Different phases of metallic alloys have a wide range of applications. However, the driving mechanisms of the phase selections can be complex. For example, the detailed pathways of the phase transitions in the devitrification process still lack a comprehensive interpretation. So, the understanding of the driving mechanisms of the phase selections is very important.

In this thesis, we focus on the study of the Al-Sm and other related metallic alloy systems by simulation and experiment. A procedure to evaluate the free energy has been developed within the framework of thermodynamic integration, coupled with extensive GPU-accelerated molecular dynamics (MD) simulations; The ``spatially-correlated site occupancy'' has been observed and measured in the $\epsilon$-Al$_{60}$Sm$_{11}$ phase. Contrary to the common belief that nonstoichiometry is often the outcome of the interplay of enthalpy of formation and configurational entropy at finite temperatures, our results from Monte Carlo (MC) and molecular dynamics (MD) simulations, imply that kinetic effects, especially the limited diffusivity of Sm is crucial for the appearance of the observed spatial correlations in the nonstoichiometric $\epsilon$ phase. Moreover, in order to overcome the time limitation in MD simulation of the nucleation process, a ``persistent-embryo method'' has been developed, which opens a new avenue to study solidification under realistic experimental conditions via atomistic computer simulation. Based on this thesis study, we have achieved deeper understanding of the driving mechanisms of the phase selections, and laid a foundation for further prediction and control of the fabrication of novel metallic alloy materials. This thesis consists of the following seven chapters:

Chapter 1 briefly introduces the history of the development of the metallic alloy materials, and their significant impact on human civilization. In particular, the research background of metallic glasses has been reviewed, and some unsolved questions have been raised.

Chapter 2 is the literature review. In the first section of it, simulation methods, including molecular dynamics (MD) simulation, Monte Carlo method (MC) simulation, and related technical issues in the computer simulation to mimic the real system have been reviewed. In the second section of it, analysis methods, including structural and dynamical analysis methods, classical nucleation theory, free energy computing algorithms, and experimental techniques have been reviewed.

Chapter 3 reports our work in a self-contained procedure to evaluate the free energy of liquid and solid phases of an alloy system. We start from the Einstein crystal as the reference system, using thermodynamic integration to solve the free energy of a single-element solid phase. Then we compute the free energy difference between the solid and liquid phases using Gibbs-Duhem integration. After that we construct an ``alchemical'' path connecting a pure liquid and a liquid alloy to calculate the mixing enthalpy and entropy. This procedure is of great importance because the evaluation of free energy is fundamental to achieving microscopic understandings of freezing and melting phenomena.

Chapter 4 elucidates the origin of the spatially-correlated site occupancy in the non-stoichiometric meta-stable $\epsilon$-Al$_{60}$Sm$_{11}$ phase. This STEM observed spatially-correlated site occupancy cannot be explained by the ``average crystal'' description from Rietveld analysis of diffraction data, or by the lowest free energy structure established in MC simulations. MD simulations of the growth of $\epsilon$-Al$_{60}$Sm$_{11}$ in undercooled liquid show that when the diffusion range of Sm is limited to $\sim 4\AA$, the correlation function of the as-grown crystal structure agrees well with that of the STEM images. Conclusion thus has been made that the kinetic effects, especially the limited diffusivity of Sm atoms plays an important role in determining the non-stoichiometric site occupancy. In addition to the free energy point of view, this result helps us to have a deeper understanding of phase selections from structural and dynamical points of views.

Chapter 5 describes the ``persistent-embryo'' method (PEM) nucleation simulation. The PEM is developed to facilitate crystal nucleation in MD simulations by preventing small crystal embryos from melting using external spring forces, so that the early state of rare nucleation events can be accessed. This method opens a new avenue to study solidification under realistic experimental conditions. The nucleation rates of pure Ni, and of B2 phase of glass former Cu-Zr alloy have been computed using PEM. We also apply PEM to the Al-Sm system to study the nucleation of $\epsilon$-Al$_{60}$Sm$_{11}$ phase in the undercooled Al-Sm liquid, complex and interesting behaviors, different from the Ni case, have been found.

Chapter 6 presents an implementation of EAM and FS inter-atomic potentials in HOOMD-blue, a GPU software designed to perform classical molecular dynamic simulations. The accuracy of the code has been verified in a variety of broad tests, the performance of the code is significantly faster than LAMMPS running on a typical CPU cluster. Furthermore, our hoomd.metal module follows HOOMD-blue code convention, which allows it to be coupled to the extensive python libraries. This package makes the MD simulations in the thesis and other related fields faster and more convenient.

Chapter 7 is a summary of my Ph.D. thesis study, and proposes a plan for future works.