Elastic Dipole Tensor Research Articles

Capture efficiencies of point defects by 1/2 〈111〉 edge dislocations in tungsten using atomistic simulations

We systematically study the interaction behaviors between a point defect (PD) and two types of 1/2 〈111〉 {110} and 1/2 〈111〉 {112} edge dislocations using molecular dynamics (MD), elastic dipole tensor, and kinetic Monte Carlo (KMC) methods in tungsten (W). We first determine the capture region of a vacancy and four types of self-interstitial atoms (SIAs) by calculating their binding energies to both edge dislocations using MD. We then find anisotropic distributions of the diffusion energy barriers of PDs in dislocation systems employing the MD and elastic dipole tensor methods. Subsequently, we utilize the KMC method to obtain the lifetime of PDs and calculate the capture efficiencies of both edge dislocations to PDs at various temperatures and dislocation densities. Results show the capture efficiency of a vacancy decreases with increasing temperature, while it first increases and then decreases with increasing temperature for SIAs. As dislocation density increases, the capture efficiency of PDs increases. Ultimately, the swelling rate is estimated based on the capture efficiency and falls within the range of experimental data. The swelling rate increases first and then decreases with increasing temperature, and the maximum swelling rate occurs around 1200 K, while it increases with increasing the dislocation density. The present results are critical for understanding the interaction behaviors between PDs and 1/2 〈111〉 edge dislocations in W, which provide an essential database for large-scale simulation methods such as rate theory and phase-field simulations.

Numerical investigation of dislocation climb under stress and irradiation

We investigate the influence of elastic properties of point defects on dislocation climb under stress and irradiation. For this purpose, elastic dipole tensors and diaelastic polarizabilities are evaluated in aluminum for vacancies and self-interstitial atoms in their stable and saddle configurations, using density functional theory calculations. These parameters are introduced in an object kinetic Monte-Carlo code and a continuous diffusion model to estimate the stress dependence of dislocation climb, using a dipole of straight dislocations. We show that both parameters have an influence on absorption of point defects under stress, in agreement with previous analytical models. However, the effect of dipole tensor is found only 5 times larger than polarizability, whereas models predict a factor up to 30. In addition, including polarizability reverses the stress angular dependence when a uniaxial stress is applied orthogonal to the dislocation line, so in general polarizability cannot be ignored for simulations under applied stress. Further comparison with analytical models shows that they give a good description of angular dependence, provided saddle point configuration of point defects is not too anisotropic. For vacancies, which are strongly anisotropic in their saddle configuration, models fail to reproduce quantitatively lattice effects on stress angular dependence observed in simulations. Calculations show that dislocation climb velocity under irradiation is expected to be the highest if the stress is approximately orthogonal to the dislocation line, especially along the Burgers vector, and the lowest if the stress is applied close to the 〈100〉 direction with the largest projection on the dislocation line.

Hydrogen-induced volume changes, dipole tensor, and elastic hydrogen-hydrogen interaction in a metallic glass

Hydrogen and its isotopes, absorbed in metals, induce local stress on the atomic structure, which generates a global expansion in proportion to the concentration of hydrogen. The dipole force tensor and its interaction with the stress fields give rise to an effective attractive nonlocal potential between hydrogen atoms---the elastic hydrogen-hydrogen interaction---which is a key quantity governing the phase transitions of hydrogen in metals. While the dipole tensor and the elastic interaction have been researched in crystalline materials, they remain experimentally unexplored in metallic glasses and it is unclear how these quantities are affected by the lack of point group symmetries. Here, we investigate both experimentally and theoretically the volume changes, the components of the force dipole tensor, and ultimately the elastic hydrogen-hydrogen interaction in the metallic glass ${\mathrm{V}}_{80}{\mathrm{Zr}}_{20}$. In situ neutron reflectometry was used to determine the deuterium-induced volume changes as a function of deuterium concentration. The one-dimensional volume expansion is found to change by more than 14% without any structural degradation, up to concentrations of one deuterium atom per metal atom. From the expansion, we determine that the out-of-plane component of the elastic dipole tensor is remarkably similar to a composition weighted sum of the ones found in crystalline vanadium and zirconium. Via ab initio calculations of both free and biaxially constrained expanded metallic structures, we determine that the trace of the dipole tensor varies with hydrogen concentration and is essentially invariant of global elastic boundary conditions. As a consequence, the elastic hydrogen-hydrogen interaction energy is found to be concentration-dependent as well, illustrating that the disordered nature of a metallic glass does not impede the mediation of the elastic attraction, but rather allows it to vary with hydrogen content.

Shear strain alters the structure and migration mechanism of self-interstitial atoms in copper

We use atomistic modeling to show that externally applied shear strain causes the lowest energy self-interstitial atom (SIA) structure in copper (Cu) to change from a ⟨100⟩-type dumbbell to a ⟨110⟩-type dumbbell. Concurrently, SIA migration switches from the three-dimensional (3D) random walk characteristic of ⟨100⟩-type dumbbells to a 1D mechanism analogous to that of crowdion SIAs. Furthermore, the relative energies of these two dumbbell structures as a function of strain are well predicted using elastic dipole tensors computed at zero strain, indicating that examination of these tensors may be used to assess the likelihood of strain-induced SIA structure transitions in other materials. Changes in lowest energy SIA structures and associated migration mechanisms stand to impact predictions of SIA behavior in irradiated solids.

Signatures of the effects of defects on the bulk moduli of crystalline solids

The small atomic region containing a defect in a crystalline solid is nonlinear elastic. In this paper, we consider a solid containing defects as a composite wherein the defected regions have a bulk modulus, K, different from that of the perfect crystal. If the volume fraction of the defected regions is sufficiently small, a rule of mixtures should apply so that K of the composite depends linearly on the volume fraction of the defected region. We identify the slope of that linear dependence as the signature, denoted S. We further show that S is related to a property of the linear elastic fields of point defects described by elastic dipole tensors, Pij. To first order, the Pij of such defects depend linearly on external strain and the strength of that dependence is the diaelastic polarizability tensor,α. We show that S is simply related to α. Atomistic models of EAM Ni were used to compute K versus reciprocal volume for several kinds of defects, namely single, di-, and tri-vacancies and interstitials, dislocations, and grain boundaries. The results show 1) when the volume fraction of the defected region is small, a rule of mixtures applies, and 2) S has a distinct value for each defect and is negative for vacancies but positive for the other defects. Thus, S depends on the effective modulus of the nonlinear region and its size. The effective bulk modulus of a spherical ball-in-hole composite model derived in the Appendix predicts that the variation of K with volume fraction is very nearly linear. The magnitudes of S, although quite small, are discussed as a potential means of monitoring defect changes in their concentration via sensitive experimental measurements of the bulk modulus.

Elastic dipole tensor of a defect at a finite temperature: Definition and properties

The concept of the elastic dipole tensor of a defect is generalized to enable the treatment of lattice distortions produced by defects at elevated temperatures. Thermodynamic and statistical mechanics treatments show the feasibility of applying the formalism to the evaluation of formation free energies and finite-temperature elastic dipole tensors of $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ prismatic self-interstitial atom dislocation loops. The method exhibits good numerical stability even in the high-temperature limit, and relates discrete atomic and continuum representations of displacement and stress and strain fields of defects.

Elastic dipole tensors and relaxation volumes of point defects in concentrated random magnetic Fe-Cr alloys

Point defects in body-centred cubic Fe, Cr and concentrated random magnetic Fe-Cr are investigated using density functional theory and theory of elasticity. The volume of a substitutional Cr atom in ferromagnetic bcc Fe is approximately 18% larger than the volume of a host Fe atom, whereas the volume of a substitutional Fe atom in antiferromagnetic bcc Cr is 5% smaller than the volume of a host Cr atom. In an alloy, elastic dipole P and relaxation volume Ω tensors of vacancies and self-interstitial atom (SIA) defects exhibit large fluctuations, with vacancies having negative and SIA large positive relaxation volumes. Dipole tensors of vacancies are nearly isotropic across the entire alloy composition range, with diagonal elements Pii decreasing as a function of Cr content. Fe-Fe and Fe-Cr SIA dumbbells are more anisotropic than Cr-Cr dumbbells. We find that fluctuations of elastic dipole tensors of SIA defects are primarily associated with the variable crystallographic orientations of the dumbbells. Statistical properties of tensors P and Ω are analysed using their principal invariants, suggesting that point defects differ significantly in alloys containing below and above 10% at. Cr. The von Mises stresses caused by dumbbells are notably larger than those caused by vacancies. The relaxation volume of a vacancy depends sensitively on whether it occupies a Fe or a Cr lattice site. A correlation between elastic relaxation volumes and magnetic moments of defects found in this study suggests that magnetism is a significant factor influencing elastic fields of defects in Fe-Cr alloys.

Dynamic model for an ensemble of interacting irradiation-induced defects in a macroscopic sample

We develop a dynamic model for the evolution of an ensemble of hundreds of interacting irradiation-induced mobile nanoscale defects in a micrometre size sample. The model uses a Langevin defect dynamics approach coupled to a finite element model, treated using the superposition method. The elastic field of each defect is described by its elastic dipole tensor, and the long-range interaction between defects is treated using the elastic Green’s function formalism. The approach circumvents the need to evaluate the elastic energy by means of volume integration, and provides a simple expression for the energy of elastic image interaction between the migrating defects and surfaces of the sample. We discuss the underlying theory, and also the parallelization and coarse-graining numerical algorithms that help speed up simulations. The model addresses the issue of imbalanced forces and moments arising as an artefact of the modified boundary problem associated with the traction free boundary condition. To illustrate applications of the method, we explore the dynamic evolution of an ensemble of interacting dislocation loops of various size and with different Burgers vectors, which proves the feasibility of performing large-scale simulations using the proposed model.

A fast efficient multi-scale approach to modelling the development of hydride microstructures in zirconium alloys

A mechanistic understanding of hydrogen diffusion and hydride precipitation at the microscale underpins the prediction of delayed hydride cracking in zirconium alloy nuclear fuel cladding. We present a novel approach to modelling the microstructures created by hydride precipitation at loaded notches in polycrystalline Zr alloys. The model is multi-scale in that it includes the elastic dipole tensor of interstitial hydrogen in α-Zr, it treats the stress-driven diffusion of hydrogen at the meso-level (mm), it calculates the thermodynamically favourable spatial arrangement of microhydrides and their assembly into macrohydride colonies, in a textured polycrystalline sample, and it treats the full elastic field of the loaded notch and all the hydrides at a scale similar to the cladding thickness. A simplifying innovation is the representation of the elastic field of a microhydride by a dislocation dipole, where the Burgers vector is set to create the experimentally measured strain in the 〈11¯00〉 direction. The model provides a predictive framework for treating elastic anisotropy, a variety of potential nucleation sites, and different grain sizes. Simulated micrographs of hydride networks in polycrystalline samples with blunt and sharper loaded notches are compared with experimental micrographs obtained at the same scale. The simulations are extremely fast and calculations typically take around tens of seconds. This makes it possible to carry out detailed sensitivity studies with respect to several pertinent metallurgical variables, as well as conducting ensemble averaging of hydride microstructures.

Nonuniversal structure of point defects in face-centered cubic metals

Using ab initio density function theory calculations, we have determined the structure of self-interstitial atom (SIA) defects in the most commonly occurring face-centered cubic (FCC) metals. The most stable SIA defects in Al, Ca, Ni, Cu, Pd, and Ag are the $\ensuremath{\langle}100\ensuremath{\rangle}$ dumbbells whereas octahedral SIA configurations have the lowest energy in Pt, Rh, and Th. The relative stability of defect configurations in Sr, Ir, Au, and Pb is less well defined, and calculations suggest that an SIA defect has the $\ensuremath{\langle}100\ensuremath{\rangle}$ dumbbell structure in Sr and Ir, a $\ensuremath{\langle}110\ensuremath{\rangle}$ crowdion/dumbbell structure in Au, and that it adopts an octahedral configuration in Pb. The occurrence of octahedral and $\ensuremath{\langle}110\ensuremath{\rangle}$ crowdion/dumbbell SIA configurations implies that defects diffuse one-dimensionally. This is fundamentally different from the three-dimensional translation-rotation migration characterizing the mobility of a $\ensuremath{\langle}100\ensuremath{\rangle}$ dumbbell. Elastic fields of point defects are defined by their elastic dipole tensors, which we compute for all the defect configurations. The magnetism of a $\ensuremath{\langle}100\ensuremath{\rangle}$ dumbbell in ferromagnetic nickel appears to have little effect on the structure of the defect. The variation of energy and elastic field of an SIA defect in copper is explored in detail as a function of its structural transformation along the migration pathway.

Multiscale analysis of dislocation loops and voids in tungsten

We performed ab initio density functional theory simulations of $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ interstitial dislocation loops, closed and open vacancy loops, $\ensuremath{\langle}100\ensuremath{\rangle}$ interstitial loops, and voids in tungsten, using simulation cells involving from 2000 to 2700 atoms. The size of the loops transcends the microscopic scale and reaches the mesoscopic scale where asymptotic elasticity treatment applies. Comparing the formation energies of dislocation vacancy loops and voids, we conclude that a void remains the most energetically favorable vacancy defect over the entire range of sizes investigated here. A closed $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ vacancy loop is more stable than an open loop if the number of vacancies in the loop is greater than $\ensuremath{\sim}45$, corresponding to the diameter of a loop of approximately 1.8 nm. We have also computed elastic dipole tensors and relaxation volumes of loops and voids, representing the source terms in continuum models for radiation induced stresses and strains in the material. A detailed analysis of metastable configurations of closed and open vacancy loops performed using molecular statics simulations shows that vacancy loop configurations are not unique, and significant fluctuations of defect structures may occur in the course of microstructural evolution under irradiation.

CALANIE: Anisotropic elastic correction to the total energy, to mitigate the effect of periodic boundary conditions

CALANIE (CALculation of ANIsotropic Elastic energy) computer program evaluates the elastic interaction correction to the total energy of a localized object, for example a defect in a material simulated using an ab initio or molecular statics approach, resulting from the use of periodic boundary conditions. The correction, computed using a fully elastically anisotropic Green’s function formalism, arises from the elastic interaction between a defect and its own periodically translated images. The long-range field of elastic displacements produced by the defect is described in the elastic dipole approximation. Applications of the method are illustrated by two case studies, one involving an ab initio investigation of point defects and vacancy migration in FCC gold, and another a molecular statics simulation of a dislocation loop. We explore the convergence of the method as a function of the simulation cell size, and note the significance of taking into account the elastic correction in the limit where the size of the defect is comparable with the size of the simulation cell. Program summaryProgram Title: CALANIE, version 2.0Program Files doi:http://dx.doi.org/10.17632/3h6xffk9h6.1Licensing provisions: Apache License, Version 2.0Programming language: C/C++Nature of problem: Periodic boundary conditions (PBCs) are often used in the context of ab initio and molecular statics atomic scale simulations. A localized defect in a crystalline material, simulated using PBCs, interacts elastically with its own periodically translated images, and this gives rise to a systematic error in the computed defect formation and migration energies. Evaluating the correction to the total energy resulting from effects of elastic interaction between a defect and its periodic images, to alleviate the contribution to the total energy arising from PBCs, is an essential aspect of any accurate total energy calculation performed using PBCs.Solution method: The energy of interaction between a localized defect and its periodically translated images is computed in the linear elasticity approximation. The energy of elastic interaction is expressed analytically in terms of the elastic dipole tensor of the defect and elastic Green’s function. Elements of the dipole tensor are computed as a part of the simulation evaluating the formation energy of the defect. Elastic Green’s function and its first and second derivatives are computed numerically from the elastic constants of the material. The method and the corresponding numerical procedures are implemented in the CALANIE computer program. The program evaluates matrix elements of the elastic dipole tensor of a localized defect and the elastic correction to the total energy arising from the use of periodic boundary conditions.Restrictions: The approach assumes the validity of the linear elasticity approximation. This limits the accuracy of evaluation of the elastic correction, which becomes less precise if the size of the defect is comparable with the size of the simulation cell.Unusual features: An open source code, containing full detail of the relevant theoretical concepts, algorithms and numerical implementation.

Relaxation volumes of microscopic and mesoscopic irradiation-induced defects in tungsten

The low-energy structures of irradiation-induced defects in materials have been studied extensively over several decades, as these determine the available modes by which a defect can diffuse or relax, and how the microstructure of an irradiated material evolves as a function of temperature and time. Consequently, many studies concern the relative energies of possible defect structures, and empirical potentials are commonly fitted to or evaluated with respect to these. But recently [S. L. Dudarev et al., Nucl. Fusion 58, 126002 (2018)], we have shown that other parameters of defects not directly related to defect energies, namely, their elastic dipole tensors and relaxation volumes, determine the stresses, strains, and swelling of reactor components under irradiation. These elastic properties of defects have received comparatively little attention. In this study, we compute relaxation volumes of irradiation-induced defects in tungsten using empirical potentials and compare to density functional theory results. Different empirical potentials give different results, but some clear potential-independent trends can be identified. We show that the relaxation volume of a small defect cluster can be predicted to within 10% from its point-defect count. For larger defect clusters, we provide empirical fits as a function of defect cluster size. We demonstrate that the relaxation volume associated with a single primary-damage cascade can be estimated from the primary knock-on atom energy. We conclude that while annihilation of defects invariably reduces the total relaxation volume of the cascade debris, there is still no conclusive verdict about whether coalescence of defects reduces or increases the total relaxation volume.

Effect of stress on vacancy formation and migration in body-centered-cubic metals

Vacancy formation and migration control self-diffusion in pure crystalline materials, whereas irradiation produces high concentrations of vacancy and self-interstitial atom defects, exceeding by many orders of magnitude the thermal equilibrium concentrations. The defects themselves, and the extended dislocation microstructure formed under irradiation, generate strongly spatially fluctuating strain and stress fields. These fields alter the local formation and migration enthalpies of defects, and give rise to the anisotropy of diffusion even if in the absence of stress the diffusion tensor is isotropic. We have performed ab initio calculations of formation and migration energies of vacancies in all the commonly occurring body-centered-cubic (bcc) metals, including alkaline, alkaline-earth and transition metals, and computed elastic dipole and relaxation volume tensors of vacancies at the equilibrium lattice positions and along the vacancy migration pathways. We find that in all the bcc metals the dipole tensor of a migrating vacancy at a saddle point exhibits an anticrowdion character. Applied external stresses or the local stresses generated by dislocations may enhance or suppress anisotropic diffusion by altering the energy barriers with respect to the direction of migration of a defect.

Universality of point defect structure in body-centered cubic metals

Density functional theory calculations show that the lowest energy structure of a self-interstitial atom defect is universal to all the nonmagnetic bcc metals. The defects adopt linear configurations with the orientation of their axes. The formation and migration energies, elastic dipole tensors, and relaxation volumes of all the point defects in all the bcc metals are tabulated in a form suitable for macroscopic simulations, for example, for predicting radiation-induced swelling. The authors also show how elastic relaxation parameters vary along the defect migration pathways.

(Invited) Computing the Anisotropic Chemical Strain in Non-Stoichiometric Oxides for Solid Oxide Fuel Cell and Li-Ion Battery Applications

Accurate characterization of chemical strain is required to study a broad range of chemical-mechanical coupling phenomena. By combining density functional theory (DFT) calculations and elastic dipole tensor theory, it is readily to predict the long-range chemical strain tensor and the chemical expansion coefficient tensor induced by dilute point defects in a crystal structure. First, we demonstrate that, even in cubic CeO2-δ, both the short-range deformation surrounding an oxygen vacancy and the long-range chemical strain (or the expansion coefficient) are anisotropic. The origin of this anisotropy is the charge disproportionation between the four cerium atoms surrounding each oxygen vacancy (two become Ce3+ and two become Ce4+) when a neutral oxygen vacancy is formed. While the short-range deformation agrees with experimentally determined Ce-O bond lengths, the predicted maximum and average chemical strains successfully bound the variety of CeO2-δ chemical strain behavior previously reported in the literature. Normally, since there are six possible disproportionation configurations, the average chemical strain is isotropic. Only under an external bias, such as an applied electric field, the chemical strain can be oriented to show the anisotropic effect. This successfully explained the giant electrostriction effect reported in doped and un-doped CeO2-δ. Next, we show strains induced by coupled vacancies in layered Li-intercalation compounds for battery applications. Li2MnO3 was investigated as Li-excess intercalation compounds containing Li2MnO3 need to be “activated” to deliver the high capacity. This activation process during the first delithiation cycle at a high voltage is believed to introduce oxygen vacancies into the system. Due to the large amount Li vacancy generated, a large number of defect configurations were sampled and the average chemical strain induced by Li vacancy concentration is obtained by Boltzmann average. Previously, we have demonstrated that it is energetically favorable to create a Li-O-Li vacancy dumbbell structure (VLi - VO - VLi) in Li2MnO3. The chemical strain of the vacancy dumbbell structure is smaller than the sum of the chemical strain of one Vo and two VLis. The chemical expansion coefficient averaged for the polycrystalline samples and the experimentally measured stress change provided a novel method to in situ track the irreversible chemical changes in Li-excess cathode materials.

Elastic fields, dipole tensors, and interaction between self-interstitial atom defects in bcc transition metals

Density functional theory (DFT) calculations show that self-interstitial atom (SIA) defects in nonmagnetic body-centered-cubic (bcc) metals adopt strongly anisotropic configurations, elongated in the $\ensuremath{\langle}111\ensuremath{\rangle}$ direction [S. Han et al., Phys. Rev. B 66, 220101 (2002); D. Nguyen-Manh et al., Phys. Rev. B 73, 020101 (2006); P. M. Derlet et al., Phys. Rev. B 76, 054107 (2007); S. L. Dudarev, Annu. Rev. Mater. Res. 43, 35 (2013)]. Elastic distortions, associated with such anisotropic atomic structures, appear similar to distortions around small prismatic dislocation loops, although the extent of this similarity has never been quantified. We derive analytical formulas for the dipole tensors of SIA defects, which show that, in addition to the prismatic dislocation looplike character, the elastic field of a SIA defect also has a significant isotropic dilatation component. Using empirical potentials and DFT calculations, we parametrize dipole tensors of $\ensuremath{\langle}111\ensuremath{\rangle}$ defects for all the nonmagnetic bcc transition metals. This enables a quantitative evaluation of the energy of elastic interaction between the defects, which also shows that in a periodic three-dimensional simple cubic arrangement of crowdions, long-range elastic interactions between a defect and all its images favor a $\ensuremath{\langle}111\ensuremath{\rangle}$ orientation of the defect.

Influence of elastic strain on the thermodynamics and kinetics of lithium vacancy in bulkLiCoO2

The influence of elastic strain on the lithium vacancy formation and migration in bulk LiCoO2 is evaluated by means of first-principles calculations within density functional theory (DFT). Strain dependent energies are determined directly from defective cells and also within linear elasticity theory from the elastic dipole tensor (Gij) for ground state and saddle point configurations. We analyze finite size-effects in the calculation of Gij, compare the predictions of the linear elastic model with those obtained from direct calculations of defective cells under strain and discuss the differences. Based on our data, we calculate the variations in vacancy concentration and mobility due to the presence of external strain in bulk LiCoO2 cathodes. Our results reveal that elastic in-plane and out-of-plane strains can significantly change the ionic conductivity of bulk LiCoO2 by an order of magnitude and thus strongly affect the performance of Li-secondary batteries.

First-principles calculation of the elastic dipole tensor of a point defect: Application to hydrogen inα-zirconium

The elastic dipole tensor is a fundamental quantity relating the elastic field and atomic structure of a point defect. We review three methods in the literature to calculate the dipole tensor and apply them to hydrogen in $\ensuremath{\alpha}$-zirconium using density functional theory (DFT). The results are compared with the dipole tensor deduced from earlier experimental measurements of the $\ensuremath{\lambda}$ tensor for hydrogen in $\ensuremath{\alpha}$-zirconium. There are significant errors with all three methods. We show that calculation of the $\ensuremath{\lambda}$ tensor, in combination with experimentally measured elastic constants and lattice parameters, yields dipole tensor components that differ from experimental values by only 10%--20%. There is evidence to suggest that current state-of-the-art DFT calculations underestimate bonding between hydrogen and $\ensuremath{\alpha}$-zirconium.

Light-element diffusion in Mg using first-principles calculations: Anisotropy and elastodiffusion

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.