External magnetic field suppression of carbon diffusion in iron

TL;DR

The paper addresses why external magnetic fields suppress carbon diffusion in BCC iron and develops a first-principles framework to quantify diffusion under field and temperature. It combines spin-space averaging (SSA) with density functional theory (DFT) by sampling magnetic moments from Monte Carlo simulations of a Heisenberg model under field to compute diffusion barriers $Q(B_\text{ext},T)$ and diffusivity using $D(B_\text{ext},T)=\frac{1}{6}a_0^2(T)\nu^*(T)f_C(T)\exp\left(-\frac{Q(B_\text{ext},T)}{k_B T}\right)$. The results reproduce the observed diffusion suppression under a 6 T field near $T_C$ and show that magnetic disorder flattens the LDOS, isotropizes the octahedral cage, and lowers the diffusion barrier, with field increasing order and raising the barrier. This work provides a mechanistic link between magnetic ordering and diffusion and a general approach applicable to diffusion under magnetic fields in other materials.

Abstract

External magnetic fields reduce diffusion of carbon in BCC iron, but the physical mechanism is not understood. Using DFT calculations with magnetic moments sampled from a Heisenberg model, we calculate diffusivities of carbon in iron at high temperatures and with field. Our model reproduces the measured suppression of diffusivity from field. We find that increasing magnetic disorder flattens the electron density of states compared with the ferromagnetic case, which distorts the octahedral cages around carbon, lowering the activation barrier to diffusion; an applied field reverses these trends.

Figures (5)

• Figure 1: Net magnetization in BCC Fe with temperature and field in experiment and with a parameterized Heisenberg model. Dashed lines are experimentally observed values in the zero-field Potter1934 and externally applied field Crangle1971, with solid lines for the model.
• Figure 2: Magnetic environments from Heisenberg model sampling in a BCC Fe$_{54}$C supercell at the Curie temperature of 1043 K in the zero-field case (left) and with an externally applied 6 T magnetic field (right). All 25 sets of moments sampled for DFT calculations are visualized simultaneously, with moments color-coded according to their component parallel to the field direction. Histograms below each plot show the distributions of component magnitudes after DFT relaxation.
• Figure 3: Diffusivity of carbon in BCC Fe at conditions of interest as modeled by spin-space averaged (SSA) calculations. The SSA models closely agree with experimental observations made by Fujii and Tsurekawa Fujii2011, and are notably more accurate than predictions that can be obtained by simple ferromagnetic (FM) or disordered local moment (DLM) models, or Ruch model interpolations between the two.
• Figure 4: Effect of magnetic ordering on Fe–C nearest-neighbor (NN) and second-nearest-neighbor (2NN) interatomic distances when carbon sits at $\langle$100$\rangle$ octahedral sites and tetrahedral transition states (TS). Geometric insets illustrate carbon and its NNs and 2NNs for each configuration. The shaded region in each panel indicates the octahedral or tetrahedral cage, while the black lines outline the octahedral cage in both panels.
• Figure 5: Density of states plots for the nearest (NN) and second nearest (2NN) iron neighbors of carbon in the octahedral and tetrahedral configurations, with comparison made to bulk iron. Magnetic disorder increases counterclockwise from the upper-left ferromagnetic (FM) panel, with the disordered local moment (DLM) configuration having randomly oriented moments.