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Microscopically, broken grain boundary particles or segregations form sites of cleavage initiation whereupon the crack may further propagate along favorably oriented crystallographic planes of the neighboring grains.
The first micromechanical model to simulate crack initiation and propagation within the ductile-brittle transition region was proposed in [4] incorporating so-called “cleavage grains”.
Nodular cast iron was chosen as model material as its graphite particles are relatively soft and loosely bonded allowing to model them as a priori existent voids so that the number of model parameters is reduced.

Proving it is effective to measure surface of cement clinker mineral, figures of hydration C-S-H grains and outlines, pore structure of concrete section.
The natural fractal which are made by discrete bodies, such as the broken body of concrete, decentralized state of cement particle, the distribution of planet in universe, can be defined with box dimension as： (2) In this formula: N(r)——the numbers of discrete structure whose sizes are beyond r C——the constant of material Another form in this formula show the relation between the number and radius.
That is to say, when you use different rounds which have different radius to cover discrete body, and then count out the number M of it in the round with the radius of r, if this discrete body is the fractal distribution, the number and radius should be followed the next formula: (3) The dimension getting in this formula is named Cluster dimension.

Ore-processing had made 100 mesh, 200 mesh, 400 mesh and 800 mesh grain size in four different test samples and each grain size of samples are 50kg.
It is a must to grasp the rate between the nuclei and the crystal grain production if wanting to control the crystal size of the product.
Generally, going up the temperature can accelerate the reaction rate and the nuclei of the precipitation, as well as the growth of grains.
Determination the appropriate of material's number and reaction time can not only benefit to the control of production process, but also the reduce of production costs.
Using the method of coarse-grained level and grade purification achieves the separation of silica and impurities.

As an example, it can be observed that a quartz grain (SEM original photo, on right and below) it is majority formed by SiO2, once Si and O are the major chemical elements detected (see mapping-photos with green colour for Si and blue for O, Fig.4).
Fig. 4: Microstructure (right and below) and EDS analysis of a quartz grain, after 1% HF during 6 hours.
These damages were dependent on the fly ash grain size, but in general it was detected some predictable situations: the external coating in the mullite and hematite grains were almost destroyed; the mullite grain showed some internal disaggregation due the removal of internal vitreous phase; the hematite grain denote less internal damage than mullite; and the quartz lost its rounded surface probably due the vitreous phase removal.
Furthermore, the 5% HF-attack showed a strong destruction in a large part of the present grains, in such a way that the fly ash acquired an unrecognizable microstructure (see Fig. 6) also noted by a drastic change in grain size.
However, most of the grains are very small with only 2 µm, as typical for clay particles (a natural well-known aluminosilicate mineral).

In general Ag NP’s are used for a number of applications due to the special electrical and biochemical properties [13] [14].
The number of laser pulses did not affect the ablation of atoms of the oxides (nickel and silver) as show in figure 2b and c.
Can show the grain size equal 19.83 nm for AgO contains several nanoparticles with average sizes equal to 15nm.
The grain size 23.71nm and average particles size20nm.
The vertical axis displays the number of x-ray counts whereas the horizontal axis displays energy in KeV.

Cu addition generates the appearance of α phase sheets inside the β phase grains.
The obtained microstructure of Ti34Nb alloy was mainly β phase (bcc), with α phase (hcp) only appearing in the grain boundaries.
Ag addition did not modify the microstructure of the alloys, while Cu addition favored the growth of α phase in form of needles from the grain boundaries, Fig. 2 d and e.
Sample Maximum strength[MPa] E [GPa] Ti34Nb 990,89 76,79 Ti34Nb1,5Ag 930,05 72,34 Ti34Nb3Ag 956,13 68,89 Ti34Nb1,5Cu 849,45 90,33 Ti34Nb3Cu 761,54 92,59 Conclusions Microstructure and mechanical properties of new Ti34Nb-xCu, Ag alloys (x=1.5 and 3), where number indicates the %wt of the alloying elements, obtained by powder metallurgy have been studied.

The bonding between the particles attributed to the rise in temperature will increase evaporation of molten salts and lead to sintering between the grains.
It is similar to the higher temperature, a longer isothermal time also will increase evaporation of molten salts and lead to sintering between the grains.
But higher temperature and longer isothermal time will increase evaporation of molten salts and lead to sintering between the grains.
With the increase relative amount of salt, it provides a greater growth space, makes the grains move more easily in molten salt and eventually promotes the reaction, all these lead to an increase of relative of particles[11-12].
With increasing time the number of particles does not change but they grow in size.

Introduction Laves phase [1] is one of the common intermetallic phases that appear in a number of alloy systems [2,3].
The precipitation of a second phase is observed at the grain interior of the Ir2Y matrix in the as-cast alloy.
A magnified micrograph of an Ir2Y grain interior in the annealed alloy (Fig. 2(a)) is converted into a binarized image (Fig. 2(b)).
(a) A magnified micrograph of an Ir2Y grain interior, (b) a binarized image of (a), and (c) an Ir-rich portion of the Ir-Y binary phase diagram.
TEM bright field images of Ir2Y grain interiors: (a) as-cast and (b) annealed at 1973 K for 100 h.

Residual Pr values of the thin film doped with La or Nd by 109 circles are about 80％ initial value .And Pr values of BNT thin film decreased slower with cycle number increase.
Fig.2 Diagram of the electric hysteresis loops Fig.3 Diagram of the anti fatigue performance of doping BTO thin film of doping BTO thin film Microstructures Fig.4 and Fig.5 is respectively surface morphology figure of BLT thin film Zoomed to 35,000 times and BLNT thin film Zoomed to 80,000 times.From the figs ,it shows that thin film surface is smooth and compact, rod-like and discoid grains can still be observed, grain size is between 100nm and 200nm.
Grain size is uniform, it is made by two grains of rod-like and discoid.

To reveal the grain structure of the as-sintered composites, representative samples were polished and thermally etched.
Compared to the plain YSZ, the densification of the CeO2-YSZ composites was hindered by CeO2 addition, as both grain growth and relative density decreased.
Sintering parameters, grain size and density for studied composites Sample Sintering Temperature (°C) Sintering Time (min) Grain Size (µm) Density (g/cm3) Relative Density (%) YSZ 1400 7 9.84±0.53 5.83 94.4±1.1 5 mol% CeO2 + YSZ 1300 5 1.58±0.26 5.37 87.0±0.8 10 mol% CeO2 + YSZ 1400 7 3.78±0.67 5.53 88.3±0.9 15 mol% CeO2 + YSZ 1400 7 2.07±0.17 5.53 87.3±1.3 Corrosion Rates.
Weight loss during SCW corrosion test Sample Sample Number Weight Loss (g) Corrosion Rate (mm/y) Comments YSZ 1 0.1923 120.06 Preferential Degradation 2 0.3994 259.65 Disintegrated 3 0.1704 165.84 Disintegrated 5 mol% CeO2 + YSZ 1 0.0169 11.62 Spallation 2 0.0021 1.77 Intact 3 0.0051 3.90 Spallation 10 mol% CeO2 + YSZ 1 0.0677 51.06 Spallation 15 mol% CeO2 + YSZ 1 0.0022 1.53 Spallation 2 0.1240 84.48 Spallation 3 0.0047 4.13 Spallation Phase Stability.