journal article·2023-11Open access

Reconciliation between simulated and measured microstructures of metastable FeCr alloys: A phase field approach

O. Tissot, P. Gokelaere, P. Garcia, L. Pauchard, C. Pareige, L. Luneville, D. Simeone

Acta Materialia· Volume 260

Abstract

This work presents a novel phase field method for modeling the microstructure induced by the thermal decomposition of immiscible metastable binary alloys. This approach bypasses the problem associated with the modeling of the nucleation process introducing a random distribution of critical precipitates as an initial condition for the Cahn–Hilliard equation, extensively used to model the microstructure in the spinodal regime. The comparison between simulated and measured microstructures obtained from atom probe tomography measurements performed on ultra pure Fe 0 . 81 Cr 0 . 19 samples justifies the validity of our method. In particular, we succeeded modeling the evolution of the chemical composition of α ′ clusters produced during annealing. Such an evolution has been many times reported from atom probe tomography measurements but never explained. Moreover, these simulations allowed proposing a physical mechanism to explain the increase of the yield strength, observed in many annealed FeCr samples.
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Research context

OpenAlex topics: Advanced Materials Characterization Techniques · nanoparticles nucleation surface interactions · Solidification and crystal growth phenomena

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References (74)

Show source-provided references
1. Neutron small-angle scattering study of unmixing in FeCr alloys10.1016/0956-7151(92)90094-U ↗
2. Tissot · 2017
3. Kinetic study of phase transformation in a highly concentrated Fe–Cr alloy: Monte Carlo simulation versus experiments10.1016/j.actamat.2010.12.038 ↗
4. Atomic scale analysis and phase separation understanding in a thermally aged Fe–20at.Cr alloy10.1016/j.jnucmat.2008.10.008 ↗
5. Comparison between sans and apt measurements in a thermally aged Fe- 19 at. Cr alloy10.1016/j.matchar.2019.03.027 ↗
6. Nucleation–growth versus spinodal decomposition in Fe–Cr alloys: An experimental verification by atom probe tomography and small angle neutron scattering10.1093/micmic/ozac052 ↗
7. A combined apt and sans investigation of alpha prime phase precipitation in neutron irradiated model FeCral alloys10.1016/j.actamat.2017.02.077 ↗
8. Spinodal decomposition in Fe-Cr alloys studied by small angle neutron scattering10.1016/0378-4363(83)90411-4 ↗
9. Early stages of spinodal decomposition in Fe–Cr resolved by in-situ small-angle neutron scattering10.1063/1.4908250 ↗
10. Decomposition kinetics in iron–chromium alloys10.1016/0378-4363(83)90413-8 ↗
11. J. Langer, Theory of spinodal decomposition in alloys, Ann. Phys. 65 (53).10.1016/0003-4916(71)90162-X ↗
12. Kinetics of nucleation in near-critical fluids10.1103/PhysRevA.21.948 ↗
13. Non-classical theory of crystal nucleation: application to oxide glasses: review10.1016/S0022-3093(99)00354-3 ↗
14. Effect of concentration dependent gradient energy coefficient on spinodal decomposition in the FeCr system10.1016/j.commatsci.2017.11.043 ↗
15. Simulation of nonclassical nucleation in binary alloys10.1134/S1063783415060232 ↗
16. Decomposition kinetics of Fe-Cr solid solutions during thermal aging10.1103/PhysRevB.86.224109 ↗
17. On spinodal decomposition10.1016/0001-6160(61)90182-1 ↗
18. Scaling and multi scaling in the ordereing kinetics of a conserved order paameter10.1103/PhysRevLett.68.1559 ↗
19. Microstructural development involving nucleation and growth phenomena simulated with the phase field method10.1016/j.msea.2003.09.019 ↗
20. Incorporating diffuse-interface nuclei in phase-field simulations10.1016/j.scriptamat.2010.02.028 ↗
21. Dynamics of nucleation in solids: a self-consistent phase field approach10.1103/PhysRevLett.131.117101 ↗
22. Tolédano · 1986
23. A study of the effect of ageing temperature on phase-separation in Fe45-Cr alloys10.1016/0169-4332(94)00498-6 ↗
24. Spinodal decompposition in an Fe-33 at %Cr alloy during isothermal aging10.2320/matertrans.M2009029 ↗
25. Revised thermodynamic description of the Fe-Cr system based on an improved sublattice model of the sigma phase10.1016/j.calphad.2017.10.002 ↗
26. An improved thermodynamic modeling of the Fe-Cr system down to zero kelvin coupled with key experiments10.1016/j.calphad.2011.05.002 ↗
27. Tolédano · 1996
28. Landau · 1975
29. Nucleation theory near theclassical spinodal10.1016/S1359-6454(99)00441-3 ↗
30. Katchaturyan · 1983
31. A review: applications of the phase field methods in predicting microstructure and properties evolution of irradiated nuclear materials
32. Non-classical critical precipitates in a nucleation and growth regime: Reconciliation of simulation and experiment10.1063/5.0122126 ↗
33. Trans-interface diffusion-controlled coarsening10.1038/nmat1340 ↗
34. Free energy of a nonuniform system. i. interfacial free energy10.1063/1.1744102 ↗
35. Stochastic simulation of nucleation in binary alloys
36. Composition and orientation dependence of the interfacial energy in Fe-Cr stainless steel10.1002/pssb.201147123 ↗
37. Calculation of excess free energies of precipitates via direct thermodynamic integration across phase boundaries10.1103/PhysRevB.86.134204 ↗
38. On ferromagnetic ordering and lattice diffusion - a simple model
39. Darken · 1948
40. Non-classical nuclei and growth kinetics of Cr precipitates in FeCr alloys during ageing10.1088/0965-0393/22/2/025002 ↗
41. Ghoniem · 2008
42. Nicolis · 1977
43. Effect of domain morphology in phase-separation dynamics at low temperature10.1103/PhysRevB.48.6854 ↗
44. Phase-separation kinetics in a model with order parameter dependent mobility10.1103/PhysRevE.56.758 ↗
45. Puri · 2009
46. The kinetics of precipitation from supersaturated solid solution10.1016/0022-3697(61)90054-3 ↗
47. Review progress in Ostwald ripening theories and their applications to nickel-base superalloys part I: Ostwald ripening theories10.1023/A:1015388912729 ↗
48. Theory of the condensation point10.1016/0003-4916(67)90200-X ↗
49. Nucleation theory near theclassical spinodal10.1103/PhysRevB.29.2698 ↗
50. The dynamics of first order phase transitions
51. Rabinowitz · 1986
52. Free energy of a nonuniform system. II. thermodynamic basis10.1063/1.1730145 ↗
53. Phase field modeling of simultaneous nucleation and growth by explicitly incorporating nucleation events10.1016/S1359-6462(00)00517-0 ↗
54. Modelling the overlap of nucleation, growth and coarsening during precipitation10.1016/j.actamat.2004.06.024 ↗
55. Homogeneous nucleation: theory and experiment10.1088/0953-8984/4/38/001 ↗
56. Lifshitz-Slyozov scaling for late-stage coarsening with an order-parameter-dependent mobility10.1103/PhysRevB.52.R685 ↗
57. Phase field benchmark problems for nucleation10.1016/j.commatsci.2021.110371 ↗
58. Unconditionally gradient stable time marching the Cahn–Hilliard equation10.1557/PROC-529-39 ↗
59. Late stage coarsening kinetics induced by a phase-dependent mobility: A phase field study of FeCr in the spinodal regime10.1063/5.0084957 ↗
60. Morphology of critical nuclei in solid-state phase transformations10.1103/PhysRevLett.98.265703 ↗
61. Quantification of apt physical limitations on chemical composition of precipitates in Fe–Cr alloys10.1016/j.jnucmat.2019.05.022 ↗
62. Trajectory overlaps and local magnification in three-dimensional atom probe10.1063/1.126545 ↗
63. Ostwald ripening in a system with a high volume fraction of coarsening phase10.1007/BF02645806 ↗
64. The Johnson-Mehl-Avrami-Kolmogorov model: A brief review10.1007/BF03185527 ↗
65. Papon · 1999
66. Solution to the multi-particle diffusion problem with applications to Ostwald ripening—II. computer simulations10.1016/0001-6160(84)90181-0 ↗
67. Homogeneous nucleation10.1023/A:1004598332758 ↗
68. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments10.1557/JMR.1992.1564 ↗
69. Symmetry breaking resulting from long-range interactions in out of equilibrium systems: Elastic properties of irradiated AgCu10.1103/PhysRevLett.125.246103 ↗
70. Multiscale modeling of precipitation hardening: application to the Fe-Cr alloys10.1016/j.actamat.2015.05.043 ↗
71. Strengthening due to Cr-rich precipitates in Fe-Cr alloys: effect of temperature ad precipitate composition10.1063/1.3340522 ↗
72. Application of a three-feature dispersed-barrier hardening model to neutron-irradiated Fe–Cr model alloys10.1016/j.jnucmat.2014.01.024 ↗
73. Mechanisms of radiation strengthening in Fe–Cr alloys as revealed by atomistic studies10.1016/j.jnucmat.2013.03.054 ↗
74. Precipitation hardening in metals