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For the films fired at 750�, the needle-shaped grains (a-axis grains) were very fine and pores were frequently observed.
In addition, the a-axis grains disappeared as the firing temperature was increased to 775�, suggesting that the grains mainly consisted of c-axis grains.
It then decreased drastically to 54 A/cm-width with increasing number of coatings.
The film thickness increased almost linearly with increasing number of coatings up to 5 times.
XRD patterns of the films with the number of coatings

D=3ΓgbVm/(C0-Cg) with Cg the carbon concentration in grains, Γgb the grain boundary excess, and Vm the molar volume of iron.
So far the synthesis of NC iron-carbon alloys has been published in a rather small number of studies [14-18].
After the annealing treatment, a pronounced grain growth happens in the powders with low C0, e.g.
Figure 3 Grain size distributions of the ball milled Fe-0.4wt.
When GBs are saturated with defectants GB energy may become zero at high enogh chemical potentials of the defactant and in turn the grain growth will be inhibited, leading to an equilibrium grain size [1].

Experimental results and analysis Metal crystals can be regarded as a composition by grains and grain boundaries; grain boundary is the 2-d defects in metal.
It separates grain to two different interfaces.
Table 2 Austenite grain size were examined by oxidization and grain boundary etching method grade of steel Austenite Grain Size with Oxidizing Method Austenite Grain Size with grain boundary etching method level mean chord length (mm) level mean chord length (mm) 20 6(85%)+7(20%) 0.0322 6(85%)+7(15%) 0.0334 20CrMo 7(80%)+8(20%) 0.0248 7(80%)+6(20%) 0.0285 20Cr2Ni4 8～9 0.0174 7(80%)+8(20%) 0.0243 40Cr 9～10 0.0115 8～9 0.0182 45 6(50%)+8(50%) 0.0284 6(50%)+8(50%) 0.0287 In addition, because Ti6Al4V (TC4) belongs to alpha and beta dual phase titanium, so usually, TC4 has two phases, i.e. alpha and beta phases.
The grain size of TC4 alloy is large, when high-speed cutting, since cutting thickness is less than the grain size; there is a great risk of cutting off the grain in the cutting process.
From microstructure analysis, TC4 (Ti6Al4V) alloy is dual phase alloy, with high strength and low plasticity due to its low number of sliding systems.

The result shows that the influence of density-grain degree coupling on saturation loess liquefaction has a feature of segmentation, plastic index plays the main role for loose loess, whereas density is the main control factor to dense loess; Moreover, the influence of density-grain degree coupling on saturated loess liquefaction controlled by cyclic numbers of the vibration, plastic index plays the leading role while the vibration times is small, while the more vibration times, the bigger density and higher strength of liquefaction.
Thus, for the loess liquefaction, grain degree and density is the most important influence factors.
In order to study the effects to saturation loess liquefaction by density and grain degree respectively, the relationship between the initial void ratio (e) , plastic index (Ip) and the liquefaction stress ratio (σd/2σ0′) under different seismic intensity is obtained though a large number of dynamic triaxial experiments of the disturbed loess samples, which as shown in figure 3[6].
To sum up, based on summarize of the experimental results which are shown above, the influence of density-grain degree coupling on saturation loess liquefaction could be divided into the following stages, shows in Tab.2 Tab.2 The segmentation of density-grain degree coupling on saturation typical loess liquefaction e Ip Ip is smaller Ip is larger e is smaller The liquefaction stress controlled by e The liquefaction stress controlled by e & Ip, but the largest e is larger The liquefaction stress controlled by e & Ip, but the smallest The liquefaction stress controlled by Ip Secondly, the cyclic numbers of vibration has a fine effect on the density-grain degree coupling.
(3) The main property indexes of loess liquefaction influenced by cyclic numbers of the vibration, plastic index plays the leading role while vibration time is small.

At high peak temperatures, the intense grain growth took place.
An adequate cold reduction is necessary to increase the dislocation density and the number of favorable recrystallization nucleation sites for the gamma-fiber.
Grain size and hardness of annealed specimens.
According to the literature [11–13], the high HR leads to more effective nucleation during the start of recrystallization, resulting in higher number of grain nuclei and thereby a refined GS.
However, at high heating temperatures coarse grain sizes can be obtained as result of grain growth

The overall number of austenite grains decreases and the inhomogeneity of austenite grains increases as some larger austenite grains merge the smaller ones.
The austenite grains spontaneously develop to be less grain boundary area and lower grain boundary energy.
The grain boundaries of austenite are flat and the overall number of austenite grains are few as shown in Fig. 5(a).
Meanwhile, the overall number of austenite grains increases and the grain size of austenite decreases with the increasing of heating rate.
The coarse grains disappear and the percentage of austenite grains with grain size below 20 μm is 79.4%.

Accordingly, grain boundary energy should be used here.
(3) The experimental values [4, 5] of KH-P for a number of FCC metals are listed in Table 1.
After the S value is calculated, grain boundary energy density, WGB, defined as the amount of grain boundary energy per unit volume (J/m 3), can also be computed, written as, dSWGB /2γγ == , (5) where γ denoted the grain boundary surface energy, i.e. the energy per unit grain boundary area.
It is now hypothesized that an expression to demonstrate the energy-stress proportionality, similar to that shown by equation (2), should also hold for grain boundary component; as a consequence, the grain boundary stress component and grain boundary energy density must satisfy the following equation: 2 GB GBW σ∝
Furthermore, if assuming that equations (4), (5), (6) and hence also (7) are independent of grain sizes, the equation (8) obtained in the present work should hold over all grain sizes.

On the criterion of precession of the location result, there are fine-grained locating and coarse-grained locating.
The cost of coarse-grained locating is much lower.
Take the number 0 grid shown in Fig. 3 for example, its level 1 adjacent neighbor grids are the grids that immediately adjacent to it, namely, grids number 1~6.
And its level 2 adjacent neighbor grids are grids number 1~18.
Number 7~18 grids are immediately adjacent to number 1~6, and their neighbor interval to grid 0 is 1.

The grains of base metal (BM) are elongated and composed of a great quantity of low-angle grain boundaries.
Under thermal cycle, the grains here recrystallized dynamically, caused the increase of grain boundary density.
The red arrow in the figure indicated the needle-shaped precipitates, and the red numbers indicated the energy spectrum acquisition positions.
Firstly, the grain size was considered.
The reduction of grain size from 7.2 to 4.5μm generated 22% grain size strengthening, and to 5.8 um in the TMAZ, the grain size strengthening decreased to 12%.

The five-parameter grain boundary character distribution (GBCD) of a material contains both the grain boundary plane orientation and the lattice misorientation information.
The statistics that are used to quantify the differences between the synthetic and experimentally observed structures are texture or orientation distribution (OD), GBCD, number and area fractions of S3 and coherent S3 boundaries, S3 cluster distribution, and twin density.
The main simulation code used in this study is the grain orientation assignment algorithm.
To demonstrate the capability of the twin insertion algorithm, the twin grains were removed from an experimental structure, Inconel 100, and were then regenerated with the twin insertion algorithm.
The largest S3 cluster measured in the experimental Inconel 100 structure consists of 98 grains, which can only be observed by analyzing the fully-reconstructed 3D structure.