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Register a new userDiffusivity and derivatives for interstitial solutes: Activation energy, volume, and elastodiffusion tensors
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Computational atomic-scale methods continue to provide new information about geometry, energetics, and transition states for interstitial elements in crystalline lattices. This data can be used to determine the diffusivity of interstitials by finding steady-state solutions to the master equation. In addition, atomic-scale computations can provide not just the site energy, but also the stress in the cell due to the introduction of the defect to compute the elastic dipole. We derive a general expression for the fully anistropic diffusivity tensor from site and transition state energies, and three derivatives of the diffusivity: the elastodiffusion tensor (derivative of diffusivity with respect to strain), the activation barrier tensor (logarithmic derivative of diffusivity with respect to inverse temperature) and activation volume tensor (logarithmic derivative of diffusivity with respect to pressure). Computation of these quantities takes advantage of crystalline symmetry, and we provide an open-source implementation of the algorithm. We provide analytic results for octahedral-tetrahedral networks in face-centered cubic, body-centered cubic, and hexagonal closed-packed lattices, and conclude with numerical results for C in Fe.
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The high solubility of oxygen in Ti, Zr and Hf makes it difficult to stabilize the protective oxide scales on their surfaces as the subsurface regions can serve as boundless sinks that continuously dissolve oxygen. Alloying elements are crucial to reduce the oxygen solubility and diffusivity within early transition metals. Past studies have shown that substitutional alloying additions to titanium repel interstitial oxygen. Here we use first-principles calculations to show that this repulsion is short ranged and identify a variety of factors that are likely responsible for the repulsive interaction. We identify a unique hybridization phenomenon between dissolved substitutional elements and interstitial oxygen within hcp Ti that leads to a repulsive interaction at short distances, similar to that between closed-shell atoms. Calculations of Bader charges also suggest the existence of short-range Coulomb interactions due to the accumulation of charge on the substitutional solute and interstitial oxygen that is drawn from the Ti host.
The effect of a dynamo-generated mean magnetic field of Beltrami type on the mean electromotive force is studied. In the absence of the mean magnetic field the turbulence is assumed to be homogeneous and isotropic, but it becomes inhomogeneous and anisotropic with this field. Using the testfield method the dependence of the alpha and turbulent diffusivity tensors on the magnetic Reynolds number Rm is determined for magnetic fields that have reached approximate equipartition with the velocity field. The tensor components are characterized by a pseudoscalar alpha and a scalar turbulent magnetic diffusivity etat. Increasing Rm from 2 to 600 reduces etat by a factor ~5, suggesting that the quenching of etat is, in contrast to the 2-dimensional case, only weakly dependent on Rm. Over the same range of Rm, however, alpha is reduced by a factor ~14, which can qualitatively be explained by a corresponding increase of a magnetic contribution to the alpha effect with opposite sign. The level of fluctuations of alpha and etat is only 10% and 20% of the respective kinematic reference values.
The light elemental solutes B, C, N, and O can penetrate the surface of Mg alloys and diffuse during heat treatment or high temperature application, forming undesirable compounds. We investigate the diffusion of these solutes by determining their stable interstitial sites and the inter-penetrating network formed by these sites. We use density functional theory (DFT) to calculate the site energies, migration barriers, and attempt frequencies for these networks to inform our analytical model for bulk diffusion. Due to the nature of the networks, O diffuses isotropically, while B, C, and N diffuse anisotropically. We compute the elastodiffusion tensor which quantifies changes in diffusivity due to small strains that perturb the diffusion network geometry and the migration barriers. The DFT-computed elastic dipole tensor which quantifies the change in site energies and migration barriers due to small strains is used as an input to determine the elastodiffusion tensor. We employ the elastodiffusion tensor to determine the effect of thermal strains on interstitial diffusion and find that B, C, and N diffusivity increases on crystal expansion, while O diffusivity decreases. From the elastodiffusion and compliance tensors we calculate the activation volume of diffusion and find that it is positive and anisotropic for B, C and N diffusion, whereas it is negative and isotropic for O diffusion.
The adiabatic elastic modulus is often useful in the high frequency response of materials. Unfortunately, it can be much more difficult to directly measure the adiabatic elastic modulus of material than the isothermal elastic modulus. We derive the relationship between the adiabatic and isothermal elastic tensors from the first law of thermodynamics.
Because inorganic solid electrolytes are one of the key components for application to all-solid-state batteries, high-ionic-conductivity materials must be developed. Therefore, we propose a method of efficiently evaluating the activation energy of ionic diffusion by calculating a potential-energy surface (PES), searching for the optimal diffusion path by an algorithm developed using dynamic programming (DP), and calculating the corresponding activation energy by the nudged elastic band (NEB) method. Taking beta-Li3PS4 as an example, the activation energy of Li-ion diffusion was calculated as 0.43, 0.25, and 0.40 eV in the a-, b-, and c-axis directions, respectively, which is in good agreement with previously reported values. By comprehensively searching for the lowest energy path by PES-DP, the arbitrariness of the path selection can be eliminated, and the activation energy must only be calculated using the NEB method a few times, which greatly reduces the computational cost required for evaluating activation energy and enables the high-throughput screening of solid state electrolytes.
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