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.

Water quality and fish populations of the Welland River, Ontario /

The water quality and fish populations of the Welland River were observed to decline with distance downstream. This coincided with increased agricultural , domestic and industrial waste loadings. The river upstream of the City of Welland received considerable loadings from agricultural sources. Centrarchids, sciaenids, ictalurids, cyprinids and esocids characterized this upper section of the river. Most of these species were tolerant of low dissolved oxygen concentrations and the high turbidity which prevailed there . The river near Port Robinson receives many industrial and domestic wastes as evidenced by the water quality data. The fish in this section were less abundant and the observed population was comprised almost solely of cyprinids. Further downstream, near Montrose, the Welland River received shock loads of chemical wastes that exceeded a specific conductance of ISiOOO ;umhos/cm. Few fish were captured at this site and those that were captured were considered to be transients. A review of the literature revealed that none of the common indices of water quality in use today could adequately predict the observed distributions. In addition to the above, the long-term trend (l3 yrs) of water quality of the lower Welland River revealed a gradual improvement. The major factor thought to be responsible for this improvement was the operation of the Welland Sewage Treatment Plant. The construction of the New Welland Ship Canal coincided with large fluctuations of the total solids and other parameters downstream. These conditions prevailed for a maximum of three years (1972- 1975)' Furthermore, spawning times and temperatures, geographic distributions, length-weight regressions and many other descriptive aspects of the ecology of some 26 species/ taxa of fish were obtained. Several of these species are rare or new to southern Ontario.

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.

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.

Some ecological factors affecting the input and population level of total and faecal coliforms and salmonella in Twelve Mile Creek, Lake Ontario and sewage waters near St. Catharines, Ontario

Some Ecological Factors Affecting the Input and Population Levels of Total and Faecal Coliforms and Salmonella in Twelve Mile Creek, Lake Ontario and Sewage Waters Near St. Catharines, Ontario. Supervisor: Dr. M. Helder. The present study was undertaken to investigate the role of some ecological factors on sewage-Dorne bacteria in waters near St. Catharines, Ontario. Total and faecal coliform levels and the presence of Salmonella were monitored for a period of a year along with determination of temperature, pH, dissolved oxygen, total dissolved solids, nitrate N, total phosphate P and ammonium N. Bacteriological tests for coliform analysis were done according to APHA Standard Methods by the membrane filtration technique. The grab sampling technique was employed for all sampling. Four sample sites were chosen in the Port Dalhousie beach area to determine what bacteriological or physical relationship the sites had to each other. The sample sites chosen were the sewage inflow to and the effluent from the St. Catharines (Port Dalhousie) Pollution Control Plant, Twelve Mile Creek below the sewage outfall and Lake Ontario at the Lakeside Park beach. The sewage outfall was located in Twelve Mile Creek, approximately 80 meters from the creek junction with the beach and piers on Lake Ontario. Twelve Mile Creek normally carried a large volume of water from the WeIland Canal which was diverted through the DeCew Generating Station located on the Niagara Escarpment. An additional sample site, which was thought to be free of industrial wastes, was chosen at Twenty Mile Creek, also in the Niagara Region of Ontarioo 3 There were marked variations in bacterial numbers at each site and between each site, but trends to lower_numbers were noted from the sewage inflow to Lake Ontario. Better correlations were noted between total and faecal coliform population levels and total phosphate P and ammonium N in Twenty Mile Creek. Other correlations were observed for other sample stations, however, these results also appeared to be random in nature. Salmonella isolations occurred more frequently during the winter and spring months when water temperatures were minimal at all sample stations except the sewage inflow. The frequency of Salmonella isolations appeared to be related to increased levels of total and faecal coli forms in the sewage effluent. However, no clear relationships were established in the other sample stations. Due to the presence of Salmonella and high levels of total and faecal coliform indicator organisms, the sanitary quality of Lake Ontario and Twelve Mile Creek at the sample sites seemed to be impaired over the major portion of the study period.