Energies Of Different Structures Research Articles

Computing the absolute Gibbs free energy in atomistic simulations: Applications to defects in solids

The Gibbs free energy is the fundamental thermodynamic potential underlying the relative stability of different states of matter under constant-pressure conditions. However, computing this quantity from atomic-scale simulations is far from trivial. As a consequence, all too often the potential energy of the system is used as a proxy, overlooking entropic and anharmonic effects. Here we discuss a combination of different thermodynamic integration routes to obtain the absolute Gibbs free energy of a solid system starting from a harmonic reference state. This approach enables the direct comparison between the free energy of different structures, circumventing the need to sample the transition paths between them. We showcase this thermodynamic integration scheme by computing the Gibbs free energy associated with a vacancy in BCC iron, and the intrinsic stacking fault free energy of nickel. These examples highlight the pitfalls of estimating the free energy of crystallographic defects only using the minimum potential energy, which overestimates the vacancy free energy by 60% and the stacking-fault energy by almost 300% at temperatures close to the melting point.

Modeling the Self-Assembly of Bolaamphiphiles under Nanoconfinement by Coarse-Grained Molecular Dynamics.

Novel and complex nanostructures of amphiphiles assemblies facilitate realizing of many practical applications in nanotechnologies. Under different physical conditions, amphiphiles can form various morphologies. In this article, the self-assembly of bolaamphiphiles was investigated under the cylindrical confinement of carbon nanotubes by coarse-grained molecular dynamics simulation. We found that bolaamphiphiles inside a carbon nanotube with a relatively large diameter tended to self-assemble into curved cylindrical micelles, and further some of these micelles can form double helix structures which were not observed in bulk solutions. We develop an effective method to characterize different morphologies. Our analysis results showed that the formation of double helix and other amorphous morphologies of micelles in carbon nanotubes is not induced by the conformational variation of bolaamphiphiles. Moreover, through examining the potential energies of different structures, we infer that it is entropy which leads micelles to bend even to form double stranded helix structures. In addition, we analyzed the sizes of micelles and find the scission and recombination of micelles during the double helix formation process. This work indicates that the confinement of carbon nanotube is an available method to produce complex nanostructures and provides some new insights of the self-assembly of bolaamphiphiles.

Microstructure, hardness, and wear resistance of sputtering TaN coating by controlling RF input power

Abstract Tantalum nitride (TaN) layers were manufactured with different microstructures through RF magnetron sputtering. Deposition input power of 75 to 150 W was used in fabricating TaN layers with various impingement energies for different structures. A fibrous layer formed near the coating substrate interface for single-layer TaN films because of random stacking of atoms at early stage deposition, following which a compact columnar structure formed. The grain size and surface roughness decreased simultaneously with the input power. The hardness and Young's modulus for a single TaN layer deposited at 150 W were approximately 26.0 and 237.1 GPa, respectively. For single-layer TaN coatings, a compact structure and higher hardness were more beneficial to the wear resistance of the 150 W deposited TaN film than for those deposited at other input powers. Further study on TaN coatings in multilayer systems was conducted to examine protective behaviour. The multilayer TaN coatings consisted of alternately stacked TaN layers fabricated at input powers of 75/150 and 100/150 W. Characteristics of the multilayer coatings, including surface morphology, hardness, Young's modulus, and tribological behaviour, were investigated. The structure of the multilayer TaN films comprised a mixture of the single-layer TaN films. An average hardness between those of crystalline and featureless TaN layers was expected. However, tribological behaviour analysis revealed narrower wear scar and limited film failure on the wear track for multilayer systems. Consequently, the multilayer TaN systems showed greater durability than did the single-layer TaN films.

Self-assembly of 21-arm star-like diblock copolymer in bulk and under cylindrical confinement.

Phase behaviors of a 21-arm star-like diblock copolymer in bulk and under confinement were explored by using the pseudo-spectral method of a self-consistent mean field theory. An asymmetrical phase diagram in bulk was constructed by comparing the free energy of different structures. The gyroid phase was found to possess a large phase region when the inner block in the star-like diblock copolymer has a small volume fraction, suggesting the propensity to form the gyroid phase under this condition. Combined with the early experimental work, a scaling law correlating the period of lamellae D(multiarms) formed from multi-arm star-like block copolymers with the number of arms f was identified, that is, D(multiarms) = D/f(1/2), where D is the period of a linear diblock copolymer with the same degree of polymerization N as a star-like diblock copolymer. The scaling law was also substantiated by the scaling theory. The bridging fraction of the lamellae formed in a star-like diblock copolymer was nearly 100%, which is advantageous for improving its mechanical properties. Some interesting two-dimensional and three-dimensional morphologies were yielded under the cylindrical confinement, where a 3D double helix was found to be the most stable structure.

The pressure dependences of elastic and lattice dynamic properties of AlAs from ab initio calculations

Ab initio calculations, based on norm-conserving nonlocal pseudopotentials and density functional theory (DFT), are performed to investigate the structural, elastic, dielectric, and vibrational properties of aluminum arsenide (AlAs) with a zinc-blende (B3) structure and a nickel arsenide (B81) structure under hydrostatic pressure. Firstly, the path for the phase transition from B3 to B81 is confirmed by analyzing the energies of different structures, which is in good agreement with previous theoretical results. Secondly, we find that the elastic constants, bulk modulus, static dielectric constants, and the optical phonon frequencies vary in a nearly linear manner under hydrostatic pressure. What is more, the softening mode of the transversal acoustic mode at the X point supports the phase transition in AlAs.

Structural determination of (Al2O3)n (n = 1–7) clusters based on density functional calculation

We obtained the geometrical structures of (Al2O3)n (n=1–7) clusters via genetic algorithm plus density functional theory method. Benchmark calculations show that the B3LYP/6-311+G* method is reliable compared to CCSD(T)/aug-cc-pVTZ. However, the basis sets have great effect on relative energies of different structures. The global minimum structures are kite-shaped, cage and tea-cozy in structure for n=1, 2 and 3 respectively, disordered at n=4 and 5. At n=6 and 7, a number of lower-energy isomers are obtained compared to the most stable structures obtained by Rahane et al. (J. Phys. Chem. C 115 (2011) 18111–18121). With increasing cluster size, structures show preference of disorder and some new configurations are derived.

Thorium(IV)–Selenate Clusters Containing an Octanuclear Th(IV) Hydroxide/Oxide Core

Four Th(IV) hydroxide/oxide clusters have been synthesized from aqueous solution. The structures of [Th(8)(μ(3)-O)(4)(μ(2)-OH)(8)(H(2)O)(15)(SeO(4))(8)·7.5H(2)O] (1), [Th(8)(μ(3)-O)(4)(μ(2)-OH)(8)(H(2)O)(17)(SeO(4))(8)·nH(2)O] (2), [Th(9)(μ(3)-O)(4)(μ(2)-OH)(8)(H(2)O)(21)(SeO(4))(10)] (3), and Th(9)(μ(3)-O)(4)(μ(2)-OH)(8)(H(2)O)(21)(SeO(4))(10)·nH(2)O (4) were determined using single crystal X-ray diffraction. Each structure consists of an octanuclear core, [Th(8)O(4)(OH)(8)](16+), that is built from eight Th(IV) atoms (four Th in a plane and two up and two down) linked by four "inner" μ(3)-O and eight "outer" μ(2)-OH groups. Compounds 3 and 4 additionally contain mononuclear [Th(H(2)O)(5)(SeO(4))(4)](4-) units that link the octamers into an extended structure. The octanuclear units are invariably complexed by two selenate anions that sit in two cavities formed by four planar Th(IV) and four extra-planar Th(IV) atoms, thus making [Th(8)O(4)(OH)(8)(SeO(4))(2)](12+) a common building block in 1-4. However, changes in hydration as well selenate coordination give rise to structural differences that are observed in the extended structures of 1-4. The compounds were also characterized by Raman spectroscopy. Density functional theory calculations were performed to predict the geometries, vibrational frequencies, and relative energies of different structures. Details of the calculated structures are in good agreement with experimental results, and the calculated frequencies were used to assign the experimental Raman spectra. On the basis of an analysis of the DFT results, the compound Th(8)O(8)(OH)(4)(SeO(4))(6) was predicted to be a strong gas phase acid but is reduced to a weak acid in aqueous solution. Of the species studied computationally, the dication Th(8)O(6)(OH)(6)(SeO(6))(6)(2+) is predicted to be the most stable in aqueous solution at 298 K followed by the monocation Th(8)O(7)(OH)(5)(SeO(6))(6)(+).

ATAT@WIEN2k: An interface for cluster expansion based on the linearized augmented planewave method

We have developed an interface between the all-electron density functional theory code WIEN2k, and the MIT Ab-initio Phase Stability (MAPS) code of the Alloy-Theoretic Automated Toolkit (ATAT). WIEN2k is an implementation of the full-potential linearized augmented planewave method which yields highly accurate total energies and optimized geometries for any given structure. The ATAT package consists of two parts. The first one is the MAPS code, which constructs a cluster expansion (CE) in conjunction with a first-principles code. These results form the basis for the second part, which computes the thermodynamic properties of the alloy. The main task of the CE is to calculate the many-body potentials or effective cluster interactions (ECIs) from the first-principles total energies of different structures or supercells using the structure-inversion technique. By linking MAPS seamlessly with WIEN2k we have created a tool to obtain the ECIs for any lattice type of an alloy. We have chosen fcc Al–Ti and bcc W–Re to evaluate our implementation. Our calculated ECIs exhibit all features of a converged CE and compare well with literature results.

Orientational structures in solid para-hydrogen in the broken symmetry phase

Calculations of the rotational energies of different structures of solid hydrogen in the broken symmetry phase at $T=0\text{ }\text{K}$ are performed. A method is used that has been applied recently to estimate the pressure transition. It determines the quantum-mechanical ground-state energy of a system of infinite rotors arranged according to a specified symmetry order and interacting through an intermolecular potential. The method is relatively simple and avoids all the approximations typical of simulation techniques. The calculations are performed for five different symmetry systems and the comparison shows that the $\text{Pca}{2}_{1}$ structure is the least energetic.

Molecular simulation studies of the structure of phosphorylcholine self-assembled monolayers

We report a study of the structure of phosphorylcholine self-assembled monolayers (PC-SAMs) on Au(111) surfaces using both molecular mechanics (MM) and molecular dynamics (MD) simulation techniques. The lattice structure (i.e., packing densities and patterns) of the PC chains was determined first, by examining the packing energies of different structures by MM simulations in an implicit solvent. The chain orientation (i.e., antiparallel and parallel arrangements of the PC head groups) was then evaluated. The initial azimuthal angles of the PC chains were also adjusted to ensure that the optimal lattice structure was found. Finally, the two most probable lattice structures were solvated with explicit water molecules and their energies were compared after 1.5 ns of MD simulations to verify the optimal structures obtained from MM. We found that the optimal lattice structure of the PC-SAM corresponds to a radical7 x radical7 R19degree lattice structure (i.e., surface coverage of 50.4 A(2)molecule) with a parallel arrangement of the head groups. The corresponding thickness of the optimal PC-SAM is 13.4 A which is in agreement with that from experiments. The head groups of the PC chains are aligned on the surface in such a way that their dipole components are minimized. The P-->N vector of the head groups forms an angle of 82 degrees with respect to the surface normal. The tilt direction of molecular chains was observed to be towards their next nearest neighbor.

First-principles studies of structures and stabilities of Pb/Si(111)

Various structures of Pb/Si(111) from 1/6 ML to 4/3 ML are investigated using first-principles calculations. Our calculations for the 1/6-ML mosaic phase and 1/3-ML $\ensuremath{\beta}$-phase yield good agreement with the experimental results. The higher coverage range $1/3<\ensuremath{\theta}<4/3\mathrm{ML}$ has been controversial experimentally, especially close to 4/3 ML with several different phases being observed $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{7},$ hexagonal incommensurate, striped incommensurate, etc.). We compare the unit cell energies of different structures to deduce the energetically favorable ones. Structures consisting of very flat Pb overlayers have lower energy than missing-top-layer structures or structures with stacking faults. This is in very good agreement with experiments which measure high Pb mobility on the $\ensuremath{\alpha}$ phase.

Growth mechanism and Raman spectroscopic study of “interlinked-cone" shaped CNx nanotubes

CNx nanotubes have been generated by thermal decomposition of ferrocene/xylene over cobalt powder at 780℃—940℃ in an atmosphere of N2, H2 and NH3 released from NH4Cl pyrolyzing at 300℃. The high-resolution transmission electron microscope (HRTEM) images show that the tubes consist of unusual “interlinked-cone". The catalytic growth mechanism of CNx nanotubes is discussed based on the formation energy of different structures. Raman spectroscopic studies show that the ID/IG ratio represents the crystallinity of the CNx nanotubes. The shift of the Raman band to higher frequencies confirms the nitrogen incorporation.

Hardness and Polarizability Profiles for Intramolecular Proton Transfer in Water Dimer Radical Cation

In view of the recently reported discrepancies in the prediction of minimum energy structure (proton-transferred vs hemibonded) for the water dimer on ionization, we have performed complete active-space self-consistent field calculations followed by total energy evaluation using multiconfigurational quasi-degenerate perturbation theory to obtain very accurate relative energies of different structures and predicted the proton-transferred structure to be the most stable ones. The variations of hardness, polarizability, chemical potential, and energy for the proton-transfer process in this weakly interacting system (ionized water dimer species) are investigated through calculations using Hartree−Fock theory. It is observed that the transition state corresponding to the proton-transfer process is associated with maximum polarizability at different O−O distances for the water dimer cation, although the hardness minimum does not exactly correspond to the transition state. However, the hardness profiles scaled suitably with chemical potential are found to have minima at the transition states.

Metallization of molecular hydrogen: predictions from exact-exchange calculations.

We study metallization of molecular hydrogen under pressure using exact-exchange (EXX) Kohn-Sham density-functional theory in order to avoid well-known underestimates of band gaps associated with standard local-density or generalized-gradient approximations. Compared with the standard methods, the EXX approach leads to considerably (1-2 eV) higher gaps and significant changes in the relative energies of different structures. Metallization is predicted to occur at a density of greater, approximately greater than 0.6 mol/cm(3) (corresponding to a pressure of greater, approximately greater than 400 GPa), consistent with all previous measurements.

Determination of the high c/a ratio of hexagonal metals with a semi-empirical tight-binding method

A semi-empirical tight-binding potential is developed to reproduce the high c/a ratio of zinc and cadmium. In this scheme, we show that the calculation of the electronic energy by the standard recursion method with the Harrison model for the hopping integrals and their radius dependence is not able to predict c/a values higher than the ideal one γ0=8/3=1.633. Only, the recursion method limited to first neighbours has permitted to get the right c/a ratio of zinc and cadmium. The calculated energies of different structures (2H, 4H, 6H and 3C) show that the hexagonal compact structure (2H) is always most stable.

On the question of salt bridges of cationized amino acids in the gas phase: glycine and arginine

The geometrical shapes of the sodiated and cesiated amino acids glycine and arginine were probed in the gas phase by using the ion mobility based ion chromatography method. The data were compared to those obtained for alkali cationized methyl esters and for all the protonated species. Molecular mechanics, semiempirical, and ab initio/density functional theory (DFT) calculations were carried out to generate model structures for comparison with experiment and to determine the relative energies of different structures. For alkali cationized glycine the experimental cross sections agreed with charge solvation structures which were found by calculation to be the most stable forms as well. Both experiment and theory indicated that sodium is solvated by both the amino and the carbonyl groups, while cesium is solvated by one or both oxygen(s) of the carboxyl group. Alkali cationized arginine was found to form a salt bridge structure. The carboxylate group is stabilized by both the charged guanidinium group and the alkali ion. High level (6-311++G∗∗ and DZVP) ab initio/DFT calculations carried out on sodiated and rubidiated N amidinoglycine, which contains a guanidino group and which was used as a model for the larger arginine molecule, indicated that the salt bridge structures are ∼10 kcal/mol more stable than the charge solvation forms for both alkali ions. The structure of protonated arginine, i.e. salt bridge or charge solvation, could not be unambiguously determined.

Crystal Structures of Zirconia from First Principles and Self-Consistent Tight Binding

The origin of the relative stability of the cubic, tetragonal, and monoclinic phases of zirconia $(\mathrm{ZrO}{}_{2})$ is investigated. To obtain accurate energies we adopt a new all-electron bandstructure approach within the local density approximation, based on muffin tin orbitals. We also develop a self-consistent tight-binding model with which to study the energies for different structures. The tight-binding model enables us to analyze ab initio and experimental phase stabilities in terms of ionic versus covalent effects, including polarization of the anions, and promises to be useful for rapid simulation of more complex systems.

Theory of surfactant-mediated growth on semiconductor surfaces

The surfactant effect, first demonstrated by Copel et al. [Phys. Rev. Lett. 63 (1989) 632] by using As to promote epitaxial growth of Ge on Si(100), has now been studied in a wide variety of systems, thus making systematic studies possible. We present theoretical models that account for the observed behavior of various surfactants on semiconductor surfaces, including homo-epitaxial and hetero-epitaxial growth. The theoretical models include first-principles calculations of the relative energy of different structures associated with surfactant layers and the activation energies for diffusion and exchange mechanisms, as well as solid-on-solid Monte Carlo simulations.

C 28: the smallest stable fullerene?

The relative energies of different structures of C 28 have been studied by density functional theory using different exchange-correlation functionals, including two with exact exchange contributions. A fullerene structure with T d symmetry ( 5A 2 state) is found to be by far the most stable structure, followed at 4–6 eV by a graphite sheet fragment and at 5–7 eV by a C 14h ring. Other structures lie still higher in energy. An infrared spectrum of fingerprint quality has been computed for the fullerene and should enable its experimental identification.

Structure of Water Clusters. The Contribution of Many-Body Forces, Monomer Relaxation, and Vibrational Zero-Point Energy

The vibrationally averaged properties of small water clusters from the dimer to the hexamer are discussed. The potential energy surface used contains explicit many-body terms which allows the non-pairwise interactions to be considered. The ground vibrational states are calculated accurately using a diffusion quantum Monte Carlo algorithm which gives vibrationally averaged rotational constants in good agreement with experiment. The many-body forces cause a destabilization of the more closed structures, and there is a significant variation in the intermolecular zero-point energies for different structures. Cyclic structures are easily the most stable for the trimer and tetramer; in the latter case, this is probably due to the three- and four-body forces. The cyclic pentamer is also probably the structure with the highest dissociation energy when all effects are considered. For the hexamer, a noncyclic cagelike structure is found to be most stable and its stability is due to a relatively low zero-point energy.