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To characterize the geometry of a grain boundary, we have to determine the misorientation between the neighboring grains, and the direction of the GB-plane.
Introduction Phenomena associated with grain boundaries (GB) in metals (e.g. corrosion, energy, segregation, etc) are known to be influenced by the grain boundary geometry. [1] The characterization of the geometry of a grain boundary relies on the calculation of the orientations of both neighboring grains and on the determination of the boundary-plane normal.
The symmetry-equivalent misorientation matrices (the number of them depends on the crystal structure) are determined from the orientation matrices of the corresponding grains.
Schematic figure of the projection of a grain boundary.
This can be shown by plotting the number of the GBs against the angle they extend to the sample surface.

The Challenge of Inhomogeneous Deformation in Magnesium and its Alloys Matthew R Barnett Centre for Material and Fibre Innovation, ITRI, Deakin University matthew.barnett@deakin.edu.au Keywords: grain boundary sliding, precipitation control, magnesium, strength, extrusion Abstract It is shown that wrought magnesium alloys display a number of significant types of deformation inhomogeneities.
It has long been known that the difficulty in achieving desired low temperature ductility in magnesium alloys owes itself to the low number of deformation systems/modes in this material [1].
That is, it is quite homogeneous at the grain scale.
This leads to considerable grain to grain heterogeneity, which has a number of consequences.
Such strain heterogeneity occurs when the stress is more evenly shared over the structure and can arise in a number of cases.

The model includes: (i) a grain-boundary migration-equation driving the evolution of grain size via the mobility of grain boundaries, which is coupled with (ii) a single-internal-variable (dislocation density) constitutive model for strain hardening and dynamic recovery, and (iii) a nucleation equation governing the total number of grains by the nucleation of new grains.
For instance, grain-boundary migration plays an important role because it is one of the main phenomena controlling the final grain size.
At any time, each grain, identified by its number i, is characterized by its diameter Di and its dislocation density ρi, which is assumed to stay homogeneous within the grain.
(ii) Grain boundary migration.
(iii) Nucleation of new grains.

Under hot deformation conditions, the flow stresses can be related to the DRX grain sizes with a grain size exponent of about 0.7 [2].
The new grains are characterized by a number of dislocations within their interiors (e.g.
A number of LAGBs with misorientations less than 15° are evolved in vicinity of initial HAGBs (Fig. 3a).
"ew grain formation at T = 500°°°°C (∼∼∼∼0.45 Tm).
The numbers in (b) indicate the misorientations in degrees.

The high-purity (99.99%) copper was received in a coarse-grained state with a grain size of ~1.2 mm.
It is important to note that there is a difference in the of the creep curves between the unpressed and the pressed materials and there is a difference in the fracture strain levels for the pressed material with different numbers of ECAP passes: these differences are denoted by the numbers B1 – B12 where the numeral denotes the number of ECAP passes using the route Bc [4].
Creep curves of (a) pure aluminium and (b) pure copper for unpressed (coarse-grained) state and various number of ECAP passes.
The solid regression lines correspond to the unpressed (coarse-grained) materials (N is number of ECAP passes).
Relation between mean creep rates and the minimum creep rates for (a) aluminium, and (b) copper (N is number of ECAP passes).

The subscript numbers of the array are determined by the coordinates of the left lower corner of cubes (re.
Its value is the subscript number in the array for the cube whose coordinate of left lower corner is (x, y, z). b is the length of cubes.
Atoms affecting a are within the 27 cubes and these cubes are determined by the combinations of subscript numbers from i-1 to i+1, j-1 to j+1, k-1 to k+1.
At the early stage the numbers of atoms are rather small, and the running times of both methods are approximately equal.
Kinetic exponents of the grain growth.

It is only valid when the final grain size is much larger than the initial grain size as in titanium alloy and ultrafine grain steel weldment [3, 4].
MC technique is used to simulate the grain growth evolution in HAZ.
Table 1 Data used for the calculation of thegrain growth kinetics of SUS316 [4,5] Nomenclature Value Initial average grain size, L0 22[μm] Activation enthalpy for grain growth, Q 1.245e5 [J/mol] Grain boundary energy,γ 1[J/m 2 ] Lattice point spacing, λ 20[μm] Avagadro's number, Na 6.02e23[/mol] Planck's constant, h 6.624e-34[ Js] Model constant number, K1 0.93 Model constant number, n1 0.46 Melting point, Tl 1573[K] Results and discussion The heat transfer and fluid flow model is employed to simulate the heat and mass transfer of GTAW process of stainless steel SUS316.
But the average of the grain size in HAZ is much smaller.
The temperature gradient existing in one grain and between neighbour grains resists the grain growth at certain extent.

Through research benefiting the agriculture policy Jiangxi grain cooperatives affect the costs and benefits to help pinpoint stabilize grain production, increase grain production capacity to ensure food security direction.
Stable development of grain production, so that farmers can be indirectly controlled grain costs, increase food revenue.
Benefiting the agriculture policy of planting grain cooperatives cost-benefit analysis In recent years, farmers engaged in grain production in Jiangxi growing enthusiasm, professional big grain acres or more from 2009 to 6969 to 2011 the development of 9319, professional big grain planting area about 335.5 acres of the total acreage 6.7%, respectively, 270 and 16.4 acres increase over the previous year.
Land costs cooperatives calculated according to the actual number of traditional farmers to do the same self-folding rent, are about $ 50
Jiangxi whole number of 17,000 cooperatives (grain cooperatives which nearly 10%), farmers join 190,000, covering 20% of households, total invested 25.61 billion yuan, driven by non-farmers to more than two million members, members generally average household income farmers than non-members more than 25%

The focus is to model austenite grain size evolution.
Equipment Pass number T,  oC Strain Strain rate, s-1 Delay times, s Pre-heating furnace 1200 70 Rougher 1 1150 0.03 0.2 14 9 1110 1.08a) 2.0 90b) Finisher (web schedule) 1 1060 0.12 5.4 5 2 1060 0.13 10.2 16 12 810 0.08 18.4 28 13 785 0.07 15.5 6 14 720 1.57c) 14.8 Air cooled Finisher (Flange schedule) 1 1070 0.05 5.4 5 2 1060 0.17 10.2 16 12 980 0.11 18.4 28 13 950 0.10 15.5 6 14 890 1.90d) 14.8 Air cooled a) Total equivalent strain after pass number 9 in the rougher; b) Delay time after pass number 9 during transfer from the rougher to the finishing stands; c) and d) Total equivalent strains after pass number 14 for the web and flange parts, respectively.
Note in Table 2 that the fraction recrystallized after pass number 8 is 60% and that after pass 9 is 100%.
Austenite and ferrite grain sizes calculated by the model for the finisher: flange schedule Equipment Pass number Average dγ before pass, μm Delay times, s Recrystallized fraction, % Average dγ after delay, μm Finisher (flange schedule) 1 105 5 0 105 2 105 16 54 53 3 53 5 83 31 4 31 18 100 61 5 61 6 48 38 6 38 20 100 80 7 80 5 27 55 8 55 22 100 74 9 74 7 16 59 10 59 26 91 38 11 38 6 23 28 12 28 28 90 24 13 24 6 0 24 14 24 Air cooling -- 15* * Ferrite grain size after air cooling to room temperature.
Here, all numbers are given in weight percentages except for the case N, given in ppm.

Recrystallization and grain growth, together with phase transformations such as precipitation, are the fundamental processes of microstructural evolution which take place during the thermomechanical processing of engineering materials.
One of the main goals of this two-volume set is to show how to cover the entire set of reactions governing recrystallization and grain growth during industrial processing – termed through process modelling.
At the same time, it is important to improve the understanding of the basic mechanisms involved in transformations such as nucleation during recrystallization, grain boundary migration under the influence of various forces, and boundary interactions with solute atoms and particles.
There are also a number of papers which deal with new techniques such as laser ultrasonics and high-energy X-ray methods for characterizing deformation structures, recrystallization and grain growth during (in situ) heat treatment.
The reader will be able to find within these two volumes a wealth of up-to-date papers describing current issues, concepts, techniques and results which will, in turn, improve his understanding of recrystallization and grain growth.