We present an efficient parallel algorithm for lattice gas Monte Carlo simulations in the framework of an Ising model that allows arbitrary interaction on any lattice, a model often called a cluster expansion. Thermodynamic Monte Carlo simulations strive for the equilibrium properties of a system by exchanging atoms over a long range, while preserving detailed balance. This long-range exchange of atoms renders other frequent parallelization techniques, like domain decomposition, unfavorable due to excessive communication cost. Our ansatz, based on the Metropolis algorithm, minimizes communication between parallel processes. We present this new "partial sequence preserving'' (PSP) algorithm, as well as benchmark data for a physical alloy system (NiAl) comprised of one billion atoms.

The segregation profile of the Pt25Rh75(100) surface is studied by the combination of density functional theory calculations with the cluster-expansion method and Monte Carlo simulations. We construct the stability diagram for the surface layers, which allows the prediction of the most stable atomic configuration for a given average concentration in those layers. On this basis, we apply the cluster-expansion Hamiltonian in grand-canonical Monte Carlo simulations for the prediction of the temperature-dependent concentration profile. The experimentally found enrichment of Pt in the top layer and depletion in the second layer is nicely confirmed by the calculations.

We present a new implementation of the cluster expansion formalism. The new code, UNiversal CLuster Expansion (UNCLE), consolidates recent advances in the methodology and leverages one new development in the formalism itself. As a core goal, the package reduces the need for user intervention, automating the method to reduce human error and judgment. The package extends standard cluster expansion formalism to the more complicated cases of ternary compounds, as well as surfaces, including adsorption and inequivalent sites.

The stability of various point defects in NiAl(100) has been investigated by first-principles calculations. For Al-rich surfaces, Ni vacancies within the first Al layer are energetically most favourable. For Ni-rich surfaces, so-called double defects, consisting of both Ni-antisite atom in the first Al layer and a Ni vacancy within the second Ni layer, form the configuration of lowest energy, superior to singular Ni antisites. An additional and significant energy gain is found in both cases by mutual lateral interaction of the defects, when they are arranged in the diagonal direction. Respective [Formula: see text] ordered configurations were found as the most stable structures. A 50:50 mixture of both defect types turns out to be even lower in energy than the ideal Al-terminated NiAl(100) surface, proving the latter to be metastable only. This is in line with the often reported inability in experiments to prepare ideal NiAl(100) surfaces.

Whereas binary intermetallic compounds often appear as ordered structures with fewer than 10 atoms per cell, large-supercell structures consisting of one- and two-dimensional superstructures have long been observed in CuPd. However, whereas the stability of the ordinary one-dimensional long-period superstructures (1-D LPS) has been previously investigated by first-principles total-energy methods, two-dimensional superstructures were not amenable to such calculations because of their large number of atoms (O(103) atoms/cell). Using a cluster expansion extracted from a set of first-principles total energy calculations, we show that 2-D LPSs are likely kinetically-stabilized structures which transform into the 1-D LPS ground-state structures at thermodynamic equilibrium.

It is demonstrated for several cases that the joint application of low-energy electron diffraction (LEED) and structural calculations using density functional theory (DFT) can retrieve the correct surface structure even though single application of both methods fails. On the experimental side ( LEED) the failure can be due to the simultaneous presence of weak and very strong scatterers or to an insufficient data base leaving different structures with the same quality of fit between experimental data and calculated model intensities. On the theory side ( DFT) it can be difficult to predict the coverage of an adsorbate or two different structures may own almost the same total energy, but only one of the structures is assumed in experiment due to formation kinetics. It is demonstrated how in the different cases the joint application of both methods-which yield about the same structural precision-offers a way out of the dilemma.

Epitaxial Ni films deposited on Ir(100) were investigated by tunneling microscopy (STM), quantitative low-energy electron diffraction (LEED), and density-functional theory (DFT). For film thicknesses beyond 3 monolayers the large tensile strain (approximate to 9%) is relieved by the formation of stair-rod-like dislocations. Their favorable energetics is revealed by DFT calculations which also determine the defects' structural parameters. On the unstructured Ir(100)-(1x1) surface they develop in an irregular way, i.e., without long-range order. In STM they are visible as shallow depressions or by decoration with further adsorbed adatoms. In contrast to this case of missing long-range order, the dislocations are ordered in films on the Ir(100)-(5x1)-H surface, whereby (5x1)-periodic Ir wires at the interface act as pinning centers. So, their detailed atomic structure is accessible experimentally by quantitative LEED with crystallographic precision. Features similar to Ni are also observed for Co films.

Although modern computer codes based on density functional theory (DFT) allow the reliable prediction of many surface properties, they often cannot be applied, when the problem of interest demands a consideration of huge configuration spaces or model systems containing many thousand atoms. An important example are binary alloy surfaces where substitutional ordering phenomena on a mesoscopic scale and surface segregation are involved. It will be demonstrated how the combination of first-principle calculations with cluster expansions (CE) and Monte-Carlo (MC) simulations allows for a quantitative prediction of disordered alloy surface properties without any empirical parameters. The concept will be applied to the Pt 25 Rh 75 (111) surface. Our results are in excellent agreement with experimental studies.

The adsorption of hydrogen on the stable state of the Ir(100) surface, the quasihexagonally reconstructed phase Ir(100)-(5x1)-hex, was investigated by density functional theory (DFT) for different coverages and zero temperature. It appears that the adsorbate induces significant structural substrate modifications which are typical for the adsorption site(s) and are due to a complex interaction between adsorbate and substrate. The system's energetics, as well as the structure of the adsorbate and substrate, are provided for different coverages at which the mirror symmetry of the clean surface is either broken or saved. The total energy per H atom decreases with coverage. So, there is no island formation but always a homogeneous phase accessible by experiment. The structure of the substrate-which can be determined with high precision by experimental methods as low-energy electron diffraction-can be used by DFT as an identifier for the actual adsorbate coverage, and the corresponding adsorption sites can be determined by the usual energy minimization procedure.

The adsorption of hydrogen on the metastable, unreconstructed Ir(100)-(1x1) surface is investigated by density functional theory (DFT), quantitative low-energy diffraction (LEED), and thermal desorption spectrometry (TDS) complemented by scanning tunneling microscopy (STM). The bridge site is unequivocally identified as the adsorption site, rather unusual for metallic fcc(100) surfaces. There is excellent quantitative agreement between calculated and experimentally determined structural parameters both for the clean surface and the adsorbate covered surface. Given the uncertainty of DFT to reproduce absolute energies there is also good agreement with the measured adsorption energy (460 meV/atom). Additionally, theoretical vibrational and electronic properties are provided without, however, related experiments being available.

The geometrical and chemical structure of the CoAl(111) surface is investigated by quantitative low-energy electron diffraction and calculations applying density functional theory. The stacking sequence of the top four atomic planes is Al-Co-Co-Co, followed below by the usual alternating B2 stacking. The topmost layers thus form a unit cell of the well-known bcc-based D0(3) crystal structure [the A(3)B superlattice of bcc(111) atomic planes], although the bulk phase diagram of CoAl shows no D0(3) phase. Its occurrence and stability at the surface is due to a slight Co excess of the nominally stoichiometric sample, equivalent to the presence of Co antisite defects in the bulk. These defects are enriched in undercoordinated near-surface sites of the Al sublattice, which lowers the total energy because more At atoms can then reside in fully coordinated bulk At sites. However, all three topmost layers are undercoordinated, and the segregation of Co antisite defects competes with a general trend towards a termination of the surface by Al. In the balance, the third layer is the preferred plane for Co antisite defects.

The morphological evolution of nanoscale precipitates in Al–Cu alloys is studied by integrating first-principles calculations, the mixed-space cluster expansion, and Monte Carlo simulations. Without a priori assumptions, we predict generic precipitate morphologies dominated by strain-induced long-range interactions: single atomic layers consisting of 100%Cu atoms along {100} planes of a face-centered-cubic lattice of Al atoms, consistent with experimental measurements. We analyze the precipitation kinetics using the Johnson–Mehl–Avrami phase transformation theory and obtain a transformation exponent close to 1.5.

The combination of density-functional theory (DFT) calculations of geometrically fully relaxed binary alloy surfaces with concepts from statistical physics is applied to construct a DFT-based phase diagram for a binary alloy surface. As a first example, we studied the appearance of Co antisite atoms at CoAl(100) surfaces. The structural parameters as multilayer relaxations, surface buckling, lateral order, and segregation profile of the predicted stable surface phases are in excellent agreement with experimental structure determinations applying low-energy electron diffraction.

Properties of ultra-thin films deviate from those of the corresponding bulk material already because of the mere reduction of dimensionality and, related to that, the reduction of symmetry. This applies to all types of collective phenomena as, e.g. geometrical structure, electronic properties and magnetism [1]. Also, the alternating combination of different film material stacked perpendicular to the surface can lead to completely new physical phenomena as, e.g., the giant magnetoresistance (GMR) effect, i.e. the enhanced sensitivity of the electrical resistivity to external magnetic fields. Within only about one decade after its discovery, the first GMR-based read-head devices appeared in commercial hard disks, and the near future might bring even non-volatile magnetic random access memory (MRAM) devices based on this technology [2,3]. For these reasons, thin films of magnetic materials have attracted a great deal of research attention. Yet in addition to the reduced dimensionality, there is another factor with tremendous impact on the film properties: When the film is grown on a crystalline substrate it tends to assume the latter s lateral periodicity. Such pseudomorphic growth is realized when the energy costs for the distortion of the film s native lattice is overbalanced by the energy gained by the formation of the film–substrate interface. This is frequently the case when the substrate s binding-potential surface is strongly corrugated. In these cases, the thin film is an artificial material whose surface parallel lattice parameter deviates from that of the bulk material (usually accompanied by a tetragonal distortion). A completely different crystal structure may even result. An example for the first case is Ni on Cu(100), which simply continues the substrate lattice parameters up to a thickness of about 20 monolayers (ML) before it gradually converts towards Ni s bulk structure. In the whole pseudomorphic range, the film exhibits a constant, laterally expanded lattice parameter ( 2.5%) and likewise contracted layer distances ( 3%) [4]. In contrast, cobalt––whose native structure at room temperature

In the 1988 edition of Nature’s ‘News and Views’, J Maddox wrote that ‘one of the continuing scandals in physical sciences is that it remains in general impossible to predict the structure of even the simplest crystallographic solids from knowledge of their chemical composition’ (Maddox 1988 Nature 335 7). There is, however, the possibility of making some progress in this direction by combining two fundamental areas of physics: quantum mechanics and statistical physics. The starting point is an electronic structure theory density functional theory (DFT) (Hohenberg and Kohn 1964 Phys. Rev. 136 864B, Kohn and Sham 1965 Phys. Rev. 140 1133A) which independently establishes the range (first neighbours, second neighbours, etc), type (pairs, three body, four body, etc) and chemical character (charge transfer, atomic site effects, etc) of the interaction energies. All these can be determined from cluster expansions (CE) (Sanchez et al 1984 Physica A 128 334) which give access to both huge parameter spaces (e.g. for ground-state searches) and systems containing more than a million atoms (e.g. for microstructure studies). It will be shown that, together with Monte Carlo simulations, CE open the possibility of quantitatively studying alloy properties which possess a delicate temperature dependence, such as short-range-order effects, mixing enthalpies or dynamic processes like the ageing of microstructures. This method is extended to alloy surfaces in order to investigate geometric relaxations as well as surface segregation, i.e. the enrichment of one component in the near-surface region. To establish a complementary, experimental view of the geometrical structure and chemical composition of surfaces, experimental low energy electron diffraction spectra are analysed by the use of a multiple-scattering theory (Pendry 1974 Low Energy Electron Diffraction (London: Academic), Van Hove and Tong 1979 Surface Crystallography by LEED (Berlin: Springer)) providing a test of our DFT predicted surface properties.

The initial stages of iron silicide growth on Si(111) were investigated using LEED, AES and STM experiments together with DFT calculations. In 1:1 stoichiometry, a cubic FeSi develops showing a (1×1) surface periodicity which is stable up to 300°C. The epitaxial strain energy stabilizes this bulk-unstable B2 (CsCl-type) phase for up to 250 Å thickness. The surface is Si terminated, the interface coordination of the so-called B8 type. After annealing at ≈ 600°C, a (2×2)-FeSi 2 phase of higher Si content is observed which possesses cubic crystal structure. It is stable below 10 monolayers (ML) initial Fe coverage and grows in an island-like morphology. In the initial growth stage, however, a c(8×4) phase forms that completely covers the surface at 1.5 ML Fe content and appears as potential template for further growth of homogeneous films. The interpretation of atomically resolved STM images suggests that the film contains three Si and two Fe layers in B2 structure with vacancies on Fe positions. The vacancy arrangement seems to be responsible for the c(8×4) periodicity displayed by the Si adatoms in T4-position.

For the example of the B2 CoAl(100) surface, we demonstrate that even slight deviations from an ordered alloy's ideal stoichiometry in a subsurface region or in the bulk can drastically affect its surface composition. By experimental surface analysis and first-principles calculations, we show that Co antisite atoms segregate to the very surface, driven by the same strong interactions which enforce order in the bulk. Our findings are consistent with the lack of antisite segregation we found earlier for the much weaker ordering FeAl(100), and resolve contradictory reports for NiAl(100).

The time evolution of the distribution of precipitate shapes and sizes in Al-Zn alloys is studied via a mixed-space cluster expansion and kinetic Monte-Carlo simulations. We find that the growth of precipitates in Al-rich Al-Zn alloys follows classical Ostwald ripening already after ageing times of a few seconds. Moreover, the distribution of the precipitates is temperature-dependent: the higher the ageing temperature, the smaller the distribution width of the precipitate size. We discuss the time evolution of the precipitates in terms of short-range order parameters and compare them with experimental data.