Dichotomy Methods



Successive dichotomy uses a totally different approach to the problem of indexing. The constants A to F in the equation



Q = A h2 + B k2 + C l2 + D kl + E hl + F hk

are assigned minimum and maximum values so that for a given hkl triplet values of Qmin and Qmax can be calculated. All of the input lines must lie within one of these Q ranges, but with no more than one line per range. The program then successively halves the range of the constants into an upper and lower range and again Q ranges are calculated. Now if some of the lines do not fall into the smaller Q ranges, then either the upper or lower range can be rejected. Thus the constants A to F are successively decreased, thus increasing their precision. The method is potentially exhaustive, but is extremely time consuming for the lowest-symmetry crystal systems.-Dichotomy Methods



Successive dichotomy uses a totally different approach to the problem of indexing. The constants A to F in the equation



Q = A h2 + B k2 + C l2 + D kl + E hl + F hk

are assigned minimum and maximum values so that for a given hkl triplet values of Qmin and Qmax can be calculated. All of the input lines must lie within one of these Q ranges, but with no more than one line per range. The program then successively halves the range of the constants into an upper and lower range and again Q ranges are calculated. Now if some of the lines do not fall into the smaller Q ranges, then either the upper or lower range can be rejected. Thus the constants A to F are successively decreased, thus increasing their precision. The method is potentially exhaustive, but is extremely time consuming for the lowest-symmetry crystal systems.