Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)




Shiwei Zhang


In this thesis, we explore two stochastic techniques to study properties of materials in realistic systems. Specifically, the kinetic Monte Carlo (KMC) method is utilized to study the crystal growth process of ferroelectric materials and the quantum Monte Carlo (QMC) approach is used to investigate the ground state properties of atoms and molecules.;In the growth simulations, we study the growth rates and chemical ordering of ferroelectric alloys using an electrostatic model with long-range Coulomb interactions. Crystal growth is characterized by thermodynamic processes involving adsorption and evaporation, with solid-on-solid restrictions and excluding diffusion. A KMC algorithm is formulated to simulate this model efficiently in the presence of long-range interactions. The growth process is simulated as a function of temperature, chemical composition, and substrate orientation. We carried out the simulations on two heterovalent binaries, those of the NaCl and the Ba(Mg1/3Nb2/3))O3(BMN) structures. Compared to the simple rocksalt ordered structures, ordered BMN grows only at very low temperatures and only under finely tuned conditions. For materials with tetravalent compositions, such as (1-x)Ba(Mg 1/3Nb2/3))O3 + x BaZrO3 (BMN-BZ), the model does not incorporate tetravalent ions at low-temperature, exhibiting a phase-separated ground state instead. at higher temperatures, tetravalent ions can be incorporated, but the resulting crystals show no chemical ordering in the absence of diffusive mechanisms.;In the second part of the thesis, we present results from an auxiliary field quantum Monte Carlo (AFQMC) study of ground state properties, in particular dissociation and ionization energy, of second-row atoms and molecules. The method projects the many-body ground state from a trial wavefunction by random walks in the space of Slater determinants. The Hubbard-Stratonovich transformation is employed to decouple the Coulomb interaction between electrons. A trial wave function is used in the approximation to control the "phase problem". We also carry out Hartree-Fock (HF) and Density Functional Theory (DFT) calculations for comparison to AFQMC results and to serve as starting wavefunctions for our AFQMC calculations. Results of dissociation energy are in excellent agreement with experimental values. Ionization energy errors are somewhat larger than those of other methods. We conclude with a discussion of several possible sources of error as well as a direction for the improvement.



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