The statistics of the atom-by-atom dissection of planes, in the atom-probe field-ion microscope, have been investigated. Tungsten specimens oriented in the  direction, with the probe hole over the center of the plane, were slowly pulsed field-evaporated on a plane-by-plane basis, and statistical analyses were made on the number of tungsten atoms detected per plane; 30 separate slow dissection experiments were performed. Observed fluctuations in the number of atoms per plane are used to infer a range of allowable values for the detection efficiency. We find that, in some cases, the number of atoms per plane can be described as following a binomial distribution. From these results detection efficiencies in the range 0.11 to 0.54 were inferred. This range of efficiencies can be understood with the aid of field-ion desorption images. In addition, a value for the detection efficiency of 0.2 was obtained under the assumption that all atoms in the area projected by the probe hole, along the specimen radius, were analyzed. Thus, we find that this geometrical procedure, a first-order approach to the problem, yields a reasonable result. Also, the results of a Monte Carlo simulation of atom-by-atom field evaporation of a large number of planes are presented. The Monte Carlo simulation shows that if a binomial distribution is obtained, the uncertainty in concentrations determined by the atom-probe technique will have only a small component owing to the uncertainty in the number of solvent specimen atoms - this is subject to the caveat that there are no special problems with the field-evaporation behavior of the solvent atoms. Although the statistical analyses were applied to a specific crystallographic plane and position, the methodology is reasonably general and can be applied to other situations.
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