Quantitative binomial distribution analyses of nanoscale like-solute atom clustering and segregation in atom probe tomography data
The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional χ2 statistics and significance testing are demonstrated to be inappropriat...
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| Published in | Microscopy research and technique Vol. 71; no. 7; pp. 542 - 550 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken
Wiley Subscription Services, Inc., A Wiley Company
01.07.2008
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1059-910X 1097-0029 1097-0029 |
| DOI | 10.1002/jemt.20582 |
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| Abstract | The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional χ2 statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, μ, is shown to normalize χ2 with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of μ over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results. Microsc. Res. Tech., 2008. © 2008 Wiley‐Liss, Inc. |
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| AbstractList | The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional 2 statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, , is shown to normalize 2 with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results. Microsc. Res. Tech., 2008. The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional χ2 statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, μ, is shown to normalize χ2 with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of μ over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results. Microsc. Res. Tech., 2008. © 2008 Wiley‐Liss, Inc. The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional chi(2) statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, mu, is shown to normalize chi(2) with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of mu over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results.The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional chi(2) statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, mu, is shown to normalize chi(2) with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of mu over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results. The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional chi(2) statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, mu, is shown to normalize chi(2) with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of mu over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results. The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional χ 2 statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, μ, is shown to normalize χ 2 with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of μ over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results. Microsc. Res. Tech., 2008. © 2008 Wiley‐Liss, Inc. |
| Author | Moody, Michael P. Ceguerra, Anna V. Ringer, Simon P. Stephenson, Leigh T. |
| Author_xml | – sequence: 1 givenname: Michael P. surname: Moody fullname: Moody, Michael P. email: m.moody@usyd.edu.au organization: Australian Key Centre for Microscopy and Microanalysis, The University of Sydney, New South Wales 2006, Australia – sequence: 2 givenname: Leigh T. surname: Stephenson fullname: Stephenson, Leigh T. organization: Australian Key Centre for Microscopy and Microanalysis, The University of Sydney, New South Wales 2006, Australia – sequence: 3 givenname: Anna V. surname: Ceguerra fullname: Ceguerra, Anna V. organization: Australian Key Centre for Microscopy and Microanalysis, The University of Sydney, New South Wales 2006, Australia – sequence: 4 givenname: Simon P. surname: Ringer fullname: Ringer, Simon P. organization: Australian Key Centre for Microscopy and Microanalysis, The University of Sydney, New South Wales 2006, Australia |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/18425800$$D View this record in MEDLINE/PubMed |
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| Publisher | Wiley Subscription Services, Inc., A Wiley Company |
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| References | Camus E,Abromeit C. 1994b. Correlation and contingency analysis of atom probe data: Diffusion-controlled dissolution of precipitates. Z Metallkd 85: 378-382. Miller MK,Cerezo A,Hetherington MG,Smith GDW. 1996. Atom probe and field ion microscopy. New York. Oxford University Press. Hetherington MG,Cerezo A,Hyde J,Smith GDW,Worrall GM. 1986. Statistical analysis of atom probe data. J de Phys 47: 495-501. Vurpillot F,Bostel A,Blavette D. 2000. Trajectory overlaps and local magnification in three-dimensional atom probe. Appl Phys Lett 76: 3127-3129. Hetherington MG,Miller MK. 1989. Some aspects of the measurement of composition in the atom probe. J de Phys 50‒C8: 535-540. Stephenson LT,Moody MP,Liddicoat PV,Ringer SP. 2007. New techniques for the analysis of fine-scaled clustering phenomena within atom probe tomography data. Microsc Microanal 13: 448-463. Sassen JM,Hetherington MG,Godfrey TJ,Smith GDW,Pumphrey PH,Akhurst KN. 1987. In: Prager M,editor. Properties of stainless steels in elevated temperature service. New York: American Society of Mechanical Engineers. p. 65. Starink MJ,Gao N,Davin L,Yan J,Cerezo A. 2005. Room temperature precipitation in quenched Al-Cu-Mg alloys: A model for the reaction kinetics and yield strength development. Philos Mag 85: 1395-1417. Ringer SP,Sakurai T,Polmeaer IJ. 1997. Origins of hardening in aged Al-u-Mg-(Ag) alloys. Acta Mater 45: 3731-3744. Danoix F,Auger P,Bostel A,Blavette D. 1991. Atom probe characterization of isotropic spinodal decompositions: Spatial convolutions and related bias. Surf 246: 260-265. Seidman DN. 2007. Three-dimensional atom-probe tomography: Advances and applications. Annu Rev Mater Res 37: 127-158. Kelly TF,Miller MK. 2007. Atom probe tomography. Rev Sci Instrum 78: 031101. Cahn JW. 1968. 1967 Institute of metals lecture spinodal decomposition. Trans Metall Soc AIME 242: 166. Everitt BS. 1977. The analysis of contingency tables. London: Chapman and Hall. Geiser BP,Kelly TF,Larson DJ,Schneir J,Roberts J. 2007. Spatial distribution maps for atom probe tomography. Microsc Microanal 13: 437-447. Tsong TT,Mc Lane SB,Ahmad M,Wu CS. 1982. Field evaporation events as Markov chains: A time-of-flight-atom-probe study of Iridium. Pt-Rh alloys and metallic glasses. J Appl Phys 53: 4180-4188. Ringer SP. 2006. Advanced nanostructural analysis of aluminium alloys using atom probe tomography. Mater Sci Forum 25: 519-521. Vaumousse D,Cerezo A,Warren PJ. 2003. A procedure for quantification of precipitate microstructures from three-dimensional atom probe data. Ultramicroscopy 95: 215-221. Vurpillot F,Renaud L,Blavette D. 2003. A new step towards the lattice reconstruction in 3DAP. Ultramicroscopy 95: 223-229. Kendall MG,Stuart A. 1961. The advanced theory of statistics. London: Griffin. Castell MR,Muller DA,Voles PM. 2003. Dopant mapping for the nanotechnology age. Nat Mater 2: 129-131. Heinrich A,Al-Kassab T,Kircheim R. 2003. Investigation of the early stages of decomposition of Cu-0.7at.% Fe with the tomographic atom probe. Mater Sci Eng A 353: 92-98. Langer JS,Bar-on M,Miller HD. 1975. New computational method in the theory of spinodal decomposition. Phys Rev A 11: 1417-1429. Gault B,Moody MP,Saxey DW,Cairney JM,Liu Z,Zheng R,Marceau RKW,Liddicoat PV,Stephenson LT,Ringer SP. Atom probe tomography at the University of Sydney. Advances in materials research series. Berlin: Springer-Verlag (in press). Moody MP,Stephenson LT,Liddicoat PV,Ringer SP. 2007. Contingency table techniques for three dimensional atom probe technology. Microsc Res Tech 70: 258-268. Camus E,Abromeit C. 1994a. Analysis of conventional and three-dimensional atom probe data for multiphase materials. J Appl Phys 75: 2373-2382. Abramowitz M,Stegun IA, editors. 1972. Handbook of mathematical functions with formulas, graphs, and mathematical tables, 9th ed. New York: Dover. pp. 940-943. Kelly TF,Gribb TT,Olson JD,Martens RL,Shepard JD,Wiener SA,Kunicki TC,Ulfig RM,Lenz DR,Strennen EM,Oltman E,Bunton JH,Strait DR. 2004. First data from a commercial local electrode atom probe (LEAP). Microsc Microanal 10: 373. Miller MK. 2000. Atom probe tomography: Analysis at the atomic level. New York. Kluwer Academic/Plenum Publisher. 1968; 242 1994a; 75 1982; 53 1997; 45 2005; 85 1996 2007; 70 1972 1975; 11 2003; 95 2007; 78 2007; 13 2003; 353 2007; 37 1977 2004; 10 1989; 50‒C8 1991; 246 2001 2000 2000; 76 1986; 47 2006; 25 2003; 2 1987 1961 1994b; 85 1904 Abramowitz M (e_1_2_1_2_1) 1972 Gault B (e_1_2_1_9_1) e_1_2_1_20_1 e_1_2_1_23_1 e_1_2_1_22_1 e_1_2_1_27_1 e_1_2_1_28_1 e_1_2_1_25_1 e_1_2_1_29_1 Sassen JM (e_1_2_1_26_1) 1987 Cahn JW (e_1_2_1_3_1) 1968; 242 Ringer SP (e_1_2_1_24_1) 2006; 25 e_1_2_1_7_1 e_1_2_1_31_1 e_1_2_1_8_1 e_1_2_1_30_1 e_1_2_1_6_1 Miller MK (e_1_2_1_21_1) 1996 e_1_2_1_4_1 Camus E (e_1_2_1_5_1) 1994; 85 e_1_2_1_10_1 e_1_2_1_33_1 e_1_2_1_11_1 Hetherington MG (e_1_2_1_12_1) 1989; 50 e_1_2_1_32_1 e_1_2_1_16_1 Hetherington MG (e_1_2_1_13_1) 1986; 47 e_1_2_1_17_1 e_1_2_1_14_1 e_1_2_1_15_1 e_1_2_1_18_1 e_1_2_1_19_1 |
| References_xml | – reference: Seidman DN. 2007. Three-dimensional atom-probe tomography: Advances and applications. Annu Rev Mater Res 37: 127-158. – reference: Gault B,Moody MP,Saxey DW,Cairney JM,Liu Z,Zheng R,Marceau RKW,Liddicoat PV,Stephenson LT,Ringer SP. Atom probe tomography at the University of Sydney. Advances in materials research series. Berlin: Springer-Verlag (in press). – reference: Miller MK. 2000. Atom probe tomography: Analysis at the atomic level. New York. Kluwer Academic/Plenum Publisher. – reference: Ringer SP,Sakurai T,Polmeaer IJ. 1997. Origins of hardening in aged Al-u-Mg-(Ag) alloys. Acta Mater 45: 3731-3744. – reference: Everitt BS. 1977. The analysis of contingency tables. London: Chapman and Hall. – reference: Tsong TT,Mc Lane SB,Ahmad M,Wu CS. 1982. Field evaporation events as Markov chains: A time-of-flight-atom-probe study of Iridium. Pt-Rh alloys and metallic glasses. J Appl Phys 53: 4180-4188. – reference: Ringer SP. 2006. Advanced nanostructural analysis of aluminium alloys using atom probe tomography. Mater Sci Forum 25: 519-521. – reference: Langer JS,Bar-on M,Miller HD. 1975. New computational method in the theory of spinodal decomposition. Phys Rev A 11: 1417-1429. – reference: Starink MJ,Gao N,Davin L,Yan J,Cerezo A. 2005. Room temperature precipitation in quenched Al-Cu-Mg alloys: A model for the reaction kinetics and yield strength development. Philos Mag 85: 1395-1417. – reference: Geiser BP,Kelly TF,Larson DJ,Schneir J,Roberts J. 2007. Spatial distribution maps for atom probe tomography. Microsc Microanal 13: 437-447. – reference: Heinrich A,Al-Kassab T,Kircheim R. 2003. Investigation of the early stages of decomposition of Cu-0.7at.% Fe with the tomographic atom probe. Mater Sci Eng A 353: 92-98. – reference: Hetherington MG,Cerezo A,Hyde J,Smith GDW,Worrall GM. 1986. Statistical analysis of atom probe data. J de Phys 47: 495-501. – reference: Stephenson LT,Moody MP,Liddicoat PV,Ringer SP. 2007. New techniques for the analysis of fine-scaled clustering phenomena within atom probe tomography data. Microsc Microanal 13: 448-463. – reference: Moody MP,Stephenson LT,Liddicoat PV,Ringer SP. 2007. Contingency table techniques for three dimensional atom probe technology. Microsc Res Tech 70: 258-268. – reference: Sassen JM,Hetherington MG,Godfrey TJ,Smith GDW,Pumphrey PH,Akhurst KN. 1987. In: Prager M,editor. Properties of stainless steels in elevated temperature service. New York: American Society of Mechanical Engineers. p. 65. – reference: Hetherington MG,Miller MK. 1989. Some aspects of the measurement of composition in the atom probe. J de Phys 50‒C8: 535-540. – reference: Vurpillot F,Bostel A,Blavette D. 2000. Trajectory overlaps and local magnification in three-dimensional atom probe. Appl Phys Lett 76: 3127-3129. – reference: Cahn JW. 1968. 1967 Institute of metals lecture spinodal decomposition. Trans Metall Soc AIME 242: 166. – reference: Danoix F,Auger P,Bostel A,Blavette D. 1991. Atom probe characterization of isotropic spinodal decompositions: Spatial convolutions and related bias. Surf 246: 260-265. – reference: Castell MR,Muller DA,Voles PM. 2003. Dopant mapping for the nanotechnology age. Nat Mater 2: 129-131. – reference: Miller MK,Cerezo A,Hetherington MG,Smith GDW. 1996. Atom probe and field ion microscopy. New York. Oxford University Press. – reference: Vurpillot F,Renaud L,Blavette D. 2003. A new step towards the lattice reconstruction in 3DAP. Ultramicroscopy 95: 223-229. – reference: Camus E,Abromeit C. 1994a. Analysis of conventional and three-dimensional atom probe data for multiphase materials. J Appl Phys 75: 2373-2382. – reference: Kelly TF,Gribb TT,Olson JD,Martens RL,Shepard JD,Wiener SA,Kunicki TC,Ulfig RM,Lenz DR,Strennen EM,Oltman E,Bunton JH,Strait DR. 2004. First data from a commercial local electrode atom probe (LEAP). Microsc Microanal 10: 373. – reference: Vaumousse D,Cerezo A,Warren PJ. 2003. A procedure for quantification of precipitate microstructures from three-dimensional atom probe data. Ultramicroscopy 95: 215-221. – reference: Abramowitz M,Stegun IA, editors. 1972. Handbook of mathematical functions with formulas, graphs, and mathematical tables, 9th ed. New York: Dover. pp. 940-943. – reference: Camus E,Abromeit C. 1994b. Correlation and contingency analysis of atom probe data: Diffusion-controlled dissolution of precipitates. Z Metallkd 85: 378-382. – reference: Kelly TF,Miller MK. 2007. Atom probe tomography. Rev Sci Instrum 78: 031101. – reference: Kendall MG,Stuart A. 1961. The advanced theory of statistics. London: Griffin. – volume: 75 start-page: 2373 year: 1994a end-page: 2382 article-title: Analysis of conventional and three‐dimensional atom probe data for multiphase materials publication-title: J Appl Phys – volume: 11 start-page: 1417 year: 1975 end-page: 1429 article-title: New computational method in the theory of spinodal decomposition publication-title: Phys Rev A – start-page: 65 year: 1987 – start-page: 27 year: 2001 end-page: 29 – volume: 45 start-page: 3731 year: 1997 end-page: 3744 article-title: Origins of hardening in aged Al‐u‐Mg‐(Ag) alloys publication-title: Acta Mater – start-page: 940 year: 1972 end-page: 943 – volume: 50‒C8 start-page: 535 year: 1989 end-page: 540 article-title: Some aspects of the measurement of composition in the atom probe publication-title: J de Phys – volume: 76 start-page: 3127 year: 2000 end-page: 3129 article-title: Trajectory overlaps and local magnification in three‐dimensional atom probe publication-title: Appl Phys Lett – year: 2000 – year: 1996 – volume: 95 start-page: 223 year: 2003 end-page: 229 article-title: A new step towards the lattice reconstruction in 3DAP publication-title: Ultramicroscopy – volume: 353 start-page: 92 year: 2003 end-page: 98 article-title: Investigation of the early stages of decomposition of Cu‐0.7at.% Fe with the tomographic atom probe publication-title: Mater Sci Eng A – volume: 37 start-page: 127 year: 2007 end-page: 158 article-title: Three‐dimensional atom‐probe tomography: Advances and applications publication-title: Annu Rev Mater Res – volume: 53 start-page: 4180 year: 1982 end-page: 4188 article-title: Field evaporation events as Markov chains: A time‐of‐flight‐atom‐probe study of Iridium. Pt‐Rh alloys and metallic glasses publication-title: J Appl Phys – volume: 10 start-page: 373 year: 2004 article-title: First data from a commercial local electrode atom probe (LEAP) publication-title: Microsc Microanal – volume: 85 start-page: 378 year: 1994b end-page: 382 article-title: Correlation and contingency analysis of atom probe data: Diffusion‐controlled dissolution of precipitates publication-title: Z Metallkd – volume: 13 start-page: 437 year: 2007 end-page: 447 article-title: Spatial distribution maps for atom probe tomography publication-title: Microsc Microanal – year: 1977 – year: 1904 – volume: 13 start-page: 448 year: 2007 end-page: 463 article-title: New techniques for the analysis of fine‐scaled clustering phenomena within atom probe tomography data publication-title: Microsc Microanal – volume: 47 start-page: 495 year: 1986 end-page: 501 article-title: Statistical analysis of atom probe data publication-title: J de Phys – year: 1961 – volume: 25 start-page: 519 year: 2006 end-page: 521 article-title: Advanced nanostructural analysis of aluminium alloys using atom probe tomography publication-title: Mater Sci Forum – volume: 95 start-page: 215 year: 2003 end-page: 221 article-title: A procedure for quantification of precipitate microstructures from three‐dimensional atom probe data publication-title: Ultramicroscopy – volume: 2 start-page: 129 year: 2003 end-page: 131 article-title: Dopant mapping for the nanotechnology age publication-title: Nat Mater – volume: 242 start-page: 166 year: 1968 article-title: 1967 Institute of metals lecture spinodal decomposition publication-title: Trans Metall Soc AIME – volume: 78 start-page: 031101 year: 2007 article-title: Atom probe tomography publication-title: Rev Sci Instrum – volume: 85 start-page: 1395 year: 2005 end-page: 1417 article-title: Room temperature precipitation in quenched Al‐Cu‐Mg alloys: A model for the reaction kinetics and yield strength development publication-title: Philos Mag – volume: 246 start-page: 260 year: 1991 end-page: 265 article-title: Atom probe characterization of isotropic spinodal decompositions: Spatial convolutions and related bias publication-title: Surf – volume: 70 start-page: 258 year: 2007 end-page: 268 article-title: Contingency table techniques for three dimensional atom probe technology publication-title: Microsc Res Tech – ident: e_1_2_1_19_1 doi: 10.1007/978-1-4615-4281-0 – ident: e_1_2_1_17_1 doi: 10.2307/3538355 – ident: e_1_2_1_31_1 doi: 10.1016/S0304-3991(02)00319-4 – ident: e_1_2_1_28_1 doi: 10.1080/14786430412331333374 – volume: 50 start-page: 535 year: 1989 ident: e_1_2_1_12_1 article-title: Some aspects of the measurement of composition in the atom probe publication-title: J de Phys – ident: e_1_2_1_11_1 doi: 10.1016/S0921-5093(02)00673-1 – ident: e_1_2_1_27_1 doi: 10.1146/annurev.matsci.37.052506.084200 – volume: 242 start-page: 166 year: 1968 ident: e_1_2_1_3_1 article-title: 1967 Institute of metals lecture spinodal decomposition publication-title: Trans Metall Soc AIME – ident: e_1_2_1_23_1 – ident: e_1_2_1_30_1 doi: 10.1063/1.331241 – ident: e_1_2_1_20_1 – ident: e_1_2_1_25_1 doi: 10.1016/S1359-6454(97)00039-6 – ident: e_1_2_1_16_1 doi: 10.1017/S1431927604040565 – volume: 47 start-page: 495 year: 1986 ident: e_1_2_1_13_1 article-title: Statistical analysis of atom probe data publication-title: J de Phys – ident: e_1_2_1_8_1 doi: 10.1007/978-1-4899-2927-3 – ident: e_1_2_1_18_1 doi: 10.1103/PhysRevA.11.1417 – start-page: 940 volume-title: Handbook of mathematical functions with formulas, graphs, and mathematical tables year: 1972 ident: e_1_2_1_2_1 – ident: e_1_2_1_14_1 – start-page: 65 volume-title: Properties of stainless steels in elevated temperature service year: 1987 ident: e_1_2_1_26_1 – ident: e_1_2_1_22_1 doi: 10.1002/jemt.20412 – ident: e_1_2_1_32_1 doi: 10.1063/1.126545 – ident: e_1_2_1_7_1 doi: 10.1016/0039-6028(91)90424-Q – volume-title: Atom probe and field ion microscopy year: 1996 ident: e_1_2_1_21_1 doi: 10.1093/oso/9780198513872.001.0001 – ident: e_1_2_1_33_1 doi: 10.1016/S0304-3991(02)00320-0 – ident: e_1_2_1_4_1 doi: 10.1063/1.356258 – volume-title: Atom probe tomography at the University of Sydney. Advances in materials research series ident: e_1_2_1_9_1 – volume: 85 start-page: 378 year: 1994 ident: e_1_2_1_5_1 article-title: Correlation and contingency analysis of atom probe data: Diffusion‐controlled dissolution of precipitates publication-title: Z Metallkd – volume: 25 start-page: 519 year: 2006 ident: e_1_2_1_24_1 article-title: Advanced nanostructural analysis of aluminium alloys using atom probe tomography publication-title: Mater Sci Forum – ident: e_1_2_1_29_1 doi: 10.1017/S1431927607070900 – ident: e_1_2_1_10_1 doi: 10.1017/S1431927607070948 – ident: e_1_2_1_6_1 doi: 10.1038/nmat840 – ident: e_1_2_1_15_1 doi: 10.1063/1.2709758 |
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| SubjectTerms | Alloys - chemistry atom probe tomography Binomial Distribution Computer Simulation frequency distribution Image Processing, Computer-Assisted Models, Statistical solute clustering solute segregation Tomography |
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| Title | Quantitative binomial distribution analyses of nanoscale like-solute atom clustering and segregation in atom probe tomography data |
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