High-entropy alloys (HEAs) generally refer to an alloy system consisting of five or more elements, with atomic concentrations concentrated between 5% and 35%. Unlike traditional alloy systems, the HEA composition is closer to the center of the phase diagram, which opens up entirely new ideas for material development, often leading to some promising properties. Accurate prediction of the phase stability of high-entropy alloys (HEAs) is of great significance for alloy design and development. There is a large deviation between the predicted results of the existing mature thermodynamic methods and the actual results.
To avoid this problem, scholars from Dalian University of Technology proposed a new simplified prediction scheme based on the experimental results of 130 HEAs combining ten elements: Al, Co, Cr, Cu, Fe, Mn, Mo, Ni, Ti, and V. Secondly, the correlation between bond enthalpy and interaction parameters was analyzed from the perspective of thermodynamics, and a new technique for quantifying inter-element interaction parameters was established. Then, the enthalpy of mixing of the solid solution with a specific crystal structure was extracted as well as the Gibbs free energy of the intermetallic compound. Therefore, by comparing the Gibbs free energy of the alloy system before and after precipitation, an overall basic method for predicting phase stability was developed. This method takes into account the change of Gibbs free energy of the solid solution after the separation of intermetallic compounds, and the calculation results are more accurate and reliable, and can indicate which complex phase (Sigma phase or Laves phase) will be precipitated in HEAs, providing a new method with high confidence in predicting the phase stability of HEAs. The work was published in Acta Materialia in a research article titled "Prediction of phase stabilities of solid solutions for high entropy alloys".
Paper Links:
https://doi.org/10.1016/j.actamat.2023.119445
In this study, we established a model to predict the phase stability of HEA by comparing the Gibbs free energy of HEA in a single solution state and the solution plus intermetallic compound state. This approach avoids the problems of ignoring too many thermodynamic parameters in traditional methods, thus ensuring the accuracy of the thermodynamic formulas employed in the model. In this study, a large number of simulation calculations based on density functional theory (DFT) are provided, and more detailed and accurate enthalpy results of atomic bonds are obtained on the basis of unified calculation standards. This study also seeks to quantify the interaction parameters, which are the basis for calculating the Gibbs free energy of solid solutions and intermetallic compounds. It is worth noting that the prediction of the phase stability of HEAs is based on the thermodynamic judgment criteria proposed in this paper. DFT calculations only provide bond energy data that cannot be directly obtained or are difficult to obtain directly from experiments or published papers, and have relatively consistent conditions for building thermodynamic models. This method can effectively give the type of precipitate in HEAs and is a reliable new method for predicting the stability of solid solutions.
Figure 1. (a), (b) Comparison of bond enthalpy estimated from Ab-initio calculations
Figure 2. (a) and (b) show the fundamental relationship between the calculated precipitation temperature Tc of the intermetallic compound IM (Sigma or Laves) and the microstructure of the HEA with the crystal structure of the solid solution (FCC). The abscissa represents the IM precipitation temperature evaluated, Tc The black box indicates the experimental results consisting of a BCC (FCC) solid solution or BCC+B2 (FCC+L12) microstructure, and the purple box indicates the precipitation of intermetallic compound IM from BCC (FCC) or BCC+B2 (FCC+L12) solid solution. The CCR value (correct classification rate) based on the classification threshold represented by the dashed dotted line is provided.
Figure 3. (a) and (b) show the basic relationship between the calculated sigma phase precipitation temperature and the microstructure of the HEA with BCC (FCC) crystal structure of the solid solution, and the microstructure of the HEA with the BCC (FCC) crystal structure of the solid solution. The abscissa represents the evaluated sigma phase precipitation temperature Tσ, the black squares represent the experimental results of BCC (FCC) solid solution or BCC+B2 (FCC+L12) microstructure composition, and the red squares represent BCC (FCC) solid solution or BCC+B2 (FCC+L12) solid solution precipitation sigma phase. The CCR value (correct classification rate) based on the classification threshold represented by the dashed dotted line is provided.
Figure 4. (a) and (b) show the basic relationship between the calculated Laves phase precipitation temperature and the microstructure of HEA with BCC (FCC) crystal structure in solid solution, and between T Laves and the microstructure of HEA with BCC (FCC) crystal structure in solid solution.
Figure 5. (a), (b) show the basic relationship between the calculated Ravis phase precipitation temperature T Laves, titanium content CTi, and the microstructure of HEA with BCC (FCC) crystal structure in solid solution. The fundamental relationship between the microstructure of HEA with a solid solution with a BCC (FCC) crystal structure.
Figure 6. The results of 105 collected literature data are presented to prove the correctness of the predictions. (a) and (b) show the calculated precipitation temperature of the intermetallic compound IM (Sigma or Lavis), the microstructure of Tc and the solid solution HEA with BCC or FCC crystal structure. (c) and (d) show the fundamental relationship between the calculated precipitation temperature Tσ of the sigma phase and the microstructure of HEA with BCC or FCC crystal structure in solid solution. (e) and (f) show the fundamental relationship between the calculated Laves phase precipitation temperature T Laves and the microstructure of HEAs with BCC or FCC crystal structures in solid solutions. (g) and (h) show the basic relationship between the calculated Ravis phase precipitation temperature T Laves, Ti element content CTi and the microstructure of HEA. The fundamental relationship between the microstructure of HEAs with BCC or FCC crystal structures in solid solutions.
Figure 7. BCC + Laves indicates that the alloy consists of a BCC solid solution and a Laves phase; FCC indicates that the alloy consists of an FCC solid solution; FCC + Sigma means that the alloy consists of an FCC solid solution and a Sigma phase. FCC + Laves indicates that the alloy consists of an FCC solid solution and a Laves phase). The CCR value (correct classification rate) is determined based on the classification threshold drawn by the dashed dots.
Figure 8. The parameters in the design database and the validation database are shown, BCC indicates that the alloy consists of a BCC solid solution; BCC + Sigma indicates that the alloy consists of a BCC solid solution and a Sigma phase. BCC + Laves indicates that the alloy consists of a BCC solid solution and a Laves phase; FCC indicates that the alloy consists of an FCC solid solution; FCC + Sigma means that the alloy consists of an FCC solid solution and a Sigma phase. FCC + Laves indicates that the alloy consists of an FCC solid solution and a Laves phase). The CCR value was determined based on the classification threshold drawn by the dashed dots.
Figure 9.Calculation of the basic relationship between the precipitation temperature of the sigma or Lavis phase and the ratio of the enthalpy of formation of the intermetallic compound to the Gibbs free energy of the solid solution
Figure 10. The fundamental relationship between the precipitation temperature Tσ or T Laves of the sigma or Lavis phases, calculated according to the Midema model, and the microstructure of HEAs with BCC or FCC crystal structures in solid solutions is shown.
Based on the Ab-initio calculation to quantify the bond enthalpy of atomic pairs in a condensed solid solution (BCC or FCC), combined with the correlation between bond enthalpy and interaction parameters, an established method for evaluating the enthalpy of solid solution mixing is established, which in turn develops a more accurate overall quantification method for the Gibbs free energy of solid solutions, providing a simplified method for correctly estimating the thermodynamic parameters of HEA. On the basis of fully considering the change of Gibbs free energy after precipitation, the precipitation temperature is taken as the basic parameter to predict phase stability. The stability of 130 HEAs was theoretically evaluated and predicted, and 105 HEAs were calculated, verifying the effectiveness of the method, indicating that the higher the precipitation temperature, the lower the stability of the solid solution, and vice versa. This new forecasting framework not only retains the advantages of Ab-initio computation, but also avoids the problem of excessive computationality. Instead, this method takes into account the change in the Gibbs free energy of the solid solution after the precipitation of the intermetallic compounds, making the calculation more accurate. At the same time, it can also give the types of complex phases precipitated in HEA, providing a reliable new method for predicting the stability of HEA. (Text: SSC)
This article is from the WeChat public account "Materials Science and Engineering". Please contact and keep the text of this box for reprinting.