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The doping elements might enter the gap of the lattice structure of TiO2, or replaced a small number of the elements on the lattice [5].
The average grain size of the doped TiO2 was 17.57 nm according to the Scherrer equation (2) (2) where D was the grain size, k the grain shape factor, about 0.89, λ the X-ray wavelength (Cu Ka radiation, 0.154056 nm), β the full width at half maximum (FWHM) of the anatase (101) diffraction line, and θ the anatase (101) Bragg angles(2θ).

Trace V is added to refine the grain.
Abrasive grains were revealed in the blade flank, resulting in the abrasive wear, which is a standard mode of the tool wear associated with the entire cutting process.
The multi-layer structure of the M3 coating exhibits a large number of interfaces and a smaller grain size.

The number and position of spot welds strongly influence the performance characteristics, such as static, dynamic and crash behaviours.
However a large number of welds is costly, and efforts have been made to reduce the number of welds without changing the rigidity of the final assembly.
The number and position of spot welds, as well as the order in which they are executed, also affect the geometrical quality of an assembly [2].
IF steels typically have in the substrate microstructure with equiaxed ferrite (ASTM grain size equal to 8.5 (17 μm)) with carbonitrides of niobium/titanium.
Fig. 3 shows the correlation between the number of spot welds with respect to weld current and weld button size.

Material behavior of the zinc coating (Eq. 2) is derived from the load-displacement curves using Nano-indentation test on various zinc grains by Song et al. [11].
N is the number of contacting bars with the tool and N* is the number of non-contacting bars that come into contact due to the rise of asperities.
Shearing length, Δsh=z-d-u which represents the shearing distance between a raising bar and its neighboring crushing bar. n is the number of sides of the bars in shearing (n=2 for 3D).
The real area of contact can be calculated by summing up the number of contacting asperities that are higher than the tool equilibrium position (asperities on the right side of vertical line on Fig. 5 (b)).
Tabor, The hardness of solids, Review of Physics in Technology, Volume 1, Number 3 (1970)

In the microstructural analyses there were observed numerous cracks at grain boundaries.
The work included the following: The first group (without erosion.): consisted of (8) tested specimens, the used loads were variable (low - high) and (high - low) with a fixed period of 10,000 cycles until the failure of the specimen to know the number of failure cycles for the specimen at that level of stress, respectively.
The following table shows the specimen numbers and (low - high) and (high - low) stress ranges.
Refer to Figs.4 & 5, which represent the state of linear stress of the metal with the stress - number of cycles curve, the accumulated damage can be expressed in the following equation [13].
Depending on Fig. 1: Xi =NfB (σi- σL)(σH- σL) (6) Where NfB = cycle number of the specimen.

The grain size distribution curve indicated that sediment is predominantly silt-sized with 60% of clay; the percentage of particles whose diameter is less than 80µm is about 78%, and tuff particle size lays mainly around 500 um, with neither fraction of particles below 5 um or above 1.25 mm.
The ceramic waste powder shows a completely different size distribution, with a large number of coarse particles (about 92% above 1 mm) and nearly 34% ultrafine (size <125 um).
Grain size distribution of studied materials.
Properties Fergoug Sediment Ceramic powder Tuff Consistency limits : NF: 94051 Liquid limit (%) 28.21 22 38.28 Plastic limit (%) 15.09 - 23 Plasticity index (%) 13.12 - 16 Specific weight NF: P 94-054 Specific weight 2.55 2.58 2.61 Grains sizes analysis NF: P 94-057 Sand (%) 14 25 18 Silt (%) 25.60 45.70 33.33 Clay (%) 60.40 34.30 48.67 Maximum dry density: γopm 1.73 1.73 1.92 Compaction NF P 94-093 Volume of blue VB (cm3) 5.50 0.12 7.52 Specific surface SST (m²/g) 111.50 2.52 157.72 (a) (b) (c) Fig. 2.

The finer of grain size, the higher the solubility [8].
The effectiveness of natural P application determined by reactivity, grain size, method and timing, natural-P measurements, crops, and cropping patterns [8].
Before the incubation process, soil mixed beforehand evenly, then sieved with a 2 mm sieve to obtain homogeneous grains of soil particles.
Response to Ameliorant Nanoparticle Phosphate Rock and Phosphate Solubilizing Fungi to Soil C-organic (%) after One Month Incubation Nanoparticle Phosphate Rock C-organic [%] After One Month’s Incubation Phosphate Solubilizing Fungi h0 = Untreated (Control) h1 = JPF 10[g /Polybag] b0 = Untreated (Control) 2,57 B 2,37 A c b b1 = 2% of soil weight 2,39 A 2,44 A b b b2 = 4% of soil weight 2, 44 B 2,24 A bc a b3 = 6% of soil weight 2,24 A 2,20 A a A Note: The average number followed by the same letter is not different significantly according to Duncan's multiple distance test of 5%.

For the high mountains and steep on yunnan laterite area, there are a lot of lateritic slope, a long period in climate condition of warm, wet, more rainy and partial acid, In combined effects of underground water and infiltration of rainwater especially acid rain, will produce hydrolysis reactions and corrosion function to laterite particles and the connection among grains, leading to the composition of laterite happen migration with seepage flow, lead to the changes of macro and micro characteristics of slope laterite, lead to serious geological disasters.
(a) The effect of compaction energy or moisture content or temperature (b) The effect of immersion time Fig.2 The migration ability of iron ion in laterite in different effect factors The migration process of iron ion in laterite in water environment The migration process of iron ion in laterite is actually the process that adsorption iron ions in laterite grains surface dissolve and migrate into water solution in water environment.
With the extension of immersion time, the number of the iron ion migration out of the laterite is more and more large.
In the water environment especially seepage, the migration of iron ions directly affect to the linking performance between laterite grains, thereby affect to the structural stability of the laterite and even the occurrence and development of lateritic geological disasters.

., grain size can be reduced) [12], (2) Effective solidification allows for more precipitation hardening [13]; and (3) Balance Precipitation (i.e., phases detrimental to mechanics or corrosion properties) can be suppressed by rapid cooling [14].
Because traditional casting features grain separation at the contour, it requires further machining, which raises production costs [17]. 
PM avoids problems associated with the traditional smelting process, in addition to controlling the growth of the grain [21]. 
The trend analysis showed that there has been a growth in the number of publications, especially reflected in the last year; however, these publications were distributed in a wide range of journals.

The grain size of the film corresponding to (111) plane for cubic reflection has been found to be 4.5 nm.
From the image, it can be seen that the grain sizes of the film are not uniform.
Ne=N∞1-e-t/τ (5) Where Ne is the number of electron being released from trap states and reaching conduction band, N∞the value for infinite time, τ is effective time constant for recombination of charge carrier.
Chen, S.L. yang Study of grain size effect of rf sputtered CdS thin film,J.Appl.Phys.,79, (1996)9105 [24] F.