This work focuses on the chemical substitution of cations and anions in the frameworks of materials that have been known to exhibit negative thermal expansion (NTE). Zr2(PO4)2(SO4) is a member of the A(2)M(3)O(12) family which has been known to exhibit NTE. We have shown that Zr2(PO4)2(SO4) exhibits anisotropic positive thermal expansion. We have also shown that this material has been characterized in the wrong space group. Hf2(PO4)2(SO4) behaves similarly to Zr2(PO4)2(SO4) and follows this trend. Under pressure, Hf2(PO4)2(SO4) appears to undergo a phase transition. We have still yet to determine what space group the materials transitions to. While many members of the AX(2)O(7) family of frameworks have been fully characterized, the thermal expansion of PbP2O7 has yet to be reported. We were unable to obtain a reproducible procedure for synthesis of PbP2O7 from its precursor. Finally, variable temperature and variable pressure studies were performed on ZrMo2O8 in an attempt to learn more about the local structure. We found that space groups P213 and Pa-3 gave poor fits of the local structure at low r. Behavior of the nearest neighbor Zr-Mo distance was very similar to the bulk CTE. On compression, pressure induced amorphization is observed in ZrMo2O8. All interatomic correlations above 4 angstroms are washed out. Zr-O-Mo linkages remain well defined and do not massively deform as the pressure is increased. Finally, we we observed that Zr-O-Mo linkages change geometry reversibly as the pressure is increased.

This thesis explores the thermal expansion and high pressure behavior of some materials with the ReO₃ structure type. This structure is simple and has, in principle, all of the features necessary for negative thermal expansion (NTE) arising from the transverse thermal motion of the bridging anions and the coupled rotation of rigid units; however, ReO₃ itself only exhibits mild NTE across a narrow temperature range at low temperatures. ReO₃ is metallic because of a delocalized d-electron, and this may contribute to the lack of NTE in this material. The materials examined in this thesis are all based on d⁰ metal ions so that the observed thermal expansion behavior should arise from vibrational, rather than electronic, effects. In Chapter 2, the thermal expansion of scandium fluoride, ScF₃, is examined using a combination of in situ synchrotron X-ray and neutron variable temperature diffraction. ScF₃ retains the cubic ReO₃ structure across the entire temperature range examined (10-1600 K) and exhibits pronounced negative thermal expansion at low temperatures. The magnitude of NTE in this material is comparable to that of cubic ZrW₂O₈, which is perhaps the most widely studied NTE material, at room temperature and below. This is the first report of NTE in an ReO₃ type structure across a wide temperature range. Chapter 3 presents a comparison between titanium oxyfluoride, TiOF₂, and a vacancy containing titanium hydroxyoxyfluoride, Tiₓ(O/OH/F)₃. TiOF₂ was originally reported to adopt the cubic ReO₃ structure type under ambient conditions, therefore the initial goal for this study was to examine the thermal expansion of this material and determine if it displayed interesting behavior such as NTE. During the course of the study, it was discovered that the original synthetic method resulted in Tiₓ(O/OH/F)₃, which does adopt the cubic ReO₃ structure type. The chemical composition of the hydroxyoxyfluoride is highly dependent upon synthesis conditions and subsequent heat treatments. This material readily pyrohydrolyizes at low temperatures (~350 K). It was also observed that TiOF₂ does not adopt the cubic ReO₃ structure; at room temperature it adopts a rhombohedrally distorted variant of the ReO₃ structure. Positive thermal expansion was observed for TiOF₂ from 120 K through decomposition into TiO₂. At ~400 K, TiOF₂ undergoes a structural phase transition from rhombohedral to cubic symmetry. High pressure diffraction studies revealed a cubic to rhombohedral phase transition for Tiₓ(O/OH/F)₃ between 0.5-1 GPa. No phase transitions were observed for TiOF₂ on compression. In Chapter 4, an in situ variable pressure{temperature diffraction experiment examining the effects of pressure on the coefficients of thermal expansion (CTE) for ScF₃ and TaO₂F is presented. In the manufacture and use of composites, which is a possible application for low and NTE materials, stresses may be experienced. Pressure was observed to have a negligible effect on cubic ScF₃'s CTE; however, for TaO₂F the application of modest pressures, such as those that might be experienced in the manufacture or use of composites, has a major effect on its CTE. This effect is associated with a pressure-induced phase transition from cubic to rhombohedral symmetry upon compression. TaO₂F was prepared from the direct reaction of Ta₂O₅ with TaF₅ and from the digestion of Ta₂O₅ in hot hydro uoric acid. The effects of pressure on the two samples of TaO₂F were qualitatively similar. The slightly different properties for the samples are likely due to differences in their thermal history leading to differing arrangements of oxide and uoride in these disordered materials. In Chapter 5, the local structures of TiOF₂ and TaO₂F are examined using pair distribution functions (PDFs) obtained from X-ray total scattering experiments. In these materials, the anions (O/F) are disordered over the available anion positions. While traditional X-ray diffraction provides detailed information about the average structures of these materials, it is not suffcient to fully understand their thermal expansion. Fits of simple structural models to the low r portions of PDFs for these materials indicate the presence of geometrically distinct M{X{M (M = Ti, Ta; X = O, F) linkages, and a simple analysis of the TaO₂F variable temperature PDFs indicates that these distinct links respond differently to temperature.

The A2Mo3O12 family, where A3+ is a large trivalent cation, can show interesting thermal properties such as negative thermal expansion, also known as thermomiotic behavior, where the overall volume of the material contracts with increasing temperature. A selection of compounds in this family, namely HfMgMo3O12, In2Mo3O12, Y2Mo3O12, Al2Mo3O12, In(HfMg)0.5Mo3O12, and In1.5(HfMg)0.25Mo3O12, have been synthesized using solid-state and mechanical activation techniques as well as a simplified sol-gel approach (Al2Mo3O12). Coefficients of thermal expansion were found to range from large-negative to low-positive in the orthorhombic phase, including near-zero in In(HfMg)0.5Mo3O12 and In1.5(HfMg)0.25Mo3O12. This set of materials provided insight into the role of low-frequency phonon modes in open-framework materials. Low-temperature heat capacity and thermal conductivity measurements confirmed that low-frequency modes were active in thermomiotic materials, and also present to some extent in all members of the open-framework A2Mo3O12 family examined. A clear correlation exists between the magnitude and sign of the coefficient of thermal expansion in the orthorhombic phase and the contribution of low-energy modes to the low-temperature heat capacity, with negative thermal expansion materials having a larger contribution. The low-frequency phonon modes result in low thermal conductivity and reduced phonon mean free paths when compared to conventional ceramics and indicate that these low values are characteristic of open-framework materials in NTE families even if the materials in the families are not thermomiotic themselves.

The research presented in this thesis focuses on the structural studies and the high pressure behavior of oxide negative thermal expansion (NTE) materials that can be classified as framework materials. First two chapters were devoted to TaO2F which adopts the ReO3-type cubic structure. Our studies under pressure revealed a rather complicated high pressure behavior for this deceivingly simple compound. The diffraction measurements at variable temperature and high pressure indicated that pressure had a significant effect on the linear coefficient of thermal expansion of TaO2F. In the remainder of the thesis, compounds that belong to the Sc2W3O12 family were examined. High-pressure in-situ powder diffraction studies were conducted on Zr2WO4(PO4)2, Zr2MoO4(PO4)2, Hf2WO4(PO4)2, and Sc2W3O12 in order to investigate the effects of pressure on the coefficients of thermal expansion, existence of phase transitions, phase transition pressures and structural changes occurring upon phase transitions.

Short-distance digital communication links, between chips on a circuit board, or between different circuit boards for example, have traditionally been built by using electrical interconnects - metallic tracks and wires. Recent technological advances have resulted in improvements in the speed of information processing, but have left electrical interconnects intact, thus creating a serious communication problem. Free-space optical interconnects, made up of arrays of vertical-cavity surface-emitting lasers, microlenses, and photodetectors, could be used to solve this problem. If free-space optical interconnects are to successfully replace electrical interconnects, they have to be able to support large rates of information transfer with high channel densities. The biggest obstacle in the way of reaching these requirements is laser beam diffraction. There are three approaches commonly used to model the effects of laser beam diffraction in optical interconnects: one could pursue the path of solving the diffraction integral directly, one could apply stronger approximations with some loss of accuracy of the results, or one could cleverly reinterpret the diffraction problem altogether. None of the representatives of the three categories of existing solutions qualified for our purposes. The main contribution of this dissertation consist of, first, formulating the mode expansion method, and, second, showing that it outperforms all other methods previously used for modelling diffraction in optical interconnects. The mode expansion method allows us to obtain the optical field produced by the diffraction of arbitrary laser beams at empty apertures, phase-shifting optical elements, or any combinations thereof, regardless of the size, shape, position, or any other parameters either of the incident optical field or the observation plane. The mode expansion method enables us to perform all this without any reference or use of the traditional Huygens-Kirchhoff-Fresnel diffraction integrals. When using the mode expansion method, one replaces the incident optical field and the diffracting optical element by an effective beam, possibly containing higher-order transverse modes, so that the ultimate effects of diffraction are equivalently expressed through the complex-valued modal weights. By using the mode expansion method, one represents both the incident and the resultant optical fields in terms of an orthogonal set of functions, and finds the unknown parameters from the condition that the two fields have to be matched at each surface on their propagation paths. Even though essentially a numerical process, the mode expansion method can produce very accurate effective representations of the diffraction fields quickly and efficiently, usually by using no more than about a dozen expanding modes. The second tier of contributions contained in this dissertation is on the subject of the analysis and design of microchannel free-space optical interconnects. In addition to the proper characterisation of the design model, we have formulated several optical interconnect performance parameters, most notably the signal-to-noise ratio, optical carrier-to-noise ratio, and the space-bandwidth product, in a thorough and insightful way that has not been published previously. The proper calculation of those performance parameters, made possible by the mode expansion method, was then performed by using experimentally-measured fields of the incident vertical-cavity surface-emitting laser beams. After illustrating the importance of the proper way of modelling diffraction in optical interconnects, we have shown how to improve the optical interconnect performance by changing either the interconnect optical design, or by careful selection of the design parameter values. We have also suggested a change from the usual 'square' to a novel 'hexagonal' packing of the optical interconnect channels, in order to alleviate the negative diffraction effects. Finally, the optical interconnect tolerance to lateral misalignment, in the presence of multimodal incident laser beams was studied for the first time, and it was shown to be acceptable only as long as most of the incident optical power is emitted in the fundamental Gaussian mode.

Short-distance digital communication links, between chips on a circuit board, or between different circuit boards for example, have traditionally been built by using electrical interconnects -- metallic tracks and wires. Recent technological advances have resulted in improvements in the speed of information processing, but have left electrical interconnects intact, thus creating a serious communication problem. Free-space optical interconnects, made up of arrays of vertical-cavity surface-emitting lasers, microlenses, and photodetectors, could be used to solve this problem. If free-space optical interconnects are to successfully replace electrical interconnects, they have to be able to support large rates of information transfer with high channel densities. The biggest obstacle in the way of reaching these requirements is laser beam diffraction. There are three approaches commonly used to model the effects of laser beam diffraction in optical interconnects: one could pursue the path of solving the diffraction integral directly, one could apply stronger approximations with some loss of accuracy of the results, or one could cleverly reinterpret the diffraction problem altogether. None of the representatives of the three categories of existing solutions qualified for our purposes. The main contribution of this dissertation consist of, first, formulating the mode expansion method, and, second, showing that it outperforms all other methods previously used for modelling diffraction in optical interconnects. The mode expansion method allows us to obtain the optical field produced by the diffraction of arbitrary laser beams at empty apertures, phase-shifting optical elements, or any combinations thereof, regardless of the size, shape, position, or any other parameters either of the incident optical field or the observation plane. The mode expansion method enables us to perform all this without any reference or use of the traditional Huygens-Kirchhoff-Fresnel diffraction integrals. When using the mode expansion method, one replaces the incident optical field and the diffracting optical element by an effective beam, possibly containing higher-order transverse modes, so that the ultimate effects of diffraction are equivalently expressed through the complex-valued modal weights. By using the mode expansion method, one represents both the incident and the resultant optical fields in terms of an orthogonal set of functions, and finds the unknown parameters from the condition that the two fields have to be matched at each surface on their propagation paths. Even though essentially a numerical process, the mode expansion method can produce very accurate effective representations of the diffraction fields quickly and efficiently, usually by using no more than about a dozen expanding modes. The second tier of contributions contained in this dissertation is on the subject of the analysis and design of microchannel free-space optical interconnects. In addition to the proper characterisation of the design model, we have formulated several optical interconnect performance parameters, most notably the signal-to-noise ratio, optical carrier-to-noise ratio, and the space-bandwidth product, in a thorough and insightful way that has not been published previously. The proper calculation of those performance parameters, made possible by the mode expansion method, was then performed by using experimentally-measured fields of the incident vertical-cavity surface-emitting laser beams. After illustrating the importance of the proper way of modelling diffraction in optical interconnects, we have shown how to improve the optical interconnect performance by changing either the interconnect optical design, or by careful selection of the design parameter values. We have also suggested a change from the usual `square' to a novel `hexagonal' packing of the optical interconnect channels, in order to alleviate the negative diffraction effects. Finally, the optical interconnect tolerance to lateral misalignment, in the presence of multimodal incident laser beams was studied for the first time, and it was shown to be acceptable only as long as most of the incident optical power is emitted in the fundamental Gaussian mode.

Short-distance digital communication links, between chips on a circuit board, or between different circuit boards for example, have traditionally been built by using electrical interconnects -- metallic tracks and wires. Recent technological advances have resulted in improvements in the speed of information processing, but have left electrical interconnects intact, thus creating a serious communication problem. Free-space optical interconnects, made up of arrays of vertical-cavity surface-emitting lasers, microlenses, and photodetectors, could be used to solve this problem. If free-space optical interconnects are to successfully replace electrical interconnects, they have to be able to support large rates of information transfer with high channel densities. The biggest obstacle in the way of reaching these requirements is laser beam diffraction. There are three approaches commonly used to model the effects of laser beam diffraction in optical interconnects: one could pursue the path of solving the diffraction integral directly, one could apply stronger approximations with some loss of accuracy of the results, or one could cleverly reinterpret the diffraction problem altogether. None of the representatives of the three categories of existing solutions qualified for our purposes. The main contribution of this dissertation consist of, first, formulating the mode expansion method, and, second, showing that it outperforms all other methods previously used for modelling diffraction in optical interconnects. The mode expansion method allows us to obtain the optical field produced by the diffraction of arbitrary laser beams at empty apertures, phase-shifting optical elements, or any combinations thereof, regardless of the size, shape, position, or any other parameters either of the incident optical field or the observation plane. The mode expansion method enables us to perform all this without any reference or use of the traditional Huygens-Kirchhoff-Fresnel diffraction integrals. When using the mode expansion method, one replaces the incident optical field and the diffracting optical element by an effective beam, possibly containing higher-order transverse modes, so that the ultimate effects of diffraction are equivalently expressed through the complex-valued modal weights. By using the mode expansion method, one represents both the incident and the resultant optical fields in terms of an orthogonal set of functions, and finds the unknown parameters from the condition that the two fields have to be matched at each surface on their propagation paths. Even though essentially a numerical process, the mode expansion method can produce very accurate effective representations of the diffraction fields quickly and efficiently, usually by using no more than about a dozen expanding modes. The second tier of contributions contained in this dissertation is on the subject of the analysis and design of microchannel free-space optical interconnects. In addition to the proper characterisation of the design model, we have formulated several optical interconnect performance parameters, most notably the signal-to-noise ratio, optical carrier-to-noise ratio, and the space-bandwidth product, in a thorough and insightful way that has not been published previously. The proper calculation of those performance parameters, made possible by the mode expansion method, was then performed by using experimentally-measured fields of the incident vertical-cavity surface-emitting laser beams. After illustrating the importance of the proper way of modelling diffraction in optical interconnects, we have shown how to improve the optical interconnect performance by changing either the interconnect optical design, or by careful selection of the design parameter values. We have also suggested a change from the usual `square' to a novel `hexagonal' packing of the optical interconnect channels, in order to alleviate the negative diffraction effects. Finally, the optical interconnect tolerance to lateral misalignment, in the presence of multimodal incident laser beams was studied for the first time, and it was shown to be acceptable only as long as most of the incident optical power is emitted in the fundamental Gaussian mode.

Thesis (M.S.)--West Virginia University, 2005 / Title from document title page. Document formatted into pages; contains vii, 57 p. Vita. Includes abstract. Includes bibliographical references (p. 46-52).

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Objective: The aim of this study was to evaluate the dentoalveolar effects of rapid maxillary expansion in children with unilateral complete cleft lip and palate in comparison with non-cleft patients. Methods: The experimental group (EG) was composed of 25 patients with unilateral and complete cleft lip and palate (9 males and 15 females) with a mean age of 10.6 years. The control group (CG) comprised of 27 patients without cleft lip and palate (14 males and 13 females) with a mean age of 9.1 years. Dental models of the maxillary dental arch were obtained immediately preexpansion (T1) and 6 months post-expansion (T2) at the time of appliance removal. Digital dental models were obtained using the 3Shape R700 3D laser scanner (3Shape A/S, Copenhagen, Denmark). Transversal widths, arch perimeter, arch length, palatal depth, palatal volume, canine and posterior tooth inclination were digitally measured. Paired t-test was used to perform interphase comparisons and independent t-test to perform intergroup comparisons (p<0.05). Results: In the experimental group, the expansion produced a ignificant increase of all maxillary transverse measurements, palatal volume, arch perimeter and palatal depth while decreased the arch length. RME caused a buccal tip of posterior teeth in patients with UCLP. No differences were observed between experimental and control groups for all the measurements performed except for the intermolar distance (6-6), which showed a greater increase in patients with cleft. Conclusion: Rapid maxillary expansion showed similar dentoalveolar effects in children with UCLP and without oral clefts. / Objective: The aim of this study was to evaluate the dentoalveolar effects of rapid maxillary expansion in children with unilateral complete cleft lip and palate in comparison with non-cleft patients. Methods: The experimental group (EG) was composed of 25 patients with unilateral and complete cleft lip and palate (9 males and 15 females) with a mean age of 10.6 years. The control group (CG) comprised of 27 patients without cleft lip and palate (14 males and 13 females) with a mean age of 9.1 years. Dental models of the maxillary dental arch were obtained immediately preexpansion (T1) and 6 months post-expansion (T2) at the time of appliance removal. Digital dental models were obtained using the 3Shape R700 3D laser scanner (3Shape A/S, Copenhagen, Denmark). Transversal widths, arch perimeter, arch length, palatal depth, palatal volume, canine and posterior tooth inclination were digitally measured. Paired t-test was used to perform interphase comparisons and independent t-test to perform intergroup comparisons (p<0.05). Results: In the experimental group, the expansion produced a ignificant increase of all maxillary transverse measurements, palatal volume, arch perimeter and palatal depth while decreased the arch length. RME caused a buccal tip of posterior teeth in patients with UCLP. No differences were observed between experimental and control groups for all the measurements performed except for the intermolar distance (6-6), which showed a greater increase in patients with cleft. Conclusion: Rapid maxillary expansion showed similar dentoalveolar effects in children with UCLP and without oral clefts.