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  • Open Access

Clustering in atom probe tomography data: Coordination number metric, percolation-based parameter scaling, and size effects

Mykola Lazarev1,* and John Banhart2,†

  • *Contact author: n.lazarev@kipt.kharkov.ua
  • †Contact author: banhart@helmholtz-berlin.de
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Phys. Rev. E 114, 044109 – Published 6 October, 2026

DOI: https://doi.org/10.1103/17ms-c7hr

Abstract

The ability to identify nanometer-scale nuclei of additional phases in atom probe tomography (APT) is often limited by the sensitivity of clustering algorithms to user-defined control parameters. Conventional approaches typically rely on the Euclidean distance metric and consider only solute atoms, thereby discarding the solvent atoms that contain most of the spatial information. Here, we introduce a coordination-number metric based on the composition and apply it to higher-order clustering. Using various metrics, we investigate percolation in typical APT structures. By scaling clustering properties to the corresponding percolation thresholds, we define a self-similar variable that is almost invariant with respect to metrics, clustering parameters, and structural disorder. This variable provides a relevant description of clustering and enables the formal transfer of optimal parameters between clustering methods. We also study the characteristic clustering behavior in small precipitates and quantify how the precipitate-matrix interface alters the composition spectrum and broadens the clustering curve. Finally, using simulations that incorporate limited spatial precision, detection efficiency, and other APT reconstruction artifacts, we show that the coordination-number-based approach effectively compensates for heterogeneous dilations and outperforms solute-density-based methods across all tested scenarios.

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Phys. Rev. E 114, 044109– Published 6 October, 2026
  • Received 1 June 2026
  • Accepted 18 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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