368 Jonathan M. Hyde et al.


Simulating the Increased Density of Atoms Associated with Local Magnification Effects Evaporation of a material composed of several phases with significant differences in field evaporation threshold induces an evolution of the steady state shape of the tip surface. The consequence is strong distortions of the ion trajectories named “local magnification” effects (Miller & Hetherington, 1991). It changes both the X, Y positions, and, to a lesser extent, the Z positions. This effect can be highlighted by the presence of high- (or low)-density regions correlated with differences in local composition (Fig. 1). When local magnification is observed, at the interface


between phases, trajectory overlaps may be present. When the difference is too big, the phase of interest can be mixed completely with the surrounding matrix (ion crossing) (Miller & Hetherington, 1991). The magnitude of ion crossing is difficult to assess. Limits can be determined based on the fact that small solute clusters can be identified. The modeling of the field evaporation of a thin needle at the atomic scale can also provide understanding of the origin of the bias in 3D reconstructions and quantitative information about their influence on chemical composition measure- ments (Blavette et al., 2001; Lefebvre et al., 2016). Local magnification of solute clusters in RPV steels will


magnification, and the associated resulting effect on atom positions in the reconstructed data, is extremely challenging to model. In this work, a pragmatic approach to consider the effect of local magnification in the simulated data files was taken and is outlined here. Assuming cylindrical symmetry on the Z axis of a single spherical cluster, the positions of atoms situated at the center


result in compression or expansion in X and Y orientations, due to the fact that the solute atoms have different evaporation fields to that of Fe, and thus clusters may appear ellipsoidal (elongated in the Z direction) rather than spherical. For example, in the case of Cu clusters in an Fe matrix a compression of the clusters is observed. The underlying physics and complexities of local


of each cluster are not modified by local magnification effects. Similarly, far away from the cluster there is no effect of local magnification. These define the boundary conditions for the transformation (either from observed APT data to a more realistic picture of the underlying microstructure, or to transform perfect simulated data into a microstructure that is more representative of what would be observed by APT). The transformation, shown schematically in Figure 2, shows that it is necessary to consider both atoms within the solute cluster (compressed in APT data) and those in the adjacent matrix (more disparate in APT data). Consider a solute cluster with radius r. As the cluster is


slowly uncovered during an APT analysis, the radius of uncovered surface will increase to ~r and then decrease to 0. The effective radius, as a function of depth z in the cluster (where −r<z<r), is therefore given by


Rz ðÞ= ffiffiffiffiffiffiffiffiffiffiffiffipr2 - z2: The schematic in Figure 3 shows the displacement of


each atom (i.e., the difference between where the atom is detected and where it would have been detected without local magnification). The displacement depends on the distance (d) in the X–Y plane to the center of the solute cluster and the


ab


Figure 2. Schematic representation of (a) observed distribution of atoms from atom probe tomography analysis resulting from local magnification effects and (b) expected distribution without local magnification effects. Plan view (X–Y plane). “Blue” atoms have a lower evaporation field than the matrix.


Figure 1. Local magnification effects for low evaporation field particle (left) or high evaporation field particle (right), and schematic drawing showing ion trajectories close to the surface of the evaporated phase (the red atoms have a lower evaporation field than the white). Note the presence of ion crossing at the interface. From Vurpillot et al. (2000).


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