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The utility of first-principles methods in the study and prediction of binary alloys is showcased by three detailed studies. In particular, the T = 0K cluster expansion methodology in conjunction with finite temperature statistical modeling by a Monte Carlo method is used to study two systems of practical interest, Mg-Li (magnesium-lithium) and Rh-W (rhodium-tungsten). Also, an empirically-informed, high-throughput approach to crystal structure prediction is shown by a study of the Pt$_8$Ti (the Pietrokowsky phase) phase and a broad and detailed analysis of binary Mg-X phases in 39 systems (X=Ag, Al, Au, Ca, Cd, Cu, Fe, Ga, Ge, Hf, Hg, In, Ir, K, La, Li, Pb, Pd, Pt, Mo, Na, Nb, Os, Rb, Re, Rh, Ru, Sc, Si, Sn, Sr, Ta, Tc, Ti, V, W, Y, Zn, Zr). These results are presented in the form of three publications (the first two are in print, and the third is nearing submission) co-authored with Gus Hart and Stefano Curtarolo.

We present and discuss results from a measurement of the hyperfine a constant of the 1s^(2)2s^(2)2p^(6)3p^(2)2P1/2 excited state in 25Mg+ and the linewidth of the same state in 24Mg+. We trapped a single ion in a linear Paul trap and laser-cooled it using the 2S1/2 -> 2P3/2 transition (in the case of 25Mg+) and the 2S1/2 -> 2P1/2 transition (in the case of 24Mg+). We optically pumped the ion into the (F=3, mp=±3) ground states and weakly probed it with a tunable fibre laser that was scanned to drive the ion from the ground state to the F'=3 and F'=2 manifolds of the 2P1/2 state. The final state of the ion was determined by counting fluorescence (or the reduction therein) from the 2S1/2 (F=3, mF=±3) -> 2P3/2 (F''=4, m''F=±4) cycling transition with a photomultiplier module. We determined that the hyperfine a constant is 102.16 ± 0.16 MHz and the natural linewidth is 42.4 ± 1.2 MHz. / Thesis / Doctor of Philosophy (PhD)

<P> There is a growing interest in magnesium and its alloys due to their high strength to weight ratio. Magnesium is of particular interest to the automotive industry as a consequence of the current pressure to reduce green house gas emissions from the transportation sector through vehicle weight reduction. However, there is a lack of knowledge concerning the formability of magnesium. As a result, the application of magnesium as a commercial material has not been fully exploited. Much has been learned from the constitutive modeling of materials such as aluminum and steel. Therefore, this thesis considers the constitutive modeling of magnesium and its alloys. </p> <p> Based on this motivation, polycrystal plasticity theories that have been established and used to characterize aluminum and steel are studied. The validity of these theories is examined with respect to magnesium and its alloys. The magnesium system is composed of the hexagonal closed-packed (HCP) crystal structure. Therefore, a strong plastic anisotropy is induced in magnesium crystals due to the limited number of slip systems that may be activated with ease. The models proposed by Taylor and Sachs neglect strain and stress heterogeneities respectively. As a result, the models are either too stiff or too soft to study magnesium due to the anisotropic nature of the crystal structure. The intermediate models; self-consistent models, which are able to consider the heterogeneities among the grains in polycrystals, are believed to be more suitable to study magnesium and its alloys. Therefore, a large strain elastic-viscoplastic self-consistent (EVPSC) model is developed for polycrystalline materials. Both rate sensitive slip and twinning are included as mechanisms of plastic deformation, while elastic anisotropy is accounted for in the elastic modulus. The transition from single crystal plasticity to polycrystal plasticity is based on a completely self-consistent approach. It is shown that the differences in the predicted stress-strain curves and texture evolutions based on the EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and Tome (1993) are negligible at large strains for monotonic loadings. For the deformations involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic transition, while the VPSC model gives a discontinuous response because the model is incapable of modeling elastic deformation. In addition, it is demonstrated that the EVPSC model can capture some important experimental features which cannot be simulated by using the VPSC model. </p> <p> Various self-consistent schemes exist for EVPSC and VPSC models. However, the evaluations of these models are not complete. Therefore, an examination of various polycrystal plasticity models is made, based on comparisons of the predicted and experimental stress responses as well as the R values, to assess their validity. It is established that, among the models examined, the self-consistent models with grain interaction stiffuess values halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options, the Affine self-consistent scheme results in the best overall performance. Furthermore, it is demonstrated that the R values under uniaxial tension and compression within the sheet plane show a strong dependence on the imposed strain. This suggests that the development of anisotropic yield functions using measured R values, must account for the strain. dependence. </p> <p> The recently developed large strain elastic visco-plastic self-consistent (EVPSC) model, which incorporates both slip and twinning deformation mechanisms, is used to study .the lattice strain evolution in extruded magnesium alloy AZ31 under uniaxial tension and compression. The results are compared against in-situ neutron diffraction measurements done on the same alloy. For the first time, the effects of stress relaxation and strain creep on lattice strain measurements in respectively displacement controlled and load controlled in-situ tests are numerically assessed. It is found that the stress relaxation, has a significant effect on the lattice strain measurements. It is also observed that although the creep does not significantly affect the trend of the lattice strain evolution, a better agreement with the experiments is found if creep is included in the simulations. </p> <p> In conjunction with the M-K approach developed by Marciniak and Kuczynski (1967), the EVPSC model is applied to study the sheet metal formability of magnesium alloys in terms of the forming limit diagram (FLO). The role of crystal plasticity models and the effects of basal texture on formability of magnesium alloy AZ31 B sheet are studied numerically. It is observed that formability in HCP polycrystalline materials is very sensitive to the intensity of the basal texture. The path-dependency of formability is examined based on different non-proportional loading histories, which are combinations of two linear strain paths. It is found that while the FLO in strain space is very sensitive to strain path changes, the forming limit stress diagram (FLSO) in stress space is much less path-dependent. It is suggested that the FLSO is much more favourable than the FLO in representing forming limits in the numerical simulation of sheet metal forming processes. The numerical results are found to be in good qualitative agreement with experimental observations. </p> / Thesis / Doctor of Philosophy (PhD)

Historically, the ability of crystal plasticity to incorporate the Schmid’s law at each integration point has been a powerful tool to simulate and predict the slip behavior at the grain level and the succeeding heterogeneous stress/strain localization and texture evolution at the macroscopic level. Unfortunately, this remarkable capability has not been replicated for materials where twinning becomes a noticeable deformation mechanism, namely in the case of low-stacking fault energy cubic, orthorhombic, and hexagonal close packed structures. This dissertation is an attempt to gain understanding on the heterogeneous deformation due to twinning through various techniques including micromechanics, discrete dislocation dipole loops, and digital image correlation (DIC) analyses, and then bring the collected small scale information up to the fullield crystal plasticity scale using fast Fourier Trans- forms. Results indicate that the twin spacing depends primarily upon the height of the twin, and the stress relaxation from the twinning depends upon the thickness of the twin. Furthermore, in a homogenous stress state, discrete dislocation dipole loop-based twinning model showed that the lenticular shape has the minimum stable energy rather than the lamellar or ellipsoidal twin morphology. Our study on the evolution of twinning under three-point bending condition in strongly basal textured magnesium alloy allowed us to build a strategy to incorporate characteristic twin spacing parameter in the crystal plasticity framework. Inspired by results from molecular dynamics (MD) simulations stressing the effect of shuffles on twin nucleation and disconnection core width, we developed an explicit twinning nucleation criterion based on hydrostatic stress gradient and volume fraction of twin inside a grain. Characteristic twin spacing parameter is used as a function of twin height to determine site specific nucleation points in case of multiple twinnings. This ap- proach offered a good reproduction of the microstructure evolution as affected by twinning in a tri-crystal system.

In this work, a crystal elasto-viscoplastic model was modified to account for the anisotropic mechanical response of magnesium aluminum alloys. Crystal plasticity may offer new understanding of these alloys by explicitly modeling the texture development that profoundly affects the properties of magnesium. The model is able to account for the individual slip systems of both the cubic and hexagonal phases. The constants of the model were determined from published experimental AZ31 data, and the plastic hardening response is shown to match these results well using a modification to the hardening rule to approximate the kinetics of twinning. Model aggregates were created with aluminum compositions representative of common magnesium structural alloys. This approach allows the effect of varying percentage of cubic phase on the hexagonal magnesium alloy aggregate to be studied both in terms of macroscopic response and the crystallographic changes occurring within the system.

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