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From the XRD spectra the dislocation density, average crystallite size, number of unit cells, and porosity were calculated and analyzed .
Characterization The phase identification and grain distribution of the sintered samples were identified using X-ray Diffractometer (XRD) (Philips: PW1830), at University of Hyderabad, A.P.
From the X-Ray diffraction studies, dislocation density, number of unit cells and porosity were evaluated.
Cisowski ,The relationship between the magnetic properties internal structure of their component Fe-oxide grains”, Geophys.
Rath.Emission of Dislocations from Grain Boundaries and Its Role in Nanomaterials, Crystals 11, 1(2021) 41. https://doi.org/10.3390/cryst11010041 [21] Indrakanti, Rajani & Rao, V & Chavan, Udaya. (2017).

It is common to obtain the FLD experimentally by measuring at critical areas, the major and minor strains from deformed circles that have been previously electroetched or imprinted on the surface of specimens from a number of different types of formability tests.
These effects are usually divided into two distinctive categories: “grain size effect” to describe the interactive effect of the grain size of the material, which is a dominant effect at micro scales; and ‘‘feature/specimen size effect’’, which depends on the process/test, referring to the size of the feature/specimen and the smallest feature to be obtained, or in other words, an indicator of the manufacturability.
The grain sizes were measured using an optical microscope and maintained constant throughout the experimental work.
The grain sizes d were measured using a commercial image editing software ImageJ.
Fig. 5 shows an almost linear evolution of the effective stress for both M and N numbers, presenting a similar trend to other observations reported in the literature [4] at similar stress levels for stainless steels, however, it will require improvements on the apparatus and experimental techniques to control the grain size in order to obtain more conclusive results.

But there are still some broken and coarse block product distributed at the grain boundary or in the interdendritic regions.
In the meantime, there are a large number of ultrafine dot-like particles in the homogenized alloy ingot, and the distribution of them are heterogeneous.
There are some ultrafine dot-like particle-free zones at the grain boundary or in the interdendritic regions which is the the end of solidification zone, or in the centre of dendrite arms which is the preliminary solidification zone during casting process (as shown in Fig. 1 (b)).
It can be seen that the grain shape of the solution-treated plate that hot-rolled from homogenization ingot is coarse and equal-axis (as shown in Fig. 5 (a)), the grain shape of the solution-treated plate that hot-rolled from homogenization-free ingot is almost fine fibrous (as shown in Fig. 5 (b)).
Because the larger number of fine, dispersive and homogeneous AlFeMnSi particles can inhibite the recrystallization behavior of α-Al matrix.

As can be seen from microstructures presented in Fig.2, the nucleation of austenite occurs preferably at the ferrite-cementite interface in pearlite colonies and to a less extent at ferrite grain boundaries due to lack of cementite particles on ferrite grain boundaries after coiling at a high temperature.
The more uniform distribution of carbon containing phases, cementite particles in particular, together with a much smaller size of ferrite grains are responsible for a larger number of austenite nuclei in the steel after a low CT.
Regardless of the higher volume of recrystallized ferrite grains in the steel coiled at a higher CT, the nucleation of austenite is more intense in the steel after a low CT.
Holding at 740 oC accelerates the recrystallization of ferrite promoting the formation of austenite nuclei at recrystallized ferrite grain boundaries (Fig.4).
The higher volume of recrystallized grains and enhanced dissolution of cementite during holding results in an increased number of austenite nuclei, which in turn assists the formation of more uniform refined microstructure in the steel coiled at a higher temperature.

Austenite nucleates at ferrite-ferrite grain boundaries or ferrite-cementite boundaries.
Spheroidization reduces the number of sites available for austenite nucleation.
Figure 2e (LCR 1019M) shows evidence of unrecrystallized grains from a combination of equiaxed, “clean” grains and pancaked, deformed grains [8].
It is possible that Ac3 is reduced at 1000 °C/s because of the greater driving force and the greater grain boundary area (due to smaller grain size) that provides nucleation sites in the final period of austenitization.
Furthermore, the Andrews equation is limited to a small number of elements and compositional ranges.

Researches on material properties were mainly focused on impurity elements (such as P, S, Mn elements), yield strength and grain boundary carbide [5-11].
Some M-A islands are semi-continuous and nearly parallel and they tend to grow along grain boundaries, which accords with the characteristics of granular bainite.
Some M-A islands distribute irregularly and grow up across grain boundaries, which corresponds to the characteristics of granular structure [14].
The grain size of three rotor steels were statistically rated through the three-circle intercept method.
Results show that the grain size numbers of 25Cr2Ni2MoV steel and 26NiCrMoV10-10 steel are 7.5~8.0 grade with a corresponding average diameter of 22.5~26.7μm and the grain size number of 30Cr2Ni4MoV is 6~7 grade with a corresponding average diameter of 31.8~44.9μm, which indicates that the grains of all three rotor steels are relatively fine and uniform.

The use of a wheel with fine abrasives is effective in improving the quality of surface roughness and reducing the thickness of a damaged layer, due to the increasing number of active grains.
The dropping of dull abrasive grains prevents both the increase of lapping force and loading of swarf.
Moreover, large grains can fall into the plate and support approximate load with other abrasives of plate, which is called 'trap' effect.
Surface roughness is tested by Mahr Perthometer S2 surface roughness measuring equipment, scan length 5.6mm, sampling number 11200, vertical resolution 0.8nm.
The dropping of dull abrasive grains prevents both the increase of lapping force and loading of swarf.

As the grain size is small, the grain boundary fraction cannot be neglected and we will study properties of both grain boundary and core grain by Mössbauer spectrometry, which is appropriate to study the specific problems of nanometer range [26].
More the number of samplings is and more the powder is contaminated.
However, it is well known that the MA process gives a distribution of the grain size, which should give a paramagnetic contribution for grains having the smallest size and a magnetic contributions for the largest grains.
For the mean grain size obtained by MA (about 10nm), the grain boundaries can be estimated to approximately 20 % of the total volume.
This fraction can be estimated using a simple spherical grains model assuming grains as a spherical crown of mean δ/2 width (grain boundary) surrounding the spherical grain core of mean diameter d.

Among machine learning algorithms, support vector regression (SVR) is one of the robust models that can observe quantitative and numbering to form predictions.
The total numbers of band gap energy for ZnO are 130 and the relevant ranging of dataset obtained covers from 2.020 eV to 5.330eV.
The dataset consists of lattice parameters a, and c, crystallite size, and grain size that were segmented into training and testing dataset with ratio of 8:2.
,xn,yn⊂X×R, where xi is the input feature of either lattice parameters a, and c, crystallite size, or grain size, and associated yi is the Eg, X is the space of the input patterns, and R is a real number.
From observation, when a high number of training dataset was trained, the better the prediction obtained.

Table 1 summarizes average grain size and volume fraction of the second phase particles.
Average grain size (µm) and volume fraction of second phase particles (%) for the alloys recrystallized at 1073K and 1273K for 1h.
First, the particle-matrix interfaces may act as dislocation sources and consequently provide a number of dislocations responsible for the plastic deformation.
Secondly, the density of dislocations generated from grain boundaries is expected to be higher in a fine-grained microstructure (i.e., the alloys with the second particles) than in a coarse-grained microstructure (without the second particles), consequently resulting in higher tensile elongation in the former alloys than in the latter alloys.
Moreover, deformation behavior in a coarse-grained microstructure is inhomogeneous causing in local stress concentration leading to a premature fracture, while deformation behavior in a fine-grained microstructure is homogeneous, resulting in the increased strain to fracture.