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  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example
  11. Auxiliary routines required.
  12. Keywords.
  13. Sources.

1. Provenance of Source Code

Kim Dae Woo
Graduate Institute of Ferrous Technology (GIFT)
Pohang University of Science and Technology
Pohang, Kyoungbuk, Republic of Korea


Added to MAP: September 2008.

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2. Purpose of code

The allotriomorphic ferrite nucleates heterogeneously at austenite grain boundaries, and although a reproducible, low-energy orientation relationship is expected to exist between the ferrite and one of the austenite grains with which it is in contact, there are reports that the ferrite can simultaneously adopt this orientation with more than one austenite grain. We examine this possibility using crystallographic theory in order to assess the probability of such events as a function of the strength of the texture within the austenite prior to its transformation.

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3. Specification

Language: Fortran 77
Product form: Source code and executable files for UNIX/Linux machines.

Complete program.

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4. Description

Austenite grains are conveniently represented as a stack of identical, space.filling Kelvin tetrakaidecahedra each of which consists of eight hexagonal and six square faces, with 36 equal edges. For ferrite nucleation at austenite grain surfaces, there are therefore 14 face-sites per grain.
The computer algorithm was constructed so that for each grain orientation relative to the sample frame of reference, it was possible to access the orientations of the fourteen neighbouring grains. A total of 1700 austenite grains was created in this way, with one of the grains having its crystallographic axes exactly parallel to those of the sample. The relationship between the sample and austenite crystal axes can be described using Euler angles. These are the three angles by which the sample reference frame must be rotated in order to coincide with that of the crystal.Non.random austenite textures were generated relative to the sample axes by setting the first austenite grain to the exact required texture, and then choosing relative to this grain, random rotation axes but with the right.handed rotation angle limited to the range of 4 to 45 degree.

Any grain of ferrite will always have an orientation relationship (a_J_r) with an austenite grain 1. However, some ferrite grains will have a special orientation relationship which corresponds to a low energy configuration. We adopt as the low energy orientation, one predicted by the crystallographic theory of martensite in order to ensure a coherent line between a and r

0.579356 0.542586 0.102537
0.014470 0.133650 -0.788984
-0.552000 0.0572979 0.086936

and when ferrite was allowed to form on a face between two austenite grains with relative orientation (r1_J_r2, the corresponding orientations with the ferrite are (r1_J_a) and (r2_JLE_a)where the latter is the low energy variant. It follows that

(r1_J_a) = (r1_J_r2)(r2_JLE_a)

Both the matrices on the right.hand side of this equation are known because the austenite orientations are set initially and (r 2_JLE_a) is given by previous table. Ferrite was allowed to nucleate on all 14 faces of each austenite grain. The ferrite in all cases had a low energy orientation with one austenite grain; since there are 24 crystallographically equivalent such orientations for any given austenite grain, the selection of the particular variant was made at random from the 24 available.

The name of source code is as follows :


This is a source code of this program. For the execution, it needs to be compiled.
compile example :
g77 allotriomorp.f -o name.out

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5. References

  1. Transformation texture of allotriomorphic ferrite in steel, Materials Science and Technology, 2009, DOI: 10.1179/174328408X365793, D. W. Kim, R. S. Qin, H. K. D. H. Bhadeshia
  2. Crystallographic Texture of Stress-Affected Bainite, Proceedings of The Royal Society A, 463 (2007) 2309-2328, S. Kundu, K. Hase and H. K. D. H. Bhadeshia
  3. S. Kundu, Transformation Strain and Crystallographic Texture in Steels, Ph.D. Thesis, University of Cambridge, U. K., 2007.
  4. H. K. D. H. Bhadeshia, Geometry of Crystals. 2nd edition, Institute of Materials, 2001
  5. More on crystallographic texture

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6. Parameter descriptions

S_J_MO(9) : Transformation matrix between seed austenite grain(crystal coordinate) and specimen coordinate
S_J_M (9) : Transformation matrix between each austenite grain and specimen coordinate
Fer_Tex(9) : Transformation matrix from austenite to ferrite
Relations(CEG,FJ2,9) : Matrix to calculate the relationship between centered austenite grain and it's neighbour grains
Fer_Ran(9) : Matrix to calculate the random orientation relationship between austenite and ferrite
FE_AX_AM(CEG,FJ2,ANF,9) : Matrix to calculate the axis_angle fair

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7. Error Indicators


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8. Accuracy estimate

No information.

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9. Any additional information


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10. Example

1. Program Compile

g77 [sourcecode name] -o [executable file name]

2. Program menu

1 : CUBE
2 : GOSS
5 : MULTI: Cube-Goss-Brass-Copper
6 : alpha-fibre: <110>//ND
7 : r-FIBRE

Select representative type:

full euler space or 45 section?
2. 45 degree section


3. Program results


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11. Auxiliary subroutines required


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12. Keywords

Texture, Allotriomorphic ferrite, Dual orientation, Crystallography

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13. Source

Download FORTRAN source code

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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