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Isothermes of grain boundary tension and grain boundary adsorption in Cu-Sn system Vaganov Danil1,a and Zhevnenko Sergey 1,b 1 Moscow State Institute of Steel and Alloys (Technological University), 4, Leninsky pr., Moscow, 119049, Russia a vaganov_d_v@pochta.ru, b sergeyng@mail.ru Keywords: Grain boundary tension; Grain boundary adsorption; Free surface tension; Zero creep method Abstract.
Today, there is a lack of such data due to the limited number of the measuring methods and possibilities of apparatus.
The groove is formed at the place of grain boundary exit to the surface.
The average grain size was 115 µm.
It is possible to evaluate the number of sites in surface monolayer A A m N N V Г 3 2 max −       = (5) 0)1ln( γ γ ++−= bc zRTdc d Г γ RT c −= bc1zbc + =Г 47.0)30001ln(102.0 ++ −= c GBγ 81.1)100001ln(148.0 ++ −= c sγwhere Vm is the tin molar volume and Na is the Avogadro number.

The high number of total lattice points with 250250250 ×× MCUs keeps the number of grains adequately for statistical analysis.
Figure 2: Temporal development of the: a - number of grains vs. grain radius and b - relative number of grains vs. relative grain size.
Fig.3b) so that the number of still existing grains during coarsening is always large enough for statistical data analysis.
Figure 5: a - Number of neighbouring grains vs. relative grain size; b - Volumetric rate of change vs. number of neighbouring grains divided into classes after 500 time steps (the three grey crosses are data that are ignored because the associated grains disappear during the considered time steps).
Acknowledgments The authors would like to thank the Deutsche Forschungsgemeinschaft for financial support under grand number GKMM 828.

The partially transformed microstructures were characterized by measuring the transformed ferrite volume fraction fvα, the mean ferrite grain size, dα, and the number of grains per unit area, NA.
The higher the number of active nuclei the smaller the ferrite grain size will be.
After saturation of the initial grain boundaries, the prior grain interiors stay almost free of ferrite grains.
It could be argued that the occurrence of some recovery in the austenite before transformation can lead to a reduction in the number of available nucleation sites through the decrease of the dislocation density.
There is experimental evidence showing that a part of the boundaries disappear, leading to a net decrease in the number of ferrite grains during transformation.

Polycrystalline materials typically contain a very large number of grains whose surrounding grain boundaries evolve over time to reduce the overall energy of the microstructure.
Thin polycrystalline films are typically composed of a large number of small grains, and the surrounding grain boundaries largely determine the microstructure of the material.
Although applications typically involve polycrystalline specimens containing a very large number of grains, it is instructive to consider small idealized systems, such as special bicrystalline systems, which can be studied in detail [2, 4, 11].
(b) The grain boundary XIII.
(b) The grain boundary XIII.

The number of faces per grain f and the average number of faces of each grain’s nearest neighbors m(f) is counted.
Fig. 2 shows the distribution of the number of grain faces in the system.
Fig. 3 plots the average number of faces of each grain’s nearest neighbors, m(f), vs. the number of faces per grain.
A distribution in the average number of faces of a grain’s neighbors is observed for a given topological class f.
Fig.3 Plot of the average number of faces of the nearest-neighbor grains, m(f), vs. the number of faces of the grains, f.

The normalised cumulative number of nuclei/grains, as generated in the simulation, has been plotted as function of the simulated transformed fraction in Fig. 3 b).
For decreasing ratios of SGB V / ˙NO (and the same nucleation rate ˙NV , see above), the same number of nuclei must form on a more and more restricted grain-boundary area and therefore nuclei are more likely to appear close to each other.
This positive correlation of nucleation positions is exhibited in Fig. 1 c) and is the reason for the retardation of the transformation kinetics as observed (Fig. 1 a): The closer to each other nuclei form, the sooner they impinge which leads to slow transformation kinetics and a high number of small grains.
Moreover, for such parent microstructures, the last part of the transformation is further slowed down because there are a number of very large parent grains (which can be transformed only by product grains nucleated at grain boundaries of these grains).
fraction as function of the transformed fraction predikted by the JMAK-like model and b) normalised cumulative number of nuclei/grains during the simulation as function of simulated transformed fraction.

The grains became thinner and elongated to the rolling direction with increasing the number of ARB cycles.
In addition, the fraction of high-angle grain boundaries increased with the number of ARB cycles and reached about 0.7 after 8 cycles.
Figure 4 shows the variation of mean spacing and the fraction of high-angle grain boundaries with the number of ARB cycles.
Summary The grains became thinner and elongated to the rolling direction with increasing the number of ARB cycles.
In addition, the fraction of high-angle grain boundaries increased with the number of ARB cycles, reached about 0.7 after 8 cycles.

The samples exhibited a large number of intermetallic particles on polished sections in each case.
No appreciable difference was found in the number density of particles between the base alloy sample and the grain-refined sample.
A total of 63 such particles were captured from a large number of randomly selected viewing fields and probed at 20 kV.
It can be inferred from the Al-Mn phase diagram [7] that this master alloy splatter may contain a large number of metastable intermetallic phase particles such as ε-AlMn.
Therefore, we can make the assumption that the nucleant is ε-AlMn in commercial AZ alloys, a b c d although the number density of these ε-AlMn particles is much lower than for Al8Mn5.

Briefly, the microstructure to be modeled is discretized, and the orientation number at each grid point is associated with a 3-parameter crystallographic orientation.
Each voxel i in a simple cubic lattice of N=100x100x100=10 6 elements was assigned an orientation number Si=500.
The misorientation distribution (MDF) was quantified by counting the number of voxels adjacent to a different grain and sorting them by misorientation type.
Journal Title and Volume Number (to be inserted by the publisher) 5 (i) (ii) Fig. 3.
Journal Title and Volume Number (to be inserted by the publisher) 7 Figure 6 illustrates the behavior of several systems.

The initial austenite grain size plays an important role in the obtained ferrite nucleation number, and the potential nucleation cells are increased.
Fig.4 shows the ferrite nucleated cell number as a function of austenite grain size.
As shown in this figure, as the initial austenite grain size is increased, the ferrite nucleated number is decreased.
Therefore, as the initial austenite grains size become small, the nucleated ferrite grain numbers large.
Thus, increasing potential nucleation number and improving nucleation probability of each nucleation position can be helpful in obtaining fined ferrite grains.