The effect of solid solution Dy element on Nd diffusivity in (Nd_1−xDy_x)₂Fe₁₄B phase: Insights from density functional theory

The effect of solid solution Dy element on Nd diffusivity in (Nd_1−xDy_x)₂Fe₁₄B phase was investigated using a vacancy mediated self-diffusion coefficient calculation method on the basis of density functional theory. The thermodynamic calculation results revealed that Nd vacancy preferentially formed at 4f position, and the primary diffusion path of Nd atoms in (Nd_1−xDy_x)₂Fe₁₄B phase was 4g→4f. As Dy concentration x increased from 0 to 0.25, Nd diffusion coefficient increased from 9.00 × 10⁻³⁷ to 2.64 × 10⁻²¹ cm²/s. Once the value of x rose to 0.375, Nd diffusivity abruptly decreased to 2.08 × 10⁻⁴² cm²/s and became even smaller than that in Nd₂Fe₁₄B phase. It was found that the Nd atomic volume and diffusion channel size characterized by coordination environment in (Nd_1−xDy_x)₂Fe₁₄B phase synergistically affected Nd diffusivity. The size matching degree between the two factors in the diffusion process, which is represented by the coordination environment distortion degree between initial and transition states, was the underlying physical reason influencing the Nd diffusivity. The largest Nd diffusivity in (Nd_0.75Dy_0.25)₂Fe₁₄B phase was ascribed to the smallest coordination environment distortion degree in the diffusion process. This work deepens the understanding of Nd diffusion mechanism in (Nd_1−xDy_x)₂Fe₁₄B phase and provides significant theoretical guidance for regulating rare earth element diffusion and distribution in magnetic (Nd_1−xDy_x)₂Fe₁₄B grains.