Materials Algorithms Project
Program Library

Subroutine MAP_CRYSTAL_ROTAT

1. Provenance of code.
2. Purpose of code.
3. Specification.
4. Description of subroutine's operation.
5. References.
6. Parameter descriptions.
7. Error indicators.
8. Accuracy estimate.
9. Any additional information.
10. Example of code
11. Auxiliary subroutines required.
12. Keywords.
13. Download source code.
14. Links.

Provenance of Source Code

H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

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Purpose

To calculate the 23 axis-angle pairs which are equivalent to a given axis-angle pair in a cubic lattice.

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Specification

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Description

The orientation relation between two cubic crystals can be described by either an axis-angle pair [P1,P2,P3] and THETA, or using a rotation matrix R. Cubic crystals have a high degree of symmetry so there are, in general, 24 crystallographic descriptions of the same orientation relationship. MAP_CRYSTAL_ROTAT generates the 23 alternative descriptions for a given axis-angle pair. This axis is described by the direction cosines [P1,P2,P3] and the right-handed angle of rotation THETA.

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References

1. H.K.D.H. Bhadeshia, Worked Examples in the Geometry of Crystals, Institute of Materials, London, 1987.

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Parameters

Input parameters

P1, P2, P3 - reals

P1, P2, P3 are the direction cosines.

THETA - real

THETA is the right-handed angle of rotation (in degrees).

BEC - real array of dimension 24x9

BEC contains 24 rotation matrices, each describing a rotation matrix which is a symmetry operation on the cubic lattice.

PI - real

PI is pi.

Output parameters

Q1, Q2, Q3 - real arrays of dimension 23

Q1, Q2, Q3 contain the 23 sets of direction cosines from the equivalent axis-angle pairs.

THET - real array of dimension 23

THET contains the 23 angles from the axis-angle pairs.

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Error Indicators

None.

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Accuracy

No information supplied.

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Further Comments

Used by the crystal analysis program MAP_CRYSTAL_PROG

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Example

1. Program text

       REAL P1, P2, P3, THETA, BEC(24,9), Q1(23), Q2(23), Q3(23), THET(23), PI
       INTEGER I
       INCLUDE 'map_constants_pi.f'
       READ (5,*) P1, P2, P3
       READ (5,*) THETA
       CALL MAP_CRYSTAL_ORIENT(BEC)
       CALL MAP_CRYSTAL_ROTAT(P1, P2, P3, THETA, BEC, Q1, Q2, Q3, THET, PI)
       DO 10  I=1,23
       WRITE (6,*) Q1(I), Q2(I), Q3(I), THET(I)
10     CONTINUE
       STOP
       END

2. Program data

1.0   3.0   2.0

3. Program results

-0.572046    -0.476419    -0.667674&   185.328
 0.502397     0.574353     0.646309&   296.046
-0.244854    -0.634860     0.732802&   348.786
 0.588009    -0.784600     0.196592&   337.544
 0.830744    -0.146912    -0.536919&   348.786
-0.930605     0.358917    -7.17835E-02 171.808
 0.173850     0.983066     5.79499E-02 230.278
-0.796225    -0.596720    -9.97522E-02 314.869
 0.704643    -0.616365    -0.351528&   206.353
 0.393561    -0.472558     0.788542&   244.484
 0.209532    -6.98440E-02 -0.975304&   328.192
 0.946556     6.32553E-02  0.316276&   202.587
-0.542144     4.94474E-02 -0.838829&   326.249
 0.313171     0.156585    -0.936699&   154.651
-0.514478     0.735537     0.440792&   279.366
-0.745192    -0.330368     0.579263&   225.945
-0.141423    -0.987420     7.07116E-02 312.092
-8.76349E-02 -0.960834     0.262905&   135.708
 5.04440E-02 -0.754847    -0.653959&   303.376
-0.120637&    0.241274     0.962930&   216.735
 0.758459&    0.530512    -0.378547&   262.227
-0.314565&    0.709546    -0.630550&   244.484
-0.968245&    0.138677    -0.208015&   344.134

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Auxiliary Routines

Utility Subroutines:
MAP_UTIL_NORM
MAP_UTIL_PROD
MAP_UTIL_ROT

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Keywords

axis-angle

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Download

Download source code

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