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Fig. 1 Relationship between grain size and lattice constant From Fig 1 it is shown that lattice constants increased with the decrease of particle sizes.
The shift essence of infrared spectrum absorption peaks is attribute to the change of molecule vibration frequency, and the magnitude of molecule vibration frequency ν%(shown by wave number) is expressed by formula (2)
If the number of atomic in boundary far less than internal, the main characteristic of the crystal is mainly depend on internal atomic, so it can be seen as a non-boundary system.
Fig. 7 indicates that the change of vibration wave number when the internal “force constant k2” stay the same of 75 and the external force constant changes constantly, therein green stands for σ1, black stands for σ2, blue stands for σ3, red stands for σ4.
Fig. 8 Relationship between k2 and wavenumber of magnesia（k1=75） （green σ1, black , blue σ3, red σ4） Fig. 8 shows that the change of vibration wave number when the external“force constant k1”stays the same of 75 and the internal force constant changes continually, green stands for σ3, black stands for σ1, blue stands for σ4, red stands for σ2.

After this transient a number of important features can be highlighted: • For the solution treated and overaged samples an apparent saddle region is observed in Fig. 2(a) and 2(b) at strain values smaller than 3%
Linear summation, i.e. n =1 holds for the situations where a high density of weak obstacles and a small number of strong obstacles co-exist, e.g. the initial stages of aging featuring a large number of shearable precipitates.
At higher stress levels a number of relaxation processes, e.g. formation and glide of prismatic dislocation loops [10], become potentially active thereby affecting the average storage rate of dislocations due to the particles.
Fig. 3(a) and 3(b) show the surface of the exposed grains for the peak and overaged samples, respectively.
In Fig. 3(a), one can observe a series of parallel slip lines in most grains (usually dominated by a single orientation).

The parameter is determined in terms of the material properties which are crystal grain surface area and crystal boundary volume.
In terms of the Young’s moduli the constitutive equation for the axial deformation is given by Here is the total number of particles in elementary volume, denotes the number of the particles connected by virgin bonds, is the number of hydrogen particles attached to a lattice.
The number of the lattice-settled hydrogen particles depends on the stress state of the lattice at every point and, generally, on time.
Despite the seeming simplicity of this approach and the large number of published data, not all of them can be used for the approximation.
Wokulski, Effect of hydrogen charging on stress-strain curves for iron whiskers, Acta Metallurgica, V. 30, I. 12, 1982, p. 2173-2179 [21] Yihong Nie, Yuuji Kimura,Tadanobu Inoue, Fuxing Yin, Eiji Akiyama,Kaneaki Tsuzaki,Hydrogen Embrittlement of a 1500-MPa Tensile Strength Level Steel with an Ultrafine Elongated Grain, Metallurgical and Materials Trans.

The work piece is thus simultaneously subject to heating due to electrical sparks occurring between the metal bonded grinding wheel and the work piece, and abrasion by diamond grains.
The projection of diamond grain on the bonding material of wheel is called protrusion height and gap between the work piece and bonding material is called gap width.
The quality characteristics measured are MRR and ASR Table 1 Selection of controllable factors and their levels Symbol Factors Units Level 1 2 3 A Current Amp. 3 5 7 B Pulse-on time μs 50 100 150 C Duty Factor - 0.526 0.660 0.704 D Wheel RPM - 700 1000 1300 Selection of Orthogonal Array for experimentation In the present case four parameters taken at three different levels assuming no interaction between factors, the total degree of freedom (dof) has been calculated by using the following formula: dof = (number of levels-1) for each factor + (number of levels -1) (number of levels -1) for each interaction +1,so that the dof = (3 - 1) × 4 + 1 = 9 [3].Selection of the orthogonal array is based on the calculation of the degree of freedom of all the factors.
For Smaller-the-better type problem MSD = ( y12 +y22 +y33+…….)/ n Table 2 Experimental observations using L9 Taguchi Orthogonal Arrey MRR ASR 0.00236 1.33 0.01192 1.02 0.0210 1.41 0.0172 0.96 0.00785 1.24 0.0148 1.18 0.0186 1.41 0.0199 0.94 0.0059 2.84 and for Higher-the-better type problem MSD = ( 1/y12 +1/y22 +1/y33+…….)/ n where, y1,y2,y3,………………yn are results of the experiments and n is the number of repetitions of yi.
The TNQL can be identified using If the wi represents the weighting factor for the ith quality feature, q is the number of quality features and yij is the loss function associated with the ith quality features at the jth trial conditions.

For extruded micro gear, the grain size of tooth-shaped portion is smaller than that of the central; the extruded micro gears are generally stronger than the hydraulic manufactured gears.
The tooth number of bigger gear is 24 with a module of 0.15mm; while the tooth number of smaller gear is 20 with a module of 0.12mm.
The most important parameters are the module, m, the number of teeth, Z, other parameters such as the pitch circle radius, r, the base circle radius,, the root circle radius,, addendum circle radius,,etc. can be calculated by the geometric relation
The tooth number, N, of bigger gear is 24 with a module of 0.15mm; while the tooth number of smaller gear is 20 with a module of 0.12mm.
Chang, Superplastic micro-forming with a fine grained Zn–22Al eutectoid alloy using hot embossing technology, Journal of Materials Processing Technology, 180, pp.17-22, 2006

In the process of generating grinding, grinding worm are subject to wear, the grinding grains loose their cutting ability and the grinding worm have thus to be redressed to recover the macro and micro geometry by using diamond based dressing tools.
So the is represented in by the equation: (5) In general, the number of threads of grinding worm is 1, the number of pinion teeth is Z.
Table 1 The major design parameters of helical gear Gear 1 2 Number of teeth /Z 40 Normal module/Mn 5 Normal Pressure angle/ o 20o Helical angle/ o 20o Modification value/ 0 According to the above calculation process, the contact line between grinding worm and pinion is a space spiral line on surface of grinding worm as shown in Fig. 2.

During recent decades, the mesoscale modelling of the microstructural formation in material processing has progressed markedly based on Cellular Automaton (CA) formulations, especially in the fields of recrystallized structures, of grain structure formation in solidification processes and of dendritic growth.
In the current model, the homogeneous damage initiation is adopted, and a initiation probability NUCp at any cell is determined by CAN tN p NUCNUC ∆ = & , where NUCN& is initiation rate, t∆ is the time length of each time step, and NCA is the cell number of the CA lattice.
For each site, a random number r ( 10 <≤ r ) is generated and compared with the initiation probability.
A non-void cell will become void if it has void cells and its generated transition random number chgr ( 10 <≤ chgr ) is smaller than the growth probability rowpg of one void cell neighboring to the non-void cell.

Based upon this information, one might suppose that limited number of forms can be made between the sylinder and sphere, considering the limits of formation of the potter's wheel.
In the first phase 10%-20% bazalt grains are mixed in the clay and kneaded; the piece is then centralized on the potters wheel, a cone-shaped and tall sylinder is formed.

Cemetery of Geometric Pattern Unearthed Woolen Fabric from Xinjiang S/N Region Cemetery 1 Lop Nur Area of Bayingolin Mongolian Autonomous Prefecture Gumugou Burial Ground of Kongque River, Xiaohe Cemetery, Ancient Loulan Tombs,Yingpan Burial Ground 2 Hami Wubao Cemetery, Aiskexiaer Cemetery, Yanblak Cemetery in Hami 3 The Southwestern Tarim Basin No.2 period of Zhagunluke Cemetery, Northern Cemetery 4 The Southern Foot of the middle of Xinjiang’s Tianshan Mountain Range Ancient Chawuhugou Cemetery in Hejing County 5 Turpan Ancient Subeixi Cemetery in Shanshan County, Ancient Yanghai Cemetery in Shanshan County,Ancient Alagou Cemetery 6 Kashgar Tuokuzisalai Site 7 Hotan Niya Site in Minfeng County, Ancient Shanpula Cemetery, Ancient Site of Keriya, Ancient Bujak Cemetery Types of Geometric Pattern Unearthed Woolen Fabric from Xinjiang The unearthed geometric patterns mainly include triangle grain, ling plaid, checkered, stripes and connection lines.
Table.2.The Types of Geometric Patterns of Unearthed Woolen Fabric S/N Composition Name of the Patterns Real Photos Isography and Restored Images 1 One Geometric Pattern Triangle pattern Diamond lattice patterns Check pattern Stripe Zigzag pattern 2 Two Types of Geometric Patterns Triangular lozenge Rhombic cross pattern Stars and stripes Zigzag and Hook pattern Check pattern 3 Two or more Geometrical Patterns Reticulate -striate 4 Geometric Patterns and Figurative Patterns Diamond lattice and four petal flower patterns The Connection between Geometric Patterns of Unearthed Potteries and Unearthed Woolen Fabric’s A large number of potteries with exquisite geometric patterns were also found in the ruins of ancient tombs of Xinjiang.

Several modifications on computational fluid dynamics (CFD) have been made to increase the number of unknown variables.
The pore size and grain size were generated randomly, and the shape of porous structure was designed just like the surface image of sandstone as shown in Figure 1.
The model is three dimensional with anisotropic structure of pore and grain. 2.
This method can be used to develop a tool for the characterization of reservoir by increasing the data sets and large number of measurements can be carried out.