popLA Manual (PDF) - Materials Science and Engineering

For hexagonal materials start with the 4-index notation (e.g., 2 110 ). Rearrange it so that the first two
indices are positive (112 0 ). Then leave the third index out (which is the negative sum of the first two,
anyway). The last index remains untouched. The final form for this example is (110) or (11•0). This is the label
for pole figures. Note, however, that in inverse pole figures and SODs, as well as in DIOR and LApp, we use
ortho-hexagonal axes with x = [21 1 0 ] ≡ (11•0) and y = [01 1 0 ] ≡ (01•0).
Higher orders (which may be the first measurable; e.g., 220 in FCC) are treated the same as the first order
(110). This leads to a problem only in materials (such as quartz) where, e.g., (006) and (009) give different
information; these can, in any case, not be treated by any of the distributed popLA programs. (There is a special
private version by Kallend and Wenk, "MIXWIMV", with which one can analyze overlapping peaks.)
B6 Format of Discrete Grains Files (TEXfiles, .WTS files)
• 1st Line: Title. The first 8 characters are used by other programs as file name (with some new extension
attached). It is always good practice to use the rest of the line for comments for later identification.
• 2nd Line: Explanation of 3rd line.
• 3rd Line: Grain shape description by the deformation gradient matrix that would have made this shape (and
orientation with respect to the sample axis) from a sphere. You must enter this by hand after the WTS file
has been made if you wish to have LApp take account of Relaxed Constraints. (The fist number must be
nonzero to activate F-matrix reading.) In some files, the end of the 2nd and 3rd lines lists the number of state
parameters for each grain; i.e. the number of columns in excess of 4.
• 4th Line: Explanation of the Euler angles and state parameters listed below. The first character on this line
identifies the Kocks, Roe (Matthies), and Bunge notations by K, R, and B, respectively. In some older
programs, any other character is interpreted as Canova angles; now these are defined by C. At the end of the
4th line, there may be a notation " X Y Z= 1 2 3". This relates the Euler-angle sample coordinates X, Y, Z to
how you may have labeled your sample (faces 1, 2, and 3) and how the sample axes are labeled in plots (1, 2,
and 3). See Appendix C.
• Data: Must be in nf8.2 format, with n•3. Some programs will interpret all nonexistent further numbers as
ones. But to be on the safe side, set all the weights in the fourth column to 1, if they are not otherwise
specified. It does not matter whether the angles are specified in the range 0° to 360° or 180° to 180°. But it
is best to keep the pole distance positive and < 180° (or better < 90°).
A sample .WTS file follows:
texreg.wts:for 4/mmm.Cubics:average triplets! diad:3456(/3),ort:1728(/3)
Evm F11 F12 F13 F21 F22 F23 F31 F32 F33
0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000
Kocks:Psi Theta phi weight (up to 6 state parameters, f8.2) 1 2 3
2.45 1.00 44.95 0.14
137.50 89.29 89.29 0.14
47.50 89.29 0.71 0.14
7.45 4.00 44.95 0.12
142.43 87.17 87.17 0.12
52.57 87.18 2.83 0.12
2.45 7.00 44.95 0.39
137.29 85.05 85.04 0.39
47.71 85.06 4.97 0.39
2.45 10.00 44.95 0.18
137.06 82.94 82.90 0.18
47.94 82.95 7.11 0.18
7.45 25.00 44.95 0.51
139.69 72.60 71.77 0.51
55.31 72.63 18.26 0.51
2.45 37.00 44.95 0.08
131.11 64.79 61.97 0.08
53.89 64.84 28.07 0.08
2.45 48.00 44.95 0.07
126.28 58.27 51.88 0.07
58.71 58.33 38.17 0.07
7.45 54.74 44.95 0.15
127.49 54.70 45.02 0.15
67.50 54.77 45.03 0.15
APPENDICES 44