Thermodynamics of Quasi-One Oxides

Quasi-one-dimensional materials are of interest because of the large variety of phase transitions they exhibit, such as charge-density-wave (CDW), spin-density -wave (SDW), spin-Peierls (SP) and superconducting transitions. Thermodynamic measurements are important to our understanding of the nature and magnitude of the phase transitions and the effect of fluctuations. Two quasi-one-dimensional inorganic oxides are comprehensively investigated in this thesis. First, CuGeO _3 undergoes a spin-Peierls transition at 14 K, and second, K_{0.3}MoO _3 shows a charge-density-wave ground state below the transition temperature of 180 K. We measured the heat capacity of CuGeO _3, using a high resolution ac calorimeter, both in the absence and presence of magnetic field. For the zero-field data, a sharp discontinuity at its spin -Peierls phase transition (~14 K) is observed. The magnitude of the jump is consistent with mean-field theory, indicating a nearest neighbor exchange interaction ~75 K, and that low-dimensional fluctuations have a small effect in depressing T_{c}. A temperature -dependent activation energy is observed at very low temperature. Between 5 and 10 K, we observed an activation energy Delta ~ 24K ~ 1.76 T_{c}, suggesting that the gap opens up more quickly below T_{c} than predicted by mean-field theory. The ratio of the specific heat anomaly and temperature derivative of the magnetic susceptibility at T _{c} equals the observed value of rm d^2T_{c}/dH ^2 at T_{c}, as expected in mean-field theory, but this ratio deviates from mean-field behavior below the transition. The depression of T_{c } in the presence of a magnetic field agrees well with mean-field theory, and there are no signs of suppression and broadening of the specific heat peaks due to external magnetic fields. The activation energy appears to be temperature dependent in all fields, but there is no clear evidence of reducing the activation energy in higher fields, suggesting that there is no creation of solitons up to 7 Tesla. In addition, the variation of c_{P} vs. magnetic field is approximately consistent with excitation of (triplet) magnons. Most interestingly, scaling of the Arrhenius plot of c_{P} - beta T^3 in various fields is observed. We present the measurements of the specific heat (by ac calorimetry), Young's modulus (by a vibrating reed technique), and susceptibility (with a Faraday balance) on the same crystal of blue bronze rm K_ {0.3}MoO_3 for which the thermal expansion had previously been measured. All these measured thermodynamic response functions were fitted by using the free energy expression developed by Chen, Albright, and Sengers (CAS) in the 3D XY (d = 3, n = 2) model. The small variation of critical fitting parameters obtained for the five CAS fits indicates that the same function fits all quantities well, which allows the prefactors in the Testardi and Ehrenfest relations to be unambiguously determined, which had not previously been possible for a phase transition in a quasi-one-dimensional material. While the large value of one fitting parameter (u), raises a yet unresolved question about the microscopic meaningfulness of the CAS approach for CDW's, the model provides a useful fitting function from which thermodynamic properties can be unambiguously extracted for comparison with microscopic models.