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Subroutine MAP_CRYSTAL_PAIR

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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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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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Specification

Language:	FORTRAN
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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Description

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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References

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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Parameters

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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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