188 research outputs found
Lattice Green's function for crystals containing a planar interface
Flexible boundary condition methods couple an isolated defect to a
harmonically responding medium through the bulk lattice Green's function; in
the case of an interface, interfacial lattice Green's functions. We present a
method to compute the lattice Green's function for a planar interface with
arbitrary atomic interactions suited for the study of line defect/interface
interactions. The interface is coupled to two different semi-infinite bulk
regions, and the Green's function for interface-interface, bulk-interface and
bulk-bulk interactions are computed individually. The elastic bicrystal Green's
function and the bulk lattice Green's function give the interaction between
bulk regions. We make use of partial Fourier transforms to treat in-plane
periodicity. Direct inversion of the force constant matrix in the partial
Fourier space provides the interface terms. The general method makes no
assumptions about the atomic interactions or crystal orientations. We simulate
a screw dislocation interacting with a twin boundary in Ti using
flexible boundary conditions and compare with traditional fixed boundary
conditions results. Flexible boundary conditions give the correct core
structure with significantly less atoms required to relax by energy
minimization. This highlights the applicability of flexible boundary conditions
methods to modeling defect/interface interactions by \textit{ab initio}
methods
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).Comment: 15 pages, 7 figure
Convergence rate for numerical computation of the lattice Green's function
Flexible boundary condition methods couple an isolated defect to bulk through
the bulk lattice Green's function. The inversion of the force-constant matrix
for the lattice Green's function requires Fourier techniques to project out the
singular subspace, corresponding to uniform displacements and forces for the
infinite lattice. Three different techniques--relative displacement, elastic
Green's function, and discontinuity correction--have different computational
complexity for a specified numerical error. We calculate the convergence rates
for elastically isotropic and anisotropic cases and compare them to analytic
results. Our results confirm that the discontinuity correction is the most
computationally efficient method to compute the lattice Green's function.Comment: 12 pages, 4 figure
Thermal Stabilization of the HCP Phase in Titanium
We have used a tight-binding model that is fit to first-principles
electronic-structure calculations for titanium to calculate quasi-harmonic
phonons and the Gibbs free energy of the hexagonal close-packed (hcp) and omega
crystal structures. We show that the true zero-temperature ground-state is the
omega structure, although this has never been observed experimentally at normal
pressure, and that it is the entropy from the thermal population of phonon
states which stabilizes the hcp structure at room temperature. We present the
first completely theoretical prediction of the temperature- and
pressure-dependence of the hcp-omega phase transformation and show that it is
in good agreement with experiment. The quasi-harmonic approximation fails to
adequately treat the bcc phase because the zero-temperature phonons of this
structure are not all stable
Systematic pathway generation and sorting in martensitic transformations: Titanium alpha to omega
Structural phase transitions are governed by the underlying atomic
transformation mechanism; martensitic transformations can be separated into
strain and shuffle components. A systematic pathway generation and sorting
algorithm is presented and applied to the problem of the titanium alpha to
omega transformation under pressure. In this algorithm, all pathways are
constructed within a few geometric limits, and efficiently sorted by their
energy barriers. The geometry and symmetry details of the seven lowest energy
barrier pathways are given. The lack of a single simple geometric criterion for
determining the lowest energy pathway shows the necessity of atomistic studies
for pathway determination.Comment: 11 pages, 2 figure
A New Mechanism for the Alpha to Omega Martensitic Transformation in Pure Titanium
We propose a new direct mechanism for the pressure driven alpha to omega
martensitic transformation in pure titanium. A systematic algorithm enumerates
all possible mechanisms whose energy barriers are evaluated. A new, homogeneous
mechanism emerges with a barrier at least four times lower than other
mechanisms. This mechanism remains favorable in a simple nucleation model.Comment: 4 pages, 4 figure
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