The effects of diffusional couplings on compositional trajectories and interfacial free energies during phase separation in a quaternary Ni-Al-Cr-Re model superalloy

Sung Il Baik; Zugang Mao; Qingqiang Ren; Fei Xue; Carelyn E. Campbell; Chuan Zhang; Bicheng Zhou; Ronald D. Noebe; David N. Seidman

doi:10.1016/j.actamat.2022.118020

The effects of diffusional couplings on compositional trajectories and interfacial free energies during phase separation in a quaternary Ni-Al-Cr-Re model superalloy

Sung Il Baik, Zugang Mao, Qingqiang Ren, Fei Xue, Carelyn E. Campbell, Chuan Zhang, Bicheng Zhou, Ronald D. Noebe, David N. Seidman

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The temporal evolution of ordered γ′(L1₂)-precipitates and the compositional trajectories during phase-separation of the γ(face-centered-cubic (f.c.c.))- and γ′(L1₂)-phases are studied in a Ni–0.10Al-0.085Cr-0.02Re (mole-fraction) superalloy, utilizing atom-probe tomography, transmission electron microscopy, and the Philippe-Voorhees (PV) coarsening model. As the γ′(L1₂)-precipitates grow, the excesses of Ni, Cr and Re, and depletion of Al in the γ(f.c.c.)-matrix develop because of diffusional fluxes crossing the γ(f.c.c.)/γ′(L1₂) heterophase interfaces. The coupling effects on diffusional fluxes are introduced (PV coarsening model) in terms of the diffusion tensor, D, and the second-derivative tensor of the molar Gibbs free energies, G^″, obtained employing Thermo-Calc and DICTRA calculations. The Gibbs interfacial free energies, σ^{γ/γ^′}, are (6.9 ± 1.4) mJ/m² with all terms in D and G^″, which changes to (18.9 ± 2.1) mJ/m², (37.7 ± 3.3) mJ/m², and (-7.5 ± 1.2) mJ/m² when not including the off-diagonal terms in D, G^″, and both D and G^″, respectively. The experimental APT compositional trajectories are displayed and compared with the PV model in a partial quaternary phase-diagram, employing a partial tetrahedron. The compositional trajectories measured by APT exhibit curvilinear behavior in the nucleation and growth regimes, t < 16 h, which become vectors, moving simultaneously toward the γ(f.c.c.) and γ′(L1₂) conjugate solvus-surfaces, for the quasi-stationary coarsening regime, t ≥ 16 h. The compositional trajectories for t ≥ 16 h are compared to the PV model with and without the off-diagonal terms in D and G^″. The directions, including the off-diagonal terms in the D and G^″tensors, are consistent with the APT experimental data.

Original language	English
Article number	118020
Journal	Acta Materialia
Volume	234
DOIs	https://doi.org/10.1016/j.actamat.2022.118020
State	Published - Aug 1 2022
Externally published	Yes

Funding

This research was supported by the National Science Foundation, Division of Materials Research (DMR) grant number DMR-1610367-001, Profs. Diana Farkas and Gary Shiflet, grant officers. Atom-probe tomography was performed at the Northwestern University Center for Atom-Probe Tomography (NUCAPT), which is a core facility of Northwestern University. The LEAP500XS tomograph at NUCAPT was purchased and upgraded with grants from the NSF-MRI (DMR-0420532) and ONR-DURIP (N00014-0400798, N00014-0610539, N00014-0910781, N00014-1712870) programs. This work made also use of the MatCI Facility and EPIC facility of Northwestern University's NUANCE Center. NUCAPT, MatCI, and EPIC facilities receive support from the MRSEC program (NSF DMR-1720139), SHyNE Resource (NSF ECCS-2025633), the IIN, and the Initiative for Sustainability and Energy (ISEN) at Northwestern University. The synchrotron x-ray diffraction measurements were performed at the Advanced Photon Source at Argonne National Laboratory, Lemont, IL. We thank research professor Dennis Keane for his important help with these measurements. SB and ZM thank Dr. Fan Zhang, Dr. Jun Zhu, Dr. Duchao Lv, and Dr. Weisheng Cao at Computherm LLC (Madison, WI) for their help in representing the quaternary phase diagram. DNS thanks Georges Martin (CEA Saclay, France) and Peter Voorhees (Northwestern) for many illuminating discussions concerning coarsening (Ostwald ripening) and mean-field modeling in general during many years. We also thank research associate professor Dr. Dieter Isheim for managing NUCAPT. This research was supported by the National Science Foundation, Division of Materials Research (DMR ) grant number DMR-1610367-001 , Profs. Diana Farkas and Gary Shiflet, grant officers. Atom-probe tomography was performed at the Northwestern University Center for Atom-Probe Tomography (NUCAPT), which is a core facility of Northwestern University. The LEAP500XS tomograph at NUCAPT was purchased and upgraded with grants from the NSF-MR I ( DMR-0420532 ) and ONR-DURIP ( N00014-0400798 , N00014-0610539, N00014-0910781 , N00014-1712870 ) programs. This work made also use of the MatCI Facility and EPIC facility of Northwestern University's NUANCE Center. NUCAPT, MatCI, and EPIC facilities receive support from the MRSEC program ( NSF DMR-1720139 ), SHyNE Resource ( NSF ECCS-2025633 ), the IIN, and the Initiative for Sustainability and Energy (ISEN) at Northwestern University. The synchrotron x-ray diffraction measurements were performed at the Advanced Photon Source at Argonne National Laboratory, Lemont, IL. We thank research professor Dennis Keane for his important help with these measurements. SB and ZM thank Dr. Fan Zhang, Dr. Jun Zhu, Dr. Duchao Lv, and Dr. Weisheng Cao at Computherm LLC (Madison, WI) for their help in representing the quaternary phase diagram. DNS thanks Georges Martin (CEA Saclay, France) and Peter Voorhees (Northwestern) for many illuminating discussions concerning coarsening (Ostwald ripening) and mean-field modeling in general during many years. We also thank research associate professor Dr. Dieter Isheim for managing NUCAPT.

Keywords

Atom-probe tomography
Coarsening
Diffusion tensor
Ni-based superalloys
Philippe-Voorhees (PV) model
Rhenium
Transmission electron microscopy

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@article{08c493df401a423cbc15b83924bd6d0b,

title = "The effects of diffusional couplings on compositional trajectories and interfacial free energies during phase separation in a quaternary Ni-Al-Cr-Re model superalloy",

abstract = "The temporal evolution of ordered γ′(L12)-precipitates and the compositional trajectories during phase-separation of the γ(face-centered-cubic (f.c.c.))- and γ′(L12)-phases are studied in a Ni–0.10Al-0.085Cr-0.02Re (mole-fraction) superalloy, utilizing atom-probe tomography, transmission electron microscopy, and the Philippe-Voorhees (PV) coarsening model. As the γ′(L12)-precipitates grow, the excesses of Ni, Cr and Re, and depletion of Al in the γ(f.c.c.)-matrix develop because of diffusional fluxes crossing the γ(f.c.c.)/γ′(L12) heterophase interfaces. The coupling effects on diffusional fluxes are introduced (PV coarsening model) in terms of the diffusion tensor, D, and the second-derivative tensor of the molar Gibbs free energies, G″, obtained employing Thermo-Calc and DICTRA calculations. The Gibbs interfacial free energies, σγ/γ′, are (6.9 ± 1.4) mJ/m2 with all terms in D and G″, which changes to (18.9 ± 2.1) mJ/m2, (37.7 ± 3.3) mJ/m2, and (-7.5 ± 1.2) mJ/m2 when not including the off-diagonal terms in D, G″, and both D and G″, respectively. The experimental APT compositional trajectories are displayed and compared with the PV model in a partial quaternary phase-diagram, employing a partial tetrahedron. The compositional trajectories measured by APT exhibit curvilinear behavior in the nucleation and growth regimes, t < 16 h, which become vectors, moving simultaneously toward the γ(f.c.c.) and γ′(L12) conjugate solvus-surfaces, for the quasi-stationary coarsening regime, t ≥ 16 h. The compositional trajectories for t ≥ 16 h are compared to the PV model with and without the off-diagonal terms in D and G″. The directions, including the off-diagonal terms in the D and G″tensors, are consistent with the APT experimental data.",

keywords = "Atom-probe tomography, Coarsening, Diffusion tensor, Ni-based superalloys, Philippe-Voorhees (PV) model, Rhenium, Transmission electron microscopy",

author = "Baik, {Sung Il} and Zugang Mao and Qingqiang Ren and Fei Xue and Campbell, {Carelyn E.} and Chuan Zhang and Bicheng Zhou and Noebe, {Ronald D.} and Seidman, {David N.}",

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doi = "10.1016/j.actamat.2022.118020",

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T1 - The effects of diffusional couplings on compositional trajectories and interfacial free energies during phase separation in a quaternary Ni-Al-Cr-Re model superalloy

AU - Baik, Sung Il

AU - Mao, Zugang

AU - Ren, Qingqiang

AU - Xue, Fei

AU - Campbell, Carelyn E.

AU - Zhang, Chuan

AU - Zhou, Bicheng

AU - Noebe, Ronald D.

AU - Seidman, David N.

PY - 2022/8/1

Y1 - 2022/8/1

N2 - The temporal evolution of ordered γ′(L12)-precipitates and the compositional trajectories during phase-separation of the γ(face-centered-cubic (f.c.c.))- and γ′(L12)-phases are studied in a Ni–0.10Al-0.085Cr-0.02Re (mole-fraction) superalloy, utilizing atom-probe tomography, transmission electron microscopy, and the Philippe-Voorhees (PV) coarsening model. As the γ′(L12)-precipitates grow, the excesses of Ni, Cr and Re, and depletion of Al in the γ(f.c.c.)-matrix develop because of diffusional fluxes crossing the γ(f.c.c.)/γ′(L12) heterophase interfaces. The coupling effects on diffusional fluxes are introduced (PV coarsening model) in terms of the diffusion tensor, D, and the second-derivative tensor of the molar Gibbs free energies, G″, obtained employing Thermo-Calc and DICTRA calculations. The Gibbs interfacial free energies, σγ/γ′, are (6.9 ± 1.4) mJ/m2 with all terms in D and G″, which changes to (18.9 ± 2.1) mJ/m2, (37.7 ± 3.3) mJ/m2, and (-7.5 ± 1.2) mJ/m2 when not including the off-diagonal terms in D, G″, and both D and G″, respectively. The experimental APT compositional trajectories are displayed and compared with the PV model in a partial quaternary phase-diagram, employing a partial tetrahedron. The compositional trajectories measured by APT exhibit curvilinear behavior in the nucleation and growth regimes, t < 16 h, which become vectors, moving simultaneously toward the γ(f.c.c.) and γ′(L12) conjugate solvus-surfaces, for the quasi-stationary coarsening regime, t ≥ 16 h. The compositional trajectories for t ≥ 16 h are compared to the PV model with and without the off-diagonal terms in D and G″. The directions, including the off-diagonal terms in the D and G″tensors, are consistent with the APT experimental data.

AB - The temporal evolution of ordered γ′(L12)-precipitates and the compositional trajectories during phase-separation of the γ(face-centered-cubic (f.c.c.))- and γ′(L12)-phases are studied in a Ni–0.10Al-0.085Cr-0.02Re (mole-fraction) superalloy, utilizing atom-probe tomography, transmission electron microscopy, and the Philippe-Voorhees (PV) coarsening model. As the γ′(L12)-precipitates grow, the excesses of Ni, Cr and Re, and depletion of Al in the γ(f.c.c.)-matrix develop because of diffusional fluxes crossing the γ(f.c.c.)/γ′(L12) heterophase interfaces. The coupling effects on diffusional fluxes are introduced (PV coarsening model) in terms of the diffusion tensor, D, and the second-derivative tensor of the molar Gibbs free energies, G″, obtained employing Thermo-Calc and DICTRA calculations. The Gibbs interfacial free energies, σγ/γ′, are (6.9 ± 1.4) mJ/m2 with all terms in D and G″, which changes to (18.9 ± 2.1) mJ/m2, (37.7 ± 3.3) mJ/m2, and (-7.5 ± 1.2) mJ/m2 when not including the off-diagonal terms in D, G″, and both D and G″, respectively. The experimental APT compositional trajectories are displayed and compared with the PV model in a partial quaternary phase-diagram, employing a partial tetrahedron. The compositional trajectories measured by APT exhibit curvilinear behavior in the nucleation and growth regimes, t < 16 h, which become vectors, moving simultaneously toward the γ(f.c.c.) and γ′(L12) conjugate solvus-surfaces, for the quasi-stationary coarsening regime, t ≥ 16 h. The compositional trajectories for t ≥ 16 h are compared to the PV model with and without the off-diagonal terms in D and G″. The directions, including the off-diagonal terms in the D and G″tensors, are consistent with the APT experimental data.

KW - Atom-probe tomography

KW - Coarsening

KW - Diffusion tensor

KW - Ni-based superalloys

KW - Philippe-Voorhees (PV) model

KW - Rhenium

KW - Transmission electron microscopy

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DO - 10.1016/j.actamat.2022.118020

M3 - Article

AN - SCOPUS:85131079749

SN - 1359-6454

VL - 234

JO - Acta Materialia

JF - Acta Materialia

M1 - 118020

ER -

The effects of diffusional couplings on compositional trajectories and interfacial free energies during phase separation in a quaternary Ni-Al-Cr-Re model superalloy

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