Skip to main content
Erschienen in: Physics of Metals and Metallography 11/2021

01.11.2021 | THEORY OF METALS

Model of Decomposition of Alloy with Two Magnetic Components: the BCC FeCr System

Erschienen in: Physics of Metals and Metallography | Ausgabe 11/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A sequential model of the decomposition of the bcc FeCr binary alloy is formulated that takes into account the configurational and magnetic contributions to the free energy. Using the results of ab initio calculations, the theory of regular solutions is generalized by considering the contributions of the magnetic entropy, the concentration dependence of the exchange interactions, and the mixing energies. The resulting expression for the free energy makes it possible to construct the boundaries of the two-phase region of the bcc FeCr alloy in good agreement with the experimental data, as well as to predict the position of the spinodal, below which the formation of highly dispersed states should be expected when starting from a homogeneous state.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat S. I. Porollo, A. M. Dvoriashin, A. N. Vorobyev, and Yu. V. Konobeev, “The microstructure and tensile properties of Fe–Cr alloys after neutron irradiation at 400°C to 5.5–7.1 dpa,” J. Nucl. Mater. 256, 247–253 (1998).CrossRef S. I. Porollo, A. M. Dvoriashin, A. N. Vorobyev, and Yu. V. Konobeev, “The microstructure and tensile properties of Fe–Cr alloys after neutron irradiation at 400°C to 5.5–7.1 dpa,” J. Nucl. Mater. 256, 247–253 (1998).CrossRef
2.
Zurück zum Zitat F. Garner, M. B. Toloczko, and B. H. Sencer, “Comparison of swelling and irradiation creep behavior of fcc-austenitic and bcc-ferritic/martensitic alloys at high neutron exposure,” J. Nucl. Mater. 276, 123–142 (2000).CrossRef F. Garner, M. B. Toloczko, and B. H. Sencer, “Comparison of swelling and irradiation creep behavior of fcc-austenitic and bcc-ferritic/martensitic alloys at high neutron exposure,” J. Nucl. Mater. 276, 123–142 (2000).CrossRef
3.
Zurück zum Zitat R. O. Williams and H. W. Paxton, “The nature of aging of binary iron–chromium alloys around 500°C,” J. Iron Steel Institute, 358–374 (1957). R. O. Williams and H. W. Paxton, “The nature of aging of binary iron–chromium alloys around 500°C,” J. Iron Steel Institute, 358–374 (1957).
4.
Zurück zum Zitat P. Olsson, I. A. Abrikosov, and J. Wallenius, “Electronic origin of the anomalous stability of Fe-rich bcc Fe–Cr alloys,” Phys. Rev. B 73, 104416 (2006).CrossRef P. Olsson, I. A. Abrikosov, and J. Wallenius, “Electronic origin of the anomalous stability of Fe-rich bcc Fe–Cr alloys,” Phys. Rev. B 73, 104416 (2006).CrossRef
5.
Zurück zum Zitat T. P. C. Klaver, R. Drautz, and M. W. Finnis, “Magnetism and thermodynamics of defect-free Fe–Cr alloys,” Phys. Rev. B 74, 094435 (2006).CrossRef T. P. C. Klaver, R. Drautz, and M. W. Finnis, “Magnetism and thermodynamics of defect-free Fe–Cr alloys,” Phys. Rev. B 74, 094435 (2006).CrossRef
6.
Zurück zum Zitat A. V. Ruban, P. A. Korzhavyi, and B. Johansson, “First-principles theory of magnetically driven anomalous ordering in bcc Fe–Cr alloys,“ Phys. Rev. B 77, 094436 (2008).CrossRef A. V. Ruban, P. A. Korzhavyi, and B. Johansson, “First-principles theory of magnetically driven anomalous ordering in bcc Fe–Cr alloys,“ Phys. Rev. B 77, 094436 (2008).CrossRef
7.
Zurück zum Zitat W. Xiong, P. Hedström, M. Selleby, J. Odqvist, M. Thuvander, and Q. Chen, “An improved thermodynamic modeling of the Fe–Cr system down to zero Kelvin coupled with key experiments,” Calphad 35, 355–366 (2011).CrossRef W. Xiong, P. Hedström, M. Selleby, J. Odqvist, M. Thuvander, and Q. Chen, “An improved thermodynamic modeling of the Fe–Cr system down to zero Kelvin coupled with key experiments,” Calphad 35, 355–366 (2011).CrossRef
8.
Zurück zum Zitat M. I. Gol’dshtein, S. V. Grachev, Yu. G. Veksler, Special Steels (Mosk. Inst. Stali i Splavov, Moscow, 1999). M. I. Gol’dshtein, S. V. Grachev, Yu. G. Veksler, Special Steels (Mosk. Inst. Stali i Splavov, Moscow, 1999).
9.
Zurück zum Zitat E. C. Stoner and C. P. Wohlfarth, “A mechanism of magnetic hysteresis in heterogeneous alloys,“ Philos. Trans. Roy. Soc. A 240, 599–642 (1948). E. C. Stoner and C. P. Wohlfarth, “A mechanism of magnetic hysteresis in heterogeneous alloys,“ Philos. Trans. Roy. Soc. A 240, 599–642 (1948).
10.
Zurück zum Zitat B. O. Mukhamedov, A. V. Ponomareva, and I. A. Abri-kosov, “Spinodal decomposition in ternary Fe–Cr–Co system,“ J. Alloys Compd. 695, 250–256 (2017).CrossRef B. O. Mukhamedov, A. V. Ponomareva, and I. A. Abri-kosov, “Spinodal decomposition in ternary Fe–Cr–Co system,“ J. Alloys Compd. 695, 250–256 (2017).CrossRef
11.
Zurück zum Zitat A. A. Mirzoev, M. M. Yalalov, and D. A. Mirzaev, “Calculation of the energy of mixing for the Fe–Cr alloys by the first-principles methods of computer simulation,“ Phys. Met. Metall. 103, 83–87 (2007).CrossRef A. A. Mirzoev, M. M. Yalalov, and D. A. Mirzaev, “Calculation of the energy of mixing for the Fe–Cr alloys by the first-principles methods of computer simulation,“ Phys. Met. Metall. 103, 83–87 (2007).CrossRef
12.
Zurück zum Zitat D. A. Mirzaev and A. A. Mirzoev, “Magnetic component of mixing enthalpy for bcc Fe–Cr alloys: ab initio based model,” J. Phys.: Conf. Ser. 1389, 012007 (2019). D. A. Mirzaev and A. A. Mirzoev, “Magnetic component of mixing enthalpy for bcc Fe–Cr alloys: ab initio based model,” J. Phys.: Conf. Ser. 1389, 012007 (2019).
13.
Zurück zum Zitat I. K. Razumov and I. G. Shmakov, " The model of decomposition of a Fe–Cu alloy with concentration-depending interatomic interactions,“ Phys. Solid State 61, 952–961 (2019).CrossRef I. K. Razumov and I. G. Shmakov, " The model of decomposition of a Fe–Cu alloy with concentration-depending interatomic interactions,“ Phys. Solid State 61, 952–961 (2019).CrossRef
14.
Zurück zum Zitat I. K. Razumov, Yu. N. Gornostyrev, and M. I. Katsnelson, “Towards the ab initio based theory of phase transformations in iron and steel,“ Phys. Met. Metallogr. 118, 362–388 (2017).CrossRef I. K. Razumov, Yu. N. Gornostyrev, and M. I. Katsnelson, “Towards the ab initio based theory of phase transformations in iron and steel,“ Phys. Met. Metallogr. 118, 362–388 (2017).CrossRef
15.
Zurück zum Zitat G. Inden, “The mutual influence of magnetic and chemical ordering,“ MRS Proc. 19, 175–188 (1982). G. Inden, “The mutual influence of magnetic and chemical ordering,“ MRS Proc. 19, 175–188 (1982).
16.
Zurück zum Zitat A. Kuronen, S. Granroth, M. H. Heinonen, R. E. Perälä, T. Kilpi, P. Laukkanen, J. Lång, J. Dahl, M. P. J. Punkkinen, K. Kokko, M. Ropo, B. Johansson, and L. Vitos, “Segregation, precipitation, and α–α' phase separation in Fe–Cr alloys,“ Phys. Rev. B 92, 214113 (2015).CrossRef A. Kuronen, S. Granroth, M. H. Heinonen, R. E. Perälä, T. Kilpi, P. Laukkanen, J. Lång, J. Dahl, M. P. J. Punkkinen, K. Kokko, M. Ropo, B. Johansson, and L. Vitos, “Segregation, precipitation, and α–α' phase separation in Fe–Cr alloys,“ Phys. Rev. B 92, 214113 (2015).CrossRef
17.
Zurück zum Zitat D. Nguyen-Manh, M. Yu. Lavrentiev, and S. L. Dudarev, “The Fe–Cr system: atomistic modelling of thermodynamics and kinetics of phase transformations,“ C. R. Phys. 9, 379–388 (2008).CrossRef D. Nguyen-Manh, M. Yu. Lavrentiev, and S. L. Dudarev, “The Fe–Cr system: atomistic modelling of thermodynamics and kinetics of phase transformations,“ C. R. Phys. 9, 379–388 (2008).CrossRef
18.
Zurück zum Zitat J. B. J. Chapman, P. W. Ma, and S. L. Dudarev, “Dynamics of magnetism in Fe–Cr alloys with Cr clustering,“ Phys. Rev. B 99, 184413 (2019).CrossRef J. B. J. Chapman, P. W. Ma, and S. L. Dudarev, “Dynamics of magnetism in Fe–Cr alloys with Cr clustering,“ Phys. Rev. B 99, 184413 (2019).CrossRef
19.
Zurück zum Zitat M. Levesque, E. Martinez, C.-C. Fu, M. Nastar, and F. Soisson, “Simple concentration-dependent pair interaction model for large-scale simulations of Fe–Cr alloys,“ Phys. Rev. B 84, 184205 (2011).CrossRef M. Levesque, E. Martinez, C.-C. Fu, M. Nastar, and F. Soisson, “Simple concentration-dependent pair interaction model for large-scale simulations of Fe–Cr alloys,“ Phys. Rev. B 84, 184205 (2011).CrossRef
20.
Zurück zum Zitat W. Xiong, M. Selleby, Q. Chen, J. Odqvist, and Y. Du, “Evaluation of phase equilibria and thermochemical properties in the Fe–Cr system,” Crit. Rev. Solid State Mater. Sci. 35, 125–152 (2010).CrossRef W. Xiong, M. Selleby, Q. Chen, J. Odqvist, and Y. Du, “Evaluation of phase equilibria and thermochemical properties in the Fe–Cr system,” Crit. Rev. Solid State Mater. Sci. 35, 125–152 (2010).CrossRef
21.
Zurück zum Zitat W. Xiong, J. Odqvist, P. Hedström, M. Selleby, M. Thuvander, and Q. Chen, “An improved thermodynamic modeling of the Fe–Cr system down to zero kelvin coupled with key experiments,“ CALPHAD 35, 355–366 (2011).CrossRef W. Xiong, J. Odqvist, P. Hedström, M. Selleby, M. Thuvander, and Q. Chen, “An improved thermodynamic modeling of the Fe–Cr system down to zero kelvin coupled with key experiments,“ CALPHAD 35, 355–366 (2011).CrossRef
22.
Zurück zum Zitat J. W. Christian, The Theory of Transformations in Metals and Alloys (Pergamon, New York, 2002). 806 c. J. W. Christian, The Theory of Transformations in Metals and Alloys (Pergamon, New York, 2002). 806 c.
23.
Zurück zum Zitat J. Strečka and M. Jaščur, “A brief account of the Ising and Ising-like models: mean-field, effective-field and exact results,” Acta Phys. Slovaca 65, No. 4, 235–367 (2015). J. Strečka and M. Jaščur, “A brief account of the Ising and Ising-like models: mean-field, effective-field and exact results,” Acta Phys. Slovaca 65, No. 4, 235–367 (2015).
24.
Zurück zum Zitat J. M. Sanchez, “Generalized cluster description of multicomponent systems,” Physica A 128, 334–350 (1984).CrossRef J. M. Sanchez, “Generalized cluster description of multicomponent systems,” Physica A 128, 334–350 (1984).CrossRef
25.
Zurück zum Zitat M. Yu. Lavrentiev, S. L. Dudarev, and D. Nguyen-Manh, J. Nucl. Mater. 386–388, 22–25 (2009).CrossRef M. Yu. Lavrentiev, S. L. Dudarev, and D. Nguyen-Manh, J. Nucl. Mater. 386388, 22–25 (2009).CrossRef
26.
Zurück zum Zitat M. Yu. Lavrentiev, J. S. Wrobel, D. Nguyen-Manh, S. L. Dudarev, and M. G. Ganchenkova, “Magnetic cluster expansion model for random and ordered magnetic face-centered cubic Fe–Ni–Cr alloys,” J. Appl. Phys. 120, 043902 (2016).CrossRef M. Yu. Lavrentiev, J. S. Wrobel, D. Nguyen-Manh, S. L. Dudarev, and M. G. Ganchenkova, “Magnetic cluster expansion model for random and ordered magnetic face-centered cubic Fe–Ni–Cr alloys,” J. Appl. Phys. 120, 043902 (2016).CrossRef
27.
Zurück zum Zitat J. S. Smart, Effective Field Theories of Magnetism (Saunders, 1968). J. S. Smart, Effective Field Theories of Magnetism (Saunders, 1968).
28.
Zurück zum Zitat I. K. Razumov, Yu. N. Gornostyrev, and M. I. Katsnelson, “Effect of magnetism on kinetics of γ–α transformation and pattern formation in iron,” J. Physics: Condens. Matter 25, No. 13. 135401 (2013). I. K. Razumov, Yu. N. Gornostyrev, and M. I. Katsnelson, “Effect of magnetism on kinetics of γ–α transformation and pattern formation in iron,” J. Physics: Condens. Matter 25, No. 13. 135401 (2013).
29.
Zurück zum Zitat Dzh. Zaiman, Models of Disorder (Mir, Moscow, 1982) [in Russian] Dzh. Zaiman, Models of Disorder (Mir, Moscow, 1982) [in Russian]
30.
Zurück zum Zitat Y. Wang, H. Hou, J. Yin, S. Hu, X. Liu, F. Xue, C. H. Jr. Henager, and J. Wang, “The magnetic effects on the energetic landscape of Fe–Cu alloy: A model Hamiltonian approach,” Comp. Mater. Sci. 145, 163–173 (2018).CrossRef Y. Wang, H. Hou, J. Yin, S. Hu, X. Liu, F. Xue, C. H. Jr. Henager, and J. Wang, “The magnetic effects on the energetic landscape of Fe–Cu alloy: A model Hamiltonian approach,” Comp. Mater. Sci. 145, 163–173 (2018).CrossRef
31.
Zurück zum Zitat G. Kirchner, T. Nishizawa, and B. Uhrenius, “The distribution of chromium between ferrite and austenite and the thermodynamics of the α/γ equilibrium in the Fe–Cr and Fe–Mn Systems,” Metall. Trans. 4, 167–174 (1973).CrossRef G. Kirchner, T. Nishizawa, and B. Uhrenius, “The distribution of chromium between ferrite and austenite and the thermodynamics of the α/γ equilibrium in the Fe–Cr and Fe–Mn Systems,” Metall. Trans. 4, 167–174 (1973).CrossRef
32.
Zurück zum Zitat H. Kaneko, M. Homma, and K. Nakamura, “Phase diagram of Fe–Cr–Co permanent magnet system,” IEEE Trans. Magn., No. 5, 1325–1327 (1977). H. Kaneko, M. Homma, and K. Nakamura, “Phase diagram of Fe–Cr–Co permanent magnet system,” IEEE Trans. Magn., No. 5, 1325–1327 (1977).
33.
Zurück zum Zitat A. V. Ponomareva, A. V. Ruban, B. O. Mukhamedov, and I. A. Abrikosov, “Effect of multicomponent alloying with Ni, Mn and Mo on phase stability of bcc Fe–Cr alloys,” Acta Mater. 150, 117–129 (2018).CrossRef A. V. Ponomareva, A. V. Ruban, B. O. Mukhamedov, and I. A. Abrikosov, “Effect of multicomponent alloying with Ni, Mn and Mo on phase stability of bcc Fe–Cr alloys,” Acta Mater. 150, 117–129 (2018).CrossRef
34.
Zurück zum Zitat M. L. Bernshtein et al. Metal Science and Heat Treatment of Steel and Cast Iron, Ed. by A. G. Rakhshtadt (Intermet Inzheniring, Moscow, 2005), vol. 2. M. L. Bernshtein et al. Metal Science and Heat Treatment of Steel and Cast Iron, Ed. by A. G. Rakhshtadt (Intermet Inzheniring, Moscow, 2005), vol. 2.
35.
Zurück zum Zitat K. Binder, “Nucleation barriers, spinodals, and the Ginzburg criterion,” Phys. Rev. A 29, 341–349 (1984).CrossRef K. Binder, “Nucleation barriers, spinodals, and the Ginzburg criterion,” Phys. Rev. A 29, 341–349 (1984).CrossRef
36.
Zurück zum Zitat D. Chandra and L. Schwartz, “Mössbauer effect study on the 475°C decomposition of Fe–Cr,” Metall. Trans. 2, No. 9, 511–519 (1971).CrossRef D. Chandra and L. Schwartz, “Mössbauer effect study on the 475°C decomposition of Fe–Cr,” Metall. Trans. 2, No. 9, 511–519 (1971).CrossRef
37.
Zurück zum Zitat B. Fultz, “Vibrational thermodynamics of materials,” Prog. Mater. Sci. 55, 247–352 (2010).CrossRef B. Fultz, “Vibrational thermodynamics of materials,” Prog. Mater. Sci. 55, 247–352 (2010).CrossRef
Metadaten
Titel
Model of Decomposition of Alloy with Two Magnetic Components: the BCC FeCr System
Publikationsdatum
01.11.2021
Erschienen in
Physics of Metals and Metallography / Ausgabe 11/2021
Print ISSN: 0031-918X
Elektronische ISSN: 1555-6190
DOI
https://doi.org/10.1134/S0031918X21110120

Weitere Artikel der Ausgabe 11/2021

Physics of Metals and Metallography 11/2021 Zur Ausgabe