Andrei V. Ruban

The surface energy of metals

Abstract 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, Cu, Mo, Ta, Pt and Pb.

Surface electronic structure and reactivity of transition and noble metals

We present self-consistent density functional calculations using the LMTO-ASA method of the variations in the surface electronic structure for pseudomorfic overlayers and impurities of Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt, and Au on the other metals. Knowledge of these variations is of importance in understanding trends in the reactivity of metal surfaces. A simple model is presented which gives a description of the overall trends in the self-consistently calculated results.

Configurational thermodynamics of alloys from first principles : effective cluster interactions

Phase equilibria in alloys to a great extent are governed by the ordering behavior of alloy species. One of the important goals of alloy theory is therefore to be able to simulate these kinds of phenomena on the basis of first principles. Unfortunately, it is impossible, even with present day total energy software, to calculate entirely from first principles the changes in the internal energy caused by changes of the atomic configurations in systems with several thousand atoms at the rate required by statistical thermodynamics simulations. The time-honored solution to this problem that we shall review in this paper is to obtain the configurational energy needed in the simulations from an Ising-type Hamiltonian with so-called effective cluster interactions associated with specific changes in the local atomic configuration. Finding accurate and reliable effective cluster interactions, which take into consideration all relevant thermal excitations, on the basis of first-principles methods is a formidable task. However, it pays off by opening new exciting perspectives and possibilities for materials science as well as for physics itself. In this paper we outline the basic principles and methods for calculating effective cluster interactions in metallic alloys. Special attention is paid to the source of errors in different computational schemes. We briefly review first-principles methods concentrating on approximations used in density functional theory calculations, Greens function method and methods for random alloys based on the coherent potential approximation. We formulate criteria for the validity of the supercell approach in the calculations of properties of random alloys. The generalized perturbation method, which is an effective and accurate tool for obtaining cluster interactions, is described in more detail. Concentrating mostly on the methodological side we give only a few examples of applications to the real systems. In particular, we show that the ground state structure of Au3Pd alloys should be a complex long-period superstructure, which is neither DO22 nor DO23 as has been recently predicted.

Calculated surface segregation in transition metal alloys

Abstract We outline a combination of numerical techniques which recently has been used to calculate heats of solution, surface energies and segregation energies for a large number of metals and alloys. The basic ingredients are density functional theory, a Greens function approach to the one-electron problem formulated within a linear muffin-tin orbitals basis, the coherent potential approximation corrected for charge transfer effects by the screened impurity model, and the atomic sphere approximation corrected for the higher multipoles of the charge density. We discuss the accuracy of the combined numerical technique and present results for the surface segregation of single impurities, the stability of pseudomorphically grown overlayers on Ni, and segregation profiles in Rh 75 Pt 25 .

Screened Coulomb interactions in metallic alloys. I. Universal screening in the atomic-sphere approximation

We have used the locally self-consistent Greens-function (LSGF) method in supercell calculations to establish the distribution of the net charges assigned to the atomic spheres of the alloy components in metallic alloys with different compositions and degrees of order. This allows us to determine the Madelung potential energy of a random alloy in the single-site, mean-field approximation. The Madelung potential makes density-functional calculations by the conventional single-site, coherent potential approximation practically identical to the more rigorous LSGF supercell results obtained with a single-site local interaction zone. We demonstrate that the basic mechanism that governs the charge distribution is the screening of the net charges of the alloy components that makes the direct Coulomb interactions short ranged. In the atomic-sphere approximation, this screening appears to be almost independent of the alloy composition, lattice spacing, and crystal structure. A formalism which allows a consistent treatment of the screened Coulomb interactions within the single-site mean-field approximation is outlined. We also derive the contribution of the screened Coulomb interactions to the S ( 2 ) formalism and the generalized perturbation method.

Growth of Co on Cu(111): subsurface growth of trilayer Co islands

Abstract The growth of cobalt on Cu(111) has been studied using a variable-temperature scanning tunneling microscope (STM). At a deposition temperature of 150 K, one observes the growth of three-layer Co islands with one subsurface layer. The Co islands are surrounded by a brim of Cu. The distinction between Co and Cu is made by adsorption of CO which adsorbs only on Co at room temperature, resulting in a Co(111)-(√3 × √3)R30°-CO structure. After heating the surface, or depositing Co at higher temperatures, the Cu brims gradually disappear, and vacancy islands form in the Cu(111) surface. The top-layer CoCu composition changes slowly at room temperature with Co being replaced by Cu on a timescale of ∼ 1 h, consistent with earlier ion-scattering studies. The experimental findings are in accordance with ab-initio total-energy calculations showing the thermodynamically stable island configuration to be several cobalt layers capped with one copper layer.

Screened Coulomb interactions in metallic alloys. II. Screening beyond the single-site and atomic-sphere approximations

A quantitative description of the configurational part of the total energy of metallic alloys with substantial atomic size difference cannot be achieved in the atomic-sphere approximation: It needs to be corrected at least for the multipole-moment interactions in the Madelung part of the one-electron potential and energy. In the case of a random alloy such interactions can be accounted for only by lifting the atomic-sphere and single-site approximations, in order to include the polarization due to local environment effects. Nevertheless, a simple parametrization of the screened Coulomb interactions for the ordinary single-site methods, including the generalized perturbation method, is still possible. We obtained such a parametrization for bulk and surface NiPt alloys, which allows one to obtain quantitatively accurate effective interactions in this system.

Submonolayer growth of Pd on Cu(111) studied by scanning tunneling microscopy

Abstract The growth mode of sub-monolayer amounts of Pd on Cu(111) in the temperature range −80–300°C has been investigated by scanning tunneling microscopy (STM), Rutherford backscattering spectroscopy (RBS) and Auger electron spectroscopy (AES). Below ≈100°C, the Pd induced phase nucleates at ascending steps in fingered brims and, on large terraces, in fingered islands. The lack of order suggests that the brims and islands are a disordered alloy formed by exchange between Pd and Cu from the layer underneath. For temperatures exceeding ≈160°C, Cu is dug out from the surface in extended, monolayer deep pits, and concurrently, the brims and islands increase in height by one layer. High-resolution STM images of brims and islands in this phase are interpreted as evidence for Cu capping. For Pd evaporation at temperatures of 220–300°C, the surface is characterized by the appearance of individual Pd atoms substituted into the first layer and the presence of subsurface Pd. A short-range order that excludes the population of nearest-neighbour, in-plane sites is revealed by pair-correlation analysis. The Pd atoms form bands in the upper terrace next to steps. These bands are surprisingly stable against further diffusion, possibly due to an attractive interaction with second- and third-nearest (in-plane) neighbours and with subsurface Pd. The lack of any ordering is explained, based on a calculation of the surface energy. Once the population of nearest-neighbour sites is excluded, there is practically no energy gain by ordering.

Unified cluster expansion method applied to the configurational thermodynamics of cubic Ti1-xAlxN

We study the thermodynamics of cubic Ti1-xAlxN using a unified cluster expansion approach for the alloy problem. The purely configurational part of the alloy Hamiltonian is expanded in terms of concentration- and volume-dependent effective cluster interactions. By separate expansions of the chemical fixed lattice, and local lattice relaxation terms of the ordering energies, we demonstrate how the screened generalized perturbation method can be fruitfully combined with a concentration-dependent Connolly-Williams cluster expansion method. Utilizing the obtained Hamiltonian in Monte Carlo simulations we access the free energy of Ti1-xAlxN alloys and construct the isostructural phase diagram. The results show striking similarities with the previously obtained mean-field results: The metastable c-TiAlN is subject to coherent spinodal decomposition over a larger part of the concentration range, e.g., from x >= 0.33 at 2000 K.

Pareto-optimal alloys

Large databases that can be used in the search for new materials with specific properties remain an elusive goal in materials science. The problem is complicated by the fact that the optimal material for a given application is usually a compromise between a number of materials properties and the cost. In this letter we present a database consisting of the lattice parameters, bulk moduli, and heats of formation for over 64 000 ordered metallic alloys, which has been established by direct first-principles density-functional-theory calculations. Furthermore, we use a concept from economic theory, the Pareto-optimal set, to determine optimal alloy solutions for the compromise between low compressibility, high stability, and cost.