A Statistical Methodology to Reconstruct Nucleation Pathways in the Fe-Cu System

Abstract:

In precipitation strengthened ferritic alloys, the Fe-Cu binary system is a well-studied model system. Still, many unsettled questions remain about the early stages of bcc Cu precipitation, most of which refer to the shape and composition of the critical and post-critical nuclei. Since the critical nucleation states are hard to investigate by experimental methods, we propose a computational strategy to reconstruct precipitation pathways and identify the nucleation states making use of Monte Carlo simulations combined with Rare Event Sampling methods. The precipitation process is reproduced by Monte Carlo simulations with an energy description based on the Local Chemical Environment approach, applying efficient pair potentials, which are dependent on the chemical environment, and the Forward Flux Sampling technique. This method provides profound insight into the shape and composition of the early-stage precipitates and also the critical cluster size and shape in dependency of the temperature and supersaturation.

• Periodical: Materials Science Forum (Volume 879)
• Pages: 1529-1534
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.879.1529
• Online since: November 2016
• Authors: Lin Qin*, Alice Redermeier, Ernst Kozeschnik, Carina Karner, Christoph Dellago
• Keywords: Monte Carlo Simulation, Nucleation Kinetics, Rare Event Sampling

References

[1] E. Hornbogen and R. C. Glenn, A metallographic study of precipitation of copper from alpha iron, Tran. Met. Soc. AIME 218 (1960) 1067–1070.

[2] P. J. Othen, M. L. Jenkins, G. Smith, and W. J. Phytian, Transmission electron-microscope investigations of the structure of copper precipitates in thermally-aged Fe-Cu and Fe-Cu-Ni, Philps. Mag. Lett. 64 (1991) 383–391.

DOI: 10.1080/09500839108215121

[3] D. Isheim and D. N. Seidman, Nanoscale studies of segregation at coherent heterophase interfaces in alpha-Fe based systems, Surf. Interface Anal 36 (2004) 569–574.

DOI: 10.1002/sia.1703

[4] D. Isheim, M. S. Galiano, M. E. Fine, and D. N. Seidman, Interfacial segregation at Cu-rich precipitates in a high-strength low-carbon steel studied on a sub-nanometer scale, Acta Mater. 54 (2006) 841–849.

DOI: 10.1016/j.actamat.2005.10.023

[5] M. Schober, E. Eidenberger, H. Leitner, P. Staron, D. Reith, and R. Podloucky, A critical consideration of magnetism and composition of (bcc) Cu precipitates in (bcc) Fe, Appl. Phys. A 99 (2010) 697–704.

DOI: 10.1007/s00339-010-5725-x

[6] M. K. Miller, B. D. Wirth, and G. R. Odette, Precipitation in neutron-irradiated Fe-Cu and Fe-Cu-Mn model alloys: a comparison of APT and SANS data, Mater. Sci. Eng. A 353 (2003) 133–139.

DOI: 10.1016/s0921-5093(02)00679-2

[7] E. Kozeschnik, Thermodynamic prediction of the equilibrium chemical composition of critical nuclei: Bcc Cu precipitation in α-Fe, Scr. Mater. 59 9 (2008) 1018 – 1021.

DOI: 10.1016/j.scriptamat.2008.07.008

[8] F. Soisson, A. Barbu, and G. Martin, Monte carlo simulations of copper precipitation in dilute iron-cooper alloys during thermal aging and under electron irradiation, Acta Mater. 44 (1996) 3789–3800.

DOI: 10.1016/1359-6454(95)00447-5

[9] F. Soisson and C. C. Fu, Cu-precipitation kinetics in alpha-Fe from atomistic simulations: Vacancy-tranping effects and Cu-cluster mobility, Phys. Rev. B 76 (2007) 214102.

DOI: 10.1103/physrevb.76.214102

[10] P. Warczok, D. Reith, M. Schober, H. Leitner, R. Podloucky, and E. Kozeschnik, Investigation of Cu precipitation in bcc-Fe – Comparison of numerical analysis with experiment, IJMR 102 (2011) 709–716.

DOI: 10.3139/146.110524

[11] R. J. Allen, P. B. Warren, and P. R. ten Wolde, Sampling Rare Switching Events in Biochemical Networks, Phys. Rev. Lett. 94 1 (2005) 018104.

DOI: 10.1103/physrevlett.94.018104

[12] S. Jungblut and C. Dellago, Caveats of mean first-passage time methods applied to the crystallization transition: Effects of non-Markovianity, J. Chem. Phys. 142 (2015) 064103.

DOI: 10.1063/1.4907364

[13] R. J. Allen, D. Frenkel, and P. R. ten Wolde, Simulating rare events in equilibrium or nonequilibrium stochastic systems, J. Chem. Phys. 124 (2006).

DOI: 10.1063/1.2140273

[14] T. S. van Erp, D. Moroni, and P. G. Bolhuis, A novel path sampling method for the calculation of rate constants, J. Chem. Phys. 118 17 (2003) 7762–7774.

DOI: 10.1063/1.1562614

[15] J. H. ter Horst and D. Kashchiev, Determination of the nucleus size from the growth probability of clusters, J. Chem. Phys. 119 (2003) 2241–2246.

DOI: 10.1063/1.1585020

[16] J. Wedekind, R. Strey, and D. Reguera, New method to analyze simulations of activated processes, J. Chem. Phys. 126 (2007) 134103.

DOI: 10.1063/1.2713401

[17] information on http: /matcalc. at.

[18] G. Stechauner and E. Kozeschnik, Thermo-kinetic modeling of Cu precipitation in α-Fe, Acta Mater. 100 (2015) 135–146.

DOI: 10.1016/j.actamat.2015.08.042