Contingency table techniques for three dimensional atom probe tomography

A contingency table analysis procedure is developed and applied to three dimensional atom probe data sets for the investigation of fine-scale solute co-/anti-segregation effects in multicomponent alloys. Potential sources of error and inaccuracy are identified and eliminated from the technique. The conventional P value testing techniques associated with chi(2) are shown to be unsatisfactory and can become ambiguous in cases of large block numbers or high solute concentrations. The coefficient of contingency is demonstrated to be an acceptable and useful basis of comparison for contingency table analyses of differently-conditioned materials. However, care must be taken in choice of block size and to maintain a consistent overall composition between experiments. The coefficient is dependent upon block size and solute composition, and cannot be used to compare analyses with significantly different solute compositions or to assess the extent of clustering without reference to that of the randomly ordered case. It is shown that as clustering evolves into larger precipitates and phases, contingency table analysis becomes inappropriate. Random labeling techniques are introduced to infer further meaning from the coefficient of contingency. We propose the comparison of experimental result, mu(exp), to the randomized value, micro(rand), as a new method by which to interpret the quantity of solute clustering present in a material. It is demonstrated that how this method may be utilized to identify an appropriate size of contingency table analysis blocks into which the data set is partitioned to optimize the significance of the results.