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Date of Award

1998

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Supervisor

Dr. B. D. Gaulin

Abstract

Scattering techniques are an essential tool in the experimental study of properties in the vicinity of a critical phase transition. Such techniques have been aplied to the study of the spin-Peierls transition in pure and doped samples of CuGeO₃ and in the organic compound MEM(TCNQ)₂. The spin-Peierls phase transition occurs in one-dimensional S-1/2 Heisenberg spin chains with short-range, antiferromangetic interactions. Such a system is unstable against a dimerization of the chains with the subsequent appearance of a gap in the magnetic excitation spectrum. Such a gap acts to lower the magnetic energy in the system and, in the presence of coupling with the lattice, causes phase transition to a dimerized, spin-Peierls, state. High temperature stability measurement of the order parameter associated with this transition in the inorganic compound CuGeO₃ indicate a continuous phase transition at a temperature of 14.05 K with a corresponding critical exponent β of 0.345±0.03. This value is in agreement with conventional 3D univerality and in closest agreement with 3D XY behaviour. We also observe a narrow as asymptotic critical region which is largely responsible for the inconsistency in previously reported results. High resolution measurements of relative lattice constant changes, performed using a novel approach, indicate spontaneous strains which scale with the square of the order parameter expect near the transition temperature where differences are observed. Similar order parameter measurements were performed on samples of CuGeO₃ doped with Zn, Si, and Cd. For the case of Zn and Si doping, we obtain and exponent β consistent with that for the pure material. Measurements on two Cd doped samples indicate results which clearly deviate from that observed in pure CuGeO₃ with an exponent β of about 0.5 consistent with mean field behaviour. We explain this change in behaviour as resulting from local strains induced by the presence of the much larger Cd²⁺ dopant ion. Relative lattice constant measurements indicate spontaneous strains which scale with the square of the order parameter for the doped samples as was the case for pure CuGeO₃. X-ray scattering measurements of both the order parameter and critical scattering in the vicinity of the transition temperature have been performed for the organic spin-Peierls compound MEM(TCNQ)₂. Order parameter measurements indicate a value of the exponent β 0.35±0.06 consistent with 3D universality, as was observed in the inorganic spin-Peierls material CuGeO₃, and inconsistent with previous measurements which suggested mean-field behaviour. Critical scattering measurements suggest a lineshape not described by a traditional Ornstein-Zernike, Lorentzian, form but well described by a Lorentzian with a varying power or a Lorentzian + Lorentzian². The latter form is reminiscent of recent x-ray scattering measurements of critical phenomena associated with structural phase transitions in perovskites or with magnetic x-ray scattering measurerments on Ho, Tb, and some U-based compounds. Differences between this and previous measurements are discussed.

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