A statistical method to detect ordering and phase separation by APFIM

A method for evaluation of atom probe field ion microscopy (APFIM) data to test if a material exhibits phase separation or ordering tendencies is presented. In this method the standard error (s) of the frequency distribution for a large number of block sizes is compared with the standard deviation (σ) of the binomial distribution (BD). The BD is expected for a solid solution, where the atoms are randomly distributed. For an ordered material the experimental s will be smaller than σ for the BD. A large s, on the other hand, can be the consequence of phase separation. Simulations were used to determine the probability that an observed large or small s, indicating some feature of the material, could have been obtained from a random distribution. Also, simulations were used to reveal the influence of detection efficiency on the possibility to detect ordering. Examples from four materials are presented to illustrate the applicability of the method.