Dynamical scattering image simulations for two-phase γ–γ′ microstructures: A theoretical model

•We describe a dynamical scattering matrix approach for two-phase materials.•We incorporate defect displacement fields into the scattering formalism.•We compute dynamical diffraction patterns for overlapping second phase particles.•We apply the method to a synthetic–0 microstructure in a Ni-base sup...

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Published in:	Ultramicroscopy Vol. 185; pp. 32 - 41
Main Authors:	Singh, S., Mills, M.J., Graef, M. De
Format:	Journal Article
Language:	English
Published:	Netherlands Elsevier B.V 01-02-2018
Subjects:	Dynamical scattering Image simulation Scattering matrix Two-phase microstructure Dynamical scattering Two-phase microstructure Scattering matrix Image simulation
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Abstract	•We describe a dynamical scattering matrix approach for two-phase materials.•We incorporate defect displacement fields into the scattering formalism.•We compute dynamical diffraction patterns for overlapping second phase particles.•We apply the method to a synthetic–0 microstructure in a Ni-base superalloy. We introduce an extension of the Darwin–Howie–Whelan (DHW) equations for the case of coherent L12 precipitates in an FCC matrix. The equations are similar in form to the conventional DHW equations and are sufficiently general to account for the different translational variants of the precipitate phase as well as for the displacement fields of arbitrary lattice defects. An approximate scheme to perform fast and accurate image simulations using a pre-computed list of scattering matrices is also introduced. Finally, the results of diffraction pattern and image simulations are shown for two synthetic microstructures for a Ni–Al alloy generated using phase field simulations. The dynamical scattering equations reveal that the precipitate phase superlattice beams can propagate through the disordered matrix, but they are fully decoupled from the fundamental waves.
AbstractList	We introduce an extension of the Darwin-Howie-Whelan (DHW) equations for the case of coherent L12 precipitates in an FCC matrix. The equations are similar in form to the conventional DHW equations and are sufficiently general to account for the different translational variants of the precipitate phase as well as for the displacement fields of arbitrary lattice defects. An approximate scheme to perform fast and accurate image simulations using a pre-computed list of scattering matrices is also introduced. Finally, the results of diffraction pattern and image simulations are shown for two synthetic microstructures for a Ni-Al alloy generated using phase field simulations. The dynamical scattering equations reveal that the precipitate phase superlattice beams can propagate through the disordered matrix, but they are fully decoupled from the fundamental waves. We introduce an extension of the Darwin-Howie-Whelan (DHW) equations for the case of coherent L1 precipitates in an FCC matrix. The equations are similar in form to the conventional DHW equations and are sufficiently general to account for the different translational variants of the precipitate phase as well as for the displacement fields of arbitrary lattice defects. An approximate scheme to perform fast and accurate image simulations using a pre-computed list of scattering matrices is also introduced. Finally, the results of diffraction pattern and image simulations are shown for two synthetic microstructures for a Ni-Al alloy generated using phase field simulations. The dynamical scattering equations reveal that the precipitate phase superlattice beams can propagate through the disordered matrix, but they are fully decoupled from the fundamental waves. •We describe a dynamical scattering matrix approach for two-phase materials.•We incorporate defect displacement fields into the scattering formalism.•We compute dynamical diffraction patterns for overlapping second phase particles.•We apply the method to a synthetic–0 microstructure in a Ni-base superalloy. We introduce an extension of the Darwin–Howie–Whelan (DHW) equations for the case of coherent L12 precipitates in an FCC matrix. The equations are similar in form to the conventional DHW equations and are sufficiently general to account for the different translational variants of the precipitate phase as well as for the displacement fields of arbitrary lattice defects. An approximate scheme to perform fast and accurate image simulations using a pre-computed list of scattering matrices is also introduced. Finally, the results of diffraction pattern and image simulations are shown for two synthetic microstructures for a Ni–Al alloy generated using phase field simulations. The dynamical scattering equations reveal that the precipitate phase superlattice beams can propagate through the disordered matrix, but they are fully decoupled from the fundamental waves.
Author	Singh, S. Graef, M. De Mills, M.J.
Author_xml	– sequence: 1 givenname: S. surname: Singh fullname: Singh, S. organization: Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA – sequence: 2 givenname: M.J. surname: Mills fullname: Mills, M.J. organization: Department of Materials Science and Engineering, Ohio State University, Columbus, OH 43210, USA – sequence: 3 givenname: M. De surname: Graef fullname: Graef, M. De email: mdg@andrew.cmu.edu organization: Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
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Keywords	Dynamical scattering Two-phase microstructure Scattering matrix Image simulation
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Snippet	•We describe a dynamical scattering matrix approach for two-phase materials.•We incorporate defect displacement fields into the scattering formalism.•We... We introduce an extension of the Darwin-Howie-Whelan (DHW) equations for the case of coherent L1 precipitates in an FCC matrix. The equations are similar in... We introduce an extension of the Darwin-Howie-Whelan (DHW) equations for the case of coherent L12 precipitates in an FCC matrix. The equations are similar in...
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SubjectTerms	Dynamical scattering Image simulation Scattering matrix Two-phase microstructure
Title	Dynamical scattering image simulations for two-phase γ–γ′ microstructures: A theoretical model
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