Phonon spectra and thermodynamic properties of rare gas solids based on empirical and semi-empirical (ab initio) two-body potentials : a comparative study /

We study the phonon dispersion, cohesive and thermal properties of raxe gas solids Ne, Ar, Kr, and Xe, using a variety of potentials obtained from different approaches; such as, fitting to crystal properties, purely ab initio calculations for molecules and dimers or ab initio calculations for solid crystalline phase, a combination of ab initio calculations and fitting to either gas phase data or sohd state properties. We explore whether potentials derived with a certain approaxih have any obvious benefit over the others in reproducing the solid state properties. In particular, we study phonon dispersion, isothermal ajid adiabatic bulk moduli, thermal expansion, and elastic (shear) constants as a function of temperatiue. Anharmonic effects on thermal expansion, specific heat, and bulk moduli have been studied using A^ perturbation theory in the high temperature limit using the neaxest-neighbor central force (nncf) model as developed by Shukla and MacDonald [4]. In our study, we find that potentials based on fitting to the crystal properties have some advantage, particularly for Kr and Xe, in terms of reproducing the thermodynamic properties over an extended range of temperatiures, but agreement with the phonon frequencies with the measured values is not guaranteed. For the lighter element Ne, the LJ potential which is based on fitting to the gas phase data produces best results for the thermodynamic properties; however, the Eggenberger potential for Ne, where the potential is based on combining ab initio quantum chemical calculations and molecular dynamics simulations, produces results that have better agreement with the measured dispersion, and elastic (shear) values. For At, the Morse-type potential, which is based on M0ller-Plesset perturbation theory to fourth order (MP4) ab initio calculations, yields the best results for the thermodynamic properties, elastic (shear) constants, and the phonon dispersion curves.

Evolution of an Archean greenstone belt in the Stormy Lake - Kawashegamuk Lake area (stratigraphy, structure and geochemistry) - Western Wabigoon Subprovince, Northwest Ontario /

330 km 2 of the easter-n part of the Archean Manitou Lakes - Stormy Lake metavolcanic - metasedimentary belt have been mapped and sampled. A large number of rocks ~.vere analyzed for the major and trace constituents including the rare-earth elements (REE). The Stormy Lake - Kawashegamuk Lake area may be subdivided into four major lithological groups of supracrustal rocks 1) A north-facing mafic assemblage, consisting of pillowed tholeiitic basalts and gabbro sills characterized by flat REE profiles, is exposed in the south part of the map area and belongs to a 8000 m thick homoclinal assemblage outside the map area. Felsic pyroclastic rocks believed to have been issued from a large central vent conformably overlie the tholeiites. 2) A dominantly epiclastic group facing to the north consists of terrestrial deposits interpreted to be an alluvial fan deposit ; a submarine facies is represented by turbiditic sediments. 3) The northeastern part of the study area consists of volcanic rocks belonging to two mafic - felsic cycles facing to the southuest ; andesitic flows with fractionated REE patterns make up a large part of the upper cycle, whereas the lower cycle has a stronger chemical polarity being represented by tholeiitic flows, with flat REE, which a r e succeeded by dacitic and rhyolitic pyroclasti cs. iii 4) A thick monotonous succession of tholeiitic pillmled basalt f lows and gabbro sills with flat REE represent the youngest supracrustal rocks. TIle entire belt underwent folding, faulting and granitic plutonism during a tectono-thermal event around 2700 Ma ago. Rocks exposed in the map area were subjected to regional greenschist facies metamorphism, but higher metamorphic grades are present near late granitic intrusions. Geochemical studies have been useful in 1) distinguishing the various rock units ; 2) relating volcanic and intrusive rocks 3) studying the significance of chemical changes due to post magmatic processes 4) determining the petrogenesis of the major volcanic rock types. In doing so, two major volcanic suites have been recognized : a) a tholeiitic suite, mostly represented by mafic rocks, was derived from partial melting of upper mantle material depleted in Ti, K and the light REE ; b) a calc-alkalic suite which evolved from partial melting of amphibolite in the lower crust. The more differentiated magma types have been produced by a multistage process involving partial melting and fractional crystallization to yield a continuum of compos i t i ons ranging from basaltic andesite to rhyolite. A model for the development of the eastern part of the Manitou Lakes - Stormy Lake belt has been proposed.

An application of cell-cluster theory to a rare gas crystal /|n[by] K. Westera. - 260 St. Catharines [Ont.] : Dept. of Physics, Brock University,

The Lennard-Jones Devonshire 1 (LJD) single particle theory for liquids is extended and applied to the anharmonic solid in a high temperature limit. The exact free energy for the crystal is expressed as a convergent series of terms involving larger and larger sets of contiguous particles called cell-clusters. The motions of all the particles within cell-clusters are correlated to each other and lead to non-trivial integrals of orders 3, 6, 9, ... 3N. For the first time the six dimensional integral has been calculated to high accuracy using a Lennard-Jones (6-12) pair interaction between nearest neighbours only for the f.c.c. lattice. The thermodynamic properties predicted by this model agree well with experimental results for solid Xenon.

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.

Modified statistical methods to calculate rare gas interaction potentials

New density functionals representing the exchange and correlation energies (per electron) are employed, based on the electron gas model, to calculate interaction potentials of noble gas systems X2 and XY, where X (and Y) are He,Ne,Ar and Kr, and of hydrogen atomrare gas systems H-X. The exchange energy density functional is that recommended by Handler and the correlation energy density functional is a rational function involving two parameters which were optimized to reproduce the correlation energy of He atom. Application of the two parameter function to other rare gas atoms shows that it is "universal"; i. e. ,accurate for the systems considered. The potentials obtained in this work compare well with recent experimental results and are a significant improvement over those from competing statistical modelS.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Patterns of faunal change at an upper Cambrian trilobite extinction event, Nolichucky Formation, Tennessee and Virginia

During the Upper Cambrian there were three mass extinctions, each of which eliminated at least half of the trilobite families living in North American shelf seas. The Nolichucky Formation preserves the record of one of these extinction events at the base of the Steptoean Stage. Sixty-six trilobite collections were made from five sections In Tennessee and Virginia. The lower Steptoean faunas are assigned to one low diversity, Aphelaspis-dominated biofacies, which can be recognized in several other parts of North America. In Tennessee, the underlying upper Marjuman strata contain two higher diversity biofacies, the Coosella-Glaphyraspis Biofacies and the Tricrepicephalus-Norwoodiid Biofacies. At least four different biofacies are present in other parts of North America: the Crepicephalus -Lonchocephalus Biofacies, the Kingstonia Biofacies, the Cedaria Biofacies, and the Uncaspis Biofacies. A new, species-based zonation for the Nolichucky Formation imcludes five zones, three of which are new. These zones are the Crepicephalus Zone, the Coosella perplexa Zone, the Aphelaspis buttsi Zone, the A. walcotti Zone and the A. tarda Zone. The Nolichucky Formation was deposited within a shallow shelf basin and consists largely of subtidal shales with stormgenerated carbonate interbeds. A relative deepening is recorded In the Nolichucky Formation near the extinction, and is indicated In some sections by the appearance of shale-rich, distal storm deposits above a carbonate-rich, more proximal storm deposit sequence. A comparable deepening-upward sequence occurs near the extinction in the Great Basin of southwestern United States and in central Texas, and this suggests a possible eustatic control. In other parts of North America, the extinction IS recorded In a variety of environmental settings that range from near-shore to slope. In shelf environments, there is a marked decrease in diversity, and a sharp reduction in biofacies differentiation. Although extinctions do take place in slope environments, there IS no net reduction in diversity because of the immigration of several new taxa.

Slide - Celebrity Ice Wine Event

A slide from the Inniskillin Celebrity Ice Wine event featuring: Michael Burgess, Ron Barbaro; Jonathan Welsh.

Major Sport Event Operational Planning Issues and Strategies: A Multi-Case Delphi Study

This study examined the operational planning, implementation and execution issues of major sport events, as well as the mitigation and management strategies used to address these issues, with the aim of determining best practices in sport event operational planning. The three Research Questions were: 1) What can previous major sport events provide to guide the operational management of future events? 2) What are the operational issues that arise in the planning and execution of a major sport event, how are they mitigated and what are the strategies used to deal with these issues? 3) What are the best practices for sport event operational planning and how can these practices aid future events? Data collection involved a modified Delphi technique that consisted of one round of in-depth interviews followed by two rounds of questionnaires. Both data collection and analysis were guided by an adaptation of the work of Parent, Rouillard & Leopkey (2011) with a focus on previously established issue and strategy categories. The results provided a list of Top 26 Prominent Issues and Top 17 Prominent Strategies with additional issue-strategy links that can be used to aid event managers producing future major sport events. The following issue categories emerged as having had the highest impact on previous major sport events that participants had managed: timing, funding and knowledge management. In addition, participants used strategies from the following categories most frequently: other, formalized agreements and communication.