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A number of studies have been done to clarify the subsurface fatigue crack generation for titanium alloys and some models have been proposed how the facet may be formed.
In this model, the grain is divided into weak grain and strong grain.
Second model is that strain incompatibility at grain boundaries due to the rearrangement of dislocation structure produces a local stress concentration in the strong grain [6].
A sufficient number of boundary dislocations would promote crack initiation and make it propagating along the slip band on (0001) [12].
Here the strain incompatibility between neighboring grains could be considered as an important factor for subsurface crack initiation, but effect of the neighboring grain was not mentioned in the study.

The values of the average grain size are listed in table 1.
These results show that grain and grain boundary decrease with increasing temperature for all samples.
When the Fe concentration increases, the number of oxygen vacancies also increases, and thus the activation energy decreases.
The SEM images of PZTFx ceramics show quasi-spherical grains and the evolution of the average grain size shows a minimum at x=0.075.
B, Condensed matter The American Physical Society vol 61, (2000) number 13

The formation of equiaxed grain structure with a grain size of about 170 nm (fig.1 a) have been observed in the HPT samples.
A great number of spots uniformly arranged in circles on electron diffraction pattern testify to the formation of grain boundaries mainly of a high angle type.
The grain size determined with EBSD for ECAP samples lower than grain size from TEM.
The grain boundary statistics were measured using more than 1000 grains for the HPT and 300 grains for ECAP samples.
Numbers of twin and numbers of special grain boundaries in both states is identical to within experimental error.

The random distribution of the nuclei is compared with Journal Title and Volume Number (to be inserted by the publisher) 3 the preferential distribution for some particular sites.
In the simulation, when this nucleation type is selected, the development of the new grains near the grain boundaries in the highly deformed areas (zones of the matrix associated with an intense deformation, i.e. smaller grain size distribution, high local misorientation) is favored (Fig. 1).
At the end of the simulation process, the microstructure presents a non-uniform grain size distribution.
Journal Title and Volume Number (to be inserted by the publisher) 5 The recrystallization kinetics are shown in Fig. 4.
Rollet : Recrystallization and Grain Growth, Proceedings of the First Joint International Conference, Eds G.

The improved current-voltage properties are attributed to the band structure difference in both sides of grains, due to the different ion concentration and species in both sides of grain boundary.
Similarly, at the inter-face the grain size in layer A is larger than in layer B.
Schottky Barrier for Grain Boundary Between Layer A and B.
The band diagram of the grain boundary before contact is shown in Fig. 5(a) where EFG and EFB are the EF − EV in the grain and grain boundary, respectively.
The current density JS, which is related to the voltage barrier and to temperature, follow the equation [15,16]: (3) where A* is the Richardson’s constant, is the interface potential barrier height, E is the electric field and is a constant related to the potential barrier width by the relation: (4) where r* is the number of grains per unit length andis the voltage barrier width.

Experimental and testing Page Numbers.
A steel forging more complex organization, obviously deformed grains, grain boundaries are not very clear, to judge from the morphology phase composition of γ+ε+α'-M; B steel substantially equiaxed grain size of about 100μm or so, phase composition of γ+ε; C steel grain size smaller is about 40μm, grains smaller deformation, grain boundary carbide precipitation, its phase composition as γ+ carbide, which show that C content increases, the forging process at the grain boundary carbide precipitation, inhibit grain growth, It can effectively reduce the grain size.
Although grain C after forging compared B grains smaller, but after solution treatment, no precipitation of carbides at the grain boundaries, grain growth, that is to say, in this heat treatment process, Carbon and aluminum elements no major impact on the grain size.
Although the chemical composition of the grain size no big impact, but the phase composition and deformation mechanism were closely related the grain size.
Steel A and B occurred TRIP effect, but due to Steel A already contains a large number of α'-M, so the TRIP effect is weaker than the steel B.

The grain diameter decreased with increasing Zr content.
The response time was approximately proportional to the square of the grain diameter.
As the oxygen partial pressure in the atmosphere decreases, the number of oxygen vacancies in the oxide semiconductor increases, which is accompanied by an increase in charge carriers and a decrease in electrical resistance.
The grain diameter was varied by changing sintering temperature.
The grain diameter of Ce0.8Zr0.2O2 element was 86 nm.

The addition of P to the Cu-Ni-Si alloy caused no change in the grain size after the solution treatment, but the addition of Cr to the Cu-Ni-Si-P alloy changed the grain size from about 100µm to 80µm.
The large precipitates restricted the growth of recrystallized grains, so that the average grain size was refined to 15µm.
The grain refinement brings about an increase in elongation without reducing strength (Fig. 3).
Owing to the grain refinement to 4µm, elongation was greatly improved (Fig. 3).
The number density N of the δ-Ni2Si precipitates was yielded from r and f.

Since the Burgers orientation relationship holds only if the β grains are nucleated within the α grains, the outcome of this question greatly affects texture-modeling efforts for this system.
The transformation of α to β can occur either by the growth of β grains pre-existing at room temperature, or by fresh nucleation of β phase within α grains.
A large number of fine precipitates are observed populating the β regions, which are probably secondary α or martensite.
This is a very interesting observation, indicating that the Burgers orientation relationship between the α grains and these early β grains is destroyed.
This indicates that the α grains nucleate within the β grains, consistent with the absence of any other nucleation site in the fully transformed material.

A small number of ferrite and ferrite dual-phase structure existed in martensite when quenching temperature was low.
Compared with conventional once quenched at 830°C, grains are refined.
It is well known that the smaller nucleation energy and the large nucleation rate can result in the finer austenite grains.
When the temperature exceed 790°C,Martensite grains become coarse gradually.
(2) The austenite grain size of 65Mn steel can be refined by austenite inverse transformation quenching