Relaxed Surface Energies Research Articles

Ab initiocalculations ofBaTiO3andPbTiO3(001) and (011) surface structures

We present and discuss the results of calculations of surface relaxations and rumplings for the (001) and (011) surfaces of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$ and $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_{3}$ using a hybrid B3PW description of exchange and correlation. On the (001) surfaces, we consider both $A\mathrm{O}$ ($A=\mathrm{Ba}$ or Pb) and $\mathrm{Ti}{\mathrm{O}}_{2}$ terminations. In the former case, the surface $A\mathrm{O}$ layer is found to relax inward for both materials, while outward relaxations of all atoms in the second layer are found at both kinds of (001) terminations and for both materials. The surface relaxation energies of BaO and $\mathrm{Ti}{\mathrm{O}}_{2}$ terminations on $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$ (001) are found to be comparable, as are those of PbO and $\mathrm{Ti}{\mathrm{O}}_{2}$ on $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_{3}$ (001), although in both cases the relaxation energy is slightly larger for the $\mathrm{Ti}{\mathrm{O}}_{2}$ termination. As for the (011) surfaces, we consider three types of surfaces, terminating on a TiO layer, a Ba or Pb layer, or an O layer. Here, the relaxation energies are much larger for the TiO-terminated surface than for the Ba- or Pb-terminated surfaces. The relaxed surface energy for the O-terminated surface is about the same as the corresponding average of the TiO- and Pb-terminated surfaces on $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_{3}$, but much less than the average of the TiO- and Ba-terminated surfaces on $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$. We predict a considerable increase of the Ti-O chemical bond covalency near the $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$ and $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_{3}$ (011) surfaces as compared to both the bulk and the (001) surface.

Water adsorption and dissociation on BeO(001) and (100) surfaces

Plateaus in water adsorption isotherms on hydroxylated BeO surfaces suggest significant differences between the hydroxylated (1 0 0) and (0 0 1) surface structures and reactivities. Density functional theory structures and energies clarify these differences. Using relaxed surface energies, a Wulff construction yields a prism crystal shape exposing long (1 0 0) sides and much smaller (0 0 1) faces. This is consistent with the BeO prisms observed when beryllium metal is oxidized. A water oxygen atom binds to a single surface beryllium ion in the preferred adsorption geometry on either surface. The water oxygen/beryllium bonding is stronger on the surface with greater beryllium atom exposure, namely the less-stable (0 0 1) surface. Water/beryllium coordination facilitates water dissociation. On the (0 0 1) surface, the dissociation products are a hydroxide bridging two beryllium ions and a metal-coordinated hydride with some surface charge depletion. On the (1 0 0) surface, water dissociates into a hydroxide ligating a Be atom and a proton coordinated to a surface oxygen but the lowest energy water state on the (1 0 0) surface is the undissociated metal-coordinated water. The (1 0 0) fully hydroxylated surface structure has a hydrogen bonding network which facilitates rapid proton shuffling within the network. The corresponding (0 0 1) hydroxylated surface is fairly open and lacks internal hydrogen bonding. This supports previous experimental interpretations of the step in water adsorption isotherms. Further, when the (1 0 0) surface is heated to 1000 K, hydroxides and protons associate and water desorbs. The more open (0 0 1) hydroxylated surface is stable at 1000 K. This is consistent with the experimental disappearance of the isotherm step when heating to 973 K.

First-principles calculations of structural and electronic properties of monoclinic hafnia surfaces

We have carried out a systematic theoretical study of the surfaces of monoclinic hafnia $(\mathrm{Hf}{\mathrm{O}}_{2})$ using plane waves and density functional theory based on the generalized gradient approximation. The fully relaxed structures of the bulk phases of $\mathrm{Hf}{\mathrm{O}}_{2}$ are found to be in excellent agreement with experimental data, the monoclinic phase being the most stable. Simulations of the monoclinic phase surfaces indicate a large relaxation which reduces the total surface energy of all nine faces considered by between 23% and 36%, with a strong correlation between the unrelaxed and relaxed surface energies. Our calculations predict that the $(\overline{1}11)$ and (111) faces of the monoclinic phase have the lowest surface energies and are hence the most stable faces. An analysis of the total and partial electronic density of states of bulk monoclinic $\mathrm{Hf}{\mathrm{O}}_{2}$ reveals that the outer valence band significantly mixes the O $2p$ and Hf $5d$ atomic states indicating some covalency of the Hf-O bonds. The total density and partial density of states of the monoclinic surfaces exhibit a surface state corresponding to the surface O $2s$ states in the inner valence band region.

Second-moment interatomic potential for gold and its application to molecular-dynamics simulations

We have obtained a new interatomic potential for Au in the framework of the second-moment approximation to the tight-binding model by fitting the total energy of the metal as a function of the volume computed by first-principles calculations. The scheme was validated by calculating the bulk modulus, elastic constants, vacancy formation energy and relaxed surface energies of Au, which were found to be in fair agreement with experiment. We also have performed molecular-dynamics simulations at various temperatures and we have determined the temperature dependence of the lattice constant, mean-square displacements, as well as the phonon density of states and the phonon dispersion curves of the metal. The agreement with the available experimental data is much better than previous works based on the same approximation.

Universal binding-energy relation for crystals that accounts for surface relaxation

We present a universal relation for crack surface cohesion including surface relaxation. Specifically, we analyze how N atomic planes respond to an opening displacement at its boundary, producing structurally relaxed surfaces. Via density-functional theory, we verify universality for metals (Al), ceramics $(\ensuremath{\alpha}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}),$ and semiconductors (Si). When the energy and opening displacement are scaled appropriately with respect to N, the uniaxial elastic constant, the relaxed surface energy, and the equilibrium interlayer spacing, all energy-displacement curves collapse onto a single universal curve.

Computational Study on Surface Structure and Crystal Morphology of γ-Fe2O3: Toward Deterministic Synthesis of Nanocrystals

This work is the first application of classical atomistic theory to a comprehensive treatment of γ-Fe2O3 surfaces. The surface energy and attachment energy of several low-index surfaces of γ-Fe2O3 have been calculated by the classical atomistic simulation methods. A mean-field approximation involving scaling the short-range potentials, charges, and force constants of the iron ions by a fraction corresponding to the partial occupation of octahedral iron sites in the spinel structure was employed. Reconstruction of the polar surfaces was required to remove the dipole perpendicular to the surface and to achieve structural stability. This was accomplished through the addition of vacancies. The two-dimensional periodic calculations were carried out with the MARVIN code. The (112) surface consisting of iron and oxygen ions had the smallest relaxed surface energy of 1.86 J/m2, while several others including (001), (011), and (012) were within 0.1 J/m2 of this value. The calculated surface energies of these plane...

Tight-binding simulations of Nb surfaces and surface defects

We study the properties of low-index Nb surfaces using the NRL-tightbinding (TB) method. We develop a new TB Hamiltonian for Nb using the basic NRL-TB framework with an expanded fitting database that includes additional bulk structures and frozen phonon calculations. The resulting Hamiltonian is validated by comparing to several bulk-zero-temperature and finite temperature properties. Using this Hamiltonian we simulate the three low-index surfaces, $(001),$ $(110),$ and $(111),$ in slab geometries. We find that substantial slab thickness and Brillouin zone sampling is needed for convergence. Our results show that the surface layer contracts in agreement with experiment, and that the direction of relaxation of the near surface layers oscillates with depth. Both the magnitude of the surface layer contraction and the relaxed surface energies are in good agreement with available experiments and previous simulations. The electronic structure of the surface samples shows distinct surface bands near the Fermi level that are strongly affected by atomic relaxation. The surface phonon spectra show distinct features that correspond to the binding strength of the surface atoms. We also calculate the formation energies of surface defects including adatoms and vacancies. Relaxation around the defects usually involves mainly the first-neighbor atoms, except on the $(111)$ surface where atoms in up to three layers under the defect move significantly.

Surface structures and defect properties of pure and doped La2NiO4

Computer modelling techniques are used to investigate the surface properties and defect chemistry of the La2NiO4 material. Relaxed surface structures and energies are calculated for the low index planes which are used to predict the equilibrium crystal morphology. The {111} surface is calculated to dominate in the absence of impurities, water or surface irregularities, with significant contributions from the {100} and {001} surfaces. Isovalent doping of the Ni site by Fe and Cu is found to affect the crystal morphology by increasing the expression of the {001} surface, although Fe doping is predicted to create the {011} face which is not present in the undoped crystal. The Sr dopant at the La site is calculated to be the most soluble of the alkaline earth metals, in accord with observation. Charge compensation is predicted to occur via the formation of Ni(III), which is consistent with bulk calculations and catalytic models in which Ni(III) species are correlated to the observed catalytic activity.

Atomistic Simulation of the Surface Energy of Spinel MgAl2O4

Atomistic simulations with atomic potentials including anion polarizibility have been performed for the low‐index surfaces of spinel MgAl2O4 with various terminations. The calculations show that for the most stable surface the surface energy is 2.27 J/m2 for the {100}, about 2.85 J/m2 for the {110}, and 3.07 J/m2 for the {111} orientation. The ratio between the experimental values to the calculated relaxed surface energies is about 1.5. Strong surface relaxation was found for the {110} and {111} orientation but only moderate surface relaxation for the {100} surface.

Defect chemistry and surface properties of LaCoO3

Atomistic computer simulation techniques are used to investigate the surface properties and defect chemistry of the LaCoO3 perovskite. The theoretical techniques are based upon efficient energy minimisation routines, a ‘two-region’ strategy and the Mott–Littleton methodology for the accurate modelling of surface and bulk defects. Sr and Ca dopants are calculated to be the most soluble of the alkaline earth metals, in accord with observation. Charge compensation is predicted to occur via oxygen ion vacancies which are believed to be key sites with regard to catalytic activity. Relaxed surface energies are calculated for the low index surfaces and the order of stability is found to be {110} > {100} > {111}. The equilibrium morphology of LaCoO3 is predicted from the surface energies, in which the {110} surface is calculated to dominate in the absence of impurities or surface irregularities, with a lesser contribution from the {100} surface. The surface defect energies are generally lower than in the bulk crystal implying that the dopants and oxygen vacancies will segregate to the surfaces, thus enhancing their catalytic and electrochemical activity.

Computer simulation of the structure and stability of forsterite surfaces

The aim of this paper is to demonstrate that atomistic simulations can be used to evaluate the structure of mineral surfaces and to provide reliable data for forsterite surfaces up to a plane index of 2 using the code METADISE. The methods used to calculate the surface structure and energy which have more commonly been used to study ceramics are briefly explained as is a comparison with experimental data, most notable the crystal morphology. The predicted morphologies show that all the methods (Donnay-Harker, Attachment energies and equilibrium) show most of the surfaces that are expressed in observed crystals. The equilibrium morphology calculated from the relaxed surface energies is the only method which expresses the {201} surfaces and the {101} surfaces, which appear only upon relaxation. The more stable surfaces are shown to be those which have the highest surface density and more closely resemble close packed structures with highly coordinated surface ions and silicon as far from the surface as possible. The most stable surfaces the {100} which has alternating layers of MgO and SiO2 terminating with an MgO layer. The structure is similar to the MgO {100} surfaces and has a similar energy (1.28 Jm−2 compared to 1.20). The second most stable are the {201} which have a stepped surface topology, but is also compact with a relaxed surface energy of 1.56 Jm−2. The results indicate that atomistic simulation is well suited to the prediction of surface structure and morphology although care must be taken in choosing potentials which model the structure and elastic properties accurately.

Tight-binding interatomic potentials based on total-energy calculation: Application to noble metals using molecular-dynamics simulation

We present an alternate approach to parametrizing the expression for the total energy of solids within the second-moment approximation (SMA) of the tight-binding theory. In order to obtain the necessary parameters, we do not use the experimental values of the lattice constant, the elastic constants, and the cohesive energy, but we fit to the total energy obtained from first-principles augmented-plane-wave calculations as a function of volume. In addition, we shift the total-energy graphs uniformly so that at the minimum they give the experimental value of the cohesive energy. We have applied the above methodology to perform molecular-dynamics simulations of the noble metals. For Cu and Ag our results for vacancy formation energies, relaxed surface energies, phonon spectra, and various temperature-dependent quantities are of comparable accuracy to those found by the standard SMA, which is based on fitting to several measured data. However, our approach does not seem to work as well for Au.

Determination of a transferable interatomic potential for alkali-metal perchlorates and its application to morphological modelling

The development of an interatomic potential for alkali-metal perchlorates is presented. The potential is fitted to orthorhombic sodium perchlorate and transferred to the perchlorates of caesium, potassium and rubidium. The derived potential data provide a consistent fit to the known crystal structures and elastic constants. Transferability of the potential to the cubic phase of sodium perchlorate leads to a poorer match to experimental data, which perhaps reflects the fact that this phase only stabilises at a high temperature. Unrelaxed and relaxed surface and attachment energies for the low-index crystal planes are calculated for potassium perchlorate, from which crystal morphologies are predicted. The simulations provide a good match to experimental growth morphologies using the Hartman–Perdok attachment energy model, but a poorer one using the more classical Gibbs–Wulff surface-energy model. Potential growth mechanisms, based on these observations, are discussed.

First-principles calculations of the energetics of stoichiometric TiO2 surfaces.

We present self-consistent ab initio total-energy calculations of the equilibrium relaxed structures and surface energies of the stoichiometric (1\ifmmode\times\else\texttimes\fi{}1) (110), (100), (001), and (011) surfaces of ${\mathrm{TiO}}_{2}$. The relaxations of atoms on these surfaces are found to be substantial, and are responsible for a large reduction of the calculated surface energies. A Wulff construction is used to display the relative energetics of these surfaces. The (100) surface is found to be stable with respect to forming macroscpic (110) facets, while the (001) surface is nearly unstable with respect to forming macroscopic (1\ifmmode\times\else\texttimes\fi{}1) (011) facets. These results shed light on published experimental results on the structures of these surfaces.