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The five phases are the extradendritic melt, the solid dendrite and interdendritic melt inside the equiaxed grains, the solid dendrite and interdendritic melt inside the columnar grains.
The averageand, grain number density of equiaxed crystals (), and mold and ingot temperatures of the as-filled state are used to initialize the solution of the 5-phase simulation of ingot solidification.
As shown in Fig.3, the higher the number of jets, the more quiescent is the flow.
Increasing number of jets reduces the kinetic energy per jet.
The number density of equiaxed grains (Fig.7c) is high at the ingot core.

If the number of boxes of size d with the same probability is ，for multifractal，the following scaling relationship holds： （3） where f（aij）is a kind of fractal dimension of aij subset．The dependence of f（aij） on aij is multifractal spectrum，which is one way of describing the multifractal structure．It usually is smooth bell or hook shape curve．
A series of samples of TB8 alloy（15.3Mo，2.9Nb，2.9Al，0.08Fe，0.18Si，0.03C，0.011N， 0.10O、0.01H，others Ti）were compressed at strain rates of 0.01 and 1s-1 to the reductions of 40% in height at different temperatures and immediately cooled to room temperature in water．Then solution heat treatment at 850for 20min and quench were conducted．Fig.1 illustrates the binary images transformed from microstructures of TB8 alloy samples deformed at different conditions．It can be seen that the obtained microstructures include two parts：the initial coarse deformed grains and the fine recrystallized grains．The recrystallized grain size（dr），recrystallized grain volume percent（r）and deformed grain size（d）vary with the deformation conditions．
（a） （b） （c） Fig.1 Binary images transformed from microstructures of TB8 alloy （a）t=750，=0.01s-1 （b）t=1100，=0.01s-1 （c）t=750，=1s-1 As we know，at higher strain rate and lower temperature，the dislocation density in deformed microstructure increases and deformation energy stored in deformed alloy increases also．Moreover，finer grains are obtained and the grain boundary area per unit volume increases．It will lead to the nucleation sites in deformed microstructure increase．Therefore，in following solution treatment，the driving force for recrystallization increases and the recrystallized grains nucleate more easily．The recrystallized grain volume percent increases and the recrystallized grain size increases also．The microstructure is fine and uniform．
Table 1 Key parameters of the microstructures and multifractal spectra t=750 =0.01s-1 t=1100 =0.01s-1 t=750 =1s-1 amin 1.857 1.889 1.908 f(amin) 0.067 0.327 0.394 amax 2.646 2.621 2.510 f(amax) 0 0.259 0 Da 0.789 0.732 0.602 Df 0.067 0.068 0.394 dr（mm） 34.7 39.6 43.8 r（%） 15 23 36 d（mm） 124 112.3 103.5 Da reflects state of microstructure distribution and is related to locations of grains．So Da describes the physical properties of fractal structure at different locations．Whereas，parameters such as recrystallized grain size，deformed gain size，recrystallized grain volume percent，are statistical average values of microstructure in the whole domain．They are related to grain numbers throughout the whole domain and independent of grain locations．So such parameters can not serve to describe the local microstructure precisely and roundly．Furthermore，although the size of each grain can be calculated，the distribution state of each grain can not be characterized．However multifractal spectrum
Conclusions On the basis of MATLAB software，recrystallization microstructures of TB8 alloy after hot deformation and solution treatment have been studied with multifractal theory．And multifractal spectra of the microstructure images have been calculated．The studies show that in current scaling range，the recrystallization microstructure of TB8 alloy has the characteristic of multifractal．And the microstructure can be reflected more objectively and accurately by the shape and width of the multifractal spectrum．With increase of the recrystallized grain size and decrease of the deformed grain size，the width of spectrum Da decreases．A narrower spectrum curve indicates a uniform microstructure．Otherwise，with increase of the recrystallized grain volume percent，the range of Df increases．Recrystallized grains are the leading distribution，the microstructure is more uniform and finer．

Notice: each grain misorienting with the neighbour grains was differentiated by certain colour in Fig. 3.
It was found that the grain boundaries in the original steel were consisted of the high angle grain boundaries (HAGB).
The variation of the average misorientation decreased from 38.71˚ (original steel) to 37.54˚ (after one period service) and 32.12˚ (after 30 days service), and correspondingly, the fraction of the LAGB increased from 17% to 24% and 36%. 10 20 30 40 50 60 0.00 0.05 0.10 0.15 0.20 Number Fraction Misorientation Angles (degrees) 10 20 30 40 50 60 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Number Fraction Misorientation Angles (degrees) 10 20 30 40 50 60 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Number Fraction Misorientation Angles (degrees) Fig. 5 Corresponding profiles for grain orientations a. original steel; b. after 150 hours service; c. after 30 days service Comparing to the service temperature below 900ºC, the present "recovery and recrystallization" process was accelerated due to the dislocation fast movement and their intensive interaction during 1200ºC super high temperature servicing.
Generally, grain boundary is a contact region between nearby grains which exhibits different orientation and is consisted of dislocations.
However, the grain growth mechanism still met the well-accepted dislocation model of subgrain combination induced grain growth.

A large number of primary equiaxed α grains are retained after two phase zone deformation under conventional heating method.
The initial sample is consisted of a large number of α phase, a small amount of β phase and Al-rich α phase by comparing XRD pattern of the initial sample.
A large number of primary equiaxed α phase retain in the microstructure after (α+β) two phase zone(900℃) deformation under conventional heating method when martensite transformation occurs obviously in the water quenching microstructure which is composed of fine flakiness α' phase, β phase and the grain boundary α phase under β phase zone heating method.
The flakiness α' martensites with large aspect ratio end at the grain boundaries of original β grains where a small amount of α phase precipitate.
The reason is that a large number of primary equiaxed α grains can only retain in the microstructure after 900℃ thermal deformation under conventional heating method.

The results show that the yield strength of hot-rolled ribbed wire rod is 510MPa, the tensile strength is 622MPa, and the elongation is 23.35%, but the content of Mn can be decreased 58.13%, the content of Si can be decreased 67.50% compared with the national standard upper limit value in HRB400; The grain size scale of edge microstructure is 9.0 at the 1# flying shear in the rolling process, the grain size scale of core microstructure is 8.5, and the edge microstructure of hot-rolled ribbed wire rod after rolling is the tempered sorbite, the grain size scale is 13.5, the core microstructure is the ferrite-pearlite, the grain size scale is 12.0, and the depth of hardening is 0.50mm.
Along with the rapid development of national economy, the consumption of Hot-rolled ribbed wire rod has increased sharply, and the requirements of comprehensive performance are also more and more high[4-5], but the energy and transportation resources are limited in China, so it can’t meet the dramatic growth of steel production capacity, we must purchase a large number of foreign resources, so it lead to the global steel production of raw material supply tension, and the prices are soaring, which will directly endanger the health of the steel industry sustainable development.
Fig.2 The stress-strain curve of hot-rolled ribbed wire rod Table 2 The mechanical properties results Sample Yield strength (MPa) Tensile strength (MPa) Elongation (%) 01 500 625 24.58 02 522 624 22.16 03 508 616 23.32 Average Value 510 622 23.35 Table 3 The measured chemical composition of material Material Chemical compositionWt, (%) C Mn Si P S Microalloy Nb, V, Ti National standard of HRB400 ≤0.25 ≤1.60 ≤0.80 ≤0.045 ≤0.045 Microscale Sample 0.22 0.67 0.26 0.019 0.023 - The microstrucucture morphology at 1#-flying shear in the rolling process as shown in Fig.3, the grain size scale of edge microstructure is 9.0, the grain size scale of core microstructure is 8.5, and the microstrucucture morphology of hot-rolled ribbed wire rod after rolling as shown in Fig.4, the edge microstructure is the tempered sorbite, the grain size scale is 13.5, the core microstructure is the ferrite-pearlite, the grain size scale is 12.0, and the depth of hardening is 0.50mm.
(a)edge (b)core Fig.3 The microstrucucture morphology at 1#-flying shear (a)edge (b)core Fig.4 The microstrucucture morphology of products Summary Through optimizing the rolling process, and the yield strength of hot-rolled ribbed wire rod is 510MPa, the tensile strength is 622MPa, and the elongation is 23.35%, but the content of Mn can be decreased 58.13%, the content of Si can be decreased 67.50% compared with the national standard upper limit value in HRB400, and there is no microalloying elements; The grain size scale of edge microstructure is 9.0 at the 1# flying shear in the rolling process, the grain size scale of core microstructure is 8.5, and the edge microstructure of hot-rolled ribbed wire rod after rolling is the tempered sorbite, the grain size scale is 13.5, the core microstructure is the ferrite-pearlite, the grain size scale is 12.0, and the depth of hardening is 0.50mm.
Wen: Ultra fine grain steel (Metallurgical industry press, Beijing 2003)

The sample serial number and the roasting situation are given as following Table 1.
The sample serial number and the roasting situation are given as following Table 1.
Table.1 The sample serial number and the roasting situation Sample number Roasting temperature Roasting situation 1# 800 Ceramic crucible inwall non-adhesion 2# 850 Ceramic crucible inwall non-adhesion 3# 900 Ceramic crucible inwall non-adhesion 4# 950 SG abrasives sticks light powdery on the clay crucible inwall, may wipe off 5# 1000 SG abrasives sticks the quantity on clay crucible's inwall to increase, the partial crystal grain adherency, cannot wipe off completely 6# 1150 SG abrasives in clay crucible the adherency basically is the crystal grain, cannot wipe off 7# 1200 SG abrasives in clay crucible the adherency is the crystal grain, cannot wipe off Fig.1.
It could be seen that the ceramic corundum (SG) abrasives big grain edges and corners are unusual clarity, and the grains crack increases, even a part of grains already have break.
Some grains with small edges and corners present to matrix, in addition, the grains present some liquid organize.

However for applications such as YBCO HTS tapes the objective is to develop a grain structure with as many very low angle grain boundaries as possible.
Measurements of a large number of points within a grain of orientation g with a real mosaicity of χ results in a distribution of orientations with mean orientation g and spread > χ.
For each texture spread the misorientation at which 70% of the grains are connected decreases in an approximately linear fashion with increasing orientation noise (some deviation from linearity is seen due to the relatively small number of grains used in the simulations).
The reason for this is straightforward: because of the statistical nature of the orientation noise in EBSP data, the greater the number of measurements along a given grain boundary, the greater will be the chance that a measured misorientation along the boundary will be significantly lower than the real grain boundary misorientation.
Acknowledgements This work was supported by the National Natural Science Foundation of China under contract numbers 50231030 and 50371041.

In order to enhance the material’s strength, refining the prior austenite grain size through repeated-heating was investigated in our previous work.
In the case of high-carbon high-chromium steels, refining the prior austenite grain size improves the material strength.
In the modified S-N diagram, the relation between stress amplitudes at the crack origin depths and the numbers of cycles to failure is shown.
The grain sizes of Q1T1 and Q3T1were approximately 15 mm and 7 mm, respectively.　
Prior austenite grain size of Q2T1 sample in the present observation is less than that of Q1T1 sample.

The varistor voltage increases with increasing number of ZnO grain boundaries between the electrodes.
Therefore, to fabricate varistors with low breakdown voltages, it is necessary to reduce the number of ZnO grain boundaries between the electrodes.
Adding only Ba to Bi-based ZnO varistors promotes grain growth, which enables large ZnO grains to be obtained [2].
This is because compounds containing both Ba and Mn do not form at grain boundaries between ZnO grains.
Excess Zn2+ ions at interstitial sites in ZnO grains have been reported to diffuse from inside the grains to the grain boundaries during annealing at approximately 700 °C [7].

The result shows the difference of electrochemical behavior between X plane and Y plane is still exist, and even in the unodd number passes for “route C” of ECAP process.
It provides extremely large imposed strains repeatedly in bulk without fracture to realize grain refinement and significant hardening through extremely line-grained structure formed by simple shear.
Several studies have showed that the extrusion direction can affect the microstructure of UFG materials especially in odd number passes for ECAP process, but the effect on the even number passes is weaken.
The aim of this experiment is investigated the effect of the even number passes.
The grain size in X plane is more uniform than that in Y plane.