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Main reason is that: (a)rare earth elements driving force of grain growth is lesser, inhibits nickel base alloy grains growing up and improving the nucleation rate, which have the effect of grain refining strengthening; (b) rare earth elements promote the diffusion process of WC particles and matrix, makes the WC grain refinement, diffuse distribution and thus has the effect of dispersion strengthened; (c) rare earth elements have great affinity with oxygen, sulfur and other impurities, during the fusion, it plays a good role in removing impurity, make the coating structure becoming compact and improve the coating hardness; (d) But CeO2 content has higher melting point when adding too much, it will make the energy of fusion to be bound to increase and lead to decrease in the number of effective nucleation grain coarsening, so in the same fusion under the condition of adding excessive amounts of rare earth elements makes the coating hardness and organization to become to poor.
This is because the CeO2 is partial in the grain boundary extremely easily, reduce the driving force of grain growth, make the grain refinement, so as to improve the micro-hardness of the coating.
Think commonly, alloys grain is fine some of the hard phase, such as alloy carbides, nitrides dispersion degree are better, the alloy wear resistance is better.
When CeO2 addition amount was 0.75%, the coating on the surface of WC and defect are small, forming micro cell number is relatively small, so the corrosion resistance is better.

In particular, it can lead to grain refinement.
Other equations relate to the activation of slip and twinning systems in grains.
The initial textures was represented by 19200 grains.
A polycrystalline sample containing 150 grains was attached to each finite element of the C3D8R type (8-nodes linear brick with reduced number of integration points).
Acknowledgements This study was financed by the Polish National Centre for Science (NCN) under decision numbers DEC-2011/01/B/ST8/07394 and DEC-2011/01/D/ST8/07399.

The results showed that homogeneous distribution of Si3N4 particles along the grain boundaries has increased the hardness of the SAC107 - Si3N4 composite solders compared to monolithic SAC107 solder alloy.
Reducing the Ag content of the SAC alloys, such as Sn–1.0Ag–0.7Cu (SAC107) alloy gives rise to more primary β-Sn phase (large β-Sn grains) and decreases the number of Ag3Sn IMC particles.
Result and Discussion Microstructural Analyses.The Si3N4 (black) particles were well distributed between the grains of SAC107.
The function of reinforcement concentration between the grains will tend to hold the grains preventing from grain dislocation and retards the grain growth.
Fig. 2: SEM micrographs for SAC107 - Si3N4 grains structure with 1000x magnification: a) SAC107 - 0.25 wt. % Si3N4, b) SAC107 - 0.5 wt. % Si3N4, c) SAC107-0.75 wt. % Si3N4, d) SAC107- 1.0 wt. % Si3N4.

σx= σhomogeneous deformation+σfriction+σadditional deformation+σbearing (3) In a multi-stage process, the sequence design or draft will be constituted by a number of consecutive stages (n) and the current stage is defined as i.
Besides, the Hall-Petch Equation (10) allows to predict the grain size in a metal that has been plastically deformed [26].
Summary of results from the FEM and analytical models and grain size calculation.
Modelling of grain size evolution with different approaches via FEM when hard machining of AISI 4140.
Six decades of the Hall–Petch effect – a survey of grain-size strengthening studies on pure metals.

A typical basket-weave Widmanstätten microstructure with an α grain boundary in the prior β grains from annealed 1050°C samples exists in Figure 1(j) (1050A).
The grain size tends to be coarse.
The number indicates the heat-treatment temperature.
In spite of that a few small lamellar grains (w10 mm) are also observed.
(3) Those microstructural parameters which vary significantly are percentage of alpha phase, size and number of alpha grains per unit area, and grain boundary area of alpha grain

This process introduces a considerable number of defects and mechanical stresses which leads to the degradation of the coercivity.
It represents a new and reliable method to prepare nanopowders and was successfully applied in the last years for a number of magnetic complex oxides [28-35].
One may appreciate that the grain size is situated somewhere around 50 nm.
One can see that the crystallite size of ceramics ranges between 0.2 and 1 µm so that the great majority of grains are still below the single domain size.
The reasons for such values consisted in that the energy of magnetic particles in external magnetic fields is proportional to their sizes via the number of molecules of single domain grains.

It has recently become possible at least on the laboratory scale to fabricate ultrafine grained (UFG) metallic materials with mean grain sizes smaller than 1-2 mm [1].
Peak temperature and Dmax as a function of number of ECAP pass.
The height of internal friction peak increases uniformly with the number of ECAP pass.
Terada, Managing both strength and ductility in ultrafine grained steels, ISIJ Inter. 48 (2008) 1114-1121
Langdon, Principle of equal-channel angular pressing for the processing of ultra-fine grained materials, Scr.

Consequent calcination, resulted in the reformation of strontium hexaferrite but now with a much finer grain size.
The first column is the number of times that the initial hexaferrite hydrogenated and recalcined (i.e.
Table 1 The effect of number of HTR cycles on the powder magnetic properties of Sr-hexaferrite Number Mr (J/Tkg) Hci (kA/m) Ms (J/Tkg) 0 38.1 314.6 67.55 1 36.5 413.3 65.51 2 37.9 404.4 69.25 3 36.9 401.3 67.69 4 36.9 403.3 66.94 Fig.1 The magnetization curve of the initial powder.
Fig.3 The effect of number of cycles on the intrinsic coercivity.
The plot of number of cycles versus intrinsic coercivity is exhibited in Fig.3.

The mixturer was divided into a number of copies, each copy was 15 grams(Li2CO3 was 4.3g and TiO2 was 10.7g).
Figure (b) was the image at 900˚C for 12h, the powder grain was also uniform and fine, the grain size was mainly between 1μm and 1.2μm.
A very small number of particles were larger, even the size of a few partilces were 5μm or so.
The grains grew up which compared with those of figure (a).
If crystal grain is too small, numbers of crystal boundaries are advantageous to insertion-extraction of Li+ very much by the additional energy which are provided by crystal boundaries, so the amount of charge/discharge capacity reduces very quickly.

On the current efficiency of the sample was calculated, its micro-hardness, tensile strength and stress were measured; and its XRD tests, analysis of the micro-strain, grain size and position electrical castings dislocation density.
Grain size and distribution of dislocations and strength, hardness and fatigue failure between closely related.
In this paper, single-line Fourier analysis method[3,4] for the broadening effect of X-ray diffraction spectra were analyzed draw microscopic strain <ε_L^2> and dislocation density ρ_s, grain size calculated by Scherrer formula.
The data listed in Table 2 is calculated according to the following diagram and the grain size of XRD lattice strain.
Range analysis using the data can not distinguish between the causes of fluctuations due to changes in experimental conditions or due to experimental error, and the various factors on the effects of fluctuations in the size of the data can not give the exact number of estimates, in order to compensate for the lack of range analysis, analysis of variance.