Rings sliding on a honeycomb network: Adsorption contours, interactions, and assembly of benzene on Cu(111)

Using a van der Waals density functional (vdW-DF) [Phys. Rev. Lett. 92, 246401 (2004)], we perform ab initio calculations for the adsorption energy of benzene (Bz) on Cu(111) as a function of lateral position and height. We find that the vdW-DF inclusion of nonlocal correlations (responsible for dispersive interactions) changes the relative stability of eight binding-position options and increases the binding energy by over an order of magnitude, achieving good agreement with experiment. The admolecules can move almost freely along a honeycomb web of "corridors" passing between fcc and hcp hollow sites via bridge sites. Our diffusion barriers (for dilute and two condensed adsorbate phases) are consistent with experimental observations. Further vdW-DF calculations suggest that the more compact (hexagonal) Bz-overlayer phase, with lattice constant a = 6.74 \AA, is due to direct Bz-Bz vdW attraction, which extends to ~8 \AA. We attribute the second, sparser hexagonal Bz phase, with a = 10.24 \AA, to indirect electronic interactions mediated by the metallic surface state on Cu(111). To support this claim, we use a formal Harris-functional approach to evaluate nonperturbationally the asymptotic form of this indirect interaction. Thus, we can account well for benzene self-organization on Cu(111).Comment: 13 pages, 7 figures, 3 tables, submitted for publication Accepted for publication in Phys. Rev. B. This version contains improved notation (with corresponding relabeling of figures), very small corrections to some tabulated values, and corrections concerning lattice lengths and subsequent discussion of commensurability of unit-cell dimension

Response of the Shockley surface state to an external electrical field: A density-functional theory study of Cu(111)

The response of the Cu(111) Shockley surface state to an external electrical field is characterized by combining a density-functional theory calculation for a slab geometry with an analysis of the Kohn-Sham wavefunctions. Our analysis is facilitated by a decoupling of the Kohn-Sham states via a rotation in Hilbert space. We find that the surface state displays isotropic dispersion, quadratic until the Fermi wave vector but with a significant quartic contribution beyond. We calculate the shift in energetic position and effective mass of the surface state for an electrical field perpendicular to the Cu(111) surface; the response is linear over a broad range of field strengths. We find that charge transfer occurs beyond the outermost copper atoms and that accumulation of electrons is responsible for a quarter of the screening of the electrical field. This allows us to provide well-converged determinations of the field-induced changes in the surface state for a moderate number of layers in the slab geometry.Comment: 11 pages, 6 figures, 4 tables; accepted for publication by Phys. Rev. B; changes from v1 in response to referee comments, esp. to Sections I and V.B (inc. Table 4), with many added references, but no change in results or conclusion

Math, Science, and Engineering Integration in a High School Engineering Course: A Qualitative Study

Engineering in K-12 classrooms has been receiving expanding emphasis in the United States. The integration of science, mathematics, and engineering is a benefit and goal of K-12 engineering; however, current empirical research on the efficacy of K-12 science, mathematics, and engineering integration is limited. This study adds to this growing field, using discourse analysis techniques to examine whether and why students integrate math and science concepts into their engineering design work. The study focuses on student work during a unit from a high school engineering course. Video data were collected during the unit and were used to identify episodes of students discussing math and science concepts. Using discourse analysis, the authors found that students successfully applied math and science concepts to their engineering design work without teacher prompting when the concepts were familiar. However, explicit teacher prompting and instruction regarding the integration of less familiar concepts did not seem to facilitate student use of those concepts. Possible explanations and implications are discussed

In pursuit of consensus: Disagreement and legitimization during small group argumentation

In recent years, an emphasis on scientific argumentation in classrooms has brought into focus collaborative consensus-building as an instructional strategy. In these situations, students with differing and competing arguments are asked to work with one another in order to establish a shared perspective. However, the literature suggests that consensus-building can be challenging for students because their interpretations of the argumentative task and context may not enable their productive engagement with counter-arguments and evidence. In this paper, our goal is to explore the ways in which interactions of students support or inhibit their consensus-building. To that end, we examine and describe three cases that represent different ways in which initially dissenting students try to work towards a consensus with their peers. Through these cases, we demonstrate that legitimization of disparate or incorrect ideas can enable students whose arguments rely on incorrect ideas to feel that their ideas were heard and valued by the rest of their group. As such, we suggest that this legitimization is important because it can help students ‘save face’. This enables students to move away from the competitive and persuasive aspects of argumentation towards interactions that align more closely with sensemaking and consensus-building

Lattice thermal conductivity of Tix_xZry_yHf1−x−y_{1-x-y}NiSn half-Heusler alloys calculated from first principles: Key role of nature of phonon modes

In spite of their relatively high lattice thermal conductivity $\kappa_{\ell}$, the XNiSn (X=Ti, Zr or Hf) half-Heusler compounds are good thermoelectric materials. Previous studies have shown that $\kappa_{\ell}$ can be reduced by sublattice-alloying on the X-site. To cast light on how the alloy composition affects $\kappa_\ell$, we study this system using the phonon Boltzmann-transport equation within the relaxation time approximation in conjunction with density functional theory.The effect of alloying through mass-disorder scattering is explored using the virtual crystal approximation to screen the entire ternary Ti$_x$Zr$_{y}$Hf$_{1-x-y}$NiSn phase diagram. The lowest lattice thermal conductivity is found for the Ti$_x$Hf$_{1-x}$NiSn compositions; in particular, there is a shallow minimum centered at Ti$_{0.5}$Hf$_{0.5}$NiSn with $\kappa_l$ taking values between 3.2 and 4.1 W/mK when the Ti content varies between 20 and 80\%. Interestingly, the overall behavior of mass-disorder scattering in this system can only be understood from a combination of the nature of the phonon modes and the magnitude of the mass variance. Mass-disorder scattering is not effective at scattering acoustic phonons of low energy. By using a simple model of grain boundary scattering, we find that nanostructuring these compounds can scatter such phonons effectively and thus further reduce the lattice thermal conductivity; for instance, Ti$_{0.5}$Hf$_{0.5}$NiSn with a grain size of $L= 100$ nm experiences a 42\% reduction of $\kappa_{\ell}$ compared to that of the single crystal

Graphene Nanogap for Gate Tunable Quantum Coherent Single Molecule Electronics

We present atomistic calculations of quantum coherent electron transport through fulleropyrrolidine terminated molecules bridging a graphene nanogap. We predict that three difficult problems in molecular electronics with single molecules may be solved by utilizing graphene contacts: (1) a back gate modulating the Fermi level in the graphene leads facilitate control of the device conductance in a transistor effect with high on/off current ratio; (2) the size mismatch between leads and molecule is avoided, in contrast to the traditional metal contacts; (3) as a consequence, distinct features in charge flow patterns throughout the device are directly detectable by scanning techniques. We show that moderate graphene edge disorder is unimportant for the transistor function.Comment: 8 pages, 6 figure

Evaluation of New Density Functional with Account of van der Waals Forces by Use of Experimental H2 Physisorption Data on Cu(111)

Detailed experimental data for physisorption potential-energy curves of H2 on low-indexed faces of Cu challenge theory. Recently, density-functional theory has been developed to also account for nonlocal correlation effects, including van der Waals forces. We show that one functional, denoted vdW-DF2, gives a potential-energy curve promisingly close to the experiment-derived physisorptionenergy curve. The comparison also gives indications for further improvements of the functionals

Stochastic B-series and order conditions for exponential integrators

We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential integrators. The resulting general order theory covers both It\^{o} and Stratonovich integration

Understanding adhesion at as-deposited interfaces from ab initio thermodynamics of deposition growth: thin-film alumina on titanium carbide

We investigate the chemical composition and adhesion of chemical vapour deposited thin-film alumina on TiC using and extending a recently proposed nonequilibrium method of ab initio thermodynamics of deposition growth (AIT-DG) [Rohrer J and Hyldgaard P 2010 Phys. Rev. B 82 045415]. A previous study of this system [Rohrer J, Ruberto C and Hyldgaard P 2010 J. Phys.: Condens. Matter 22 015004] found that use of equilibrium thermodynamics leads to predictions of a non-binding TiC/alumina interface, despite the industrial use as a wear-resistant coating. This discrepancy between equilibrium theory and experiment is resolved by the AIT-DG method which predicts interfaces with strong adhesion. The AIT-DG method combines density functional theory calculations, rate-equation modelling of the pressure evolution of the deposition environment and thermochemical data. The AIT-DG method was previously used to predict prevalent terminations of growing or as-deposited surfaces of binary materials. Here we extent the method to predict surface and interface compositions of growing or as-deposited thin films on a substrate and find that inclusion of the nonequilibrium deposition environment has important implications for the nature of buried interfaces.Comment: 8 pages, 6 figures, submitted to J. Phys.: Condens. Matte

Benchmarking van der Waals Density Functionals with Experimental Data: Potential Energy Curves for H2 Molecules on Cu(111), (100), and (110) Surfaces

Detailed physisorption data from experiment for the H_2 molecule on low-index Cu surfaces challenge theory. Recently, density-functional theory (DFT) has been developed to account for nonlocal correlation effects, including van der Waals (dispersion) forces. We show that the functional vdW-DF2 gives a potential-energy curve, potential-well energy levels, and difference in lateral corrugation promisingly close to the results obtained by resonant elastic backscattering-diffraction experiments. The backscattering barrier is found selective for choice of exchange-functional approximation. Further, the DFT-D3 and TS-vdW corrections to traditional DFT formulations are also benchmarked, and deviations are analyzed.Comment: 15 pages, 9 figure