Structural and chemical embrittlement of grain boundaries by impurities: A general theory and first-principles calculations for copper

First-principles calculations of the Sigma 5(310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However, numerical results show a striking equivalence between the alkali metal Na and the semimetal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unraveled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the net reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect.

Multi-zone TAP-reactors theory and application - IV. Ideal and non-ideal boundary conditions

We study the influence of non-ideal boundary and initial conditions (BIC) of a temporal analysis of products (TAP) reactor model on the data (observed exit flux) analysis. The general theory of multi-response state-defining experiments for a multi-zone TAP reactor is extended and applied to model several alternative boundary and initial conditions proposed in the literature. The method used is based on the Laplace transform and the transfer matrix formalism for multi-response experiments. Two non-idealities are studied: (1) the inlet pulse not being narrow enough (gas pulse not entering the reactor in Dirac delta function shape) and (2) the outlet non-ideality due to imperfect vacuum. The effect of these non-idealities is analyzed to the first and second order of approximation. The corresponding corrections were obtained and discussed in detail. It was found that they are negligible. Therefore, the model with ideal boundary conditions is proven to be completely adequate to the description and interpretation of transport-reaction data obtained with TAP-2 reactors.

General rules for predicting where a catalytic reaction should occur on metal surfaces: A density functional theory study of C-H and C-O bond breaking/making on flat, stepped, and kinked metal surfaces

To predict where a catalytic reaction should occur is a fundamental issue scientifically. Technologically, it is also important because it can facilitate the catalyst's design. However, to date, the understanding of this issue is rather limited. In this work, two types of reactions, CH4 CH3 + H and CO C + 0 on two transition metal surfaces, were chosen as model systems aiming to address in general where a catalytic reaction should occur. The dissociations of CH4 - CH3 + H and CO --> C + O and their reverse reactions on flat, stepped, and kinked Rh and Pd surfaces were studied in detail. We find the following: First, for the CH4 Ch(3) + H reaction, the dissociation barrier is reduced by similar to0.3 eV on steps and kinks as compared to that on flat surfaces. On the other hand, there is essentially no difference in barrier for the association reaction of CH3 + H on the flat surfaces and the defects. Second, for the CO C + 0 reaction, the dissociation barrier decreases dramatically (more than 0.8 eV on Rh and Pd) on steps and kinks as compared to that on flat surfaces. In contrast to the CH3 + H reaction, the C + 0 association reaction also preferentially occurs on steps and kinks. We also present a detailed analysis of the reaction barriers in which each barrier is decomposed quantitatively into a local electronic effect and a geometrical effect. Our DFT calculations show that surface defects such as steps and kinks can largely facilitate bond breaking, while whether the surface defects could promote bond formation depends on the individual reaction as well as the particular metal. The physical origin of these trends is identified and discussed. On the basis of our results, we arrive at some simple rules with respect to where a reaction should occur: (i) defects such as steps are always favored for dissociation reactions as compared to flat surfaces; and (ii) the reaction site of the association reactions is largely related to the magnitude of the bonding competition effect, which is determined by the reactant and metal valency. Reactions with high valency reactants are more likely to occur on defects (more structure-sensitive), as compared to reactions with low valency reactants. Moreover, the reactions on late transition metals are more likely to proceed on defects than those on the early transition metals.

General insight into CO oxidation: A density functional theory study of the reaction mechanism on platinum oxides

CO oxidation on PtO2(110) has been studied using density functional theory calculations. Four possible reaction mechanisms were investigated and the most feasible one is the following: (i) the O at the bridge site of PtO2(110) reacts with CO on the coordinatively unsaturated site (CUS) with a negligible barrier; (ii) O-2 adsorbs on the bridge site and then interacts with CO on the CUS to form an OO-CO complex; (iii) the bond of O-OCO breaks to produce CO2 with a small barrier (0.01 eV). The CO oxidation mechanisms on metals and metal oxides are rationalized by a simple model: The O-surface bonding determines the reactivity on surfaces; it also determines whether the atomic or molecular mechanism is preferred. The reactivity on metal oxides is further found to be related to the 3rd ionization energy of the metal atom.

Dazed and Confused: Accidental Mixtures of Goods and the Theory of Acquisition of Title

This paper explores the law of accidental mixtures of goods. It traces the development of the English rules on mixture from the seminal nineteenth century case of Spence v Union Marine Insurance Co to the present day, and compares their responses to those given by the Roman law, which always has been claimed as an influence on our jurisprudence in this area. It is argued that the different answers given by English and Roman law to essentially the same problems of title result from the differing bases of these legal systems. Roman a priori theory is contrasted with the more practical reasoning of the common law, and while both sets of rules are judged to be coherent on their own terms, it is suggested that the difference between them is reflective of a more general philosophical disagreement about the proper functioning of a legal system, and the relative importance of theoretical and pragmatic considerations.

Dimension theory and nonstable K1 of quadratic modules

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E2n(A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G2n(A, ) G2n0(A, ) G2n1(A, ) E2n(A, ) of the general quadratic group G2n(A, ) such that G2n(A, )/G2n0(A, ) is Abelian, G2n0(A, ) G2n1(A, ) is a descending central series, and G2nd(A)(A, ) = E2n(A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K1,2n(A, ) is solvable when d(A) <.

Insight into the solvent effect: A density functional theory study of cisplatin hydrolysis

The solvent effect on reactions in solutions is crucial for many systems. In this study, the reaction barrier with respect to the number of solvent molecules included in the system is systematically studied using density function theory calculations. Our results show that the barriers rapidly converge with respect to the number of solvent molecules. The solvent effect is investigated by calculating cisplatin hydrolysis in several types of solvents. The results are analyzed and a linear relationship between the reaction barrier and the interaction strength of solvent-reactants is found. Insight into the general solvent effect is obtained. (c) 2006 American Institute of Physics.

Identifying an O-2 supply pathway in CO oxidation on Au/TiO2(110): A density functional theory study on the intrinsic role of water

Au catalysis has been one of the hottest topics in chemistry in the last 10 years or so. How O-2 is supplied and what role water plays in CO oxidation are the two challenging issues in the field at the moment. In this study, using density functional theory we show that these two issues are in fact related to each other. The following observations are revealed: (i) water that can dissociate readily into OH groups can facilitate O-2 adsorption on TiO2; (ii) the effect of OH group on the O-2 adsorption is surprisingly long-ranged; and (iii) O-2 can also diffuse along the channel of Ti (5c) atoms on TiO2(1 10), and this may well be the rate-limiting step for the CO oxidation. We provide direct evidence that O-2 is supplied by O-2 adsorption on TiO2 in the presence of OH and can diffuse to the interface of Au/TiO2 to participate in CO oxidation. Furthermore, the physical origin of the water effects on Au catalysis has been identified by electronic structure analyses: There is a charge transfer from TiO2 in the presence of OH to O-2, and the O-2 adsorption energy depends linearly on the 02 charge. These results are of importance to understand water effects in general in heterogeneous catalysis.

CO oxidation and NO reduction on metal surfaces: density functional theory investigations

This article reviews the accumulated theoretical results, in particular density functional theory calculations, on two catalytic processes, CO oxidation and NO reduction on metal surfaces. Owing to their importance in automotive emission control, these two reactions have generated a lot of interest in the last 20 years. Here the pathways and energetics of the involved elementary reactions under different catalytic conditions are described in detail and the understanding of the reactions is generalized. It is concluded that density functional theory calculations can be applied to catalysis to elucidate mechanisms of complex surface reactions and to understand the electronic structure of chemical processes in general. The achieved molecular knowledge of chemical reactions is certainly beneficial to new catalyst design.

Insight into association reactions on metal surfaces: Density-functional theory studies of hydrogenation reactions on Rh(111)

Hydrogenation reaction, as one of the simplest association reactions on surfaces, is of great importance both scientifically and technologically. They are essential steps in many industrial processes in heterogeneous catalysis, such as ammonia synthesis (N-2+3H(2)-->2NH(3)). Many issues in hydrogenation reactions remain largely elusive. In this work, the NHx (x=0,1,2) hydrogenation reactions (N+H-->NH, NH+H-->NH2 and NH2+H-->NH3) on Rh(111) are used as a model system to study the hydrogenation reactions on metal surfaces in general using density-functional theory. In addition, C and O hydrogenation (C+H-->CH and O+H-->OH) and several oxygenation reactions, i.e., C+O, N+O, O+O reactions, are also calculated in order to provide a further understanding of the barrier of association reactions. The reaction pathways and the barriers of all these reactions are determined and reported. For the C, N, NH, and O hydrogenation reactions, it is found that there is a linear relationship between the barrier and the valency of R (R=C, N, NH, and O). Detailed analyses are carried out to rationalize the barriers of the reactions, which shows that: (i) The interaction energy between two reactants in the transition state plays an important role in determining the trend in the barriers; (ii) there are two major components in the interaction energy: The bonding competition and the direct Pauli repulsion; and (iii) the Pauli repulsion effect is responsible for the linear valency-barrier trend in the C, N, NH, and O hydrogenation reactions. For the NH2+H reaction, which is different from other hydrogenation reactions studied, the energy cost of the NH2 activation from the IS to the TS is the main part of the barrier. The potential energy surface of the NH2 on metal surfaces is thus crucial to the barrier of NH2+H reaction. Three important factors that can affect the barrier of association reactions are generalized: (i) The bonding competition effect; (ii) the local charge densities of the reactants along the reaction direction; and (iii) the potential energy surface of the reactants on the surface. The lowest energy pathway for a surface association reaction should correspond to the one with the best compromise of these three factors. (C) 2003 American Institute of Physics.

General trends in the barriers of catalytic reactions on transition metal surfaces

A catalyst preparation by design is one of the ultimate goals in chemistry. The first step towards this goal is to understand the origin of reaction barriers. In this study, we have investigated several catalytic reactions on some transition metal surfaces, using density functional theory. All the reaction barriers have been determined. By detailed analyses we obtain some insight into the reaction barrier. Each barrier is related to (i) the potential energy surface of reactants on the surface, (ii) the total chemisorption energy of reactants, and (iii) the metal d orbital occupancy and the reactant valency. (C) 2001 American Institute of Physics.

General trends in CO dissociation on transition metal surfaces

Dissociative adsorption is one of the most important reactions in catalysis. In this communication we propose a model aiming to generalize the important factors that affect dissociation reactions. Specifically, for a dissociation reaction, say AB -->A + B, the model connects the dissociation barrier with the association barrier, the chemisorption energies of A and B at the final state and the bonding energy of AB in the gas phase. To apply this model, we have calculated CO dissociation on Ru(0001), Rh(111), Pd(111) (4d transition metals), Os(0001), Ir(111), and Pt(111) (5d transition metals) using density function theory (DFT). All the barriers are determined. We find that the DFT results can be rationalized within the model. The model can also be used to explain many experimental observations. (C) 2001 American Institute of Physics.

Imitation and 'theory of mind' competencies in discrimination of autism from other neurodevelopmental disorders

Several studies have reported imitative deficits in autism spectrum disorder (ASD). However, it is still debated if imitative deficits are specific to ASD or shared with clinical groups with similar mental impairment and motor difficulties. We investigated whether imitative tasks can be used to discriminate ASD children from typically developing children (TD) and children with general developmental delay (GDD). We applied discriminant function analyses to the performance of these groups on three imitation tasks and tests of dexterity, motor planning, verbal skills, theory of mind (ToM). Analyses revealed two significant dimensions. The first represented impairment of dexterity and verbal ability, and discriminated TD from GDD children. Once these differences were accounted for, differences in ToM and the three imitation tasks accounted for a significant proportion of the remaining intergroup variance and discriminated the ASD group from other groups. Further analyses revealed that inclusion of imitative tasks increased the specificity and sensitivity of ASD classification and that imitative tasks considered alone were able to reliably discriminate ASD, TD and GDD. The results suggest that imitation and theory of mind impairment in autism may stem from a common domain of origin separate from general cognitive and motor skill.

Electro-thermal theory of intermodulation distortion in lossy microwave components

An analytic formulation of dynamic electro-thermally induced nonlinearity is developed for a general resistive element, yielding a self-heating circuit model based on a fractional derivative. The model explains the 10 dB/decade slope of the intermodulation products observed in two-tone testing. Two-tone testing at 400 MHz of attenuators, microwave chip terminations, and coaxial terminations is reported with tone spacing ranging from 1 to 100 Hz.