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The impedance spectrum of Ho-doped sample indicates that consist of semiconducting grain and moderately insulating grain boundary regions.
Generally, the formula of doped bismuth titanate is (Bi2O2)2+(Am–1BmO3m+1)2– , where A means mono-, di-, or trivalent ions, or a mixture of them; B means quadri- or quinque-valence ions, such as Ti4+, Nb5+, Ta5+; and m means integer number > 1.
Ho-doped sample exhibits randomly oriented and plate-like grains, and the average grain area of the sample was approximately 10×10μm2, and thickness was less than 2μm in general.
In general, the capacitance C of grain and grain boundary are typically of the order of pFcm–1and nFcm–1, respectively.
The Ho-doped bismuth titanates consist of grain and grain boundary regions.

Because of these special performances, engineering ceramics are expected to be used increasingly in a number of high-performance applications ranging from electronic and optical devices to heat- and wear-resistant parts [1-2].
Then, the material removal rate by one grain is given by: r 4 V CCM hL o �����= . (5) where, � is the rotation speed of the tool; r is the radius of the grain’s track.
Assuming that the density of effective cutting grains is � in terminal face of drilling tool, the number of effective grains in area dA (see Fig.5) is: drr2dAn ���� �=� = . (6) Then, the material removal rate of the tool is: ( )RRCC rCC 3 1 3 2 hL 2 2 hL 2 v 3 8 dr R R 8M 2 1 
����� ��=������ ��= � � � . (7) 1 2 3 4 1.
Fig.3 Schematic of diamond tool drilling process Journal Title and Volume Number (to be inserted by the publisher) 409 The number of effective grains in the terminal face of the tool is [10]: ( )RR d K 2 1 2 2 3 2 g 2 0 1 6 AN
��� � � 
 � � � � � � �=� = � . (8) where, ( )RRA 2 1 2 2
=� , R2 is the external radius of the diamond wheel; R1 is the internal radius of the diamond wheel; K1 is a proportional constant; � g is the concentration of abrasive grains; do is the mean diameter of the abrasive grains.
Acknowledgement The work described in this paper is supported by National Nature Science Foundation of China(Subject number: 50275087).

As the time change from t to t + δt, grains position will also change to , where it holds in general that
Function sign() in Eq. (5) is defined as (6) and the overlap between grains ξij is defined as in [11] , (7) where Di is diameter of grains i.
Experiment Two dimension grains are represented by small and thin disks, which are distributed artificially.
Each configuration is recorded and then analyzed using tailored software to get particles position and number of contacts on each particle.
Each particle position and contacts are obtained from tailored software, where illustration of the observed contacts between grains is given in Fig. 2.

Microstructure of wires fabricated usin 800 rpm consists finer equiaxed mg grains with finer precipitates homogeneously distributed along the grain boundaries.
To fabricate the magnesium based components, machining is main process and as the number of applications increasing with the use of magnesiumm, the scrap volume is also increasing.
It consists of approximately equiaxed grains of 100 µm with the grain boundaries discontinuously covered by the precipitates.
The microstructure consists of larger grains surrounded by finer grains with precipitates at their grain boundaries.
The average grain size at higher rotational speeds is 180 µm which is much higher than the as cast base metal grain size.

Microstructures of CGP processed Al experienced diffe- rent number of pressings (εef) at room temperature: a) top groove ε ~ 0; b) top groove ε ~ 0; c) sheared area ε ~ 0.58; d) 1 pass ε ~ 1.16.
The interior of these new grains is free of disloca- tions; grain boundaries are straight and they have a similar morphology of polygonized subgrains.
TEM microstructure analysis results also indicates a very low fraction of submicron grains with high angle grain boundaries even in case the strain applied is the highest.
Considering fact, as to the subgrains and grains size, the CGP method for grain refinement in pure Al appeared to be not so effective.
A distinction between the values for the initial state and the deformed plates subjected to CGP straining due to different number of pressings is evident.

The grains decreased -gradually with the increase of the fire time [5].
Comparison and Analysis of Measured Grain Size with Calculated Results.
The final grain size of end face is 4 grades approximately.
(2) With the increase of fire time and the reduction, the domain of uniform and fine grains enlarges and the grain size could be fined in the multi-fire forging process
(Item number: 50675146).

The parameters used in the HCPEB surface treatment were as follows: the accelerating voltage 27 kV, the numbers of pulses 35, the pulse duration 5 μs, peak current density 6J/ cm2.
Clusters grow outward until contacting adjacent grains.
However, these nodule units are not grain while boundaries of the cluster organization are not grain boundary.
A large number of craters are found when samples are observed at a certain tilt angle.
As for grain size, the surface grain size can be less than 200nm after electron beam irradiation.

That is, a big deformation is conduced to grain refinement.
Fig. 3 Effect of deformation ratio on the austenite grain size (a): 0.83 and (b): 0.65 The volume fraction of austenite grain boundary is measured through analysis system (Sisc IAS8.0).
Owing to the finer austenite grain and bigger volume fraction of grain boundary, the spread and development of crack would be restrained, leading to the austenite grain more fastening which makes the better strength and toughness ultimately.
Furthermore, there are number of precipitates with the size between 0.5μm to 1.5μm on the impact fracture.
Whereas, fine precipitates in the grain internal are beneficial to the toughness of material attributing to their refining effect on grains and microstructures.

Grain Refinement and Mechanical Properties of Magnesium Alloy by Hydrogenation Treatment S.
Each was cooled in water after undergoing the predetermined number of cycles.
It shows that after they rolling and recrystallization, the treated material has an average grain size of 9 µm in diameter, whereas the untreated material has an average grain size of 6 µm.
There was no great difference for grain size distribution after dehydrogenation.
Fig.7 Relationship between hydrogen content and grain size.

larger (sub)grains developed under lower stresses.
The prior austenite grains size was about 20 µm.
Therefore, the grain size represents the inter-boundary spacing.
The block/grain size is about 2 µm.
The volume fraction of fine carbonitrides is about 0.002, which was estimated by counting the number of particles per unit volume, �V = 2 × 1022.