Nickel-based alloys are widely used in harsh environments due to their excellent high-temperature properties, including yield strength, oxidation and corrosion resistance, and fatigue and creep properties. However, surface oxidation and corrosion are common causes of material degradation in harsh environments. The oxygen (O) diffusion process plays a crucial role in oxidation, oxide scale growth, environmental embrittlement, stress corrosion cracking, oxide formation, and changes in mechanical properties, making it essential to study. Despite its importance, the available data on oxygen diffusion in Ni-based alloys in the literature is limited due to experimental and theoretical challenges. Experimental measurements face challenges such as high temperatures, high pressures, and/or long equilibrium times, while theoretical predictions mainly focus on oxygen diffusion in face-centered cubic (fcc) nickel.
Methods
This study employs density functional theory (DFT)-based transition state theory, combined with a vacancy (Va) modified mechanism, to investigate O diffusion in Ni-based alloy Ni30VaXO, where X represents 22 alloying elements. The diffusion jump rates are predicted by DFT-based phonon calculations and the quasiharmonic approach (QHA). Additionally, machine learning (ML) based correlation analysis is conducted to understand the prediction results. Specific methods include:
DFT calculations: DFT calculations are performed using the VASP code, employing the PBEsol exchange-correlation functional and the quasiharmonic approximation (QHA) to calculate the Gibbs free energy of oxygen diffusion.
Transition state theory: The climbing image nudged elastic band (CINEB) method is used to calculate the transition state and minimum energy pathway.
Phonon calculations: Phonon calculations are carried out using the Yphon code to predict phonon density of states (pDOS) and force constants, which are used to evaluate the diffusion jump rate and examine phase stability.
Correlation analysis: Correlation analysis is performed using MATLAB, including linear fitting, sequential feature selection (SFS), and Shapley value, to identify the relationship between oxygen diffusivity and the electronic structure of alloying element X.
Findings
Effects of alloying elements: The study found that reactive elements (e.g., Y, Hf, Al, and Cr) that easily form oxides increase the O diffusivity, while noble Pt-group elements (e.g., Pt, Pd, Ir, and Rh) that are difficult to oxidize decrease the O diffusivity in Ni-based alloys. This indicates that the bonding strength between X and O, determinable by Ellingham diagram, plays a critical role in affecting O diffusion in Ni.
Correlation with electronic structures: Correlation analysis using linear fitting, sequential feature selection, and Shapley value indicates that the O diffusivity in Ni30VaXO is closely related to the electronic structures of alloying element X, such as work function, electronegativity, and valence electrons.
Outliers: The identified outliers by correlation analysis are mainly alloying elements Y and Mn, which are correlated with O diffusion in Ni30VaXO.
Fig. 2. Predicted diffusion coefficients of oxygen in Ni30VaXO for 22 alloying elements X's with their activation energies increasing from 0.67 eV for Y to 2.18 eV for Pt.
This study systematically investigated the vacancy-modified oxygen diffusion mechanism in Ni-based alloys through DFT calculations and machine learning analysis. It revealed the influence of alloying elements on oxygen diffusivity and discovered a close correlation between oxygen diffusivity and the electronic structure of alloying elements. These findings provide a crucial theoretical basis for understanding and predicting oxygen diffusion behavior in Ni-based alloys, and offer guidance for designing Ni-based alloys with improved oxidation and hot corrosion resistance.
Fig. 3. Correlation analyses using linear fits to examine O diffusion in Ni30VaXO: (a) activation energy Q vs. work function (WorkFunc) of alloying element X and (b) pre-factor log10(𝐷0) vs. electronegativity (EleNeg).
