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.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

Dechanneling of 2 Mev Heâ ½ in gold

Thick gold single crystals of high quality were prepared for Rutherford Backscattering Dechanneling studies by electropolishing and annealing. The variation.; with temperature of the Random Fraction versus Depth spectrtnn for 2 MeV He+ on < 110> gold was extracted from measured Aligned and Random (Energy) Spectra. The measured dechanneling rate showed a sixfold increase in going from 4loK to 293°K and is in reasonable agreement with calculations made using the Steady Increase in Transverse Energy (SITE) approximation.

On the formulation and the calculation of the harmonic contributions to the Debye-Waller factor in metals (sodium)

The algebraic expressions for the anharmonic contributions to the Debye-Waller factor up to 0(A ) and 0 L% ) £ where ^ is the scattering wave-vector] have been derived in a form suitable for cubic metals with small ion cores where the interatomic potential extends to many neighbours. This has been achieved in terms of various wave-vector dependent tensors, following the work of Shukla and Taylor (1974) on the cubic anharmonic Helmholtz free energy. The contribution to the various wave-vector dependent tensors from the coulomb and the electron-ion terms in the interatomic metallic potential has been obtained by the Ewald procedure. All the restricted multiple whole B r i l l o u i n zone (B.Z.) sums are reduced to single whole B.Z. sums by using the plane wave representation of the delta function. These single whole B.Z. sums are further reduced to the •%?? portion of the B.Z. following Shukla and Wilk (1974) and Shukla and Taylor (1974). Numerical calculations have been performed for sodium where the Born-Mayer term in the interatomic potential has been neglected because i t is small £ Vosko (1964)3 • *n o^er to compare our calculated results with the experimental results of Dawton (1937), we have also calculated the r a t io of the intensities at different temperatures for the lowest five reflections (110), (200), (220), (310) and (400) . Our calculated quasi-harmonic results agree reasonably well with the experimental results at temperatures (T) of the order of the Debye temperature ( 0 ). For T » © ^ 9 our calculated anharmonic results are found to be in good agreement with the experimental results.The anomalous terms in the Debye-Waller factor are found not to be negligible for certain reflections even for T ^ ©^ . At temperature T yy Op 9 where the temperature is of the order of the melting temperature (Xm) » "the anomalous terms are found to be important almost for all the f i ve reflections.

Benefits, challenges, and limitations of fair trade as a social justice movement

This thesis answers some important questions about how Fair Trade is experienced and perceived by some Northern sellers, consumers, activists, advocates, practitioners, and an importer. As it relates to sellers, I focus only on small scale independent businesses (i.e. I do not include large corporate businesses in my interview sample). Fair Trade works to establish a dignified livelihood for many producers in the South. Some of the most important actors in the Fair Trade movement are the people who buy, sell, and/or advocate for Fair Trade in the North. Fair Trade is largely a consumer movement which relies on the purchase of Fair Trade products. Without consumers purchasing Fair Trade products, retailers providing the products for sale, and activists raising awareness of Fair Trade, the movement, as it is presently constituted, would be non-existent. This qualitative research is based on 19 in-depth i.nterviews with nine interviewees involved with Fair Trade in Canada. I focus on benefits, challenges, and limitations of Fair Trade in the context of their involvement with it. I describe and analyze how people become involved with Fair Trade, what motivates them to do so, what they hope to achieve, and the benefits of being involved. I also describe and analyze how people understand and deal with any challenges and limitations associated with their involvement with Fair Trade. I also explore whether involvement with Fair Trade influences how people think about other products that they purchase and, if so, in what ways. I focus mainly on the commodity of coffee, but my discussion is not limited to this single commodity. Interviewees' experiences with and participation in Fair Trade vary in terms of their level of involvement and interest in the broader Fair Trade movement (as opposed to just participating in the market component). This research reveals that while Fair Trade is a small movement, sellers, consumers, and activists have had much success in the advancement of Fair Trade. While challenges have not deterred interviewees from continuing to participate in Fair Trade, analysis and explanation of such challenges provides the opportunity for Fair Trade practitioners to develop effective solutions in an effort to meet the needs of various Fair Trade actors.

Investigation of Changes in Prescribed and Voluntary Job Roles in Community Service Delivery for People who have Intellectual Disabilities after the Implementation of the 3 Rs; Rights, Respect and Responsibility Project

The purpose of this thesis was to explore whether there is change in organizational citizenship behaviours in community agency staff following agency adoption of a rights - based service philosophy. Four community agency support staff were interviewed to investigate how residential care providers in services for persons who have intellectual disabilities describe their voluntary job related behaviours following training about human rights. The major finding was that the participants were actively engaged in displaying civic virtue, courtesy, and altruism discretionary behaviours. There was evidence of a post rights training shift in communication patterns with support staff reporting that they used language that prom,oted and advocated for human rights, and reported increased communication exchanges among persons supported by the agency, support staff and managers. Participants also suggested that the individuals they support asserted their rights more frequently and they were more active in their own life choices following rights training.