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The annihilation kinetics of the nanoscale antiphase domain boundary in B2 alloys: phase field characterization at the atomistic level

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Abstract

The microstructure evolution and coarsening kinetics of ordered domain depend on the annihilation behavior in ordered metallic materials. In this work, the annihilation phenomenon of nanoscale B2 antiphase domain boundary (APDB), at various compositions and temperatures, is investigated by establishing an atomic phase field approach. The effect of uniaxial compressive stress is also included. Kinetically, the annihilation behavior of nanoscale APDB presents a staged feature during the dynamic evolution process. Qualitatively, the analyses of area and radius reveal that APDB annihilation evolves along a fixed path. Further, the annihilation rate of APDB is characterized by composition and temperature dependence, which is a result of synergy among the temperature, composition and uniaxial compressive stress. Thermodynamically, the energy analyses reveal that solute depletion at the homophase interface acts energetically for the migration of B2-APDB. The uniaxial compressive stress significantly influences the micromorphology, solute depletion and evolution of APDB, which provides theoretical insight for controlling the nanoscale APDB. Moreover, simulation results show reasonable agreement with previous theoretical results.

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References

  1. Liu L, Wu X, Wang R, Li W, Liu Q (2015) First principle study on the temperature dependent elastic constants, anisotropy, generalized stacking fault energy and dislocation core of NiAl and FeAl. Comput Mater Sci 103:116–125. https://doi.org/10.1016/j.commatsci.2015.03.024

    Article  Google Scholar 

  2. Li D, Zhou L, Xi Y, Liu L, Liu Z, Si J, Zhu K (2017) Phase transformation behavior of alumina grown on FeAl alloys with reactive element dopants at 1273 K. J Alloys Compd 692:427–433. https://doi.org/10.1016/j.jallcom.2016.09.092

    Article  Google Scholar 

  3. Kant R, Prakash U, Agarwala V, Satya Prasad VV (2015) Wear behaviour of an FeAl intermetallic alloy containing carbon and titanium. Intermetallics 61:21–26. https://doi.org/10.1016/j.intermet.2015.02.013

    Article  Google Scholar 

  4. Mondal D, Banik S, Kamal C, Nand M, Jha SN, Phase DM, Sinha AK, Chakrabarti A et al (2016) Electronic structure of FeAl alloy studied by resonant photoemission spectroscopy and Ab initio calculations. J Alloys Compd 688:187–194. https://doi.org/10.1016/j.jallcom.2016.07.121

    Article  Google Scholar 

  5. Zheng Y, Wang F, Ai T, Li C (2017) Structural, elastic and electronic properties of B2-type modified by ternary additions FeAl-based intermetallics: first-principles study. J Alloys Compd 710:581–588. https://doi.org/10.1016/j.jallcom.2017.03.308

    Article  Google Scholar 

  6. Viguier B, Martinez M, Lacaze J (2017) Characterization of complex planar faults in FeAl(B) alloys. Intermetallics 83:64–69. https://doi.org/10.1016/j.intermet.2016.12.005

    Article  Google Scholar 

  7. Starostenkov M, Chaplygin P, Chaplygina A, Potekaev A (2017) Investigation of growth ordered phases in the alloy NiAl equiatomic composition during stepwise cooling. Procedia IUTAM 23:78–83. https://doi.org/10.1016/j.piutam.2017.06.007

    Article  Google Scholar 

  8. Rong TS (2003) Serrated yielding in the B2-ordered Nb–15Al–20V alloy. Intermetallics 11(2):151–155. https://doi.org/10.1016/S0966-9795(02)00196-6

    Article  Google Scholar 

  9. Gilles R, Hofmann M, Johnson F, Gao Y, Mukherji D, Hugenschmidt C, Pikart P (2011) Analysis of antiphase domain growth in ternary FeCo alloys after different cooling rates and annealing treatments using neutron diffraction and positron annihilation. J Alloys Compd 509(2):195–199. https://doi.org/10.1016/j.jallcom.2010.09.075

    Article  Google Scholar 

  10. Zhang Y, Wang X, Kong F, Chen Y (2018) A high-performance β-stabilized Ti–43Al–9V–0.2Y alloy sheet with a nano-scaled antiphase domain. Mater Lett 214:182–185. https://doi.org/10.1016/j.matlet.2017.12.002

    Article  Google Scholar 

  11. Tanimura M, Koyama Y (2006) The role of antiphase boundaries in the kinetic process of the L12 → D022 structural change of an Ni3Al0.45V0.50 alloy. Acta Mater 54(16):4385–4391. https://doi.org/10.1016/j.actamat.2006.05.031

    Article  Google Scholar 

  12. Lefebvre W, Masquelier N, Houard J, Patte R, Zapolsky H (2014) Tracking the path of dislocations across ordered Al3Zr nano-precipitates in three dimensions. Scr Mater 70:43–46. https://doi.org/10.1016/j.scriptamat.2013.09.014

    Article  Google Scholar 

  13. Yasuda HY, Nakajima T, Umakoshi Y (2007) Temperature dependence of pseudoelasticity in Fe3Al single crystals. Intermetallics 15(5–6):819–823. https://doi.org/10.1016/j.intermet.2006.10.006

    Article  Google Scholar 

  14. Cugini F, Righi L, van Eijck L, Brück E, Solzi M (2018) Cold working consequence on the magnetocaloric effect of Ni50Mn34 in 16 Heusler alloy. J Alloys Compd 749:211–216. https://doi.org/10.1016/j.jallcom.2018.03.293

    Article  Google Scholar 

  15. Mangler C, Gammer C, Karnthaler HP, Rentenberger C (2010) Structural modifications during heating of bulk nanocrystalline FeAl produced by high-pressure torsion. Acta Mater 58(17):5631–5638. https://doi.org/10.1016/j.actamat.2010.06.036

    Article  Google Scholar 

  16. Gammer C, Mangler C, Karnthaler HP, Rentenberger C (2011) Growth of nanosized chemically ordered domains in intermetallic FeAl made nanocrystalline by severe plastic deformation. Scr Mater 65(1):57–60. https://doi.org/10.1016/j.scriptamat.2011.03.002

    Article  Google Scholar 

  17. Mangler C, Gammer C, Hiebl K, Karnthaler HP, Rentenberger C (2011) Thermally induced transition from a ferromagnetic to a paramagnetic state in nanocrystalline FeAl processed by high-pressure torsion. J Alloys Compd 509:S389–S392. https://doi.org/10.1016/j.jallcom.2010.12.023

    Article  Google Scholar 

  18. Golovin IS, Balagurov AM, Bobrikov IA, Cifre J (2016) Structure induced anelasticity in Fe3Me (Me = Al, Ga, Ge) alloys. J Alloys Compd 688:310–319. https://doi.org/10.1016/j.jallcom.2016.06.277

    Article  Google Scholar 

  19. Gammer C, Karnthaler HP, Rentenberger C (2017) Reordering a deformation disordered intermetallic compound by antiphase boundary movement. J Alloys Compd 713:148–155. https://doi.org/10.1016/j.jallcom.2017.04.045

    Article  Google Scholar 

  20. Koizumi Y, Allen SM, Ouchi M, Minamino Y, Chiba A (2011) Phase-field simulation of D03-type antiphase boundary migration in Fe3Al with vacancy and solute segregation. Solid State Phenom 172–174:1313–1319. https://doi.org/10.4028/www.scientific.net/SSP.172-174.1313

    Article  Google Scholar 

  21. Koizumi Y, Allen SM, Ouchi M, Minamino Y (2010) Effects of solute and vacancy segregation on antiphase boundary migration in stoichiometric and Al-rich Fe3Al: a phase-field simulation study. Intermetallics 18(7):1297–1302. https://doi.org/10.1016/j.intermet.2009.12.016

    Article  Google Scholar 

  22. Wang K, Wang Y, Cheng Y (2018) The formation and dynamic evolution of antiphase domain boundary in FeAl alloy: computational simulation in atomic scale. Mater Res. https://doi.org/10.1590/1980-5373-mr-2017-1048

    Google Scholar 

  23. Alster E, Elder KR, Hoyt JJ, Voorhees PW (2017) Phase-field-crystal model for ordered crystals. Phys Rev E 95(2):22105. https://doi.org/10.1103/PhysRevE.95.022105

    Article  Google Scholar 

  24. Hu S, Chen Z, Xi W, Peng Y (2017) Phase-field-crystal study on the evolution behavior of microcracks initiated on grain boundaries under constant strain. J Mater Sci 52(10):5641–5651. https://doi.org/10.1007/s10853-017-0799-x

    Article  Google Scholar 

  25. Fallah V, Langelier B, Ofori-Opoku N, Raeisinia B, Provatas N, Esmaeili S (2016) Cluster evolution mechanisms during aging in Al–Mg–Si alloys. Acta Mater 103:290–300. https://doi.org/10.1016/j.actamat.2015.09.027

    Article  Google Scholar 

  26. Khachaturyan AG (1983) Theory of structural transformations in solids. Wiley, New York

    Google Scholar 

  27. Ustinovshikov Y, Koretsky V (1998) Computer simulation of the intermetallics formation process. Comput Mater Sci 11(1):74–86. https://doi.org/10.1016/S0927-0256(97)00191-2

    Article  Google Scholar 

  28. Chen L, Wang Q (1998) Concentration overshooting caused by compositional relaxation in a one-dimensional bcc binary model alloy: a computer simulation on microscopic master equations. Scr Mater 39(8):1113–1118. https://doi.org/10.1016/S1359-6462(98)00273-5

    Article  Google Scholar 

  29. Poduri R, Chen LQ (1998) Computer simulation of atomic ordering and compositional clustering in the pseudobinary Ni3Al–Ni3V system. Acta Mater 46(5):1719–1729. https://doi.org/10.1016/S1359-6454(97)00335-2

    Article  Google Scholar 

  30. Wang HY, Wang Y, Tsakalakos T, Semenovskaya S, Khachaturyan AG (1996) Indirect nucleation in phase transformations with symmetry reduction. Philos Mag A 74(6):1407–1420. https://doi.org/10.1080/01418619608240732

    Article  Google Scholar 

  31. Khachaturyan AG, Wang YZ, Wang HY (1994) Metastable phases and nuclei: computer modeling. Mater Sci Forum 155–156:345–366. https://doi.org/10.4028/www.scientific.net/MSF.155-156.345

    Article  Google Scholar 

  32. Chen LQ, Khachaturyan AG (1993) Dynamics of simultaneous ordering and phase separation and effect of long-range Coulomb interactions. Phys Rev Lett 70(10):1477–1480. https://doi.org/10.1103/PhysRevLett.70.1477

    Article  Google Scholar 

  33. Chen L, Wang Y, Khachaturyan AG (1992) Kinetics of tweed and twin formation during an ordering transition in a substitutional solid solution. Philos Mag Lett 65(1):15–23. https://doi.org/10.1080/09500839208215143

    Article  Google Scholar 

  34. Chen L, Wang Y, Khachaturyan AG (1991) Transformation-induced elastic strain effect on the precipitation kinetics of ordered intermetallics. Philos Mag Lett 64(5):241–251. https://doi.org/10.1080/09500839108214618

    Article  Google Scholar 

  35. Zhang J, Chen Z, Wang Y, Tao Y (2013) The temporal evolution of microstructures during structural transition of D022 and L12 involved with transient phases. Superlattice Microst 64:251–264. https://doi.org/10.1016/j.spmi.2013.09.020

    Article  Google Scholar 

  36. Lu Y, Zhang L, Chen Y, Chen Z, Wang Y (2013) Phase-field study for the pre-precipitation process of L12-Ni3Al phase in Ni–Al–V alloy. Intermetallics 38:144–149. https://doi.org/10.1016/j.intermet.2013.02.014

    Article  Google Scholar 

  37. Hou H, Zhao Y, Zhao Y (2009) Simulation of the precipitation process of ordered intermetallic compounds in binary and ternary Ni–Al-based alloys by the phase-field model. Mater Sci Eng A 499(1–2):204–207. https://doi.org/10.1016/j.msea.2007.11.140

    Article  Google Scholar 

  38. Lu Y, Lu G, Liu F, Chen Z, Tang K (2015) Phase-field study on the pre-precipitated phase of ordered intermetallic compounds in binary and ternary Ni–Al base alloys. J Alloys Compd 637:149–154. https://doi.org/10.1016/j.jallcom.2015.03.006

    Article  Google Scholar 

  39. Yang K, Zhang M, Chen Z, Fan X (2012) Microscopic phase-field study for mechanisms of directional coarsening and the transformation of rafting types in Ni–Al–V ternary alloys. Comput Mater Sci 62:160–168. https://doi.org/10.1016/j.commatsci.2012.05.046

    Article  Google Scholar 

  40. Lu Y, Chen Z, Li X, Tang K (2015) Microscopic phase-field study of the effect of temperature on the pre-precipitates of Ni–Al–Cr alloy. Comput Mater Sci 99:247–252. https://doi.org/10.1016/j.commatsci.2014.11.042

    Article  Google Scholar 

  41. Poduri R, Chen LQ (1998) Computer simulation of morphological evolution and coarsening kinetics of δ′ (Al3Li) precipitates in Al–Li alloys. Acta Mater 46(11):3915–3928. https://doi.org/10.1016/S1359-6454(98)00058-5

    Article  Google Scholar 

  42. Zhao R, Zhu J, Liu Y, Lai Z (2012) The phase field investigation of B2 (FeAl) phase antisite defect during homogenous transformation of Fe–24Al alloy. J Mater Sci 47(7):3376–3382. https://doi.org/10.1007/s10853-011-6181-5

    Article  Google Scholar 

  43. Rahnama A, Kotadia H, Sridhar S (2017) Effect of Ni alloying on the microstructural evolution and mechanical properties of two duplex light-weight steels during different annealing temperatures: experiment and phase-field simulation. Acta Mater 132:627–643. https://doi.org/10.1016/j.actamat.2017.03.043

    Article  Google Scholar 

  44. Wang Y, Chen L, Khachaturyan AG (1992) Particle translational motion and reverse coarsening phenomena in multiparticle systems induced by a long-range elastic interaction. Phys Rev B 46(17):11194–11197. https://doi.org/10.1103/PhysRevB.46.11194

    Article  Google Scholar 

  45. Vaithyanathan V, Chen LQ (2000) Coarsening kinetics of δ′-Al3Li precipitates: phase-field simulation in 2D and 3D. Scr Mater 42(10):967–973. https://doi.org/10.1016/S1359-6462(00)00323-7

    Article  Google Scholar 

  46. Liu L, Chen Z, Wang Y, Zhang M (2017) The split of dendritic precipitates with interfacial anisotropy in solid transformations in alloys. J Alloys Compd 703:321–329. https://doi.org/10.1016/j.jallcom.2017.01.283

    Article  Google Scholar 

  47. Liu L, Chen Z, Wang Y (2016) Elastic strain energy induced split during precipitation in alloys. J Alloys Compd 661:349–356. https://doi.org/10.1016/j.jallcom.2015.11.201

    Article  Google Scholar 

  48. Chen L, Khachaturyan AG (1991) Computer simulation of decomposition reactions accompanied by a congruent ordering of the second kind. Scr Metall Mater 25(1):61–66. https://doi.org/10.1016/0956-716X(91)90354-4

    Article  Google Scholar 

  49. Haraguchi T, Yoshimi K, Yoo MH, Kato H, Hanada S, Inoue A (2005) Vacancy clustering and relaxation behavior in rapidly solidified B2 FeAl ribbons. Acta Mater 53(13):3751–3764. https://doi.org/10.1016/j.actamat.2005.04.027

    Article  Google Scholar 

  50. Kass M, Brooks CR, Falcon D, Basak D (2002) The formation of defects in Fe–Al alloys. Intermetallics 10(10):951–966. https://doi.org/10.1016/S0966-9795(02)00115-2

    Article  Google Scholar 

  51. Zhao M, Yoshimi K, Nakamura J, Yubuta K, Sugawara T (2014) High-temperature elastic anisotropy of B2-type FeAl. Scr Mater 82:37–40. https://doi.org/10.1016/j.scriptamat.2014.03.016

    Article  Google Scholar 

  52. Pollock TM, Lu DC, Shi X, Eow K (2001) A comparative analysis of low temperature deformation in B2 aluminides. Mater Sci Eng A 317(1–2):241–248. https://doi.org/10.1016/S0921-5093(01)01163-7

    Article  Google Scholar 

  53. Cadel E, Fraczkiewicz A, Blavette D (2001) Atomic scale observation of Cottrell atmospheres in B-doped FeAl (B2) by 3D atom probe field ion microscopy. Mater Sci Eng A 309–310:32–37. https://doi.org/10.1016/S0921-5093(00)01688-9

    Article  Google Scholar 

  54. Hadef F, Otmani A, Djekoun A, Grenèche JM (2011) Nanocrystalline FeAl intermetallics obtained in mechanically alloyed Fe50Al40Ni10 powder. Superlattice Microstruct 49(6):654–665. https://doi.org/10.1016/j.spmi.2011.04.003

    Article  Google Scholar 

  55. Kopecek J, Hausild P, Jurek K, Jarosova M, Drahokoupil J, Novák P, Sima V (2010) Precipitation in the Fe–38 at.% Al–1 at.% C alloy. Intermetallics 18(7):1327–1331. https://doi.org/10.1016/j.intermet.2010.03.027

    Article  Google Scholar 

  56. Hadef F (2017) Synthesis and disordering of B2 TM-Al (TM = Fe, Ni, Co) intermetallic alloys by high energy ball milling: a review. Powder Technol 311:556–578. https://doi.org/10.1016/j.powtec.2017.01.082

    Article  Google Scholar 

  57. Koizumi Y, Allen SM, Minamino Y (2009) Effects of solute and vacancy segregation on migration of a/4 〈111〉 and a/2 〈100〉 antiphase boundaries in Fe3Al. Acta Mater 57(10):3039–3051. https://doi.org/10.1016/j.actamat.2009.03.012

    Article  Google Scholar 

  58. Feng WM, Yu P, Hu SY, Liu ZK, Du Q, Chen LQ (2006) Spectral implementation of an adaptive moving mesh method for phase-field equations. J Comput Phys 220(1):498–510. https://doi.org/10.1016/j.jcp.2006.07.013

    Article  Google Scholar 

  59. Kim SG, Park YB (2008) Grain boundary segregation, solute drag and abnormal grain growth. Acta Mater 56(15):3739–3753. https://doi.org/10.1016/j.actamat.2008.04.007

    Article  Google Scholar 

  60. Koizumi Y, Allen SM, Minamino Y (2008) Solute and vacancy segregation to a/4 〈111〉 and a/2 〈100〉 antiphase domain boundaries in Fe3Al. Acta Mater 56(19):5861–5874. https://doi.org/10.1016/j.actamat.2008.08.007

    Article  Google Scholar 

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Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant numbers 51475378, 51575452, 51704243, 51674205).

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Wang, K., Hu, S. & Wang, Y. The annihilation kinetics of the nanoscale antiphase domain boundary in B2 alloys: phase field characterization at the atomistic level. J Mater Sci 54, 14440–14455 (2019). https://doi.org/10.1007/s10853-019-03972-0

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