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The average grain size of the powders obtained after hydrothermal treatment at 160ºC for 9h was about 30nm with cubic structure.
A number of important physical, chemical, mechanical or mixed procedures have been proposed, among which the hydrothermal method has been found to be very promising for the preparation of well optimized and non-agglomerated powders [5-10].
The grain size of the powders was estimated using the Scherer's equation: θβλ cos/kd = (3) where d is the grain size, k sharp factor(0.9), λ the wave length of X-ray (0.15406nm), β the full width at half maximum(FWHM), and θ the Bragg angle.
average grain size was about 30nm with uniform distribution, which was in good agreement with the grain size determined from XRD.
Acknowledgements This work was partly financially supported by National Hi-Tech Research and Development Program of the People's Republic of China (Project Number: 2004AA32G090 ).

BaFe12O19 substituted sample shows a single semicircle at lower temperature and two overlapped arcs at 120 and 160 oC due to grain and grain boundary.
The electrical resistivity contribution by the bulk material (grain), grain boundaries or electrode can be identified from the arcs [3].
BaTiO3 phase was indexed based on the standard JCPDS data number 05-0626 for tetragonal structure.
R1 is much higher compared to R2 due to difficulty of the charges to move in the grain boundary compared to in the grain.
From 25 to 80 oC, the grain boundary relaxation peak frequency decreases with temperature but the Z“ value increases showing an increment in the grain boundary capacitance.

The results show that the specimens have uneven microstructure, and the grains are relatively small.
The grains grow mainly by the form of columnar and cluster-like, and there are obviously preferred orientation in the (220) plane.
Grain size: Considering the diffraction peak broadening caused by the grain size, the relationship between grain size D and the width of its real point β can be given by Scherrer formula: D (h k l) =k λ/β cos θ
Grain size of each small columnar is about 5μm.
Since the whole grain is in equilibrium, when the LIGA Ni micro-structure only exist micro-stress, the grain in a certain part is tensile stress, while the other part is the compressive stress.

Finite element modelling can be used to enable the manufacturing of complex-shaped parts economically as the number of experimental trials can be reduced.
The finite element calculations take into account also grain size evolution.
This included two aspects as follows: Grain Growth.
(1) The static grain growth ̇dstatic in Eq. 2 captures the grain growth by atomic diffusion due to the high temperatures in the absence of deformation conditions.
Fig. 1 also shows that the grain size values of Ti64 alloy are higher than those of Ti54M alloy as the rate of grain growth of Ti64 alloy was higher than that of Ti54M alloy and the initial grain size of Ti64 alloy was greater than that of Ti54M alloy.

Chromium diffusion along the grain boundaries is more favorable.
The carbide formation reveals that the distance between carbides increases and the number of grains in the steel decreases as carbides grow.
Fujibayashi et al. also observed cavities with dimensions of less than 5 µm in small grains [5].
This progression can happen either inside the grains or at the grain boundaries, depending on the microstructure and stress state of the material.
In this study, Fig. 5b confirmed that cavities located near grain boundaries were due to high load, under which, the stress concentrated on the grain boundaries, leading to the formation of cavities near these positions.

For the calculations presented below, the initial deformed state was described by a two dimensional set of grains, similar to an EBSD map, containing approximately 2000 grains.
The grain structure is represented by vertices with positions       = k k k y x r r , where N,...,1k = (N is the number of vertices in the structure).
Each (sub) grain has its orientation On and the stored energy value En.
The initial positions of vertices in grains are the corners of a Voronoi structure.
During recrystallization process, the grain structure undergoes topological changes.

Results and Discussion Before ECAP the microstructure of the alloy had uniform equiaxed grains with the average size of about 9 µm.
It is seen that the ECAP route used gives rise to an ultrafine-grained structure of the alloy with the average grain size ~ 1-5 µm.
The observed changes in the texture are a consequence of the ECAP features and depend on the route of pressing chosen and the total number of passes.
At the same time, a pronounced microstructure refinement at the level of the grains and subgrains occurs.
This texture, in combination with the grain size refinement down to the average grain size of ~ 1-5 µm, is responsible for the observed improvement of ductility.

In addition, that the nano-particles adsorbed on the surface of grains will hinder the growth of grains and lead to refine grains and increase the grain boundaries, thus melting caused by slight changes in the temperature.
The microstructure of Sn-30Bi-0.5Cu after adding nano-Ag was shown in Figure 2, indicating a large number of Ag3Sn micro-nano particles were adsorbed on grain boundaries [22].
(2)The Grain boundary strengthening.
Due to the high melting point of these particles and no reaction with the matrix, the added inert nano-particles such as TiO2, Al2O3, ZrO2, and so on, may become the core of heterogeneous nucleation, to increase grain numbers, and particles adsorbed on grain boundaries will impede the migration of grain boundaries, refining grains.
The generated IMC adsorbed at grain boundaries and dispersed in the matrix, will hinder the migration of grain boundaries, refining grains.

The power of grain size was taken from a regression model developed previously that is able to predict the static recrystallisation kinetics of vast number of carbon and microalloyed steel grades.
It was reported that due to the pinning effect exerted by sulphur-rich particles, grain growth is delayed up to reheating temperatures as high as 1250°C, thus resulting in a fine austenite grain size prior to subsequent deformation.
No specific study was undertaken to vary the grain size and to estimate the grain size exponent (s) for two reasons: first, it is quite difficult to get large variations in grain size owing to the presence of sulphide inclusions, which retard the grain growth process up to at least 1250°C [2] and secondly, the grain size exponent has also been found to be strongly grain size dependent [8-10].
Hence, the equation developed for the grain size exponent (s) in the previous regression model [8-10] has been employed here in predicting the SRX kinetics.
Similarly, systematic relaxation tests carried out on a number of C/CMn steels yielded strain rate exponent values in the range -0.75 to -0.8.

The grain size was 1-4µm.
When the substrate temperature was 600°C, the sheet had sharp irregular polyhedral grain, and when the substrate temperature was 700°C the sheet had quite regular grains.
The grains are with sharp irregular polyhedral shape.
As the number of turns of the substrate is 12 round/min, the upward vertical acceleration introduced by bonding force or adsorption affinity is calculated to be 8.5m/s-2.
The grain size is 1-4µm.