The relationship between the mean square vibrational amplitude of the atoms of a crystalline solid and the thermal expansion of that solid is derived from basic principles, assuming a simple potential energy function between atoms. The functional accuracy of this relationship is proven for several cubic lattice elements and compounds by experimental data reported in the literature. The constants of the relationship are calculated for the materials investigated. / Master of Science

Two framework oxide materials of the MO��� network type have been synthesized and structurally characterized by synchrotron and X-ray powder diffraction and the Rietveld method in the temperature range 25~500 K. The results show one of them to be a low thermal expansion material. Theoretical studies of negative thermal expansion (NTE) in framework oxides were conducted with two methods, geometrical modeling by Rigid Unit Mode (RUM) method and lattice dynamic calculations by free energy minimization (FEM) method, the results are compared with each other as well as with experimental observations. RUM analysis of all five types of framework oxide structures negates any simple and direct correlation between presence or absence of RUMs in a structure and the sign of its thermal expansion. Instead, results suggest that NTE of a crystalline solid can not be explained by pure geometrical considerations over its structure alone, and for a better understanding of structure-relationship in negative thermal expansion structures, specific interatomic interactions present in each one must be brought in explicitly. FEM calculation of two negative thermal expansion structures indicates on a structure by structure basis NTE could be predicted and understood within the Gruneisen model, which attributes NTE of a structure to special vibration modes in a structure that softens when the lattice shrinks. The soft NTE modes are, however, not necessarily RUM or RUM like vibration motions. / Graduation date: 2003

LOW TEMPERATURE SYNTHESIS AND CHARACTERIZATION OF SOME LOW POSITIVE AND NEGATIVE THERMAL EXPANSION MATERIALS Kathleen Madara White 151 pages Directed by Dr. Angus P. Wilkinson Low temperature non-hydrolytic sol-gel synthesis was used to explore the possibility of lowering the crystallization temperatures of some known AIVMV2O7 compounds. Crystallization temperatures for ZrP2O7 and ZrP2O7 were unaffected by the use of non-hydrolytic sol-gel methods; however, successful synthesis of these compounds broadens the range of materials that can be produced using this method and suggests the possibility of synthesizing solid solutions (or composites) including ZrP2O7 or ZrV2O7. This research presents for the first time the direct synthesis of ZrP2O7 from separate zirconium and phosphorus starting materials using mild autoclave methods. Characterization of some AIVMV2O7 compounds, using lab and high resolution synchrotron powder XRD, led to the assignment of a new symmetry for CeP2O7 and to the suggestion that the reported structure for PbP2O7 was inadequate. Studies using in situ high temperature lab and synchrotron powder XRD for PbP2O7 and CeP2O7 provided the opportunity to report their thermal properties for the first time, and to compare their behavior to that of some other AIVMV2O7. High pressure diffraction measurements on CeP2O7 provided data for the estimation of bulk moduli and suggested two possible pressure-induced phase transitions. A broad range of MIIIMVP4O14 compounds were prepared using low temperature hydrolytic sol-gel synthesis. Thermal studies revealed nearly linear trends in CTEs and lattice constants with respect to the sizes of MIIIMV cations. Some lower ionic radii compounds had CTEs comparable to that of ZrP2O7 at low temperature, suggesting a similar superstructure. Three compounds were found to exhibit temperature-induced phase transitions.