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Phase-field modeling of microstructure evolution of Cu-rich phase in Fe–Cu–Mn–Ni–Al quinary system coupled with thermodynamic databases

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Abstract

Quinary phase-field model was extended and constructed, and the diffusion-controlled phase decomposition and morphology in thermal aging Fe–Cu–Mn–Ni–Al quinary system coupled with CALPHAD thermodynamic databases were successfully studied. The effects of Manganese composition on the morphology, volume fraction, number density, particles size and growth and coarsening of Cu-rich precipitates were investigated systematically. The simulation results showed that Cu-rich α phase was firstly formed, and the Ni, Al and Mn atoms were partitioned to the Cu-rich phase, leading to the formation of a Ni–Al–Mn-rich intermetallic ring/Cu-rich core precipitate morphology and final conversion of Cu-rich phase to Cu-rich γ phase. The curves of volume fraction and free energy variation with simulation time indicated that Mn element can promote nucleation driving force to overcome the nucleation barrier in initial stage and can also accelerate the precipitation of Cu-rich phase and promote the growth and coarsening processes. Through the analysis of number density (ND) and average particle size (APS), we found that the values of ND and APS of Cu-rich particles increase with the rising of Mn content, which indicates that the higher Mn content will boost the nucleation and growth rate. Moreover, the time exponent at the later precipitation was 0.41, 0.42 and 0.37, respectively, which had deviations with the 0.33 of the LSW’s value, and the growth and coarsening of Cu-rich precipitates were under the mixed mechanisms of Ostwald ripening and coalescence coarsening of neighboring precipitates. These results provided useful information for the preparation of multi-component alloyed steel with excellent mechanical properties to some extent.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. U1610123, 51674226, 51574207, 51574206, 51774254, 51774253, 51701187), Science and Technology Major Project of Shanxi Province (No. MC2016-06).

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  1. School of Materials Science and Engineering, North University of China, Taiyuan, 030051, People’s Republic of China

    Sun Yuanyang, Zhao Yuhong, Zhao Baojun, Yang Wenkui & Hou Hua

  2. School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Li Xiaoling

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  1. Sun Yuanyang
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Appendix: Gibbs energies of pure i element \( G_{i}^{\varphi } \) and the binary and ternary interaction parameters \( L_{i,j}^{\varphi } \) and \( L_{{_{i,j,k} }}^{\varphi } \)

Appendix: Gibbs energies of pure i element \( G_{i}^{\varphi } \) and the binary and ternary interaction parameters \( L_{i,j}^{\varphi } \) and \( L_{{_{i,j,k} }}^{\varphi } \)

\( G_{i}^{\varphi } \) is the Gibbs energies of φ phase of pure i component; \( L_{i,j}^{\varphi } \) and \( L_{{_{i,j,k} }}^{\varphi } \) represent the binary and ternary interaction parameters of φ phases, In this simulation, we mainly study the phase separation of Cu-rich phase and its transformation process from α(bcc) phase to γ(fcc) phase; thus, we just consider all of binary interaction parameters and parts of ternary interaction parameters related to Cu constituents and assume other ternary interaction parameters as 0. Concrete interaction parameters as function of composition and temperature and Gibbs energies of pure i component are applied the following data [67,68,69,70,71,72,73]:

$$ L_{1,2}^{\alpha } { = }41033 - 6. 0 2 2T $$
$$ L_{1,3}^{\alpha } { = } - 2759 + 1.237T $$
$$ L_{1,4}^{\alpha } { = } - 956.63 - 1.28726T + \left( {1789.03 - 1.92912T} \right)\left( {c_{1} - c_{4} } \right) $$
$$ L_{1,5}^{\alpha } { = } - 122960 + 31.989T - \left( {2945.2} \right)\left( {c_{1} - c_{5} } \right) $$
$$ L_{2,3}^{\alpha } { = }11190 - 6T - 9865\left( {c_{2} - c_{3} } \right) $$
$$ L_{2,4}^{\alpha } { = }8366 + 2.8T $$
$$ L_{2,5}^{\alpha } { = } - 104600 + 27.5T - \left( {9800 + 20T} \right)\left( {c_{2} - c_{5} } \right) $$
$$ L_{3,4}^{\alpha } { = } - 51638.31 + 3.64T + 6276\left( {c_{3} - c_{4} } \right) $$
$$ L_{3,5}^{\alpha } { = } - 120077 + 52.851T - \left( { - 40652 + 29.276T} \right)\left( {c_{3} - c_{5} } \right) $$
$$ \begin{aligned} &L_{4,5}^{\alpha } { = } - 264500 - 119T + 23TInT \\ &\quad - \left( - 107000 + 559T - 67TInT \right)\left( {c_{4} - c_{5} } \right) \\ & \quad + \left( {414000 - 800T + 95TInT} \right)\left( {c_{4} - c_{5} } \right)^{2} \\ &\quad - \left( - 118000 + 970T - 99TInT \right)\left( {c_{4} - c_{5} } \right)^{3} \\ \end{aligned} $$
$$ L_{1,2,3}^{\alpha } { = 30000} $$
$$ L_{1,2,4}^{\alpha } { = }L_{2,3,4}^{\alpha } { = 0} $$
$$ L_{1,2,5}^{\alpha } { = } - 1 5 0 0 0c_{ 1} + 3 5 0 0 0c_{2} - 1 6 0 0 0 0c_{5} $$
$$ L_{2,3,5}^{\alpha } { = 36000} $$
$$ L_{2,4,5}^{\alpha } { = }\left( { - 28000 + 40T} \right)c_{1} + \left( { - 133000 + 40T} \right)c_{2} + \left( { - 200000 - 100T} \right)c_{5} $$
$$ L_{1,2}^{\gamma } { = }53360 - 12.626T - \left( {11512 - 7.095T} \right)\left( {c_{1} - c_{2} } \right) $$
$$ L_{1,3}^{\gamma } { = }\left( { - 7762 + 3.865T} \right) - 259\left( {c_{1} - c_{3} } \right) $$
$$ L_{1,4}^{\gamma } { = } - 12054.355 + 3.27413T + \left( {11082.1315 - 4.45077T} \right)\left( {c_{1} - c_{4} } \right) - 725.8051\left( {c_{1} - c_{4} } \right)^{2} $$
$$ L_{1,5}^{\gamma } { = } - 76066.1 + 18.6758T - \left( {21167.4 + 1.3398T} \right)\left( {c_{1} - c_{5} } \right) $$
$$ L_{2,3}^{\gamma } { = }11820 - 2.3T{ + }\left( { - 10600 + 3T} \right)\left( {c_{2} - c_{3} } \right) + \left( { - 4850 + 3.5T} \right)\left( {c_{2} - c_{3} } \right)^{2} $$
$$ L_{2,4}^{\gamma } { = }8366 + 2.802T + \left( { - 4359.6 + 1.812T} \right)\left( {c_{2} - c_{4} } \right) $$
$$ L_{2,5}^{\gamma } { = } - 64400 + 10T - 34000\left( {c_{2} - c_{5} } \right) $$
$$ L_{3,4}^{\gamma } { = } - 58158 + 10.878T + 6276\left( {c_{3} - c_{4} } \right) $$
$$ L_{3,5}^{\gamma } { = } - 69300 + 25T - 8800\left( {c_{3} - c_{5} } \right) $$
$$ \begin{aligned} & L_{4,5}^{\gamma } = - 162408 + 16.213T - \left( {73418 - 36.914T} \right)\left( {c_{4} - c_{5} } \right) \\ & \quad + \left( {33471 - 9.837*T} \right)\left( {c_{4} - c_{5} } \right)^{2} \\ & \quad - \left( { - 30758 + 10.253T} \right)\left( {c_{4} - c_{5} } \right)^{3} \\ \end{aligned} $$
$$ L_{1,2,3}^{\gamma } { = } - 68000{ + }50T $$
$$ L_{1,2,4}^{\gamma } { = } - 73272 + 30.9T $$
$$ L_{1,2,5}^{\gamma } { = }\left( { - 240000 + 100T} \right)c_{1} + \left( { - 180000 + 100T} \right)c_{2} + \left( { - 180000{ + }100T} \right)c_{5} $$
$$ L_{2,3,4}^{\gamma } { = }\left( { - 115000 + 10T} \right)c_{2} - 33000c_{3} - 33000c_{4} $$
$$ L_{2,3,5}^{\gamma } { = 17000} $$
$$ L_{2,4,5}^{\alpha } { = }\left( { - 100000 - 50T} \right)c_{2} + \left( { - 50000 - 20T} \right)c_{4} + \left( { - 240000 - 50T} \right)c_{5} $$
$$ G_{1}^{\alpha } { = }0 $$
$$ G_{2}^{\alpha } { = }4017 - 1.255T $$
$$ G_{3}^{\alpha } { = } - 3235.3 + 127.85T - 23.7TInT - 0.0074271T^{2} + 60000/T $$
$$ G_{4}^{\alpha } { = }8715.084 - 3.556T $$
$$ \begin{aligned} & G_{5}^{\alpha } = - 1193.24 + 218.235446T - 38.5844296TInT \\ & \quad+ 18.531982 3 {{E - 3}}T^{2} - 5.764227{{E - }}6T^{3} + 74092T^{ - 1} \\ \end{aligned} $$
$$ G_{1}^{\gamma } { = } - 1462.4 + 8.282T - 1.15TInT + 6.4E{ - }6T^{2} $$
$$ G_{2}^{\gamma } { = }0 $$
$$ G_{3}^{\gamma } { = } - 3439.3 + 131.884T - 24.5177TInT - 0.006T^{2} + 69600/T $$
$$ G_{4}^{\gamma } { = }0 $$
$$ \begin{aligned} & G_{5}^{\gamma } { = } - 11276.24 + 233.048446T - 38.5844296TInT \\ & \quad + 18.531982{{E - }}3T^{2}- 5.764227{{E - }}6T^{3} + 74092T^{ - 1} \\ \end{aligned} $$

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Yuanyang, S., Yuhong, Z., Baojun, Z. et al. Phase-field modeling of microstructure evolution of Cu-rich phase in Fe–Cu–Mn–Ni–Al quinary system coupled with thermodynamic databases. J Mater Sci 54, 11263–11278 (2019). https://doi.org/10.1007/s10853-019-03678-3

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