A versatile approach for simulation of APT measurements is presented. The model is founded on a Voronoi cell partition of 3D space. The partition is used in dual role: First, the atomic structure of the field emitter is depicted in a one to one relationship by single Wigner-Seitz cells. Second, the construction of an adaptive tetrahedral mesh enables solving the Poisson equation on length scales covering seven orders of magnitude. Ion trajectories are computed in full-length comparable to experiments. Contrary to former simulation approaches the sequence of desorbing atoms is determined by field-induced polarization forces. Both results for cubic lattices in <001>, <011>, and <111> orientation are presented and the simulation of an APT measurement of a complex crystalline/amorphous layer structure is demonstrated. The example of a grain boundary addresses the new possibility of constructing models with structural defects. In this case, the simulation reveals strong artifacts in the reconstruction even if homogenous evaporation threshold is assumed.
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