Ph. D.

We develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points. For such systems the formalism yields one-dimensional systems with many-body infinite range interactions for which the thermodynamics is well defined while the Gibbs states are not. (Piecewise linear systems of this kind yield the soluble, in a sense, Fisher models.) We prove that such systems exhibit phase transitions, the order of which depends on the behavior at the indifferent fixed points. We obtain the critical exponent describing the singularity of the pressure and analyse the decay of correlations of the equilibrium states at all temperatures. Our technique relies on establishing and exploiting a relationship between the transfer operators of the original map and its suitable (expanding) induced version. The technique allows one to also obtain a version of the Bowen-Ruelle formula for the Hausdorff dimension of repellers for maps with indifferent fixed points, and to generalize Fisher results to some non-soluble models. / Ph. D.

The change in the number of phase transitions for perturbations of finite range interactions is studied. A Monte-Carlo simulation was performed for a translation invariant spin 1/2 ferromagnetic model in Z² with fundamental bonds A = {(0,0);(0,1)} B = {(0,0);(2,0)} C = {(0,0);(0,1);(1,1);(1,0)} The model exhibits one phase transition if the coupling constant J(A) is zero, but two phase transitions were found when J(A) is non zero and small enough. The generalization of this situation is provided by a construction, due to J. Slawny, which through a sequence of progressively smaller perturbations yields models with an arbitrary minimum number of phase transitions. However, such construction requires the existence of interactions with one fundamental bond such that for all values of the coupling constants the Gibbs state is unique even when the interaction is perturbed by an arbitrary finite range perturbation of small enough norm. In this work it is proven that such property is exhibited by some translation invariant systems in Z^ν with finite state space at each point. The proof applies to models with real interactions and whose fundamental bonds are all multiple of a single bond which is of prime order and which is obtained as the product—in the group ring structure of the dual space—of one dimensional bonds whose non trivial projections at each lattice site are unique. The proof is based on the Dobrushin-Pecherski criterion concerning the uniqueness of Gibbs states under perturbations. Such criterion is restated so that only transition functions on sets of simple geometry are involved. In addition, an algebraic characterization is presented for the set of Gibbs states for ferromagnetic systems for which the state space at each lattice site is a compact abelian group. This is a generalization of the theory originally introduced by Slawny for spin 1/2 ferromagnetic models and later extended by Pfister to ferromagnetic models for which the state space at each point is a finite product of tori and finite abelian groups. / Ph. D.

The current understanding of the mechanical properties and deformation behavior of some individual phases in titanium alloys is limited due to the fine scale at which these phases precipitate within the β-phase matrix. The α and ω phases represent the most widely observed phases in titanium alloys depending on the alloy composition and also the heat treatment procedure adopted during processing. The possibility of precipitating ω-phase depends on the content of the β-stabilizers within the system. Although a significant compositional partitioning occurs within ω-phase upon aging treatment, the knowledge of ω-phase mechanical properties as a function of composition is very limited. The initial part of the current work focuses on the effect of common β-stabilizers elements on the phase stability and mechanical properties of the ω-phase using first-principles calculations. A relation between the bonding nature, the phase stability, and elastic properties was proposed. Thereafter αʺ martensitic phase was investigated in Ti-Nb and Ti-Nb-O alloys. The phase stability and martensitic start temperature of αʺ-phase was studied as a function of Nb and oxygen content. Also, the effect of the lattice shear distortion induced by oxygen atom on stabilizing β-phase was investigated. Subsequently the effect of the β-stabilizers' elements on stacking faults energy and ductility in α-Ti alloys was studied. Both prismatic and basal slip system were investigated with different concentration of β-stabilizers at the slip plane. Lastly, while the Tadmor and Bernstein model was employed to predict the partial dislocation emission and twinning propensity, the Rice criterion was used to estimate the effect of different β-stabilizers on the ductility of α-Ti alloys.

"The goal of heat treating manufactured steel components is to enhance the characteristics of the metal so that the components meet pre-specified quality assurance criteria. However, the heat treatment process often creates considerable distortion, dimensional change, and residual stresses in the components. These are caused mainly by thermal stresses generated by a non-uniform temperature distribution in the part, and/or by transformation stresses due to the volume mismatch between the parent phase and product phases that may form by phase transformation. With the increasing demand for tighter dimensional tolerances and better mechanical properties from heat treated components, it is important for the manufacturer to be able to predict the ability of a component to be heat treated to a desired hardness and strength without undergoing cracking, distortion, and excessive dimensional change. Several commercial softwares are available to accurately predict the heat treatment response of wrought steel components. However, these softwares cannot be used to predict the heat treatment response of steel components that are made by powder metallurgy (PM) processes since these components generally contain pores which affect the mechanical, thermal, and transformation behavior of the material. Accordingly, the primary objective of this research is to adapt commercially available simulation software, namely DANTE, so that it can accurately predict the response of PM steel components to heat treatment. Additional objectives of the research are to characterize the effect of porosity on (1) the mechanical properties, (2) the heat transfer characteristics, and (3) the kinetics of phase transformation during heat treatment of PM steels."

No description available.

The physical properties of single crystals of samarium monosulfide exhibit a first order semiconductor-to-metal transition near 6.5 kbar. However, thin films of SmS show only a gradual change in their properties on applying pressure and this renders the technical utilization of the material difficult. Several mechanisms have been proposed as the cause of the smoothing of the transition. They include intrinsic stress, impurities, grain size, improper stoichiometry, and porosity, all of which can be traced to the physical vapor deposition techniques employed in preparing the films. In contrast, chemical vapor deposition was employed in this study because previous work had shown that it could minimize these detrimental modifications in thin films. A new CVD system was tested using a volatile organometallic as the samarium source and reacting it with H₂S. The deposited films contained considerable amounts of oxygen as evidenced by structure analysis, and the origin was traced to the samarium organometallic. The reaction of oxygen-free samarium tricyclopentadienyl with H₂S as well as chemical transport are suggested for deposition of stress-free SmS thin films in future work.

No description available.

No description available.

No description available.