Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Science, 1982. / Microfiche copy available in Archives and Science / Bibliography: leaves 42-44. / by Harvey Hartman Haines. / M.S.

Finite element optimum meshes are synthesized by the use of thermal expansion principles in conjunction with an analogous temperature field computed from the element strain energy contents. Elements having high strain energy contents are shrunk and those with low strain energy contents are expanded until all elements contain the same amount of strain energy. Deviatoric strain energy is also used in place of the strain energy as the objective function for the optimization method. Both objective functions yield significant improvements of the meshes after only a few iterations. In one test case, the errors in the maximum stresses are reduced by more than 1/3 after 1 iteration. In another test case, the error in the stress concentration factor is reduced by more than 3/4 after 7 iterations. / M.S.

Thermal expansion in a crystal may be completely described from a phenomenological point of view by a second rank tensor whose elements are defined by λ_ij=(∂l_ij/∂T)_σ Or ε_ij=(∂e_ij/∂T)_σ Where the l_ij and the e_ij are the elements of the linear Lagrangian and Eulerian strain tensors respectively. These λ_ij and ε_ij have been formulated in terms of crystal cell parameters. For example, for a monoclinic crystal the λ_ij are of the form: λ₁₁(T) = 1/a₀sinβ₀ d[a(T)sinβ(T)]/dT , λ₁₃(T) = ½ (1/a₀sinβ₀ d[a(T)cosβ(T)]/dT - cotβ₀/c₀ dc(T)/dT) , λ₂₂(T) = 1/b₀ db(T)/DT , and λ₃₃(T) = 1/c₀ dc(T)/dT where a₀, b₀, c₀, and β₀ are the crystal’s cell parameters at some reference temperature T₀. By expressing the crystal cell parameters as power series expansions in the temperature, thermal expansion coefficients have been computed for indialite (hexagonal cordierite), emerald and beryl and for the clinopyroxenes: diopside, hedenbergite, jadeite, ureyite, acmite, and spodumene. The extended Grüneisen equation has been used to further examine the nature of the thermal expansion in emerald, beryl, and diopside. The crystal structures of the synthetic clinopyroxenes CaCoSi₂O₆ (cobalt diopside) and CaNiSi₂O₆ (nickel diopside) have also been determined. / Doctor of Philosophy

Vibrations of nuclei in crystals govern various properties such as thermal expansion, phase transitions, and elasticity, and the quasiharmonic approximation (QHA) is the simplest nontrivial approximation which includes the effects of vibrational anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate the quasiharmonic approximation by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (ThO₂) using density functional theory with three exchange-correlation functionals. The convergence of the two complementary strain parametrizations is evaluated for the computed thermal expansion. The temperature dependent lattice parameter and thermal expansion computed within the QHA is compared with experimental measurements. The QHA results are compared to measurements of the elastic constant tensor using time domain Brillouin scattering and inelastic neutron scattering. We then demonstrate the generalized quasiharmonic approximation in a non-cubic material, ferroelectric lead titanate, computing the temperature and stress dependence of the full elastic constant tensor. The irreducible derivative approach is employed for computing strain dependent phonons using finite difference, explicitly including dipole-quadrupole contributions. We use density functional theory, computing all independent elastic constants and piezoelectric strain coefficients at finite temperature and stress. There is good agreement between the quasiharmonic approximation and the experimentally measured lattice parameters close to 0 K. The quasiharmonic approximation overestimates the measured temperature dependence of the lattice parameters and elastic constant tensor, demonstrating that a higher level of strain dependent anharmonic vibrational theory is needed. The next material we study is zirconium nitride, employing the quasiharmonic approximation with the irreducible derivative approach to compute the phonons and thermal expansion. Density functional theory is used with two exchange-correlation functionals. We investigate the difference between the measured and computed optical phonon branches, showing that volume effects, two-phonon scattering, and nitrogen vacancies do not explain the discrepancy between the measurement and computation. The temperature dependent lattice parameter is computed within the QHA, where the thermal expansion is overestimated as compared with existing experimental measurements.

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.

Two-phase flow, boiling, and condensation in microchannels have received considerable attention in the recent past due to the growing interest in the high heat fluxes made possible by these channels. This dissertation presents a study on the condensation of refrigerant R134a in small hydraulic diameter (100 < Dh < 160 mm) channels. A novel technique is used for the measurement of local condensation heat transfer coefficients in small quality increments, which has typically been found to be difficult due to the low heat transfer rates at the small flow rates in these microchannels. This method is used to accurately determine pressure drop and heat transfer coefficients for mass fluxes between 300 and 800 kg/m2-s and quality 0 < x < 1 at four different saturation temperatures between 30 and 60oC. The results obtained from this study capture the effect of variations in mass flux, quality, saturation temperature, hydraulic diameter, and channel aspect ratio on the observed pressure drop and heat transfer coefficients. Based on the available flow regime maps, it was assumed that either the intermittent or annular flow regimes prevail in these channels for the flow conditions under consideration. Internally consistent pressure drop and heat transfer models are proposed taking into account the effect of mass flux, quality, saturation temperature, hydraulic diameter, and channel aspect ratio. The proposed models predict 95% and 94% of the pressure drop and heat transfer data within ±25%, respectively. Both pressure drop and heat transfer coefficient increase with a decrease in hydraulic diameter, increase in channel aspect ratio and decrease in saturation temperature. A new non-dimensional parameter termed Annular Flow Factor is also introduced to quantify the predominance of intermittent or annular flow in the channels as the geometric parameters and operating conditions change. This study leads to a comprehensive understanding of condensation in microchannels for use in high-flux heat transfer applications.

Out-of-plane displacement (warpage) is one of the major thermomechanical reliability concerns for board-level electronic packaging. Printed wiring board (PWB) and component warpage results from CTE mismatch among the materials that make up the PWB assembly (PWBA). Warpage occurring during surface-mount assembly reflow processes and normal operations may cause serious reliability problems. In this research, a convective reflow and projection moire warpage measurement system was developed. The system is the first real-time, non-contact, and full-field measurement system capable of measuring PWB/PWBA/chip package warpage with the projection moire technique during different thermal reflow processes. In order to accurately simulate the reflow process and to achieve the ideal heating rate, a convective heating system was designed and integrated with the projection moire system. An advanced feedback controller was implemented to obtain the optimum heating responses. The developed system has the advantages of simulating different types of reflow processes, and reducing the temperature gradients through the PWBA thickness to ensure that the projection moire system can provide more accurate measurements. Automatic package detection and segmentation algorithms were developed for the projection moire system. The algorithms are used for automatic segmentation of the PWB and assembled packages so that the warpage of the PWB and chip packages can be determined individually. The effect of initial PWB warpage on the fatigue reliability of solder bumps on board assemblies was investigated using finite element modeling (FEM) and the projection moire system. The 3-D models of PWBAs with varying board warpage were used to estimate the solder bump fatigue life for different chip packages mounted on PWBs. The simulation results were validated and correlated with the experimental results obtained using the projection moire system and accelerated thermal cycling tests. Design of experiments and an advanced prediction model were generated to predict solder bump fatigue life based on the initial PWB warpage, package dimensions and locations, and solder bump materials. This study led to a better understanding of the correlation between PWB warpage and solder bump thermomechanical reliability on board assemblies.

The thesis is focused on structural design of unconventional experimental combustion air preheater into drawing documentation needed for production and realization. Strength and expansion control of exposed elements of construction is also included in the thesis. The final design is obtained by gradual specification of pre-designed and strength and expansion controlled elements of construction. The work also includes discussion of structural properties of the final design.

Synthesis and Characterization of Some Low and Negative Thermal Expansion Materials Tamas Varga 370 pages Directed by Dr. Angus P. Wilkinson The high-pressure behavior of several negative thermal expansion materials was studied by different methods. In-situ high-pressure x-ray and neutron diffraction studies on several compounds of the orthorhombic Sc2W3O12 structure revealed an unusual bulk modulus collapse at the orthorhombic to monoclinic phase transition. In some members of the A2M3O12 family, a second phase transition and/or pressure-induced amorphization were also seen at higher pressure. The mechanism for volume contraction on compression is different from that on heating. A combined in-situ high pressure x-ray diffraction and absorption spectroscopic study has been carried out for the first time. The pressure-induced amorphization in cubic ZrW2O8 and ZrMo2O8 was studied by following the changes in the local coordination environments of the metals. A significant change in the average tungsten coordination was found in ZrW2O8, and a less pronounced change in the molybdenum coordination in ZrMo2O8 on amorphization. A kinetically frustrated phase transition to a high-pressure crystalline phase or a kinetically hindered decomposition, are likely driving forces of the amorphization. A complementary ex-situ study confirmed the greater distortion of the framework tetrahedra in ZrW2O8, and revealed a similar distortion of the octahedra in both compounds. The possibility of stabilizing the low thermal expansion high-temperature structure in AM2O7 compounds to lower temperatures through stuffing of ZrP2O7 was explored. Although the phase transition temperature was suppressed in MIxZr1-xMIIIxP2O7 compositions, the chemical modification employed was not successful in stabilizing the high-temperature structure to around room temperature. An attempt has been made to control the thermal expansion properties in materials of the (MIII0.5MV0.5)P2O7-type through the choice of the metal cations and through manipulating the ordering of the cations by different heat treatment conditions. Although controlled heat treatment resulted in only short-range cation ordering, the choice of the MIII cation had a marked effect on the thermal expansion behavior of the materials. Different grades of fluorinert were examined as pressure-transmitting media for high-pressure diffraction studies. All of the fluorinerts studied became nonhydrostatic at relatively low pressures (~1 GPa).