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Modern Models of Grain Boundary Diffusion V.V.
Recent models of grain-boundary diffusion are briefly reviewed.
Fisher’s model of grain-boundary diffusion
Diffusion proceeds only along grain boundaries.
An unusually high effective diffusion permeability of nano-materials at low temperatures was observed in a number of publications (see, e.g. [23-25]).

The real-space distributions of texture and grain/crystallite size of HPTed steels of four torsion numbers were quantitatively visualized at once.
Five samples of the same rotation number were stacked for statistics averaged general evaluation.
The numbers of the rotation were 1/4, 1/2, 1 and 10 in the same direction.
Fig. 3: Torsion number dependence of texture and grain/crystallite size over the whole area of HPTed ultralow-carbon steels visualized by the neutron Bragg imaging combined with the RITS code.
The iteration number of FBP-EM was 30 times (k = 30).

When the vibration head dipped into the middle of the melton, the better grain refinement effect can be gotten.
It has been reported that ultrasonic vibration can generate a high number density of fine ice crystals in the solidification of water within a short time[4].
These grain refinement of the microstructures by the UV technique also have been observed in other alloys.
The grain size of Fig.2(b) is smaller than that of Fig.2 (a), especially at the bottom of the ingots.
It can be seen form Fig.2 (a) that microstructure is coarse columnar grain and the grain size is not very uniform.

Przylenk [5] claimed that material removal had some relation with the number of grains contacting with workpiece surface.
Jain [12] has studied the effects of different process parameters (number of cycles, abrasive concentration, grain size) on material removal and surface finish based on experiments.
Meantime, the active grain would slow down, and others grains around which would squeeze the active grain as shown in Fig 1(c).
Fig.6 Two types of arrangement of grain in fluid abrasive Grain squeezing forces.
The distribution state of grains could be the following two types of arrangement, as shown in Fig.6.The number of all grains could be estimated by the following equation, Where, R and L are radius and length of workpiece. r is grain size.

The mechanism of grain refinement was discussed.
The number and the misorientation angle of kink bands evolved at low strains rapidly increase with deformation, finally resulting in development of new grains in large strain.
Namely, grain refinement from 22.3µm to 0.8µm can result in enhancement of grain boundary sliding taking place in such fine-grained structures [5], leading to reduction of flow stress as well as improvement of ductility.
The average grain size was about 0.36µm.
The average grain size decreases with repeated MDF during temperature drop, resulting in evolution of the minimal grain structure of 0.36µm in ∑ε=4.8 at 423K.

The grains grows up and some grains are still intergranular crack for the samples annealed at 810 ℃.
The numbers of the intergranular crack grains decrease and the cleavage planes increase for the sample annealed for 180sec at 840℃.
As seen, there is apparent phosphorus segregated at grain boundary.
The main reason is that Ti-IF steel is cold-rolled by 75% reduction and a large number of vacancies and dislocations are introduced in the matrix.
The grains grow up and the intergranular crack grains decrease for the sample annealed for 180sec at 840oC.

The objective of this work is to study the effect of cross section of the billet, number of passes on grain refinement, mechanical properties and wear behaviour of AA 5083.
It is observed that the wear rate and coefficient of friction are reduced with number of passes in both the cases and rate of decrease is more in case of square billets. 1.
This process has great impact for developing ultra-fine grain structure consisting of equiaxed and homogeneous grains with high angle grain boundaries[6-13].
In addition to the grain refinement, the porosity and blow holes are reduced during ECAE of square billets and more homogeneous grain structure produced.
· The wear resistance of the raw material is low and is increased with increasing number of ECAP passes for square and circular billets.

During certain number of passes (six passes), the material experiences higher hardness with fair amount of ductility.
Stress Vs strain graph With further straining (increasing number of passes), these dislocations aid to form dislocation cells/sub grains, resulting in grain refinement and strength enhancement.
This grain refinement is due to the evolution of sub grains within big grain (bimodal structure).
In addition, grains are sheared resulting in oblate grain structure, with grain axis inclined to the extrusion direction.
With increasing number of passes, the material experiences a critical strain and there by obtains an oblate grain structure, which is associated with high angle grain boundaries and leads to enhancement of strength with reasonable ductility 3.

The grain refining effects of Al-Ti, Al-TiC and Al-Ti-C master alloys on commercially pure aluminum were compared, and the grain refinement mechanism of TiAl3 and TiC among master alloys was discussed.
With people’s increasingly deeper understanding of the phenomenon of grain refinement, they have put forward many ideas and theories of the mechanism of grain refinement.
Results and discussion The grain refinement effects of master alloys Al-Ti, Al-TiC and Al-Ti-C on pure aluminum.
When Ti wt% reaches 0.05%, with the increase in the addition amount of refinement agent, since TiAl3 particles added can exist stably for a long time in the melt and become cores of heterogeneous nucleation during crystallization of α-Al, thus the sample grains are refined significantly, until after the addition amount of refining agent reaches 0.07% of Ti wt%, when there exist in the melt a sufficient number of TiAl3 particles, the refining effect reaches a saturated state.
But with the extension of the heat preservation time, a large number of TiAl3 particles eventually dissolve, and only a small amount of residual TiAl3 becomes the core of aluminum nucleation.

The total number of particles per unit volume decreases in the order of Zr > Mg > Ce > Ti.
It is seen that the mean grain size decreases with increasing the number of inclusion particles.
It is seen that the effect of soluble Zr and Ce on inhibition of austenite grain growth 0 min at 1200 Co N / mmV-3 0.1 1.0 60 min at 1200 Co Fig. 3 @Relation between number of @ @ @particles, NV, and mean size @ @ @of grains, DA.
The effect of nonrandom dispersion of particles on austenite grain growth was estimated by using the fraction of oxide particles on grain boundaries, ΦA, which is defined as the ratio of the number for particles at the grain boundaries and the total number of particles per unit area.
Summary In Fe-10% Ni and Fe-0.05% C alloys deoxidized with Mn-Si, Ti and Mg, the austenite grain size can be controlled only by the number and size of inclusion particles.