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The phase states are represented by the continuous order parameter field although it has discontinuity on grain boundary in reality.
While, in the multi-phase-field method [7], each grain has its own order parameter field and it is necessary to calculate a much larger number of order parameters than the KWC model and rotation of crystal orientation is ignored, whereas the governing equations are relatively stable to calculation with large time increment.
Since analysis domain includes a number of grains whose crystal orientation can rotate, an evolution equation of crystal orientation is required in addition to that of order parameter.
In addition, the mobility of θ is set as 2 (1 )M M θ θφ= − so that the recrystallized grains do not rotate after they contact.
We can see that the high angle boundaries generate along the subgrain walls in each grain.

Different Dual Phase steels were processed with ferrite grain size between 0.7 µm and 4 µm and martensite islands dispersed along the grain boundaries of the ferrite phase.
A name was given in relation with the size of the ferritic phase : CG for Coarse Grained, FG for Fine Grained and VFG for Very Fine Grained.
The ferrite grain size, martensite grain size and martensite volume fraction are provided in Table 2.
Ferrite grain size (df), martensite grain size (dm) and martensite volume fraction (Vm).
The agreement is not so good at the lowest depth for which a small number of representative indentations was performed.

ECAP has a number of advantages compared with traditional metal processes, such as deformation without changing the shape of objective material [5,6,7,8,9].
Apparently, with the increase in the pressing temperature, the equiaxed α phase becomes smaller in number and the secondary lamellar α phase begins to be separated out.
Additionally, the number of acicular α phase at boundaries was much larger than that in the coarse β grains from Fig. 4b.
Because of no annealing softening, a large number of tangled dislocations which are produced by ECAP deformation have been seen clearly (Fig. 6).
With the increase in pressing temperature, equiaxed grains have become coarser and the number of α phase has decreased.

The grain size of porous HA was sub-micron and MgO which existed in the grain boundary of HA as a second phase particles that played the roles of inhibiting the HA grain growth.
The paper deals with the preparation and micro structure of the Mg containing porous HA with ultra-fine grain.
The specimen were heated in 1100-1200℃ for 1-3 hours for the preparation of Porous HA with ultra-fine grain containing Mg.
Characterization The porous hydroxyapatite ceramic were characterized by using a number of methods such as wide angle X-ray diffraction, transmission electron microscopy, scanning electron microscopy (SEM), SEM in combination with energy dispersive X-ray spectroscopy(SEM-EDX), X-ray photoelectron spectroscopy.
Grain size and morphology of nano HA[J].

In the grain interior, the majority of slip is generally concentrated on a limited number of active slip systems for most grain orientations.
The relative volume of the grain boundary region is a function of grain size as well as the deformation conditions [5-7].
This results in a critical grain size, below which the grain boundary region extends over the entire grain and the enclosed cell/subgrain structure dominates the substructure development [5-7].
The formation of DRX grains involves simultaneous grain boundary movement as straining proceeds.
DRX grain size; Fig. 4).

The number that comes after "E" is the number of ECAP passes as a pre-state for the plane strain compression.
Fig. 5 (a) shows the evolution of cell structure size with number of passes.
Fig. 5 (b) gives the variation of average misorientation angle with number of passes.
Fig. 5 (c) gives the area fraction with grains less than 1 mm based on a 2o grain tolerance angle.
Fig. 5 (d) represent the evolution of number fraction of high angle grain boundaries (HAGBs), that is boundaries with misorientation across them greater than 15o.

And the grain loss, less tipping and blade fracture during tool wear results from high frequency intermittent shock by SiC grain.
The wear behavior on the tool flank is mainly of grain loss.
However, the wear behavior of the rake face is not only of grain loss, but also abrasive wear of WC grain by SiC grain.
After 105~107 times of impact, impacted grains fractured and fell off to form pits.
A number of wear curves have validated the above rule [9, 10].

An alternative approach, based on recent advancements in XRD micro-focusing has enabled a limited number of XRD synchrotron facilities to quantify elastic strains in individual grains using the analysis of Laue diffraction patterns [4].
A large number of interrelated effects need to be considered when optimising the milling setup.
The gradient of this plot is used to quantify strain relief as a function of image number.
We observe, however, that the fitting Fig. 4 a) Full strain relief against grain number in directions parallel and perpendicular to the grinding direction for both the stepwise and continuous milling process. b) Full strain relief against core diameter size in grain 4.
Exceptions were grains numbered 3, 5 and 9 which demonstrated negative strain relief sign, and thus a tensile residual stress.

The shape were labeled as follows: No type – color ( e.g.: 1p - red) were No means the number that the grains had in the order table (this number is given beginning from 1 and finishing with the last value of the counted grains), type can have three values, and represent the type of the grain (p – droplet shape grain, L - elongated shape and N - the nondefine shape) and last the color, that also can take three values (red - droplet shape grain, blue - elongated shape and green - the nondefine shape) (Fig. 6).
The first thing is to count the total number of grains from each picture.
When this number is known the type of grain (droplet shape, elongated shape and undefined shape) must be analyzed in order to build a map of the distribution of grain shapes in the part (Table 1 and Table 2).
Another value that differs between the two strategies is total number of grains, and this is grater in the 30 [µm] (336 grains) while in the 50 [µm] is lower (214).
In other words using the 50 [µm] manufacturing strategy the part will have bigger grains and less of them with a droplet shape, while using the 30 [µm] manufacturing strategy the grains will be smaller and the number of droplet shape ones will be grater.

Introduction Alumina ceramic has been found a wide application in a number of abrasive wear environments, such as in balls, mills, cutting tools, dies, and so on [1].
As an additive, La2O3 decrease grain sizes and improve ceramics density [7].
The micrograph clearly shows that grain sizes of ceramic samples with Tb4O7 doped are smaller than S1, and grains become bigger with increasing of Tb4O7.
And terbium ions in liquid phases could inhibit ions migration, which prevent grain growth and make grain sizes small, to improve wear resistant of ceramic samples.
Grain size effect on abrasive wear mechanisms in alumina ceramics.