popLA Manual (PDF) - Materials Science and Engineering

(However, if output >= 1152, you’d have to increase dimensions in DIOR.)
Use DIOR (p5#7) with this file as input, and the symmetry files
actually applicable to the SOD (e.g., cub.sym and ort.sym).
Pick the axes permutation you want (need not be right-handed).
Pick SOD, 19 quadrants to 90 deg. for cubic cry./ortho.sample,
37 quadrants to 180 deg. for cubic cry./mono.sample,
37 semis to 180 deg. for at least ortho./ortho.
(lower symmetries won’t work this way).
Ask for density file, 5 x 5 degs., defaults.
Look at it (dspecnam): should have same format as original SOD,
but with different IPER’s in line 2. Done.
#3 Make .COD from .SOD (or .CHD from .SHD)
This routine converts a sample orientation distribution into a crystal orientation distribution (regardless of how
the SOD was obtained.)
#4 Make OBLIQUE sections from .SOD file
"Oblique sections" are handy to remove the last vestige of non-uniqueness at the origin; the sum (or difference)
of the two azimuthal Euler angles is used as the section parameter. popLA does this only in the "symmetric"
angle nomenclature, using the angle nu.
The resulting file extension ends on N (.SON, .CON, etc.). The azimuth in the section may be chosen in an
arbitrary manner; this distinguishes an .SON from a .CON. (A doubly oblique set is called an .OON.)
In some versions, we append the projection, in some we do not. The reason is that one typically chooses as
few sections as necessary, and then the sum of these sections is only part of the total projection.
#5 Pare to Subset for Display
Our displays typically accommodate only up to 12 figures. This option lets you pick an arbitrary selection of
SOD sections (or COD section, CON sections, etc.)
#6 Convert Miller Indices to Euler Angles
The input is either one set of Miller indices (or direction indices) or a pair describing a full orientation (by one
plane and one direction in it). For hexagonal crystals, the four-index notation is used. The program also needs a
defined CRY.SYM in the directory (or the appended path) and will use this to calculate all symmetrically
equivalent orientations for this crystal structure. The output file is called MILLER.EUL (overwriting any
previous one!) and contains all these orientations in any of the Euler angle conventions we use (Bunge, Canova,
Kocks, or Roe/Matthies). The format of this output file is that of a standard "weights file" or "discrete grains
file". (Note that when the fourth column is left blank. the weight is assumed to be 1.0.)
#7 DIOR See the description in the TUTORIAL section.
The program DIOR (for DIscrete ORientations) was introduced in the tutorial for one purpose: to convert a
discrete grains file into a density file (pole figure, inverse pole figure or any of the OD files). It also has plotting
capabilities, which will be described under page 6,#7.
Here we concentrate on its ability to manipulate an input weights file (DIORIN) and produce a new weights
file (DIOROUT). One may increase the number of grains by adding all orientations that are symmetrically
equivalent by virtue of any crystal symmetry elements or any sample symmetry elements. Conversely, one may
reduce the number of grains by only keeping those within a certain part of orientation space (such as in one
quadrant of a pole figure). The two actions often combine to leave the total number of grains constant (on
purpose). In addition, one may change the Euler angle nomenclature, and one may permute the sample axes.
(Note that, since both the input and the output are Euler angle files, the handedness must be kept the same; thus,
if the input IPER was cyclic (e.g., the default 1 2 3), you must specify a cyclic output IPER (say, 2 3 1).
When DIORIN and/or CRY.SYM and/or SAM.SYM exist in the subdirectory (or in the appended path),
DIOR will take these and print some information that helps you recognize what was used. When they do not
exist, DIOR asks you which file to use for DIORIN (e.g., MILLER.EUL), which for CRY.SYM (e.g.,
CUB.SYM -- which it will find in the appended C:\X), and which for SAM.SYM (e.g., ORT.SYM, ditto).
To do these operations, DIOR has to reserve a certain amount of memory. We have different versions: the
more recent ones use up to 540 KB of RAM (allowing up to 1002 input grains and 18 total symmetry operators).
DIOR does not use extended memory.
DETAILS 30