Skip to main content Accessibility help

Atom Probe Tomography Interlaboratory Study on Clustering Analysis in Experimental Data Using the Maximum Separation Distance Approach

  • Yan Dong (a1), Auriane Etienne (a2), Alex Frolov (a3), Svetlana Fedotova (a3), Katsuhiko Fujii (a4), Koji Fukuya (a4), Constantinos Hatzoglou (a2), Evgenia Kuleshova (a3), Kristina Lindgren (a5), Andrew London (a6), Anabelle Lopez (a7), Sergio Lozano-Perez (a8), Yuichi Miyahara (a9), Yasuyoshi Nagai (a10), Kenji Nishida (a9), Bertrand Radiguet (a2), Daniel K. Schreiber (a11), Naoki Soneda (a9), Mattias Thuvander (a5), Takeshi Toyama (a10), Jing Wang (a11), Faiza Sefta (a12), Peter Chou (a13) and Emmanuelle A. Marquis (a1)...


We summarize the findings from an interlaboratory study conducted between ten international research groups and investigate the use of the commonly used maximum separation distance and local concentration thresholding methods for solute clustering quantification. The study objectives are: to bring clarity to the range of applicability of the methods; identify existing and/or needed modifications; and interpretation of past published data. Participants collected experimental data from a proton-irradiated 304 stainless steel and analyzed Cu-rich and Ni–Si rich clusters. The datasets were also analyzed by one researcher to clarify variability originating from different operators. The Cu distribution fulfills the ideal requirements of the maximum separation method (MSM), namely a dilute matrix Cu concentration and concentrated Cu clusters. This enabled a relatively tight distribution of the cluster number density among the participants. By contrast, the group analysis of the Ni–Si rich clusters by the MSM was complicated by a high Ni matrix concentration and by the presence of Si-decorated dislocations, leading to larger variability among researchers. While local concentration filtering could, in principle, tighten the results, the cluster identification step inevitably maintained a high scatter. Recommendations regarding reporting, selection of analysis method, and expected variability when interpreting published data are discussed.


Corresponding author

*Author for correspondence: Emmanuelle A. Marquis, E-mail:


Hide All
Auger, P, Pareige, P, Welzel, S and Van Duysen, JC (2000). Synthesis of atom probe experiments on irradiation-induced solute segregation in French ferritic pressure vessel steels. J Nucl Mater 280(3), 331344.10.1016/S0022-3115(00)00056-8
Blavette, D and Chambreland, S (1986). A statistical model for deriving microstructure parameters of finely dispersed systems from atom-probe analyses. J Phys Colloq 47(C7), C7503.10.1051/jphyscol:1986784
Blum, TB, Darling, JR, Kelly, TF, Larson, DJ, Moser, DE, Perez-Huerta, A, Prosa, TJ, Reddy, SM, Reinhard, DA, Saxey, DW, Ulfig, RM and Valley, JW (2017). Best practices for reporting atom probe analysis of geological materials. In Microstructural Geochronology: Planetary Records Down to Atom Scale. Moser, DE, Corfu, F, Darling, JR, Reddy, SM and Tait, K. Wiley, pp. 369373.10.1002/9781119227250.ch18
Ceguerra, AV, Moody, MP, Stephenson, LT, Marceau, RKW and Ringer, SP (2010). A three-dimensional Markov field approach for the analysis of atomic clustering in atom probe data. Philos Mag 90(12), 16571683.10.1080/14786430903441475
Cerezo, A and Davin, L (2007). Aspects of the observation of clusters in the 3-dimensional atom probe. Surf Interface Anal 39, 184188.10.1002/sia.2486
Chen, Y, Chou, PH and Marquis, EA (2014). Quantitative atom probe tomography characterization of microstructures in a proton irradiated 304 stainless steel. J Nucl Mater 451(1–3), 130136.10.1016/j.jnucmat.2014.03.034
Couturier, L, De Geuser, F and Deschamps, A (2016). Direct comparison of Fe–Cr unmixing characterization by atom probe tomography and small angle scattering. Mater Charact 121, 6167.10.1016/j.matchar.2016.09.028
CVL (2016). CVL: Characterization Virtual Laboratory. Monash University. Available at
De Geuser, F, Lefebvre, W and Blavette, D (2006). 3D atom probe study of solute atoms clustering during natural ageing and pre-ageing of an Al–Mg–Si alloy. Philos Mag Lett 86(4), 227234.10.1080/09500830600643270
Edmondson, PD, Miller, MK, Powers, KA and Nanstad, RK (2016). Atom probe tomography characterization of neutron irradiated surveillance samples from the R. E. Ginna reactor pressure vessel. J Nucl Mater 470, 147154.10.1016/j.jnucmat.2015.12.038
Gault, B, Danoix, F, Hoummada, K, Mangelinck, D and Leitner, H (2012 a). Impact of directional walk on atom probe microanalysis. Ultramicroscopy 113, 182191.10.1016/j.ultramic.2011.06.005
Gault, B, Moody, MP, Cairney, JM and Ringer, SP (2012 b). Atom Probe Microscopy. New York: Springer-Verlag.10.1007/978-1-4614-3436-8
Gurovich, B, Kuleshova, E, Shtrombakh, Y, Fedotova, S, Maltsev, D, Frolov, A, Zabusov, O, Erak, D and Zhurko, D (2015). Evolution of structure and properties of VVER-1000 RPV steels under accelerated irradiation up to beyond design fluences. J Nucl Mater 456, 2332.10.1016/j.jnucmat.2014.09.019
Haley, D (2010). 3Depict—Visualisation and Analysis for Atom Probe. Available at
Heinrich, A, Al-Kassab, TA and Kirchheim, R (2003). Investigation of the early stages of decomposition of Cu–0.7 at% Fe with the tomographic atom probe. Mater Sci Eng A 353(1–2), 9298.10.1016/S0921-5093(02)00673-1
Hellman, OC, Vandenbroucke, JA, Rüsing, J, Isheim, D and Seidman, DN (2000). Analysis of three-dimensional atom probe data by the proximity histogram. Microsc Microanal 6, 437444.10.1007/S100050010051
Hyde, JM, Cerezo, A and Williams, TJ (2009). Statistical analysis of atom probe data: Detecting the early stages of solute clustering and/or co-segregation. Ultramicroscopy 109(5), 502509.10.1016/j.ultramic.2008.10.007
Hyde, JM, DaCosta, G, Hatzoglou, C, Weekes, H, Radiguet, B, Styman, PD, Vurpillot, F, Pareige, C, Etienne, A, Bonny, G, Castin, N, Malerba, L and Pareige, P (2017). Analysis of radiation damage in light water reactors: Comparison of cluster analysis methods for the analysis of atom probe data. Microsc Microanal 23(2), 366375.10.1017/S1431927616012678
Hyde, JM, Marquis, EA, Wilford, KB and Williams, TJ (2011). A sensitivity analysis of the maximum separation method for the characterisation of solute clusters. Ultramicroscopy 111(6), 440447.10.1016/j.ultramic.2010.12.015
Jaegle, EA, Choi, PP and Raabe, D (2014). The maximum separation cluster analysis algorithm for atom-probe tomography: Parameter determination and accuracy. Microsc Microanal 20, 16621671.10.1017/S1431927614013294
Jiao, Z and Was, GS (2011). Impact of localized deformation on IASCC in austenitic stainless steels. J Nucl Mater 408(3), 246256.10.1016/j.jnucmat.2010.10.087
Kolli, RP and Seidman, DN (2007). Comparison of compositional and morphological atom-probe tomography analyses for a multicomponent Fe–Cu steel. Microsc Microanal 13, 272284.10.1017/S1431927607070675
Kuramoto, A, Toyama, T, Nagai, Y, Inoue, K, Nozawa, Y, Hasegawa, M and Valo, M (2013). Microstructural changes in a Russian-type reactor weld material after neutron irradiation, post-irradiation annealing and re-irradiation studied by atom probe tomography and positron annihilation spectroscopy. Acta Mater 61(14), 52365246.
Lefebvre, W, Philippe, T and Vurpillot, F (2011). Application of Delaunay tessellation for the characterization of solute-rich clusters in atom probe tomography. Ultramicroscopy 111(3), 200206.10.1016/j.ultramic.2010.11.034
Lefebvre, W, Vurpillot, F and Sauvage, X (2016). Atom Probe Tomography, Put Theory Into Practice, Elsevier.
London, A (2016). AtomProbeLab: Matlab-based analysis of Atom Probe Data. Available at
Marceau, RK, Stephenson, LT, Hutchinson, CR and Ringer, SP (2011). Quantitative atom probe analysis of nanostructure containing clusters and precipitates with multiple length scales. Ultramicroscopy 111(6), 738742.
Marquis, EA, Araullo-Peters, V, Dong, Y, Etienne, A, Fedotova, S, Fujii, K, Fukuya, K, Kuleshova, E, Lopez, A, London, A, Lozano-Perez, S, Nagai, Y, Nishida, K, Radiguet, B, Schreiber, D, Soneda, N, Thuvander, M, Toyama, T, Sefta, F and Chou, P (2017). On the use of density-based algorithms for the analysis of solute clustering in atom probe tomography data. Proceedings of the 18th International Conference on Environmental Degradation of Materials in Nuclear Power Systems—Water Reactors. The Minerals, Metals and Materials Series. Springer, Cham.
Meslin, E, Lambrecht, M, Hernández-Mayoral, M, Bergner, F, Malerba, L, Pareige, P, Radiguet, B, Barbu, A, Gómez-Briceño, D, Ulbricht, A and Almazouzi, A (2010). Characterization of neutron-irradiated ferritic model alloys and a RPV steel from combined APT, SANS, TEM and PAS analyses. J Nucl Mater 406(1), 7383.10.1016/j.jnucmat.2009.12.021
Meslin, E, Radiguet, B and Loyer-Prost, M (2013). Radiation-induced precipitation in a ferritic model alloy: An experimental and theoretical study. Acta Mater 61(16), 62466254.10.1016/j.actamat.2013.07.008
Miller, MK and Hetherington, MG (1991). Local magnification effects in the atom probe. Surf Sci 246, 442449.
Miller, MK, Powers, KA, Nanstad, RK and Efsing, P (2013). Atom probe tomography characterizations of high nickel, low copper surveillance RPV welds irradiated to high fluences. J Nucl Mater 437(1–3), 107115.10.1016/j.jnucmat.2013.01.312
Miller, MK and Russell, KF (2007). Embrittlement of RPV steels: An atom probe tomography perspective. J Nucl Mater 371(1), 145160.10.1016/j.jnucmat.2007.05.003
Miller, MK, Russell, KF, Kocik, J and Keilova, E (2000). Embrittlement of low copper VVER 440 surveillance samples neutron-irradiated to high fluences. J Nucl Mater 282(1), 8388.10.1016/S0022-3115(00)00240-3
Moody, MP, Stephenson, LT, Ceguerra, AV and Ringer, SP (2008). Quantitative binomial distribution analyses of nanoscale like-solute atom clustering and segregation in atom probe tomography data. Microsc Res Technol 71(7), 542550.10.1002/jemt.20582
Pareige, P, Stoller, RE, Russell, KF and Miller, MK (1997). Atom probe characterization of the microstructure of nuclear pressure vessel surveillance materials after neutron irradiation and after annealing treatments. J Nucl Mater 249(2–3), 165174.10.1016/S0022-3115(97)00215-8
Radiguet, B, Barbu, A and Pareige, P (2007). Understanding of copper precipitation under electron or ion irradiations in FeCu 0.1 wt% ferritic alloy by combination of experiments and modelling. J Nucl Mater 360, 104117.10.1016/j.jnucmat.2006.09.007
Rose, DJ (1956). On the magnification and resolution of the field emission electron microscope. J Appl Phys 27(3), 215220.
Saxey, DW (2011). Correlated ion analysis and the interpretation of atom probe mass spectra. Ultramicroscopy 111(6), 473479.10.1016/j.ultramic.2010.11.021
Shu, S, Wirth, BD, Wells, PB, Morgan, DD and Odette, GR (2018). Multi-technique characterization of the precipitates in thermally aged and neutron irradiated Fe–Cu and Fe–Cu–Mn model alloys: Atom probe tomography reconstruction implications. Acta Mater 146, 237252.
Stephenson, LT, Moody, MP, Liddicoat, PV and Ringer, SP (2007). New techniques for the analysis of fine-scaled clustering phenomena within atom probe tomography (APT) data. Microsc Microanal 13(6), 448463.10.1017/S1431927607070900
Styman, PD, Hyde, JM, Parfitt, D, Wilford, K, Burke, MG, English, CA and Efsing, P (2015). Post-irradiation annealing of Ni–Mn–Si-enriched clusters in a neutron-irradiated RPV steel weld using atom probe tomography. J Nucl Mater 459, 127134.10.1016/j.jnucmat.2015.01.027
Styman, PD, Hyde, JM, Wilford, K and Smith, GDW (2013). Quantitative methods for the APT analysis of thermally aged RPV steels. Ultramicroscopy 132(0), 258264.10.1016/j.ultramic.2012.12.003
Takeuchi, T, Kuramoto, A, Kameda, J, Toyama, T, Nagai, Y, Hasegawa, M, Ohkubo, T, Yoshiie, T, Nishiyama, Y and Onizawa, K (2010). Effects of chemical composition and dose on microstructure evolution and hardening of neutron-irradiated reactor pressure vessel steels. J Nucl Mater 402(2), 93101.10.1016/j.jnucmat.2010.04.008
Thompson, K, Lawrence, D, Larson, DJ, Olson, JD, Kelly, TF and Gorman, B (2007). In situ site-specific specimen preparation for atom probe tomography. Ultramicroscopy 107(2–3), 131139.
Toyama, T, Kuramoto, A, Nagai, Y, Inoue, K, Nozawa, Y, Shimizu, Y, Matsukawa, Y, Hasegawa, M and Valo, M (2014). Effects of post-irradiation annealing and re-irradiation on microstructure in surveillance test specimens of the Loviisa-1 reactor studied by atom probe tomography and positron annihilation. J Nucl Mater 449, 207212.
Toyama, T, Nagai, Y, Tang, Z, Hasegawa, M, Almazouzi, A, van Walle, E and Gerard, R (2007). Nanostructural evolution in surveillance test specimens of a commercial nuclear reactor pressure vessel studied by three-dimensional atom probe and positron annihilation. Acta Mater 55(20), 68526860.
Vaumousse, D, Cerezo, A and Warren, PJ (2003). A procedure for quantification of precipitates microstructures from three-dimensional atom probe data. Ultramicroscopy 95, 215221.10.1016/S0304-3991(02)00319-4
Vurpillot, F, Bostel, A and Blavette, D (2000 a). Trajectory overlaps and local magnification in three-dimensional atom probe. Appl Phys Lett 76(21), 31273129.10.1063/1.126545
Vurpillot, F, Bostel, A, Cadel, E and Blavette, D (2000 b). The spatial resolution of 3D atom probe in the investigation of single-phase materials. Ultramicroscopy 84(3–4), 213224.10.1016/S0304-3991(00)00035-8
Vurpillot, F, De Geuser, F, Da Costa, G and Blavette, D (2004). Application of Fourier transform and autocorrelation to cluster identification in the three-dimensional atom probe. J Microsc 216, 234240.10.1111/j.0022-2720.2004.01413.x
Waugh, AR, Boyes, ED and MJ, S (1876). Investigations of field evaporation with a field-desorption microscope. Surf Sci 69(1), 109142.
Wells, PB, Yamamoto, T, Miller, B, Milot, T, Cole, J, Wu, Y and Odette, GR (2014). Evolution of manganese–nickel–silicon-dominated phases in highly irradiated reactor pressure vessel steels. Acta Mater 80, 205219.10.1016/j.actamat.2014.07.040
Williams, CA, Haley, D, Marquis, EA, Smith, GD and Moody, MP (2013). Defining clusters in APT reconstructions of ODS steels. Ultramicroscopy 132, 271278.10.1016/j.ultramic.2012.12.011
Zelenty, J, Dahl, A, Hyde, J, Smith, GD and Moody, MP (2017). Detecting clusters in atom probe data with Gaussian mixture models. Microsc Microanal 23(2), 269278.10.1017/S1431927617000320


Related content

Powered by UNSILO
Type Description Title
Supplementary materials

Dong et al. supplementary material
Appendices 1 and 2

 Word (1.1 MB)
1.1 MB

Atom Probe Tomography Interlaboratory Study on Clustering Analysis in Experimental Data Using the Maximum Separation Distance Approach

  • Yan Dong (a1), Auriane Etienne (a2), Alex Frolov (a3), Svetlana Fedotova (a3), Katsuhiko Fujii (a4), Koji Fukuya (a4), Constantinos Hatzoglou (a2), Evgenia Kuleshova (a3), Kristina Lindgren (a5), Andrew London (a6), Anabelle Lopez (a7), Sergio Lozano-Perez (a8), Yuichi Miyahara (a9), Yasuyoshi Nagai (a10), Kenji Nishida (a9), Bertrand Radiguet (a2), Daniel K. Schreiber (a11), Naoki Soneda (a9), Mattias Thuvander (a5), Takeshi Toyama (a10), Jing Wang (a11), Faiza Sefta (a12), Peter Chou (a13) and Emmanuelle A. Marquis (a1)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.