Phonon spectra and thermal properties of some fcc metals using embedded-atom potentials /

By employing the embedded-atom potentials of Mei et ai.[l], we have calculated the dynamical matrices and phonon dispersion curves for six fee metals (Cu,Ag,Au,Ni,Pd and Pt). We have also investigated, within the quasiharmonic approximation, some other thermal properties of these metals which depend on the phonon density of states, such as the temperature dependence of lattice constant, coefficient of linear thermal expansion, isothermal and adiabatic bulk moduli, heat capacities at constant volume and constant pressure, Griineisen parameter and Debye temperature. The computed results are compared with the experimental findings wherever possible. The comparison shows a generally good agreement between the theoretical values and experimental data for all properties except the discrepancies of phonon frequencies and Debye temperature for Pd, Pt and Au. Further, we modify the parameters of this model for Pd and Pt and obtain the phonon dispersion curves which is in good agreement with experimental data.

Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.

Effect of iron on reactivity of vanillin in wine models /

Phenolic compounds are important components of grapes and wines. They have been found to have important roles in grape and wine systems and properties that are beneficial for human health. Vanillin (3-methoxy-4-hydroxybenzaldehyde) is a phenolic compound coming from the oxidative degradation of lignin in oak-barrels during the aging of wine. Vanillin is an important flavour component of wine and its concentration in wine influences significantly the aroma and flavour of wine. The concentration of vanillin in wine is affected by various factors including the presence of metal ions. In this work, by using HPLC, HPLC-MS, and MS technologies, iron (III) cations were found to affect the oxidation of vanillin in a model system of wine, and the product of the oxidation was identified as divanillin. The mechanism of the redox reaction between vanillin and Fe^"^ is thought to follow that of other phenol oxidations. Increasing the concentration of Fe ^ in the model system accelerates divanillin production. The best pH condition for the divanillin production in the system is the range of 3.0 ~ 3.5. Increasing temperature from 20°C to 40°C accelerates the divanillin production. Divanillin was found to exist in three commercial red wines in this work. Keeping the storage temperature cool and decreasing the contact of grapes and wines with iron are two major measures suggested by this work in order to decrease the oxidation of vanillin during the making and aging of wine.

Half-sandwich silane complexes of ruthenium and iron : synthesis, structure and application to catalysis

The present thesis describes syntheses, structural studies, and catalytic reactivity of new non-classical silane complexes of ruthenium and iron. The ruthenium complexes CpRu(PPri3)CI(T]2-HSiR3) (1) (SiR3 = SiCh (a), SiClzMe (b), SiCIMe2 (c), SiH2Ph (d), SiMe2Ph (e» were prepared by reactions of the new unsaturated complex CpRu(PPri3)CI with silanes. According to NMR studies and X-ray analyses, the complexes la-c exhibit unusual simultaneous Si··· H and Si··· CI-Ru interactions. The complex CpRu(PPri3)CI was also used for the preparation of the first examples of late transition metal agostic silylamido complexes CpRu(PPri3)(N(T]2-HSiMe2)R) (2) (R= Ar or But), which were characterized by NMR spectroscopy. The iron complexes CpFe(PMePri2)H2(SiR3) (3) (SiR3 = SiCh (a), SiClzMe (b), SiCIMe2 (c), SiH2Ph (d), SiMe2Ph (e» were synthesized by the reaction of the new borohydride iron complex CpFe(PMePri2)(B~) with silanes in the presence NEt3. The complexes 3 exhibit unprecedented two simultaneous and equivalent Si··· H interactions, which was confirmed by X-ray analyses and DFT calculations. A series of cationic ruthenium complexes [CpRu(PR3)(CH3CN)(112-HSiR'3)]BAF (PR3 = PPri 3 (4), PPh3 (5); SiR'3 = SiCh (a), SiClzMe (b), SiClMe2 (c), SiH2Ph (d), SiMe2Ph (e» was obtained by substitution of one of the labile acetonitrile ligands in [CpRu(PR3)(CH3CNh]BAF with sHanes. Analogous complexes [TpRu(PR3)(CH3CN)(T]2 -HSiR' 3)]BAF (5) were obtained by the reaction of TpRu(PR3)(CH3CN)CI with LiBAF in the presence of silanes. The complexes 4-5 were characterized by NMR spectroscopy, and the observed coupling constants J(Si-H) allowed us to estimate the extent of Si-H bond activation in these compounds. The catalytic activity in hydrosilylation reactions of all of the above complexes was examined. The most promising results were achieved with the cationic ruthenium precatalyst [CpRu(PPri3)(CH3CN)2t (6). Complex 6 shows good to excellent catalytic activity in the hydrosilylation of carbonyls, dehydrogenative coupling of silanes with alcohols, amines, acids, and reduction of acid chlorides. We also discovered very selective reduction of nitriles and pyridines into the corresponding N-silyl imines and l,4-dihydropyridines, respectively, at room temperature with the possibility of catalyst recycling. These chemoselective catalytic methods have no analogues in the literature. The reactions were proposed to proceed via an ionic mechanism with intermediate formation of the silane a-complexes 4.

Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Modeling short-range ballistic missile defense and Israel's Iron Dome system

This paper develops a model of short-range ballistic missile defense and uses it to study the performance of Israel’s Iron Dome system. The deterministic base model allows for inaccurate missiles, unsuccessful interceptions, and civil defense. Model enhancements consider the trade-offs in attacking the interception system, the difficulties faced by militants in assembling large salvos, and the effects of imperfect missile classification by the defender. A stochastic model is also developed. Analysis shows that system performance can be highly sensitive to the missile salvo size, and that systems with higher interception rates are more “fragile” when overloaded. The model is calibrated using publically available data about Iron Dome’s use during Operation Pillar of Defense in November 2012. If the systems performed as claimed, they saved Israel an estimated 1778 casualties and $80 million in property damage, and thereby made preemptive strikes on Gaza about 8 times less valuable to Israel. Gaza militants could have inflicted far more damage by grouping their rockets into large salvos, but this may have been difficult given Israel’s suppression efforts. Counter-battery fire by the militants is unlikely to be worthwhile unless they can obtain much more accurate missiles.

Iron Mountain Route Railway schedule: the great through line St. Louis, Arkansas and Texas to the Hot Springs of Arkansas

Iron Mountain Route Railway schedule: the great through line St. Louis, Arkansas and Texas to the Hot Springs of Arkansas.

Letter to S.D. Woodruff from William Colburn with the letterhead “Office of Detroit Bridge and Iron Works”

Letter to S.D. Woodruff from William Colburn with the letterhead “Office of Detroit Bridge and Iron Works” regarding stating that he closed up the business with Dewey’s. He states that “we” now have “warranty deeds” from them for exclusive rights for all time for hunting, shooting and trapping, Mar. 20, 1884.

Letter to S.D. Woodruff from A. Jeffrey importer of Hardware, Iron, Steel, and Window Glass of St. Catharines, Ont.

Letter to S.D. Woodruff from A. Jeffrey importer of Hardware, Iron, Steel, and Window Glass of St. Catharines, Ont. A. Jeffrey says that he will be able to supply Mr. Woodruff with glass and iron pipe, June 7, 1875.

Letter to S.D. Woodruff from A. Jeffrey importer of Hardware, Iron, Steel, and Window Glass of St. Catharines, Ont.

Letter to S.D. Woodruff from A. Jeffrey importer of Hardware, Iron, Steel, and Window Glass of St. Catharines, Ont. regarding breakage and freight, June 23, 1875.

Receipt from A. Jeffrey importer of Hardware, Iron, Steel, Nails and etc

Receipt from A. Jeffrey importer of Hardware, Iron, Steel, Nails and etc. regarding payment received on glass panes, Nov. 12, 1875.

Receipt from Gourlay Brothers for iron thimble and stopper

Receipt from Gourlay Brothers for iron thimble and stopper, Sept. 9, 1876.

Receipt from Watkins and Harris, Wholesale and Retail Ironmongers, Toronto, Ontario for iron

Receipt from Watkins and Harris, Wholesale and Retail Ironmongers, Toronto, Ontario for iron, May 11, 1838.