arXiv subjects

Dallas R. Trinkle

Publications and source records attributed to Dallas R. Trinkle.

31 records · Page 2Linked to original sources

arXiv2012

Direct calculation of lattice Green function with arbitrary interactions for general crystals

Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic strain. Flexible boundary condition methods embedded a defect in infinite harmonic bulk through the lattice Green function. We demonstrate an efficient and accurate calculation of the lattice Green function from the force-constant matrix for general crystals with an arbitrary basis by extending a method for Bravais lattices. New terms appear due to the presence of optical modes and the possible loss of inversion symmetry. By separately treating poles and discontinuities in reciprocal space, numerical accuracy is controlled at all distances. We compute the lattice Green function for a two-dimensional model with broken symmetry to elucidate the role of different coupling terms. The algorithm is generally applicable in two and three dimensions, to crystals with arbitrary number of atoms in the unit cell, symmetry, and interactions.

cond-mat.mtrl-sci↗

arXiv2011

Au/TiO2(110) interfacial reconstruction stability from ab initio

We determine the stability and properties of interfaces of low-index Au surfaces adhered to TiO2(110), using density functional theory energy density calculations. We consider Au(100) and Au(111) epitaxies on rutile TiO2(110) surface, as observed in experiments. For each epitaxy, we consider several different interfaces: Au(111)//TiO2(110) and Au(100)//TiO2(110), with and without bridging oxygen, Au(111) on 1x2 added-row TiO2(110) reconstruction, and Au(111) on a proposed 1x2 TiO reconstruction. The density functional theory energy density method computes the energy changes on each of the atoms while forming the interface, and evaluates the work of adhesion to determine the equilibrium interfacial structure.

cond-mat.mtrl-sci↗

arXiv2011

Direct diffusion through interpenetrating networks: Oxygen in titanium

How impurity atoms move through a crystal is a fundamental and recurrent question in materials. The previous understanding of oxygen diffusion in titanium relied on interstitial lattice sites that were recently found to be unstable, making the diffusion pathways for oxygen unknown. Using first-principles quantum-mechanical methods, we find three oxygen interstitial sites in titanium, and quantify the multiple interpenetrating networks for oxygen diffusion. Surprisingly, no single transition dominates, but all contribute to diffusion.

cond-mat.mtrl-sci↗

arXiv2011

Prediction of thermal cross-slip stress in magnesium alloys from direct first principles data

We develop a first-principles model of thermally-activated cross-slip in magnesium in the presence of a random solute distribution. Electronic structure methods provide data for the interaction of solutes with prismatic dislocation cores and basal dislocation cores. Direct calculations of interaction energies are possible for solutes---K, Na, and Sc---that lower the Mg prismatic stacking fault energy to improve formability. To connect to thermally activated cross-slip, we build a statistical model for the distribution of activation energies for double kink nucleation, barriers for kink migration, and roughness of the energy landscape to be overcome by an athermal stress. These distributions are calculated numerically for a range of concentrations, as well as alternate approximate analytic expressions for the dilute limit. The analytic distributions provide a simplified model for the maximum cross-slip softening for a solute as a function of temperature. The direct interaction calculations predict lowered forming temperatures for Mg-0.7at.%Sc, Mg-0.4at.%K, and Mg-0.6at.%Na of approximately 250C.

cond-mat.mtrl-sci↗

arXiv2011

Nanoscale-hydride formation at dislocations in palladium: Ab initio theory and incoherent inelastic neutron scattering measurements

Hydrogen arranges at dislocations in palladium to form nanoscale hydrides, changing the vibrational spectra. An ab initio hydrogen potential energy model versus Pd neighbor distances allows us to predict the vibrational excitations for H from absolute zero up to room temperature adjacent to a partial dislocation and with strain. Using the equilibrium distribution of hydrogen with temperature, we predict excitation spectra to explain new incoherent inelastic neutron-scattering measurements. At 0K, dislocation cores trap H to form nanometer-sized hydrides, while increased temperature dissolves the hydrides and disperses H throughout bulk Pd.

cond-mat.mtrl-sci↗

arXiv2010

Energy density in density functional theory: Application to crystalline defects and surfaces

We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transformation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation.

cond-mat.mtrl-sci↗

arXiv2010

Accurate and efficient algorithm for Bader charge integration

We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid, and apply it to the Bader charge partitioning for the electron charge density. Starting with the evolution of trajectories in space following the gradient of charge density, we derive an expression for the fraction of space neighboring each grid point that flows to its neighbors. This serves as the basis to compute the fraction of each grid volume that belongs to a basin (Bader volume), and as a weight for the discrete integration of functions over the Bader volume. Compared with other grid-based algorithms, our approach is robust, more computationally efficient with linear computational effort, accurate, and has quadratic convergence. Moreover, it is straightforward to extend to non-uniform grids, such as from a mesh-refinement approach, and can be used to both identify basins of attraction of fixed points and integrate functions over the basins.

cond-mat.mtrl-sci↗

arXiv2010

First-principles calculation of H vibrational excitations at a dislocation core of Pd

Palladium is an ideal system for understanding the behavior of hydrogen in metals. In Pd, H is located both in octahedral sites and in dislocation cores, which act as nanoscale H traps and form Cottrell atmospheres. Adjacent to a dislocation core, H experiences the largest possible distortion in alpha-Pd. Ab initio density-functional theory computes the potential energy for a hydrogen in an octahedral site in alpha-Pd and in a trap site at the core of a partial of an edge dislocation. The Pd partial dislocation core changes the environment for H, distorting the H-Pd bonding which changes the local potential, vibrational spectra, and inelastic form factor for an isolated H atom. The decrease in excitation energy is consistent with experiments, and the calculations predict distortions to the H wavefunction.

cond-mat.mtrl-sci↗

arXiv2010

First-principles data for solid-solution strengthening of magnesium: From geometry and chemistry to properties

Solid-solution strengthening results from solutes impeding the glide of dislocations. Existing theories of strength rely on solute-dislocation interactions, but do not consider dislocation core structures, which need an accurate treatment of chemical bonding. Here, we focus on strengthening of Mg, the lightest of all structural metals and a promising replacement for heavier steel and aluminum alloys. Elasticity theory, which is commonly used to predict the requisite solute-dislocation interaction energetics, is replaced with quantum-mechanical first-principles calculations to construct a predictive mesoscale model for solute strengthening of Mg. Results for 29 different solutes are displayed in a "strengthening design map" as a function of solute misfits that quantify volumetric strain and slip effects. Our strengthening model is validated with available experimental data for several solutes, including Al and Zn, the two most common solutes in Mg. These new results highlight the ability of quantum-mechanical first-principles calculations to predict complex material properties such as strength.

cond-mat.mtrl-sci↗

arXiv2010

Misfit-Dislocation-Mediated Heteroepitaxial Island Diffusion

Scanning tunneling microscopy combined with molecular dynamics simulations reveal a dislocation-mediated island diffusion mechanism for Cu on Ag(111), a highly mismatched system. Cluster motion is tracked with atomic precision at multiple temperatures and diffusion barriers and prefactors are determined from direct measurements of hop rates. The non-monotonic size dependence of the diffusion barrier is in good agreement with simulations and can lead to enhanced mass transport upon coarsening, in surprising contrast to the traditional island diffusion models where diffusivity reduces with cluster size.

cond-mat.mtrl-sci↗

arXiv2009

Island Shape Controls Magic-Size Effect for Heteroepitaxial Diffusion

Lattice mismatch of Cu on Ag(111) produces fast diffusion for special "magic sizes" of islands. A size- and shape-dependent reptation mechanism is responsible for low diffusion barriers. Initiating the reptation mechanism requires a suitable island shape, a property not considered in previous studies of 1D island chains and 2D closed-shell islands. Shape determines the dominant diffusion mechanism and leads to multiple clearly identifiable magic-size trends for diffusion depending on the number of atoms whose bonds are shortened during diffusion.

cond-mat.mtrl-sci↗

arXiv2009

Cu/Ag EAM Potential Optimized for Heteroepitaxial Diffusion from ab initio Data

A binary embedded-atom method (EAM) potential is optimized for Cu on Ag(111) by fitting to ab initio data. The fitting database consists of DFT calculations of Cu monomers and dimers on Ag(111), specifically their relative energies, adatom heights, and dimer separations. We start from the Mishin Cu-Ag EAM potential and first modify the Cu-Ag pair potential to match the FCC/HCP site energy difference then include Cu-Cu pair potential optimization for the entire database. The optimized EAM potential reproduce DFT monomer and dimer relative energies and geometries correctly. In trimer calculations, the potential produces the DFT relative energy between FCC and HCP trimers, though a different ground state is predicted. We use the optimized potential to calculate diffusion barriers for Cu monomers, dimers, and trimers. The predicted monomer barrier is the same as DFT, while experimental barriers for monomers and dimers are both lower than predicted here. We attribute the difference with experiment to the overestimation of surface adsorption energies by DFT and a simple correction is presented. Our results show that the optimized Cu-Ag EAM can be applied in the study of larger Cu islands on Ag(111).

cond-mat.mtrl-sci↗

arXiv2006

Lattice Green function for extended defect calculations: Computation and error estimation with long-range forces

Computing the atomic geometry of lattice defects--point defects, dislocations, crack tips, surfaces, or boundaries--requires an accurate coupling of the local strain field to the long-range elastic field. Periodic boundary conditions used by classical potentials or density-functional theory may not accurately reproduce the correct bulk response to an isolated defect; this is especially true for dislocations. Recently, flexible boundary conditions have been developed to produce the correct long-range strain field from a defect--effectively "embedding" a defect in a finite cell with infinite bulk response, isolating it from either periodic images or free surfaces. Flexible boundary conditions require the calculation of the bulk response with the lattice Green function (LGF). While the LGF can be computed from the dynamical matrix, for supercell methods (periodic boundary conditions) it can only be calculated up to a maximum range. We illustrate how to accurately calculate the lattice Green function and estimate the error using a cutoff dynamical matrix combined with knowledge of the long-range behavior of the lattice Green function. The effective range of deviation of the lattice Green function from the long-range elastic behavior provides an important length scale in multiscale quasi-continuum and flexible boundary-condition calculations, and measures the error introduced with periodic boundary conditions.

cond-mat.mtrl-sci↗