CALPHAD-aided design of high entropy alloy to achieve high strength via precipitate strengthening

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  • ReceivedJun 20, 2019
  • AcceptedAug 27, 2019
  • PublishedSep 17, 2019


Funded by

the Fundamental Research Funds for the Central Universities of Central South University(2019zzts052)

the National Natural Science Foundation of China(51828102)


This work was supported by the Fundamental Research Funds for the Central Universities of Central South University (2019zzts052) and the National Natural Science Foundation of China (51828102).

Interest statement

The authors declare no conflict of interest.

Contributions statement

Song M designed the project. Guo L and Gong X produced the materials and performed the mechanical testing. Guo L, Gu J, and Ni S conducted the microstructural characterization. Guo L, Gu J and Song M wrote the manuscript. All authors contributed to the discussion of the results and commented on the manuscript.

Author information

Lin Guo is currently a PhD candidate at Powder Metallurgy Research Institute, Central South University, China. His current research focuses on HEAs designing and microstructural evolution.

Ji Gu is a lecturer of Powder Metallurgy Research Institute, Central South University, China. He received his PhD degree in material science and engineering in 2019 under the supervision of Prof. Min Song. His current research focuses on exploring the mechanical behaviour, deformation mechanism and structure-property relationship of HEAs and gradient structure materials.

Min Song is a Professor and Vice Dean of Powder Metallurgy Research Institute at Central South University. He serves as Associate Editor of “Materials Characterization”. He received his PhD degree in 2005 at Dartmouth College, USA. His current research interests involve deformation mechanisms of metallic materials, including: metals and alloys, bulk nanocrystalline materials, metallic glasses, HEAs and metal matrix composites.


Supplementary information

Supporting data are available in the online version of this paper.


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  • Figure 1

    Phase diagram of the (FeCoNi)92Al2.5Ti5.5 HEA calculated using Thermo-Calc software and the TTNI8 database.

  • Figure 2

    XRD patterns of the (FeCoNi)92Al2.5Ti5.5 HEA after different treatments.

  • Figure 3

    EBSD IPF maps illustrating the grain-size evolution after different thermo-mechanical processes.

  • Figure 4

    (a) KAM map and (b) grain-boundaries map of the T4 alloy.

  • Figure 5

    SEM micrographs of the: (a) T1, (b) T2, (c) T3, and (d) T4.

  • Figure 6

    Particle-size and spacing distributions of the L12 ordered precipitates in the (a, d) T2, (b, e) T3, and (c, f) T4 samples.

  • Figure 7

    TEM characterizations of the T2: (a) TEM dark-field image and corresponding SAED pattern, (b) HRTEM image of the precipitates and corresponding FFT pattern (the superlattice spots are outlined by red arrows), (c) HAADF STEM image and (c1) corresponding elemental mapping in the red-square region in (c).

  • Figure 8

    Engineering strain–stress curves of the four specimens tensile-deformed at room temperature.

  • Figure 9

    TEM micrographs showing the microstructures of the T1 at different strains: (a) 2%, (b) 30%, and (c) 60%.

  • Figure 10

    TEM micrographs showing the microstructures of the T2 alloy at different strains: (a) 2% and (b) 28%.

  • Figure 11

    (a) HRTEM image of the T2 tensile-deformed to fracture (with a total strain of about 28%), with the interface between the matrix and the precipitate being identified by the corresponding FFT pattern A, B, C, and D (the superlattice spots are outlined by red arrows), (b) HRTEM-filtered image of the precipitate–matrix interface, and (c, d) corresponding IFFT images of the HRTEM shown in (b) for the (11-1) and (1-11) planes.

  • Figure 12

    A column chart characterizing the strengthening contributions of different mechanisms, where Δσp, ΔσG, and Δσdis represent the precipitation hardening, grain-boundaries hardening, and dislocation hardening, respectively.

  • Table 1   Chemical compositions and the basic properties of the elements in (FeCoNi)AlTi alloy













    Atomicradius (Å)






    Meltingtemperature (°C)






  • Table 2   Grain size, yield strength, ultimate tensile strength and elongation of the alloy after different treatments processing


    Treatment processing

    Grain size (μm)

    Yield strength (MPa)

    Ultimate tensile strength (MPa)

    Elongation (%)


    Cold rolled (60%) + annealing at 1150°C for 10 min






    Cold rolled (85%) + annealing at 1150°C for 3min + aging at 800°C for 60 min






    Cold rolled (85%) + annealing at 1150°C for 3 min + aging at 750°C for 60 min






    Cold rolled (85%) + annealing at 970°C for 0.5 min + aging at 750°C for 60 min





  • Table 3   The values of chemical mixing enthalpy, Δ of atomic pairs between elements Fe, Co, Ni, Al, and Ti


























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