Identification of the parameters affecting the morphology of σ-phase precipitates in FCC high-entropy alloys combining experimental and simulated data with machine learning approaches

• Applicants: Professor Guillaume Laplanche, Ph.D.; Professor Dr.-Ing. Markus Stricker
• Subject Area: Thermodynamics and Kinetics as well as Properties of Phases and Microstructure of Materials ; Mechanical Properties of Metallic Materials and their Microstructural Origins
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 564857507

The topologically close-packed σ phase is one of the most frequently encountered intermetallic phases in engineering alloys, e.g., it has been reported to form in austenitic stainless steels, Ni-base superalloys, and high-entropy alloys (HEAs) when these materials are annealed at high temperatures. Its precipitation is known to be detrimental as it causes embrittlement, degrades creep resistance, fatigue properties, and corrosion resistance. Consequently, it is important to predict how the σ phase forms and how its precipitation and precipitate morphology affect material properties. In this context, we will investigate the σ-phase precipitation kinetics in two model HEAs with very different precipitate morphologies (i.e., globular and plate-like), followed by tensile tests on specimens with well-defined microstructures to determine how these morphologies affect the tensile properties. Typically, the precipitation kinetics of the σ phase is relatively slow. For example, in NiFe-base superalloys, isothermal aging for more than 4 years is required to establish equilibrium states between 600 and 800 °C. Traditionally, precipitation kinetics are investigated in situ from the changes in some physical properties (e.g., resistivity, specific heat capacity, thermal expansion coefficient). However, this cannot be applied to the precipitation kinetics of the σ phase due to its sluggishness. In this project, we will therefore systematically characterize the σ-phase morphology at different times and temperatures using quantitative metallography. Annealed samples will be metallographically prepared and systematically characterized using the backscattered electron signal in scanning electron microscopy. The recorded micrographs will be segmented using a transferable deep-learning workflow with minimal manual segmentation effort. This will result in a quantitative and statistically relevant dataset (e.g., mean size, aspect ratio, number density) of σ particles. To gain a better understanding of the nucleation, growth, soft and hard impingement, and coarsening processes, our experimental results will be systematically compared with simulations based on a Kampmann-Wagner Numerical (KWN) approach. In addition, we will develop a machine learning model based on the KWN solutions to efficiently vary input parameters (diffusivities, interfacial properties, elastic stiffness coefficients, etc.) to accelerate predictions or to infer/optimize input parameters that best match experimental results. All these efforts will then allow us to identify and quantify the governing parameters that affect the σ-phase precipitation kinetics, the morphology of its precipitates and its embrittling effect. Lastly, we expect that our results will be relevant to other widely used structural materials such as austenitic steels and Ni-base superalloys.

• DFG Programme: Research Grants