Part VII – July 1968 – Communications - Computer Program for Calculating Interplanar Angles and Indexing Back-Reflection Laue Films of Hexagonal Crystals

ThE computer program for arbitrary crystal systems reported by Camp and Clum' has been modified to make it more convenient for hexagonal crystals. The program' uses the Miller indexes (hkl) which can be confusing for hexagonal crystals while the modified program uses the Miller-Bravais indexes with four axes; e.g., the angles between the (110) planes, Fig. 1, are 0 and 90 deg but in the (hkil) system the angles between the (1150) planes are 0 and 60 deg. If a Laue photograph is taken of a crystal oriented with the prismatic planes nearly parallel to the film then the spots on the stereo graphic projection will be from high-index planes. The probable positions of the low-index planes, e.g., (0001) plane, can only be obtained from the intersection of zones and this is not accurate to 1 or 2 deg. The number of planes considered by the program (card 1)' has to be limited to the ones of low index or the program time is excessive but a solution will not be obtained if one of the spots has an index that is not being considered. To overcome this problem the program1 was modified so that if no fit was obtained at *1 deg (card 3) of the tabulated angles then ±2 or ±3 deg was tried. If still no solution was obtained either due to one of the angles not being measured correctly to ±3 deg or because one of the spots was from a high-index plane, then the last spot was discounted and a fit tried for the remaining spots at i1 deg, and so forth. The minimum number of spots that the program will try to fit is five. If the limit on any individual index is 4 (card 1) and (h + k + l + 1) is six then twenty-three planes are considered and there are over 1000 interplanar angles. Many pairs of planes have very similar interplanar angles and with the errors previously mentioned the program will often produce several alternative solutions to a group of spots particularly at ±2 or ±3 deg. However without the program the alternative solutions would probably not have been found. If a large number of spots are used the number of possible fits is reduced. In the example shown in Fig. 2, if only spots which are on the film are used (case 1) the program gives six possible solutions, Table I. However if points 7 and 8 are also used (case 2) the program gives only one fit which also agrees with a standard projection of the crystal. In addition to time-saving the program ensures that a correct solution is obtained since it is unlikely that all the alternatives would have been gound manually; the first would probably be assumed to be the correct solution. The program has been used for zirconium crystals but is equally suitable for other hexagonal materials.