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H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
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To calculate the axis-angle pair relating two cubic lattices from an input consisting of a pair of vectors from each crystal, together with an angle between the two sets. All 24 symmetry-related axis-angle pairs are computed.
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Language: | FORTRAN
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Product form: | Source code |
SUBROUTINE MAP_CRYSTAL_PAIR(H, K, L, H1, K1, L1, U1, V1, W1, U, V, W,
& BEC, R, AINVR, PI, X, Y, Z, N1, Q1, Q2, Q3, THET, PHI)
REAL H, K, L, H1, K1, L1, U1, V1, W1, U, V, W, BEC(24,9), R(9), AINVR(9),
& PI, X, Y, Z, N1, Q1(23), Q2(23), Q3(23), THET(23), PHI
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The orientation relationship between two cubic crystals may be described in terms of
an axis-angle pair [X,Y,Z] and N1, or, alternatively, using a rotation matrix R.
MAP_CRYSTAL_PAIR calculates these using a pair of vectors from each crystal and the
angle between the two sets of vectors. All the vectors are coplanar. All 24 symmetry-related
axis-angle pairs are computed.
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- H.K.D.H. Bhadeshia, Worked Examples in the Geometry of Crystals,
Institute of Materials, London, 1987.
- H.K.D.H. Bhadeshia, Chapter on crystallography in Microstructural
Characterisation of High Temperature Materials,
ed. E. Metcalfe, Institute of Metals, London, 1988.
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Input parameters
- H, K, L - real
- H, K, L are the components of vector 1A.
- H1, K1, L1 - real
- H1, K1, L1 are the components of vector 2A.
- U1, V1, W1 - real
- U1, V1, W1 are the components of vector 1B.
- U, V, W - real
- U, V, W are the components of vector 2B.
- PHI - real
- PHI is the acute angle between the vectors 2A and 2B (in degrees).
- PI - real
- PI is pi.
Output parameters
- X, Y, Z - real
- X, Y, Z is the direction cosine from the axis-angle pair.
- N1 - real
- N1 is the right-handed rotation angle (in degrees).
- R - real array of dimension 9
- R is the rotation matrix.
- AINVR - real array of dimension 9
- AINVR is the inverse of the rotation matrix.
- BEC - real array of dimension 24x9
- BEC contains the 24 rotation matrices defining the symmetry operations of a cubic lattice.
- 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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None.
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No information supplied.
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None.
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1. Program text
REAL H, K, L, H1, K1, L1, U1, V1, W1, U, V, W, PI, PHI
REAL BEC(24,9), R(9), AINVR(9), Q1(23), Q2(23), Q3(23)
REAL X, Y, Z, N1, THET(23)
INCLUDE 'map_constants_pi.f'
READ (5,*) H, K, L
READ (5,*) H1, K1, L1
READ (5,*) U1, V1, W1
READ (5,*) U, V, W
READ (5,*) PHI
CALL MAP_CRYSTAL_PAIR(H, K, L, H1, K1, L1, U1, V1, W1, U, V, W,
& BEC, R, AINVR, PI, X, Y, Z, N1, Q1, Q2, Q3, THET, PHI)
WRITE (6,10) X, Y, Z, N1
WRITE (6,30)
WRITE (6,20) (R(I), I=1,9)
WRITE (6,40)
WRITE (6,20) (AINVR(I), I=1,9)
10 FORMAT ('Direction cosines ',3F8.4, ', Angle ',F8.4)
20 FORMAT (5X, 3F8.4)
30 FORMAT (,'Rotation matrix')
40 FORMAT (,'Inverse matrix')
STOP
END
2. Program data
None supplied.
3. Program results
None supplied.
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Subroutines:
MAP_CRYSTAL_ORIENT
MAP_CRYSTAL_ROTAT
Utility Subroutines:
MAP_UTIL_INVERS
MAP_UTIL_NORM
MAP_UTIL_ROT
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cubic lattice, rotation matrix, axis-angle pair
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Download source code
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