Further remarks concerning optimization of counting times in single-crystal diffractometry: rebuttal to Killean: considerations of background counting and slewing times

Abstract

The objections raised by Killean [Acta Cryst. (1969), B25, 977] to the validity and applicability of the optimization presented by Hamilton [ACA Summer Meeting (1967), Abstract E6] and Shoemaker [Acta Cryst. (1968), A24, 136] are discussed, and shown to be not entirely substantial; it is concluded that optimized distribution of a fixed total counting time for the determination among the various reflections may still prove useful under commonly encountered experimental conditions. Modifications of the equations of Hamilton and of Shoemaker are presented. It is shown that, within the context of fixed total counting time, the addition of background to which a portion of that counting time must be allocated (in optimized ratios; see Shoemaker, 1968) results in an increase in the optimum counting time tj (scan plus background) per reflection to be assigned to relatively weak reflections that are highly sensitive to the parameters being determined, and a decrease in optimum counting time for weak reflections of low sensitivity and for all strong reflections. When a priori estimates of optimum counting times tj (without consideration of slewing between reflections) are available, as from a previous rough determination, the question may arise as to whether a low-weight reflection k should be counted at all since its omission releases not only its optimum tk, but also the slewing (circle-setting) time ts as well, for distribution among the remaining reflections. It is shown for fixed total time (counting plus slewing) that if tk < t*k where t*k ≃ (tstk0)½, the weight of the determination is increased by omitting the operations of slewing to and counting reflection k. [Here tk0 is defined (Shoemaker, 1968) as a counting time that would give a variance contribution due to counting statistics equal to the variance contribution due to all other sources.]