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The information on the grain microstructure with respect to grain size and number of grains composing different texture components obtained by orientation imaging with EBSD is given in Table 1.
A magnetic annealing also alters the number of grains in the different grain subsets.
Grain numbers, grain number fractions (% in brackets) and mean grain sizes for subsets based on orientation criteria in specimens annealed at 700°C for 180 min at zero field and in a magnetic field of 17 T.
Grain subsets Out of magnetic field In magnetic field All measured grains 10607 4857 Overall mean grain size 21.6 µm 35.3 µm Subset A (0, 35, 0) grains number (fraction%) 510 (6.6%) 217 (5.5%) mean grain size 25.6 µm 40.9 µm Subset B (0, 35, 30) grains number (fraction%) 1307 (9.8%) 585 (7.4%) mean grain size 21.7 µm 30.8 µm Subset R (including A+B) grains number (fraction%) 5318 (40.4%) 1886 (26.3%) mean grain size 21.5µm 32.0 µm Subset C* (180, 35, 0) grains number (fraction%) 494 (7.1%) 378 (15.9%) mean grain size 26.2 µm 48.9 µm Subset D* (180, 35, 30) grains number (fraction%) 1294 (9.8%) 788 (14.7%) mean grain size 21.8 µm 36.3 µm Subset L* (including C+D) grains number (fraction%) 5289 (59.6%) 2971 (73.7%) mean grain size 21.7 µm 37.4 µm Grains of size > 70µm in subset R 53 (0.5%) 100.3 µm 89 (1.8%) 93.1 µm Grains of size > 70µm in subset L* 59 (0.6%) 104.2 µm 296 (6.1%) 105.8 µm The EBSD analysis also showed that the
An increase in the fraction number of abnormally grown grains is observed for both favourably (180,35,0) and unfavourably (0,35,0) oriented grains.

Finally, statistical analyses were made such as the number of grain boundaries, the diameter and area of grains.
A certain number of points would be chosen as grain cores and each core was assigned with a grow velocity.
Fig. 2 Simulated result for 16 grains A statistical analysis of the number of grain edges in the microstructures simulated in Fig.2 and 3 was conducted and the results were shown in Table 1 and 2.
The previous research indicated that the average number of edges for a grain was nearly 5.143 under equilibrium which meant most of grains were like a pentagon or a hexagon.
With the ratio equal to 1.8, polygons with different number of edges appeared.

Each site has a grain number for the identification of individual grains.
And each grain number has orientation information which consists of three Euler angles (φ1, ω, φ2).
When these two randomly-selected sites have a different orientation number, the orientation number of the selected lattice site is replaced by that of the selected nearest neighboring site.
The number of a central grain represents the Goss orientation which has a potential to grow abnormally under favorable conditions.
When a central Goss grain contains sub-boundaries, the central grain is divided into 8 sub-grains, which have slightly different Goss orientation numbers with sub-boundary energy of 0.05.

The structural changes observed by SEM/EBSD analysis can be characterized by the evolution of many mutually crossing kink bands at low strains, continuous increase in their number and misorientation angle in moderate strain and finally full formation of a fine-grained structure in high strain.
CA shows compression axis.� &$� Fig. 3 OIM maps of AZ31 alloy with (a) D0 = 22 µm and (b) 90 µm deformed to ε = 0.15 at 573 K and at 3 x 10 -3 s-1. � &$� εεεε = 0.15� εεεε = 0.8�Further deformation to moderate strains leaded to increase in the misorientaion angle and the number of kink band, i.e. further formation of kink band in many grain interiors.
Kink band, followed by new grain formation in the fine-grained sample, is scarcely developed in the twinned grain interiors for the coarse-grained one.
(2) In fine-grained sample, kink bands are first evolved at grain boundaries and then in grain interiors at relatively low strains.
The misorientation and the number of boundaries of kink band rapidly increase with deformation, finally followed by the evolution in-situ of new grains with high angle boundaries in high strain

This work suggests that it may be possible to see past a grain growth episode to estimate the original grain shape and grain size of the polycrystal, and perhaps even reconstruct the grain boundary kinematics.
Many natural examples of this type of microstructure have been described in the literature [3,10,11,12]. 1 http://www.microstructure.uni-tuebingen.de/elle Journal Title and Volume Number (to be inserted by the publisher) 3 Figure 1.
Journal Title and Volume Number (to be inserted by the publisher) 5 Discussion The numerical simulations presented here predict that virtually all grains undergoing normal grain growth will preserve a remnant core of unswept material, and that if these cores can be identified, then it is possible to estimate the grain size, shape and chemistry of the primary material.
The variety of natural samples found suggests that finding unswept cores may not be that difficult, however, in order to apply this result to natural systems there are a number of issues that need to be addressed.
Thus the evolution of grain and grain boundary chemistry can be tracked in systems such as grain growth where the dynamics of the grain boundaries are relatively straightforward.

Introduction The main characteristic of the grain structure is the size of grains.
In 3D context it usually means the mean grain volume Ev or its reciprocal value ENV (the mean number of grains per unit volume).
The most common are the counting procedures - profile and intercept counts giving the observed number of profiles per unit area of the examined observing window NA and number of profile intercepts per unit length of examined test line NL.
Fig. 3 Histogram of grain volumes.
Numbers at point denotes CV a, gray numbers at point denotes mean number of generators in cluster.

Q is the total number of the orientations, and Si corresponds to the orientation of the grain in typical grain growth simulations.
Each set of contiguous sites with the same orientation number forms a grain in the microstructure.
The total energy is computed via the Hamiltonian: , (2) in which N is the total number of lattice sites, z is the lattice coordination (26 for a cubic voxel, considering 1st, 2nd and 3rd nearest neighbors), J(Si,Sj) is the grain-boundary energy per unit area and δ is the Kronecker delta.
The orientation number at each site was initialized at random and the inert pinning particles were randomly placed (and were not allowed to touch) until the prescribed volume fraction is reached 0.02, 0.04, 0.06, 0.08, 0.10 and 0.12.
(b) Grain Size Distributions based on the logarithm of the normalized grain size as a function of simulation time. 3.2 The effect of 2nd phase particles on the grain size distribution As described above, the size of the simulation box was 2563 and all orientation numbers were initialized at random.

Grain size or/ and continuous annealing process may affect the number of grain boundary segregation carbon atoms.
Cottrell has shown that the kinetics of bake hardening is dependent on the amount of solute carbon and the number of free dislocations.
But a great number of carbon atoms segregating to grain boundaries have a big affect on bake hardening property because final cooling was at low temperature (20-400 oC).
Discuss the effect of grain size on grain boundary segregation of carbon atoms.
As the grain size increasing accompanied by a reduction in the actual number of grains, the total area of boundary was reduced, the total amount of carbon stored in the grain boundaries should be lower than fine grain structure.

In order to account for this effect, and to test the idea, in some cases, the number of precipitates and / or their pinning strength was / were suddenly decreased by a given amount to test the stability of pinned grain structures.
Journal Title and Volume Number (to be inserted by the publisher) 3 Results To compare the topology of grains during normal growth and particle controlled growth we analyze the average size of neighboring grains versus the size of the considered grain, for all grains of various configuration.
Fig. 1 introduces this representation for normal growth; in average it is independent on the number of grains in the evolving structure, for instance the one shown in Fig. 2.
However, among a large number of different runs, we have sometimes observed some grains exhibiting a very fast growth and able to reach a size (area) up to 16 times the average grain size and up to 10 times the average size of its neighbors.
In Journal Title and Volume Number (to be inserted by the publisher) 5 one case (Fig.6a) the large grain had clearly an initial advantage in size, although still in the limits of the dispersion shown in Fig. 3b.

As with other metallic engineering alloys, a refinement in prior-β grain size in cast titanium alloys is believed to improve a number of properties including strength, ductility and fatigue resistance [1] as well offer a number of other benefits [2, 3].
A number of articles by the authors have investigated a variety of different alloying elements in titanium with a core focus on grain refinement.
Various grain refining elements were investigated in a number of studies including Si [20], B [21], Cr and Fe [22] and Be [19].
According to the model proposed by Easton and StJohn [12], the slope of the trendline through the data indicates that the particles are semi-potent, as relatively low solute additions are sufficient to activate a number of the particles.
[12] Easton, M.A. and StJohn, D.H. (2005) An analysis of the relationship between grain size, solute content, and the potency and number density of nucleant particles, Metallurgical and Materials Transactions 36A, 1911 - 1920