Role of chemical disorder in slowing down diffusion in complex concentrated alloys

The advent of multiprincipal element alloys (MPEAs) has sparked significant interest in physical metallurgy. These alloys, distinguished by their high configurational entropy aimed at minimizing free energy, have raised intriguing questions regarding the interplay of chemical disorder and chemical short-range order (CSRO) in kinetics of MPEAs. Particularly, the widely assumed phenomenon of sluggish diffusion has come under scrutiny. Here we employ atomistic simulations to quantitatively evaluate the impact of CSRO on diffusion in a representative medium-entropy alloy. We introduce a physical order parameter to establish a quantitative correlation between CSRO and diffusivity. Surprisingly, our simulations suggest that CSRO, rather than chemical disorder, serves to suppress and localize defect diffusion. The observed link between diffusion activation energy and CSRO provides a rationale for the observed deceleration in diffusion due to chemical ordering. A linear relationship between diffusion activation energy and activation entropy is unveiled, aligning with the Meyer-Neldel rule, and replicating experimental results. These insights help clarify the intricate role of chemical disorder in plastic deformation of chemically disordered materials.

Figure 1

Emergence of chemical ordering. (a) Order parameter $\phi$ for samples prepared under different Monte Carlo temperature $T_{\mathrm{MC}}$. Insets depict the corresponding atomic configurations. (b) Histograms representing the distribution of the order parameter in various configurational spaces. (c) $\phi$ calculated by considering varying levels of nearest neighbors. (d) Spatial autocorrelation functions of the order parameter. (e) Evolution of the Warren-Cowley parameters as a function of $T_{\mathrm{MC}}$. (f) $\phi$ versus the averaged absolute values of the pairwise Warren-Cowley parameters.

Figure 2

Chemical order suppresses diffusion kinetics. (a) MSD versus time in the same configuration ($\phi =0.455$) at varying temperatures. (b) MSD for different samples (varying $\phi$) at a fixed temperature (1550 K). (c) Residual MSD at $\phi =0.455$ and $T=1350\mathrm{K}$, showing “fast” regions colored in red ($\mathrm{\Delta }\mathrm{MSD}>0$) and “slow” regions ($\mathrm{\Delta }\mathrm{MSD}<0$). $\mathrm{\Delta }$ denotes deviation from linearity. (d) Asymmetric distribution of $\mathrm{\Delta }\mathrm{MSD}$ with $\phi =0.455$ and $T=1350\mathrm{K}$, fitted by the extreme value distribution.

Figure 3

Trajectories of vacancy diffusion for two specific configurations with $\phi =0.455$ (a) and $\phi =0.369$ (b) at 1300 K over a uniform time interval of 1 ns. Trajectories are color coded based on diffusion time. The starting and ending points are marked by blue and red arrows, respectively.

Figure 4

(a) Arrhenius plot illustrating diffusivity for samples with different values of $\phi$, encompassing ordered, partially ordered, and random alloys. (b) Activation energy versus annealing temperature $T_{\mathrm{MC}}$. Inset displays the correlation between activation energy and the degree of CSRO $\phi$.

Figure 5

Correlation between diffusion prefactor $D_0$ and activation energy $\mathrm{\Delta }E$, indicating the existence of the Meyer-Neldel rule in MPEAs.

Figure 6

Convergence of potential energy during the annealing procedure at 400 K (a) and 800 K (b), respectively.