Abstract
Combined with phase field simulation and experimental research, the growth and coarsening of M7C3 carbide precipitated from supersaturated austenite matrix were studied. Adopting the CALculation of PHAse Diagram (CALPHAD) method and thermodynamic database, the real Gibbs free energy of the austenite and M7C3 carbide phases in the Fe–Cr–C ternary alloy was established. The growth and coarsening of M7C3 carbide were simulated by phase field method. The microstructure and elements distribution of M7C3 carbide in Fe–Cr–C alloy were observed by field emission scanning electron microscope (FESEM) and energy-dispersive spectrometer (EDS) after various isothermal aging times (0 h, 0.5 h, 2 h) at 1273 K, respectively. Results show that the growth and coarsening of the precipitated M7C3 carbide phase undergo the following process during isothermal aging: first, a single precipitated phase nucleus is precipitated from the matrix; afterward, the single precipitated phase continues to coarsen and grow to form a plate-like structure, or two precipitated phases contact to form a single bar-like structure; then, several precipitated phase nucleuses contact to form an elongated bar shape, and finally, the elongated bar-shaped structure contacts and grows to form a typical lamellar eutectic carbide. In addition, through the analysis of the concentration field, the precipitated M7C3 carbide is a shell structure. The outer layer is a carbon-rich zone, and the inner part is a chromium-rich zone. By comparing the simulated morphology evolution with the experimental microstructure characterization and elements distribution via EDS, the correctness of the proposed phase field model has been verified.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China [Grant Nos. 51974153, U1960203].
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LL contributed to the conceptualization, methodology, formal analysis, investigation, data curation, and writing—original draft. MC was software, validation, and writing—review and editing. WL contributed to the resources, funding acquisition, and writing–review and editing. XZ and ZJ contributed to the resources and funding acquisition. BW and JJ were involved in the data curation.
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Appendix
Appendix
The molar Gibbs energy for the FCC phase was described using a two-sublattice model \({\text{(Fe,Cr)(C,Va)}}\) (Table
3).
where
where the site fraction of component \(i\) is marked as \(y_{i}\) and the relationship between site fraction and mole fraction can be expressed as:
All the \({}^{0}G\) values are given relative to the enthalpy of selected reference states for the elements at 298.15 K. The comma separates components that interact in the same sublattice and colon is used to separate between different sublattices. \(R\) and \(T\) are gas constant and temperature. The \(L_{i,j}^{\phi }\)(binary interaction parameters) can be concentration dependent according to a Redlich–Kister polynomial,
where
The M7C3 carbide was treated with the two-sublattice model \({\text{(Fe,Cr)}}_{{7}} {\text{C}}_{{3}}\) and its molar free energy was described as
where \({}^{0}G_{i:{\text{C}}}^{{{\text{M}}_{7} {\text{C}}_{3} }}\) is the Gibbs energy of a pure binary carbide, the binary interaction parameter \(L_{{\text{Cr,Fe:C}}}^{{{\text{M}}_{{7}} {\text{C}}_{{3}} }}\) in Eq. A.7 is
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Li, L., Chen, M., Li, W. et al. Growth and coarsening of eutectic M7C3 carbide in Fe–Cr–C alloy during isothermal aging: phase field simulation and experimental research. Appl. Phys. A 127, 888 (2021). https://doi.org/10.1007/s00339-021-05031-5
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DOI: https://doi.org/10.1007/s00339-021-05031-5