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.

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.

Inventory of Jane C. Woodruff Estate

An inventory of the Jane C. Woodruff estate (5 pages, handwritten). This is a copy. The last page is torn in half. n.d.

List of inventory of goods in the dwelling of S.D. Woodruff of St. Catharines

List of inventory of goods (6 pages, handwritten) in the dwelling of S.D. Woodruff of St. Catharines. This list was examined by William Walker on Oct. 30, 1862 and compiled on Oct. 27, 1862.

List of inventory of goods in the dwelling of S. D. Woodruff, Ontario Street, St. Catharines

List of inventory (5 pages, handwritten) of goods in the dwelling of S. D. Woodruff, Ontario Street, St. Catharines, n.d.

Inventory of goods and chattels belonging to Samuel Wood and delivered to the Honourable William Dickson

Inventory of goods and chattels belonging to Samuel Wood and delivered to the Honourable William Dickson (double-sided, handwritten page), Dec. 10, 1828.

Towards the development of a questionnaire of post transgression motives and behaviours /

The primary purpose of this study was to develop a questionnaire that assesses both forgiveness-seeking motives and behaviours. This questionnaire was based on the premise that, following the commitment of an offense in the context of a relationship, a perpetrator will be motivated to reduce the damage that has taken place. The . ' questionnaire examined several motives that a perpetrator might have for seeking forgiveness. These motives were divided into five proposed domains of posttransgression concerns: God, Self, Victim, Others/Society, and Relationship. Within these domains, the following more specific types of concern were explored: Avoidance of punishment, concern about public image, emotional well-being, self-image, sense of fairness/justice, loss of relationship, loss or gain of power, and loss of ability to trust. The questionnaire also assessed which behaviours (approach and avoidance) a perpetrator might use in order to address these concerns. In addition, this study explored whether or not the severity of the situation and the personality of the perpetrator influenced post transgression motives and behaviours. Participants were 221 individuals from the community and Brock University. They filled out a questionnaire package that assessed personality traits, social desirability, and forgiveness-seeking motives and behaviours. In order to answer items assessing motives and behaviours, participants were asked to imagine themselves as perpetrators in three hypothetical transgression scenarios. These scenarios ranged in severity fi^om low to high. Participants were asked to rate their motives and behaviours both in an immediate time frame (immediately following the transgression) and in the long-term (in order to move on from the situation). Results indicated that the motivation items could be classified into the following subscales:Concern about God, Damaged Self-worth Concerns, Justice Concerns, Impression Management Concerns, Victim and Others Concerns, and Relationship Concerns. The behaviour items formed the following subscales: Approach, Avoidance, Denial and Hiding, and Groveling. Results also indicated differences in motivations and behaviours based on the severity of the situation as well as the personality (assessed using the HEXACO inventory) of the perpetrator.