Investigation of Frustrated Quasi-One-Dimensional Quantum Spin-Chain Materials

Copper arsenite CuAs2O4 and Copper antimonite CuSb2O4 are S=1/2 (Cu2+ 3d9 electronic configuration) quasi-one-dimensional quantum spin-chain compounds. Both compounds crystallize with tetragonal structures containing edge sharing CuO6 octahedra chains which experience Jahn-Teller distortions. The basal planes of the octahedra link together to form CuO2 ribbon-chains which harbor Cu2+ spin-chains. These compounds are magnetically frustrated with competing nearest-neighbour and next-nearest-neighbour intrachain spin-exchange interactions. Despite the similarities between CuAs2O4 and CuSb2O4, they exhibit very different magnetic properties. In this thesis work, the physical properties of CuAs2O4 and CuSb2O4 are investigated using a variety of experimental techniques which include x-ray diffraction, magnetic susceptibility measurements, heat capacity measurements, Raman spectroscopy, electron paramagnetic resonance, neutron diffraction, and dielectric capacitance measurements. CuAs2O4 exhibits dominant ferromagnetic nearest-neighbour and weaker antiferromagnetic next-nearest-neighbour intrachain spin-exchange interactions. The ratio of the intrachain interactions amounts to Jnn/Jnnn = -4.1. CuAs2O4 was found to order with a ferromagnetic groundstate below TC = 7.4 K. An extensive physical characterization of the magnetic and structural properties of CuAs2O4 was carried out. Under the effect of hydrostatic pressure, CuAs2O4 was found to undergo a structural phase transition at 9 GPa to a new spin-chain structure. The structural phase transition is accompanied by a severe alteration of the magnetic properties. The high-pressure phase exhibits dominant ferromagnetic next-nearest-neighbour spin-exchange interactions and weaker ferromagnetic nearest-neighbour interactions. The ratio of the intrachain interactions in the high-pressure phase was found to be Jnn/Jnnn = 0.3. Structural and magnetic characterizations under hydrostatic pressure are reported and a relationship between the structural and magnetic properties was established. CuSb2O4 orders antiferromagnetically below TN = 1.8 K with an incommensurate helicoidal magnetic structure. CuSb2O4 is characterized by ferromagnetic nearest-neighbour and antiferromagnetic next-nearest-neighbour spin-exchange interactions with Jnn/Jnnn = -1.8. A (H, T) magnetic phase diagram was constructed using low-temperature magnetization and heat capacity measurements. The resulting phase diagram contains multiple phases as a consequence of the strong intrachain magnetic frustration. Indications of ferroelectricity were observed in the incommensurate antiferromagnetic phase.

Response curves of deterministic and probabilistic cellular automata in one and two dimensions

One of the most important problems in the theory of cellular automata (CA) is determining the proportion of cells in a specific state after a given number of time iterations. We approach this problem using patterns in preimage sets - that is, the set of blocks which iterate to the desired output. This allows us to construct a response curve - a relationship between the proportion of cells in state 1 after niterations as a function of the initial proportion. We derive response curve formulae for many two-dimensional deterministic CA rules with L-neighbourhood. For all remaining rules, we find experimental response curves. We also use preimage sets to classify surjective rules. In the last part of the thesis, we consider a special class of one-dimensional probabilistic CA rules. We find response surface formula for these rules and experimental response surfaces for all remaining rules.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

The influence of emotional body posture on adults' and 8-year-olds' perception facial expressions

The present set of experiments was designed to investigate the development of children's sensitivity of facial expressions observed within emotional contexts. Past research investigating both adults' and children's perception of facial expressions has been limited primarily to the presentation of isolated faces. During daily social interactions, however, facial expressions are encountered within contexts conveying emotions (e.g., background scenes, body postures, gestures). Recently, research has shown that adults' perception of facial expressions is influenced by these contexts. When emotional faces are shown in incongruent contexts (e.g., when an angry face is presented in a context depicting fear) adults' accuracy decreases and their reaction times increase (e.g., Meeren et a1. 2005). To examine the influence of emotional body postures on children's perception of facial expressions, in each of the experiments in the current study adults and 8-year-old children made two-alternative forced choice decisions about facial expressions presented in congruent (e.g., a face displayed sadness on a body displaying sadness) and incongruent (e.g., a face displaying fear on a body displaying sadness) contexts. Consistent with previous studies, a congruency effect (better performance on congruent than incongruent trials) was found for both adults and 8-year-olds when the emotions displayed by the face and body were similar to each other (e.g., fear and sad, Experiment l a ) ; the influence of context was greater for 8-year-olds than adults for these similar expressions. To further investigate why the congruency effect was larger for children than adults in Experiment 1 a, Experiment 1 b was conducted to examine if increased task difficulty would increase the magnitude of adults' congruency effects. Adults were presented with subtle facial and despite successfully increasing task difficulty the magnitude of the. congruency effect did not increase suggesting that the difference between children's and adults' congruency effects in Experiment l a cannot be explained by 8-year-olds finding the task difficult. In contrast, congruency effects were not found when the expressions displayed by the face and body were dissimilar (e.g., sad and happy, see Experiment 2). The results of the current set of studies are examined with respect to the Dimensional theory and the Emotional Seed model and the developmental timeline of children's sensitivity to facial expressions. A secondary aim of the series of studies was to examine one possible mechanism underlying congruency effe cts-holistic processing. To examine the influence of holistic processing, participants completed both aligned trials and misaligned trials in which the faces were detached from the body (designed to disrupt holistic processing). Based on the principles of holistic face processing we predicted that participants would benefit from misalignment of the face and body stimuli on incongruent trials but not on congruent trials. Collectively, our results provide some evidence that both adults and children may process emotional faces and bodies holistically. Consistent with the pattern of results for congruency effects, the magnitude of the effect of misalignment varied with the similarity between emotions. Future research is required to further investigate whether or not facial expressions and emotions conveyed by the body are perceived holistically.

Crystal Growth and Characterization of Li0.9Mo6O17

Purple bronze Li0.9Mo6O17 has attracted researchers for its low dimensionality and corresponding properties. Although it has been studied for nearly two decades, there are still some unsolved puzzles with this unique material. Single crystals of Li0.9Mo6O17 were grown using the temperature gradient flux technique in this research. The crystal growth was optimized by experimenting different conditions and good quality crystals were obtained. X-ray diffraction results have confirmed the right phase of the crystals. Resistivity measurements and magnetic susceptibility measurements were carried out, and anomalous electronic behaviors were found. All of the samples showed the metal-insulator transition near 20K, followed by behavior that differs from sample to sample: either superconducting, metallic or insulating behavior was observed below 2K. Li0.9Mo6O17 was considered as a quasi-one-dimensional crystal and also a superconducting crystal, which implies a dimensional crossover may occur at the metal-insulator transition. A two-band scenario of the Luttinger liquid model was used to fit the resistivity data and excellent results were achieved, suggesting that the Luttinger theory is a very good candidate for the explanation of the anomalous behavior of Li0.9Mo6O17. In addition, the susceptibility measurements showed Curie paramagnetism and some temperature independent paramagnetism at low temperature. The absence of any anomalous magnetic feature near 20K where the resistivity upturn takes place, suggests that a charge density wave mechanism, which has been proposed by some researchers, is not responsible for the unique properties of Li0.9Mo6O17.