Standard deviations of composition measurements in atom probe analyses. Part I: Conventional 1D atom probe

Atom probe is a very powerful instrument to measure concentrations on a sub nanometric scale [M.K. Miller, G.D.W. Smith, Atom Probe Microanalysis, Principles and Applications to Materials Problems, Materials Research Society, Pittsburgh, 1989]. Atom probe is therefore a unique tool to study and characterise finely decomposed metallic materials. Composition profiles or 3D mapping can be realised by gathering elemental composition measurements.As the detector efficiency is generally not equal to 1, the measured compositions are only estimates of actual values. The variance of the estimates depends on which information is to be estimated. It can be calculated when the detection process is known.These two papers are devoted to give complete analytical derivation and expressions of the variance on composition measurements in several situations encountered when using atom probe.In the first paper, we will concentrate on the analytical derivation of the variance when estimation of compositions obtained from a conventional one dimension (1D) atom probe is considered. In particular, the existing expressions, and the basic hypotheses on which they rely, will be reconsidered, and complete analytical demonstrations established.In the second companion paper, the case of 3D atom probe will be treated, highlighting how the knowledge of the 3D position of detected ions modifies the analytical derivation of the variance of local composition data.