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As for the properties of grain boundaries the compensation effect was observed in grain boundary diffusion [1], migration [2,3,5] and solute segregation [5].
To fulfill the condition 4, the grain boundary concentration is defined by the tangent to the Gibbs energy of the grain boundary parallel to Fig. 1 Gibbs energy in grain boundary segregation.
(9) In general, d∆H ch(Ψj) ≠ 0 and d∆Sch(Ψj) ≠ 0 are real numbers and therefore, there must exist a range of the changes of the variables Ψj within which the constant temperature Tc is defined as j PT N j j ch j PT N j j ch ch ch c ji ji S H S H T Ψ         Ψ∂ ∆∂ Ψ         Ψ∂ ∆∂ = ∆ ∆ = Ψ≠Ψ = Ψ≠Ψ = ∑ ∑ d d d d ,, 1 ,, 1
Let us comment here this connection for grain boundary segregation.
Tc is 930 K in the grain boundary segregation in α-Fe but 1386 K in the grain boundary migration in Fe-6at%Si alloy [5]).

The SPS-950 consists mainly of submicrometer-sized grains (Fig. 3a), whereas the PLS-1350 exhibits larger grain sizes, usually of several micrometer (Fig. 3b).
Generally, domain wall motion induces the degradation of Qm and thereby, higher Qm value shown in the SPS-950 was attributed to pinning the movement of the aligned domains on the large number of grain boundaries resulting from the fine grain size [7].
In addition, it is interesting to note that the Kp value is the same for both the SPS-950 (fine grains) and the PLS-1350 (larger grains), because generally as grain size decreases, the randomly oriented domains are difficult to be arranged [8].
Domain structures depending on the grain sizes in the SPS-950. was domain size�(grain size) m , which leaded to a parabolic scaling (m�1/2) [9].
Most grains are found to consist of ferroelectric domains whos e structure is similar to that in bulk, with single-domain in a few small grains.

After conventional melt-treatment, there were still a number of oxide inclusions, still distributed non-uniformly and gathered together; but their size decreased to about 10-20μm.
After high-efficient melt-treatment the number of inclusions was decreased obviously, and distributed along grain boundary or within the grain very uniformly (about or less than 4μm), and no congregation of inclusions was found in this material.
From Fig.1 it can be seen that the high-efficient melt-treatment can decrease effectively the number of inclusions and improve their existing morphologies.
The inclusions congregated in a large lump form and distributed non-uniformly along grain boundary.
After high-efficient melt-treatment, the number and content of inclusions in molten Al have decreased remarkably, and their size was very small [2-4].

Austenite final grain size was measured .
grain size.
The experiment also shows that steel with higher Nb content has lower grain growth kinetics and has the finer austenite grain size.
Higher cooling rate after hot rolling and recrystallization will produce finer autenite grain size, and steel with higher Nb content has lower grain growth kinetics and has the finer austenite grain size. 2.
Tech, vol 24, Number 2, (2008.)

This processing produced ultra-fine grained (UFG) structure with an average grain size of 0.6 μm and an average dislocation density of ~4×1014 m-2.
However, there were a limited number of reports dealt with examination of superplastic behavior of Cu alloys [1,2,4].
Grains and (sub)grains contain a large number of lattice dislocations (r~4×1014 m-2) (Fig. 1b) [10].
The formation of significant number of annealing twins occurs during dynamic grain growth [1] (Fig. 7b).
Acknowledgements The financial support received from the Ministry of Education and Science, Russia, under Grant No. 14.575.21.0005 (ID number RFMEFI57514X0005) is gratefully acknowledged.

A significant number of experimental investigations have now been performed on both columnar and equiaxed growth using a number of different alloy systems [4–6].
Currently, a number of different microgravity platforms are available, and have been used, for solidification research, e.g.
The numbered dots correspond to g-level measurements in Fig. 3.
Numbered dots correspond to the image stills in Fig. 2.
Fig. 3 shows the g-level and temperature measurements recorded during solidification, along with the time-axis locations of the images in Fig. 2 correlated by the numbered dots.

The grain sizes were expressed the grain size number G, standardized by ASTM.
As-received AZ31 sheet 1.0mm thick showed fine and uniform equiaxed structure and the average grain number was approximately 9, while specimens 1.6mm and 2.0mm thick showed the abnormal grain irregularly.
Grain size increased with annealing temperature.
The grain size numbers of as-received and annealed AZ31 sheets are shown in Fig. 6.
Fig. 6 Grain size number of AZ31 sheets Fig. 7 Vickers hardness of AZ31 sheets Fig. 8 shows the mechanical properties of AZ31 sheets annealed at different temperatures during 1 hour.

Diffusion bonding of Ti-6Al-4V titanium alloy in the coarse grained and ultrafine grained state was performed.
Since grain boundaries play a major role in diffusion, it can be assumed that reducing the grain size and increasing the surface area of grain boundaries should improve diffusion.
UFG and CG couples of samples, with average roughness Ra=50 nm, bonded at temperature of 725°C have approximately the same number of pores of similar shape (Fig. 4a and Fig. 4b).
Zhu, Grain boundary diffusion and creep of UFG Ti and Ti-6Al-4V alloy processed by severe plastic deformation, Proc. of Ultrafine Grained Materials III. (2004) 621-628
Valiev, Grain boundaries in ultrafine grained materials processed by severe plastic deformation and related phenomena, Materials Science and Engineering A. 540 (2012) 1– 12

Both XRD and TEM showed that a small difference in grain sizes remains even after 5 revolutions of HPT with smaller grain sizes at the peripheral region of the sample.
The increase in microhardness was attributed to further grain refinement, the formation of a larger fraction of high-angle grain boundaries and grain boundaries being closer to equilibrium after recovery.
Fig. 1 indicates that the local microstrain undergoes marked oscillations as a function of the number of rotations of HPT.
In the HPT state, the grain size was about 500nm, and the adjacent grains showed similar contrast, a characteristic of low-angle GBs; while in the recovered sample, many grains having sizes of about 200nm or less were observed.
Conclusions The local level of microstrain showed dynamical oscillations as a function of the numbers of rotations of HPT as a result of evolution of crystalline defects during the HPT procedure.

During annealing process, the twin grains disappeared and the original bulky organization was replaced by recrystallization grain, while the grain refinement was obvious with the grain reduction to 20-60μm.
Some initial grain steered to favor orientation by grain rotating, initiated new twin, secondary twin and crossed twin[7].
It shows that grain refinement is obvious, twins disappeared during annealing, crystal grain siae changed from 200~300μm to 20~30μm.
Put number in table 1 and R2/R1 into (1), and table 2 show the calculation results.
At the same time the size of grain decreeased to 20-60μm which indicated that the grain refinement was obvious.