popLA Manual (PDF) - Materials Science and Engineering

Discrete Grains Files
So far, we have described textures by densities in orientation space; even though they were assigned to discrete
boxes, these were contiguous and meant to represent a continuous function. Under other circumstances, one
describes textures by a set of discrete grains; for example, if they have been individually measured, or if they are
the result of a simulation. One needs a way to convert one description into the other.
Weights
This program converts continuous distributions into discrete ones. As input, one needs a “grains” file that
represents “no texture”. One can do this by picking a regular lattice of grains in orientation space or a random
distribution. The grains are specified by a set of Euler angles. (The WEIGHTS program is written for one
nomenclature only: the “symmetric” or “Kocks’” Euler angles). These grains will be assigned weights that
reflect the density in orientation space at its location. We often assign different weights (near 1.0) to different
grains even in the beginning: to make the random (or regular) distribution more isotropic. This can be tested by
converting the grains files back to orientation distributions (see below: DIOR).
• Try this for our example: p.7#2. For the initial grains file, use TEXCUB.WTS. This is a file that contains
"triplets" of grains at positions that are equivalent due to the three-fold axis of the crystal symmetry. Use the
triplets (256 of them, for a total of 768 orientations); the program will average the OD density at the three
equivalent positions and deliver only the 256 irreducible orientations.
• Another option you will have is to discard grains of low weight, such as to arrive at the smallest number of
grains that describes your texture well enough. Try discarding all grains below a weight of 0.2. When the
program is done, it will tell you how many grains are left, and what volume fraction was discarded (128, 0.05
in our case). Now you must judge whether this is tolerable, or whether the number of grains is still too large;
iterate until you are satisfied. The output file has the extension .WTS.
• Inspect the resulting file (p.1#1). You see three columns of Euler angles and one of weights. (The weights
are not necessarily normalized to 1.0: this must be done in subsequent programs.) The last line before the
data block must contain, in its first position, the letter K (as it does here, for "Kocks" angles) or B or R or C.
The first line, as always, contains the specimen name in its first 8 positions. The third line reflects the grain
shape, which you have to edit yourself if you need it for future use (advanced topic).
Figure 10 – DEMO.WTS
TUTORIAL 20