On the relation between monovacancy formation energy and surface energy for metals

Computational Materials Science, 1999

We show ab initio calculations for vacancy formation energies in Cu and Al. The calculations are based on densityfunctional theory and the full-potential Korringa±Kohn±Rostoker Green's function method for impurities. The nonlocal eect beyond the local-spin-density approximation (LSDA) for density-functional theory is taken into account within the generalized-gradient approximation (GGA) of Perdew and Wang. The lattice relaxation around a vacancy is also investigated using calculated Hellmann±Feynman forces exerted on atoms in the vicinity of a vacancy. We show that the GGA calculations reproduce very well the experimental values of vacancy formation energies and bulk properties of Cu and Al, as they correct the de®ciency of LSDA results (underestimation of equilibrium lattice parameters, overestimation of bulk moduli, and vacancy formation energies). It is also shown that the GGA calculations reduce the LSDA results for the lattice relaxation energy for a vacancy in Cu. Ó : S 0 9 2 7 -0 2 5 6 ( 9 8 ) 0 0 0 7 2 -X

Chemical Physics of Solid Surfaces, 2003

We review measurements and theory of vacancy-mediated mass transport in a metal surface. Experimentally, this transport is made visible with the use of a low density of tracer atoms, embedded in the outermost layer. The STM measurements presented in this chapter have been obtained with In and Pd atoms in the Cu(0 0 1) surface. The observations show that the diffusion of these tracer atoms through the Cu(0 0 1) surface proceeds via long jumps separated by long time intervals. Quantitative details are discussed for both systems and we introduce the theoretical framework that was developed to analyze these measurements. Differences in the energetics of the vacancy-mediated diffusion of In and Pd are discussed and the mobility of Cu atoms in Cu(0 0 1) terraces is evaluated using these measurements. 2 3 4 5 6 7 8

Materials Science Forum, 2001

The vacancy formation energy E, for Pb and Sn are determined by using the positron age-momentum correlation (AMOC) technique. The reported values of E, for them are scattered over a considerable range because their S-parameter do not saturate even close to the melting points. S, for the trapped positrons, however, are obtained by extrapolating the time dependent S-parameter S(t). We dtermined the E, for Pb and Sn using the S, thus obtained.

physica status solidi (b), 1976

I n the tight-binding approximation a complete intra-atomic screening of the charge is assumed t o evaluate the self-consistent potential near a defect in a transition metal. The importance of this potential on the relaxation near e defect is demonstrated. It can, for instance, invert the sign of the displacements for a nearly empty or full d band where the screening by the d electrons is less efficient. The agreement with the experimental results is notably improved for the vacancy formation volume of platinum.

1979

The average efficiencies of dislocation loops and the surface as sinks for supersaturated vacancies in quenched aluminum at 40°C were measured using stereo electron microscopy. The growth of dislocation loops in the region adjacent to the surface was used to investigate the competition between the surface and the growing dislocation loops for the annihilation of vacancies. Comparing the spatial dependence of the fully grown loop size with the solution of the appropriate diffusion equation, the average efficiencies of both types of sinks were determined. The values of the efficiencies are CL = 0.9 &-0.1 and Es = 0.7 f 0.1 for dislocation loops and the surface, respectively. The results indicate that dislocation loops are quite good sinks during their growth at 40°C and that the aluminum surface, which is always covered by a protective and adhesive oxide layer, is not a perfect sink for vacancy annihilation.

Chemical Physics, 2002

In this paper we calculate surface energy (SE) of monovalent, divalent and some trivalent metals. For these metals for which SE can be solely expressed by dimensionless Wigner-Seitz density parameter, r s , of delocalized electrons:

Surface Science, 2002

Statistical–mechanical description of multi-layer surface segregation in multi-component alloys, based on the free-energy concentration expansion method (FCEM), is introduced. The generalized FCEM provides simple analytical expressions for numerical minimization of the alloy free energy in the presence of short-range order (SRO).As an example, this theoretical approach is applied to unravel segregation with site competition at the (111) surface of a

arXiv (Cornell University), 2018

In this work, we present an open access database for surface and vacancy-formation energies using classical force-fields (FFs). These quantities are essential in understanding diffusion behavior, nanoparticle formation and catalytic activities. FFs are often designed for a specific application, hence, this database allows the user to understand whether a FF is suitable for investigating particular defect and surface-related material properties. The FF results are compared to density functional theory and experimental data whenever applicable for validation. At present, we have 17,506 surface energies and 1,000 vacancy formation energies calculation in our database and the database is still growing. All the data generated, and the computational tools used, are shared publicly at the following websites https://www.ctcms.nist.gov/~knc6/periodic.html, https://jarvis.nist.gov and https://github.com/usnistgov/jarvis. Approximations used during the high-throughput calculations are clearly mentioned. Using some of the example cases, we show how our data can be used to directly compare different FFs for a material and to interpret experimental findings such as using Wulff construction for predicting equilibrium shape of nanoparticles. Similarly, the vacancy formation energies data can be useful in understanding diffusion related properties.

Acta Materialia, 2002

Darken's equations are formulated for a spherical geometry and used to examine excess vacancy formation for a Cu-Ni binary system. A subsequent numerical analysis is performed to solve for the excess (above the local thermodynamic equilibrium) vacancies. The results indicate a propensity for pore formation due to the presence of supersaturated vacancies. Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.

This paper extends the embedding energy function () developed by our group in earlier works to the compilation of the surface energies for low index facets of twelve metals in the framework of the embedded atom method (EAM). The goal is to use the mathematical techniques for () which have hitherto worked for metals, to generate a consistent database for metallic elements. The () parameters are obtained through a fit to the experimental mono-vacancy formation energy of each metal and are subsequently applied to the surface energy calculation. These techniques make basic functions computationally simple and produce results with improved accuracy and reliability. Of the twelve elements considered, the surface energies of the five alkali metals follow the broken-bond model's trend () () () expected for metals while the seven transition metals do not. The accuracy of the calculated surface energy for each metal is reasonably good compared to existing theoretical data with similar background and experiments.

Physical Review B, 2015

Vacancy properties in concentrated alloys continue to be of great interest because nowadays ab initio supercell simulations reach a scale where even defect properties in disordered alloys appear to be within reach. We show that vacancy properties cannot generally be extracted from supercell total energies in a consistent manner without a statistical model. Essential features of such a model are knowledge of the chemical potential and imposition of invariants. In the present work, we derive the simplest model that satisfies these requirements and we compare it with models in the literature. As illustration we compute ab initio vacancy properties of fcc Cu-Ni alloys as a function of composition and temperature. Ab initio density functional calculations were performed for SQS supercells at various compositions with and without vacancies. Various methods of extracting alloy vacancy properties were examined. A ternary cluster expansion yielded effective cluster interactions (ECIs) for the Cu-Ni-Vac system. Composition and temperature dependent alloy vacancy concentrations were obtained using statistical thermodynamic models with the ab initio ECIs. An Arrhenius analysis showed that the heat of vacancy formation was well represented by a linear function of temperature. The positive slope of the temperature dependence implies a negative configurational entropy contribution to the vacancy formation free energy in the alloy. These findings can be understood by considering local coordination effects.

Journal of Physics F: Metal Physics

The self-consistent density functional approach has been applied to a study of electronic properties of vacancies and vacancy clusters in simple metals. The electron density profiles and potentials have been obtained for spherical voids of varying size. The formation energies and residual resistivities have been calculated for vacancies using both the perturbational and variational inclusion of discrete lattice effects. The relation of the void properties to the plane surface properties is studied, and the inadequacy of the jellium-based methods to high-index faces is demonstrated.

Journal of Physics and Chemistry of Solids, 2008

The formation mechanism of the di-vacancy in FCC metal Pt has been studied from the migration of the two vacancies by using the modified analytical embedded atom method (MAEAM). The lattice relaxation resulted from the existence of the vacancies is performed with the molecular dynamics (MD) method. For migration of an isolated vacancy in Pt, the favorable path is the first-nearest-neighbor (1NN) migration. From the minimum formation energy or the maximum binding energy of the di-vacancy, we know that the 1NN configuration of the di-vacancy is the most stable. Up to the fifth-nearest-neighbor (5NN) configuration of the di-vacancy, the migration of the two vacancies is always to approach each other in the shortest paths of 5NN-2NN-1NN, 4NN-1NN, 3NN-1NN and 2NN-1NN.

Journal of Physics: Condensed Matter, 2010

We calculate properties like equilibrium lattice parameter, bulk modulus and monovacancy formation energy for nickel (Ni), iron (Fe) and chromium (Cr) using Kohn-Sham density functional theory (DFT). We compare relative performance of local density approximation (LDA) and generalized gradient approximation (GGA) for predicting such physical properties for these metals. We also make a relative study between two different flavors of GGA exchange correlation functional, namely, PW91 and PBE.

Surface Science, 1998

We have used density functional theory to establish a database of surface energies for low index surfaces of 60 metals in the periodic table. The data may be used as a consistent starting point for models of surface science phenomena. The accuracy of the database is established in a comparison with other density functional theory results and the calculated surface energy anisotropies are applied in a determination of the equilibrium shape of nano-crystals of Fe,