Machine Learning Kinetic Monte Carlo Simulation for Point Defect Diffusion in Concentrated Solid Solution Alloys

Abstract

Concentrated solid solution alloys (CSAs), including high-entropy alloys (HEAs), have been attracting considerable interest in recent years because of their desirable properties, such as outstanding mechanical properties at both low and high temperatures, exceptional corrosion resistance, and enhanced radiation tolerance. These attractive properties are directly related to atomic transport and defect diffusion behaviors, such as sluggish diffusion, percolation, and chemically biased diffusion. In addition, the effects of short-range order (SRO) also have been reported to be crucial in influencing the above excellent properties in CSAs. However, understanding the controlling mechanism of diffusion behavior under these factors in CSAs poses significant challenges for available theoretical methodologies.

Firstly, the macroscopic atomic transport is mainly influenced by the highly rugged potential energy landscape (PEL) that is hugely time-consuming for state-of-the-art simulation methods, such as molecular dynamics (MD) simulations and transition rate-based kinetic Monte Carlo (kMC). The diffusing objects in MD may get trapped frequently under such complex PEL and lead to a requirement of exceedingly long simulation time for thoroughly sampling the trajectory to collect statistically meaningful results. Besides, the bottleneck in the transition rate-based kMC is how to incorporate the information of the versatile PEL into the calculations of transition rates, which also requires a vast computation cost in kMC modeling. This is because the commonly-used nudged elastic band (NEB) method for determining the complicated PEL at each kMC step requires huge computation costs. Thus, it is urgently needed to develop efficient simulation and theoretical methods to understand how the varying factors (i.e., PEL or concentrations) influence diffusion behavior.

Secondly, sluggish diffusion is one of the most desirable features in CSAs, because it would give the material a much longer service time before it becomes unstable or other undesired microstructure degradation occurs. However, this phenomenon has been poorly understood until now, and many experimental and simulation studies have even shown contradictory opinions about its existence. One of the essential claims of this phenomenon is that the percolation effect plays a crucial role, but how percolation may trigger sluggish diffusion in CSAs is unclear.

Thirdly, SRO is another factor that has a great influence on suppressing diffusion in CSAs. However, the development of SRO is usually tangled with structural evolution associated with diffusion-induced atomic transport, making it challenging to accurately determine the diffusion coefficients in CSAs based on conventional modeling techniques. Thus, it is still not fully understood how SRO leads to the diffusion behavior above.

Fourthly, most of the diffusion studies are focused on vacancy-mediated cases, but interstitial-mediated diffusion also plays an essential role in the phase stability and irradiation response of materials under non-equilibrium conditions in CSAs. The mechanistic understanding of diffusion behavior like sluggish and chemically-biased diffusion is still insufficient for interstitial-mediated diffusion. Besides, how to adjust the controlling factors (such as concentration or energy barriers) is another urgent issue for obtaining the desirable interstitial diffusion properties in CSAs.

In order to solve the first issues above, the Machine Learning (ML) model is developed as an efficiently on-the-fly energy barrier calculator to replace the time-consuming NEB calculation in kMC. With the help of the accelerated ML-kMC, the results suggest that self-diffusion in CSAs is predominantly governed by the PEL roughness, as characterized by the elemental-specific site energies and migration barriers. Comparisons with previously-proposed simplified models for self-diffusion in HEAs elucidate that the models based on species-averaged migration barriers may be a suitable alternative method to rapidly assess diffusion properties, though the correlation effects may be underestimated. Aided by theoretical analysis, we show that the atomic concentrations of fast-diffusing elements and the differences in the averaged migration barriers for different species are the dominant factors influencing sluggish diffusion in HEAs. Besides, as the theoretical analysis method proposed previously was limited to the binary system, we further developed a more general species-resolved analytical diffusion model that can capture essential features of self-diffusion in arbitrary alloy composition and temperature. The model results are validated through ML-kMC. The agreement between our model and ML-kMC simulations unveils that sluggish diffusion depends on the PEL and alloy composition that define the jump probability and correlation effects for each constitutive element. Furthermore, the theoretical analysis suggests that the mean energy barrier of each species, rather than the energy distribution width, has a more significant impact on diffusion.

As for the second issue, the percolation effect on diffusion is investigated. The results indicate that percolation does not always lead to sluggish diffusion. Instead, the diffusion properties are exclusively governed by the PEL that the diffusing object experiences. By comparing the reduced systems of CoNi and FeNi, the results show that the percolation effect on triggering the sluggish diffusion depends on the diffusion properties of the slow-diffuser in these systems. These results shed light on understanding the complex diffusion behaviors in CSAs, highlighting the importance of manipulating species-dependent PEL for tailoring their diffusion properties.

In terms of the third issue, the diffusion influence of SRO in CSAs is explored. The development of SRO is usually tangled with structural evolution associated with diffusion-induced atomic transport. In this study, ML-kMC is utilized to compute the self-diffusion coefficients in NiCoCr and NiFeCr CSAs with distinct SRO tendencies under long-time structural evolution. The results show that the long-term diffusion process governed by thermodynamic and kinetic factors can promote SRO formation due to chemically biased exchange between vacancy and specific components in the alloy. The results further demonstrate that accurate diffusion coefficients in CSAs can only be obtained through long-term simulations allowing for sufficient structural evolution. This study underlines the shortcomings of the presently widely employed techniques to study diffusion in CSAs and highlights the intricate coupling between SRO and diffusion.

For the last issue above, the atomic transport mediated by interstitial diffusion is studied by ML-kMC in CSAs. By comprehensively analyzing the critical diffusion controlling factors, including the tracer correlation factor and jump frequency, the results demonstrate that interstitial diffusion can be effectively regulated by tailoring the competition of these two factors. As a result, sluggish interstitial diffusion can be induced by suitable combinations of the tracer correlation factor and jump frequency depending on the concentration-dependent energy landscapes. Besides, the results further suggest that the information on formation energy differences among different interstitial dumbbells is inherently carried by the ML-learned energy barriers, leading to chemically-biased diffusion. Therefore, the transition preference for various interstitial dumbbells is the dominant factor for understanding interstitial diffusion. We finally propose a simplified kMC model based on the species-resolved mean energy barriers to efficiently and conveniently assess interstitial diffusion in CSAs. An inverse design strategy is then put forward using the model, which allows for exploring the conditions and mechanisms for maximizing the sluggish diffusion effects in CSAs.

This work developed efficient ML-kMC methods for the vacancy- and interstitial-mediated diffusion simulation, which can be applied to explore other diffusion properties in CSAs. In addition, the proposed theoretical species-resolved analytical diffusion model can capture essential features of self-diffusion in arbitrary alloy compositions and temperatures, which can be applied as an efficient and accurate method to determine the diffusion properties in CSAs. Finally, the revealing mechanism of percolation and SRO can be used to understand the sluggish diffusion and other diffusion behavior in other CSAs.

Date of Award	19 Jun 2023
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Shijun ZHAO (Supervisor) & Yong YANG (Co-supervisor)