as calculated from the SEM images.
However, a vitrified bond wheel with small grain size such as SD8000V could cut AlN grains by transcrystalline fracturing.

Although such force exists universally, it is too weak to fasten the diamond grains firmly between vitrified adhesive and diamond grain surface.
The numbers of grains falling out in each ways can be figured out by the fractography analysis with computer software aiding.
Under the first circumstance only the interface binding force plays the role, so the force equilibrium equation of grain falling out from matrix is: (1) where f1 is the pulling force of single grain (N), d the diameter of grain (M), σ1 the chemical combining strength (Pa).
(3) (4) where F is the external force loading in sample as tensile testing (N), n1 the number of grains fell out in the first way, n2 the number of grains fell out in the second way, n the total number of grains (n = n1 + n2), A the area of fracture surface (m2), A0 the area of porosity (m2).
Diameter of grains approximately equals the diamond products d50.

Under these circumstances, there exists a competition between the decrease in grain size (grain refinement) due to the imposed plastic strain and an increase in grain size (grain coarsening) due to the increased temperature of the specimen subjected to deformation.
Since the evolution of ultrafine grains takes place by thermally activated processes, the role played by the interfaces such as grain boundaries in controlling the grain size is significant.
This assumes further significance due to the presence of large number of grain boundaries in ultrafine grained materials.
During large strain deformation, as the imposed strain increases, original grain boundaries are compressed and are elongated in the direction of grain flow resulting in high aspect ratio grains, with the thickness of grains decreasing with increasing strain.
Based on Fig.3(a), it may be noted that when the thickness of the deformed grain (grain size) is smaller than the grain boundary diffusion distance, atoms diffuse and ferrite structure is fully recrystallized consisting of new equiaxed ultrafine grains; On the other hand, when the thickness of deformed grain is larger than the grain boundary diffusion distance, atoms diffuse to a short distance leaving a mixture of elongated and newly generated grains.