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The goal of this work is to metallurgically decrease stray grain formation by control of solidification behavior.
(1) where Γ is the Gibbs-Thomson coefficient, R is the dendrite tip radius, Pei is the Peclet number for i, mi is the liquidus slope, C0,i is the initial concentration for i, ki is the partition coefficient for i, ζc(Pei) is a function of the Peclet number, Iv(Pei) is the Ivantsov solution (i=Cr or Al) and Ghkl is the average temperature gradient near the dendrite tip.
Centerline grain boundary formation is imposed by intersection of [010] and [100] dendrite growth regions.
Unfavorable phenomena of competitive dendrite growth, such as centerline grain boundary formation, columnar/equiaxed transition and divergent grain boundary orientation, are decreased.
Prediction of dendrite orientation and stray grain distribution in laser surface-melted single crystal superalloy.

Each soil section was used for chemical extraction, microbial enumeration, and grain size distribution.
Most Probable Number (MPN) enumeration was conducted for soil samples to determine the number of total anaerobes for a quick screen of bacteria activity.
Grain size distribution analysis is the measurement of the proportions of the various sizes of primary soil particles.
Table 1 presents the distribution results of grain size and MPN for total anaerobes.
Distribution grain size and MPN of total anaerobes.

The defined map shows that most of the grains were elongated and the grain boundaries were serrated having a certain wavelength due to dynamic recovery accompanied with incomplete recrystallization.
Grain orientation map with inverse-pole-figure coloring with respect to the loading direction.
Considering the enhanced strain hardening behavior, a possible explanation is that dislocation generation inside the grains is the dominant mechanism for coarse grains, and the dislocation density accumulates during plastic deformation.
This suggests that slip lines represent only partial information about the deformation in grains.
By examining Fig. 7 and 8 one might suggest that neighbouring grains rotate towards the same end orientation under uniaxial loading hence making it easy for micro cracks to propagate into neighboring grains at 295K.

Ti2AlC/TiC[6] composite material only in a proportion of complex, to meet a number of performance can not improve at the same time, it can not meet the requirements in some circumstances; and the gradient material Ti2AlC/TiC is equivalent to the multilayer Ti2AlC/TiC composite superposition, and each layer with component gradient change, its properties and microstructure can be designed and controlled, the human design and control so as to realize the material strength, toughness, stiffness, thermal and electrical properties, to adapt to different application occasions.
Shown as Fig. 2, energy spectrum analysis of the sample of the 1300℃ sintering can get Ti, Al: C atom number 2.06:1. 08, Ti, Al: C atom number close to 2:1:1, because the sample is at each layer of the composite material, which contains the TiC, so the content of Ti and C more is normal, so don't consider the above factors, the influence of the Ti, Al: C atom number than Ti2AlC atomic number than the basic agreement.
It can be seen from the figure, as the TiC in Ti2AlC volume fraction is reduced, the grain size of Ti2AlC gradually increased, Ti2AlC is the main material gradient layer microstructure, TiC powder particles distribution in Ti2AlC network structure, shown as Fig. 3.
There is a mutation process at about 600℃, and in the 900-1200℃ temperature range increased rapidly, and the two temperature interval is the important stage of material densification, 600℃ is an important process of Ti and Al TiA13 production, particle quickly close to the process, which makes displacement rapid increase. 900-1200℃ is TiC and Ti - Al melt reaction and material densification process, displacement can also be a significant change, 1200-1300℃ displacement remain the same, after 1300℃, displacement tends to decrease,,because in the 1300℃ after Ti2AlC turn into Ti3AlC2, at the same time with the secondary recrystallization process of porosity inside into the grain, and along with the grain grew up, and this will lead to increased volume, displacement smaller.
TiC has a great influence on performance of materials, with the increase of the content of TiC, material grain obviously thinning, the hardness of material in the gradient direction gradually increased.

And the average grain size of the ATC is much smaller than that of the traditional AT composite.
This is because the cobalt distributed uniformly in the matrix, mostly located at the interfaces between Al2O3 and TiC grains[5].
The cobalt locating at the grain boundary reduces the free energy of the grain boundary, restrains the grain boundary movement and acts as grain boundary pinning for grain growth[6-7].
By contrast, the microstructure of the AT composite is not homogeneous with abnormal grain growth, which is disadvantageous to fracture strength.
Crack deflection plays an effective role in the ATC composite, generating a more irregular path with higher deflection angle and deflection number, which is attributed to the interaction of the tangential compressive stress and smaller radial tensile stress in Al2O3 that pins and deflects the crack, increasing crack growth resistance and consuming more fracture surface energy.

On the other hand, XRD data can be related to the estimation of theoretical densities (ρXRD) of each sample using a formula like the following [18]: ρXRD=MZNaV where, M is the molecular mass (g/mol), Z is the number of units in a unit cell, Na is Avogadro’s number (6.02 ×1023 mol-1), and V is the lattice volume obtained from XRD analysis.
This program utilizes the technique of measuring the diameter of almost all grains within the SEM image and provides a statistical calculation of the grain size.
The results of the measurements are distributed in a histogram of grain sizes, while the peak indicates the average grain size of the compound.
The solid-state synthesis methods are known to have large grain sizes but with non-homogenous grain sizes [6].
This indicates that each grain consists of several crystals [7].

Naturally grown, wood has various defects like knots, cracks and inclined grain.
As the R-L and T-L planes are the natural cleavage planes of wood, in which the crack propagates parallel to grain, the RL and TL crack thus deserve more consideration.
Table 2 Stress intensity factor KIIC [MPa·mm1/2] specimen number mean Std CV RL-10 8 68.30 16.34 23.92% RL-15 5 57.04 12.07 21.16% RL-25 8 62.35 10.70 17.17% RL-35 7 71.01 16.32 22.98% RL-45 5 66.60 5.28 7.93% Fig.4.
Effect of thickness on KIIC During the tests, specimens all failed in pure shear, crack propagated vertically along the grain.
The grain direction of the specimens and the arrangement of the electrical resistance strain gauges are shown in Fig.5.

Thus, almost all of the perovskites have the number of high dielectric constant.
Normally, the electrical response from the grain boundary should be associated with larger resistance and capacitance from those of grains.
Grain boundary’s response frequency is therefore much lower than that of grain, and it gives rise to a relatively strong peak in the impedance.
Generally, the peak frequency for grain boundaries is much lower than that for grains due to their large resistance and capacitance compared with those of grains.
Furthermore, in the part of capacitances and resistance in grain and grain boundary are summarized in Table 1.

Triangular and elongated rectangular faceted structures were directionally aligned, and (001)- and (018)-oriented grains were epitaxially grown on (001) and (11(_)0) Al2O3 substrates.
LiCoO2 grains are likely to grow in the c-axis direction owing to the highest atomic density and the lowest surface energy in a (003) plane [13, 14].
In the same manner as mentioned above, the epitaxial growth of LiCoO2 grains were expected with LiCoO2 [1(_)00]//Al2O3 [1(_)1(_)0] in-plane relationship (Fig.3 (c)).
There were a number of small polygonal facets inclined in the various directions.
This would lead the local growth of the (104)-oriented grains.

With the increase of TiO2 content, the size of the calcium oxide grains was decreased, and the formed CaTiO3 aggregated around the surface of calcium oxide grains (Fig.4 (a)-(c)).
When the TiO2 content is constant, the size of the calcium oxide grains was sharply increased, and the number of pores was decreased (Fig.4(a) and Fig.4(d)).
In this work, the promotion of hydration resistance of calcia-based ceramic core composites is considered due to the following two reasons: Firstly, the addition of TiO2, the formed CaTiO3 covered the surface of CaO grains which decreased the area of CaO grains exposed to atmosphere.
Secondly, the area of CaO grains exposed to atmosphere also related to the relative density of sintered bodies.
When the TiO2 was added in the CaO powder, CaO reacted with TiO2 to form CaTiO3, which was mainly aggregated around the CaO grains to inhibit the growth of CaO grains and decrease the area of CaO grains exposed to atmosphere.