Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Includes bibliographical references. / by David Malcolm Kundrat. / Sc.D.

A free energy formalism is developed in order to describe phase equilibria in binary alloys. The proposed phenomenological approach uses a limited number of experimental data to provide a global thermodynamic description of a system including its equilibrium and metastable phase diagrams. Emphasis is placed on the description of short range order by means of the cluster variation method. A microscopic theory is also developed in order to predict the enthalpies of formation of transition metal alloys as well as the short range order dependence of these enthalpies. The theory uses a tight-binding Hamiltonian together with the generalized perturbation method. 0ff~diagonal disorder is taken into account, and charge transfer is treated self consistently in the random alloy. All input parameters to the theory are obtained from ab-initio calculations for the pure elements. In this regard, the model can be considered parameter free. The phenomenological approach has been used to analyzed the Al-Ni, Ni~Cr, and Al~Li systems. It is found that the vibrational entropy of‘ formation plays an important role in the thermodynamics of the Al-Li and Ni-Cr alloys. The approach allows an accurate description of stable and metastable order-disorder or order-order equilibria existing in the Ni-Al or AL~Li systems. The model is used to predict a metastable clustering tendency in Al-Li alloys which appears to have been recently confirmed by experiment. The microscopic theory has been applied to the VB-VIE and IVB-VIIIB (Ni, Pt, Pd) alloys. The calculations are in good agreement with the available experimental data and phase diagram information. It is shown that off-diagonal disorder and electronic self-consistency play a crucial role in the accuracy of the results.

We present a general approach for determining the equilibrium shape of isolated, coherent, misfitting particles by minimizing the sum of elastic and interfacial energies using a synthesis of finite element and optimization techniques. The generality derives from the fact that there is no restriction on the initial or final shape, or on the elastic moduli of the particle and matrix, or on the nature of misfit. The particle shape is parameterized using a set of design variables which are the magnitudes of vectors from a reference point inside the particle to points on the particle/matrix interface. We use a sequential quadratic programming approach to carry out the optimization. Although this approach can be used to find equilibrium shapes of particles in three dimensional systems, we have presented the details of our formulation for two dimensional systems under plane strain conditions. Using our formulation, we have studied the equilibrium shapes in two dimensional systems with cubic anisotropy; the precipitate and matrix phases may have different elastic moduli, and the misfit may be dilatational or non-dilatational. The equilibrium shapes and their size dependence are analysed within the framework of symmetry-breaking shape transitions. These transitions are further characterized in terms their dependence on the cubic elastic anisotropy parameter, defined by A = 2C44/(C11 – C12), and on the modulus mismatch, defined by δ=μp/μm, where /μp and μm are the effective shear moduli of the precipitate and matrix phases, respectively. Depending on the type of misfit, the systems may be classified into the following four cases: Case A: For dilatational misfit, the equilibrium shapes in isotropic systems are circular (with an isotropic or I symmetry) at small sizes and undergo a transition at a critical size to become ellipse-like (with an orthorhombic or O symmetry). This I --O transition is continuous and is obtained only when the precipitate phase is softer than the matrix. These results are in good agreement with the analytical results of Johnson and Cahn. In cubic systems with dilatational misfit, the particles exhibit a transition from square-like shapes (with a tetragonal or T symmetry) at small sizes to rectangle-like shapes (with an O symmetry) at large sizes. This T -- O transition is continuous. It occurs even in systems with stiffer precipitates; however, it is forbidden for systems with δ >δC, where δ C represents a critical modulus mismatch. The critical size decreases with increasing cubic anisotropy (i.e., with increasing values of (A-1)/(A+1). The sides of the square-like and rectangle-like shapes are along the elastically soft directions. Case B: In these systems, the principal misfits e*xx and e*yy differ in magnitude but have the same sign. The precipitates at small sizes become elongated along the direction of lower misfit; this shape has an O symmetry. In systems with A > 1, they continue to become more elongated along the same direction, exhibiting no symmetry-breaking transition. However, in systems with A < 1, particles at large sizes are elongated along an intermediate direction between the direction of lower misfit and one of the elastically soft <11> directions; this shape has only a monoclinic or M symmetry. This O - M transition, in which the mirror symmetries normal to the x and y axes are lost, may be discontinuous or continuous. The critical size increases with δ (in the range 0.8 < δ <1.25), indicating that this transition would also be forbidden for systems with δ > δC. In systems with A < 1, the critical size decreases with increasing values of A-1/ A+1 Case C: In these systems, the principal misfits differ in both magnitude and sign, and the misfit strain tensor allows an invariant line along which the normal strain is zero. The precipitates at small sizes are elongated along the direction of lower absolute misfit, and possess an 0 symmetry. At large sizes, the mirror symmetries normal to the x and y axes are broken to yield shapes which are elongated along a direction between that of lower misfit and the invariant line. This 0 -> M transition is continuous and occurs in all the systems irrespective of the value of A The critical size increases with A and decreases with δ. Case D; The misfit in this case is a special form of that in Case C; the principal misfits have the same magnitude but opposite signs. The precipitates at small sizes have a square-like shape with its sides normal to the < 11 > axes, irrespective of the type of cubic anisotropy. At large sizes, they become rectangle-like with the long axis oriented along one of the <11> directions. Similar to Case C, this T - 0 transition is continuous and occurs in all the systems irrespective of the values of A. The critical size increases with A and decreases with δ. Thus, we have identified all the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two dimensional systems. We have identified their origin and nature, and characterized them in terms of their dependence on the anisotropy parameter and modulus mismatch.

Vapour-Liquid Equilibrium (VLE), Liquid-Liquid Equilibrium (LLE) and Vapour-Liquid-Liquid Equilibrium (VLLE) are of special interest in chemical engineering as these types of data form the basis for the design and optimization of separation processes such as distillation and extraction, which involve phase contacting. Of recent, chemical companies/industries have required thermodynamic data (especially phase equilibrium data) for chemicals that are expensive or costly to synthesize. Phase equilibrium data for such chemicals are scarce in the open literature since most apparatus used for phase equilibrium measurements require large volumes (on average 120 cm3) of chemicals. Therefore, new techniques and equipment have to be developed to measure phase equilibrium for small volumes across reasonable temperature and pressure ranges. This study covers the design of a new apparatus that enables reliable vapour pressure and equilibria measurements for multiple liquid and vapour phases of small volumes (a maximum of 18 cm3). These phase equilibria measurements include: VLE, LLE and VLLE. The operating temperature of the apparatus ranges from 253 to 473 K and the operating pressure ranges from absolute vacuum to 1600 kPa. The sampling of the phases are accomplished using a single Rapid-OnLine-Sampler- Injector (ROLSITM) that is capable of withdrawing as little as 1μl of sample from each phase. This ensures that the equilibrium condition is not disturbed during the sampling and analysis process. As an added advantage, a short equilibrium time is generally associated with a small volume apparatus. This enables rapid measurement of multiple phase equilibria. A novel technique is used to achieve sampling for each phase. The technique made use of a metallic rod (similar in dimension to the capillary of the ROLSITM) in an arrangement to compensate for volume changes during sampling. As part of this study, vapour pressure and phase equilibrium data were measured to test the operation of the newly developed apparatus that include the following systems: • VLE for 2-methoxy-2-methylpropane + ethyl acetate at 373.17 K • LLE for methanol + heptane at 350 kPa • LLE for hexane + acetonitrile at 350 kPa • VLLE for hexane + acetonitrile at 348.20 K New experimental vapour pressure and VLE data were also measured for systems of interest to petrochemical companies. These measurements include: • VLE for methanol + butan-2-one at 383.25, 398.14 and 413.20 K ABSTRACT • VLE for ethanol + butan-2-one at 383.26, 398.23 and 413.21 K • VLE for ethanol + 2-methoxy-2-methylbutane at 398.25 and 413.19 K • VLE for ethanol + 2-methylpent-2-ene at 383.20 K These measurements were undertaken to understand the thermodynamic interactions of light alcohols and carbonyls as part of a number of distillation systems in synthetic fuel refining processes which are currently not well described. Two of these above mentioned systems include expensive chemicals: 2-methoxy-2-methylbutane and 2-methylpent-2-ene. The experimental vapour pressure data obtained were regressed using the extended Antoine and Wagner equations. The experimental VLE data measured were regressed with thermodynamic models using the direct and combined methods. For the direct method the Soave-Redlich-Kwong and Peng-Robinson equations of state were used with the temperature dependent function (α) of Mathias and Copeman (1983). For the combined method, the virial equation of state with the second virial coefficient correlation of Tsonopoulos (1974) was used together with one of the following liquid-phase activity coefficient model: TK-Wilson, NRTL and modified UNIQUAC. Thermodynamic consistency testing was also performed for all the VLE experimental data measured where almost all the systems measured showed good thermodynamic consistency for the point test of Van Ness et al. (1973) and direct test of Van Ness (1995). / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2011.

Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2012.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (p. [148]-178).

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 128-145).

Thesis (Ph.D.)--Aerospace Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Seitzman, Jerry; Committee Member: Jagoda, Jechiel; Committee Member: Lieuwen, Tim; Committee Member: Menon, Suresh; Committee Member: Tan, David.

Thesis (M.Sc.)--Memorial University of Newfoundland, 2004. / Bibliography: leaves 56-61.