Dislocation core energies and magnetic exchange interactions from first-principles energy density method

Dan, Yang

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https://hdl.handle.net/2142/127385 Copy

Description

Title

Dislocation core energies and magnetic exchange interactions from first-principles energy density method

Author(s)

Dan, Yang

Issue Date

2024-12-05

Director of Research (if dissertation) or Advisor (if thesis)

Trinkle, Dallas R.

Doctoral Committee Chair(s)

Trinkle, Dallas R.

Committee Member(s)

• Schleife, André
• Bellon, Pascal
• Ertekin, Elif

Department of Study

Materials Science & Engineerng

Discipline

Materials Science & Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• density functional theory (DFT)
• energy density method (EDM)
• first-principles
• electronic structure
• spin polarization
• dislocation
• defect energy
• dislocation core energy
• magnetic exchange interaction
• mechanical properties

Abstract

We develop an energy density method with spin polarization (spin-EDM) from the formalism of spin-polarized density functional theory (spin-DFT) and the projector-augmented wave (PAW) method. The aim of the method is to decompose the DFT total energy of a system into well-defined atomic energies. Spin-EDM is a generalization of earlier formalisms of EDM to the scenarios with spin polarization, which is useful and necessary to study defects in magnetic systems. The DFT total energy decomposition by spin-EDM involves two steps. As the first step, the total energy is decomposed to energy densities in real space, including kinetic energy density, classical Coulomb energy density, exchange-correlation energy density, which are functions defined in the entire real space, and on-site energy density as delta functions located at each atom/ion. The kinetic and classical Coulomb energy densities do not have unique forms due to gauge dependence, so gauge-invariant volumes need to be used for energy integration, which ensure that these gauge-dependent terms are integrated to zero within them. Bader charge analysis can be used to find such gauge-invariant volumes, which are Bader volumes and charge-neutral volumes defined as zero-flux volumes in the gradient vector fields of pseudo electron density and the total potential, respectively. As the second step, energy densities are integrated over these gauge-invariant volumes for atomic energies, whose summation over all the atoms restores the DFT total energy up to a constant difference. We perform the first works of applying EDM to study dislocation energies, from which one is able to extract core energies. Dislocations have long-range elastic fields that are incompatible with the periodic boundary conditions, so their modeling in DFT calculations often involve dislocation dipoles to cancel out the long-range elastic field, but that requires extra effort to model the interaction energies. With EDM, we show that dislocation line energies can be calculated using geometry containing an isolated dislocation. The line energy can be calculated by summing up the atomic energies from the core to the elastic region, while excluding the spurious energies from the free surface near the domain boundaries. The analytical form of line energies can be acquired by fitting the linear part of the line energy, with the intercept being the core energy. -type screw dislocations in hexagonal close-packed (HCP) Mg are studied as the example of nonmagnetic materials, which yields the higher core energy in the prismatic screw dislocation compared to the basal screw dislocation, with the core energy difference quantitatively determined, which is useful for understanding the energy barrier of cross-slip in Mg. Edge and mixed dislocation in ferromagnetic body-centered cubic (BCC) Fe are calculated using spin-EDM as examples for magnetic materials, from which the line energies and core energies are determined. We study magnetic exchange interactions between atoms in paramagnetic face-centered cubic (FCC) Fe using magnetic structures predicted by DFT and atomic energies predicted by EDM, with spin polarization. Special quasirandom structures (SQS's) are used to approximate the disordered spin arrangements in FCC Fe, which are further used in DFT and EDM calculations. Empirical models are derived to model atomic magnetic energy from the magnetic configuration, which contains a self-spin energy term and exchange energies; the former has the form of Landau function while the latter are modeled using spin-cluster expansion (SCE) models and deep neural network (DNN) models, based on the approach of cluster expansion. The clusters are selected and ranked by importance through a greedy algorithm that evaluates the Pearson’s correlation of residues of the Landau-SCE model and the cluster functions of candidate clusters, and always keeps the cluster yielding the greatest magnitude in the Pearson’s correlation at each step. Both models suggest that their best accuracy can be achieved by incorporating the first 5 clusters selected by the greedy algorithm: 4 pair clusters containing sites from the 1st nearest neighbor up to the 4th nearest neighbor, and a tetrahedron-shaped quadruplet cluster with the sites being 1st nearest neighbors. With these 5 clusters, the Landau-SCE models and Landau-DNN models are parameterized and give similar testing RMSE errors on datasets. These parameterized models can be applied in and further tested by thermodynamics simulations for fast evaluation of the configurational energy.

Graduation Semester

2024-12

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/127385

Copyright and License Information

Copyright 2024 Yang Dan

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