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The oxygen tracer diffused quickly from the surface up to the grain boundary and then appeared as discontinuous steps at the grain boundary.
They found that non-doped BaTiO3 contained a higher number of oxygen vacancies than the La-doped BaTiO3.
Neither grain boundaries nor grain segregation were observed in any of the images.
One of the possible reasons for the blocking behavior could be the lower number of effective oxygen vacancies around the grain boundaries, compared to those in the grains themselves.
That is, the effective number of oxygen defects is reduced because of the formation of such complex defects.

The tensile properties are also improved with the refinement of grain structure.
The Al-Ti-C master alloy, as a good refiner for Al/Mg based alloy [1,2], has been extensively studied by a number of researchers.
The mean grain size was measured by linear intercept method.
Birol, Grain refining efficiency of Al-Ti-C alloys, J.
Mahmudi, Grain boundary strengthening in a fine grained aluminium alloy, Scripta Mater.

By this the amplitude and frequency of which varies in a variable voltage wide range depending on the number of blades on the rotor stage and number of blades on the stator stage and depend on also from the rotor rotation frequency.
By Boyd-Lee is shown in work [7] that the fatigue cracks were formed via nanoporosity and this is the reason of fracture at very high cycle’s number.
During EUF the chemical condition of grain boundaries was changed.
The cycle’s number was increased from 2.107 to 4 x 2.107 cycles by step-by step (40 MPa) at increased load.
By (x) in Fig. 5, b is shown HPC blade fracture at HCF strength at corresponding cycle’s number.

In the process, melt is charged and flows over a water-cooled slope, which provides high thermal supercooling, so a greater numbers of small nuclei are obtained in the melt.
Because the large number of the nuclei limit the space between them, grain size is fine.
At lower pouring temperature, rapid nucleation occurs on the cooling slope and the great numbers of nuclei limit the space between them, resulting in finer solidified grains [7].
In contrast, nucleation doesn’t occur abundantly at higher pouring temperature, which renders less numbers of nuclei, providing more space for grain growing to larger sizes.
Table 7 Pouring temperature vs. grain size (μm), Inclined slope angle vs. grain size (μm) and Melt cooling rate vs. grain size (μm).

Timber has higher tensile and compressive strength parallel to the grain but higher shear capacity when loaded perpendicular to the grain.
Timber is typically loaded axially to the grain, but in order to create folded plate structures the timber will be loaded at a range of different grain angles.
This model is based on one piece of analysis but can be extended to consider a range of connections in terms of the number of dowels and the angle of the connection.
The rods embedded at lower angles are being pulled with the grain direction and grain boundaries so there is less resistant to the timber pulling out.
Affect of grain angle on pull-out load Fig.12.

Touge ground the ceramic with the superfine grain diamond cup wheel, and found the grain and grind depth affect on removal model [10].
The grains size decreased, the amount of grains in unit volume increased.
Grains micro-morphology show as fig 5.
The hm related to each grain force.
The every grain force composed the grinding force.

Grain boundary element formulation.
Given a volume bounded by an external surface and containing grains, two kinds of grains can be distinguished: the boundary grains, intersecting the external boundary, and the internal grains, completely surrounded by other grains.
Let and be two adjacent grains.
The present formulation requires only meshing of the grain surfaces.
The grain size is ASTM G=12 (calculated number of grains per : [12]).

Two different precipitations are observed in pipeline steel X80, a class of TiN precipitations is mainly and a small number of (Nb, V)(C, N) complex precipitations in the TiN around, and the other for large number of NbC precipitations and a small amount of TiC, VC and simultaneous deposition of the complex formed precipitations.
Remarkable strengthening and grain refinement can ne caused by these precipitations.
Introduction Distance, a large number of transportation of natural gas, oil produce large pressure to the pipeline.
Fine grain strengthening is obvious, which contributed greatly to the strength and toughness of pipeline steel.
The formation of the crystal contains a large number of dislocation and subgrain, which strengthen the wrong place and sub-grain.

In homogeneous nucleation, the total number of nuclei can be obtained from the classical nucleation theory.
For a given volume of steel (V), the grain size (d) and the total number of nuclei (N) has the following approximation
Each lattice point is assigned an identification (ID) number to represent its physical state.
To nucleate M number of martensite plates with all 24 variants in equal opportunities within an austenite grain, The random number x () is called and checked if its value falls into the range of (i=1, 2, … 24).
Martensite is nucleated at either martensite grain boundary or around a inclusion within the austenite grain.

During cold rolling, the coarse-grained, random texture of the slab is transformed into the classical rolling texture of a fine-grained Al-alloy, with elongated Al-grains delimited by thin Sn-ribbons.
Grain growth within the original cold-rolled grains is fast, but once the recrystallised grain size reaches the length scale of the second-phase distribution, it slows down and both phases coarsen simultaneously, accompanied by a significant texture change.
Grains are often delimited on both sides by the Sn-ribbons, but often collections of smaller grains are present between two parallel ribbons.
In general, the appearance of “exotic” components such as M, b and c may be associated with local strain heterogeneities which are present in too small numbers to be observed in the recrystallised texture but, having originated at sites of higher stored energy may posses a size advantage when secondary recrystallisation is activated by the ongoing coarsening of the liquid Sn.
In: Recrystallisation and Grain Growth, Ed.