This dissertation presents theoretical investigations of two novel functional materials, TlBr and MoS2. TlBr is interesting due to its potential application as a high-quality room temperature radiation detector. The stability and electronic structures of three phases of TlBr are studied using Density Functional Theorem (DFT) calculations employing a hybrid functional. The calculated band gaps from DFT with the hybrid functional are in excellent agreement with experimental measurements. The influence of some interstitial and substitutional dopants on TlBr properties is further studied. DFT predicts that interstitial and substitutional C, N, and O dopants in TlBr can display large, localized magnetic moments. A simple model that employs Pauli exclusion principle and group theory is introduced to explain the magnitude of the moments. Van der Waals (VDW) bonded, layered transition metal dichalcogenides (TMDCs) are promising 2D materials and have drawn much research attention recently. A theory for the epitaxial growth on the transition metal dichalcogenides is developed and analyzed. A prototypical example of Au epitaxially grown on MoS2 is studied. It is demonstrated that if one accounts for interfacial energies and strains, the presence of misfit dislocations, and the compliance of the MoS2 substrate, the experimentally observed growth orientation (Au {111} orientation) will be energetically favored. Meanwhile, with only the top substrate layer being compliant (strained), this epitaxy method can serve as a means to exfoliate and transfer large single layers sheets of MoS2. The exfoliation of monolayer based on this epitaxy idea has been realized experimentally. This epitaxy model could prove technologically useful in 2D electronic devices and in epitaxial thin film growth applications.

Several mesoscale models have been developed to consider

a number of mechanical properties and microstructures

of Ti-V approximants to Gum Metal and steels from the atomistic scale.

In Gum Metal, the relationships between phonon properties

and phase stabilities are studied. Our results show that

it is possible to design a BCC (&beta-phase)

alloy that deforms near the ideal strength,

while maintaining structural stability

with respect to the formation of the &omega

and &alpha'' phases. Theoretical diffraction patterns reveal

the role of the soft N-point phonon

and the BCC-to-HCP transformation

path in post-deformation samples. The total energies

of the path explain the formation of the giant faults

and nano shearbands in Gum Metal.

In the study of steels, we focus on the carbon-solute dislocation

interactions. The analysis covers the Eshelby's model of point defects

and first principles calculations. It is argued that the effects

of chemistry and magnetism, omitted in the elasticity model,

do not make major contributions to the segregation energy.

The predicted solute atmospheres are in good agreement

with atom probe measurements.

Graphene is the strongest material ever discovered and has an extremely high Young's modulus (~ 1 GPa). Although stretching the sp2 covalent bonds between carbon atoms is very difficult, significant deflections do develop in graphene membranes. In fact, thermal rippling naturally emerges in graphene at any finite temperature. Moreover, the topological defects mediating plastic deformation often cause out-of-plane crumpling, an effective way to reduce the total elastic energy of the topological defect. It is even possible to design specific stress states to produce periodic wrinkles in graphene with adjustable wave lengths.

This work aims to understand how buckling influences the elastic and plastic behavior of graphene-based nanostructures. While the elastic moduli may be straightforwardly computed using structure optimization techniques with applied test stresses, it is a nontrivial task to obtain elastic properties at any specific temperature. Further, linear elastic theories are not able to describe large buckling because the second order nonlinear terms in the definition of the Lagrangian finite strain tensor cannot be neglected. In addition, the existence of topological defects and constraints need to be properly treated. Finally, buckling and defects of a curved surface such as a nanotube is even more complicated and poses other intriguing challenges.

To proceed, we employ Monte Carlo techniques to obtain fundamental elastic properties of graphene at desired temperatures, which supplies useful inputs for a nonlinear continuum model for graphene. This model not only takes into account, in a suitable manner, both large out-of-plane buckling and interactions among edge dislocations with periodic boundary conditions, but also serves as a handy tool for simulating nanoindentation experiments and the controlled wrinkling of graphene. At last, we focus on the Stone-Wales defect mediated plasticity of CNTs. Specifically, a kinetic Monte Carlo framework is designed to model the defect dynamics over a long time scale. We find that in large nanotubes, a chain of closely packed dislocations (called a "dislocation worm") may have less buckling and lower formation energy than the conventional dislocation glide under high tensile stresses.

This dissertation contains two parts. The goal of the first part is to understand the experimental observation that the friction forces between a 2D material and an amorphous substrate are sufficient to stabilize tensile and compressive strains of the order of 1\% within the 2D material. An idealized atomic scale model featuring stick-slip friction is proposed to explore the interaction between a 2D material and a substrate. The atomic scale model shows that the observed strains can be sustained by bonds with strengths of the order of van der Waals (vdW) bonds. The observed distribution of strain and force in the strain-stabilized structure suggests that the maintenance of strain can be attributed to atoms located along the boundary, within a specified width range, which corresponds well to the prediction made by a continuum model.

In the second part, the observations of interesting atomic scale structures that include vortices, anti-vortices, and other more complicated structures in the force vectors revealed by the model in the first part are discussed. The centers of the vortices and anti-vortices are identified by calculating the winding number at each atomic position. Vortices and anti-vortices are found to annihilate with each other during structural relaxation, but a significant number of vortices and anti-vortices are preserved with the friction on the order of vdW interaction. Similar simulations are repeated for a system without the friction, and the interesting structures of vortices and anti-vortices cannot be maintained. Furthermore, the size of the vortices is quantified by defining a directional correlation function to investigate the evolution of those intriguing patterns, which concludes that the average size of the vortices will increase as the system stabilizes. It is also found that vortices and anti-vortices exist in the atomic displacements, which suggests the possibility to observe those structures experimentally. Finally the effect of those structures on friction is investigated by applying constant force and constant velocity in this stick-slip friction model.

Weak interlayer interactions in van der Waals bonded layered materials enable us to isolate 2D monolayer from the bulk by means of simple mechanical exfoliation methods. Since the first time graphene was extracted from bulk graphite, this method has been used extensively to produce various 2D monolayers. Despite its success, this method is not a well-controlled process since it usually requires a random number of mechanical exfoliation steps to yield a monolayer sample and final sample size is relatively small. Recently, a thin film mediated mechanical exfoliation method has addressed these problems by enabling a one-step exfoliation scheme to achieve monolayers. This dissertation examines the process from a theory perspective.

To reveal its underlying mechanism as well as have a comprehensive understanding of the mechanical exfoliation process, we have developed a rigid layer model for van der Waals bonded layered materials. The assumption is based on the fact that, there exists very low frequency phonon vibration modes, in which the layers move nearly as rigid units and these low frequency vibration modes essentially determines the stability of the big structure. Within the framework of rigid layer model, we have analyzed the mechanical stability of vdW bonded layered system under the perturbation of external loading force and thermal noise. We have shown that the effectiveness of thin film mediated method arise from the change of soft mode. Furthermore, we found that twisting topmost layer with rotation angle has similar effect and should lead to improvement in exfoliation result as well. Finally, this rigid layer model has been compared with atomic model to show its scope of application. At zero temperature, all these atomic scale simulation results agree with the rigid layer model suggesting that the simple model captures the essential features of the exfoliation mechanisms of vdW bonded layered materials at low temperature. This simple model can serve as a reasonable and efficient way to assess the factors affecting the mechanical exfoliation results.

Chalcogen-based materials, specially those containing S, Se or Te, can can be successfully manufactured into thin films with semiconducting properties. Transition metal dichalcogenides (TMDCs) are a class of layered materials whose electronic properties are known to depend on the elastic state. Mono- and bi-layer WSe2, for example, undergoes a strain-induced direct to indirect band gap transition. This feature, in principle, could be of great use to design single-material electronic devices were circuits are “drawn” in different elastic states. While it is possible to grow TMDCs in a variety of elastic states, precise control of local strain is yet to be achieved. The first part of this dissertation develops a theoretical model for an empirically-tested method of strain release for TMDCs with built-in strain: the solvent evaporation-mediated decoupling (SEMD) method. The purpose of building such model is to generate knowledge about the underlying mechanism that allows the strain release, and once this process is better understood, to propose further generalizations and experiments that could lead to a better engineering of the elastic states.

The SEMD process consists simply in letting a droplet of liquid solvent evaporate on top of a strained layer. The process was first reported in WSe2 monolayers grown by physical vapor deposition (PVD) on top of amorphous silica; in this case, as the system cooled down from growth to room temperature, strain build up in the film due to the mismatch between its thermal expansion coefficient and that of the substrate. By finding the elastic equilibrium state of a Hamiltonian that takes into account the elastic, interfacial, and substrate-film interaction energies, the proposed model finds an in-plane deformation beyond the film’s initial strain as the main effect of the solvent droplet, and identifies it as the strain release mechanism. Furthermore, the proposes a selectivity criteria based on the contact angle that determines whether the SEMD process would be successful for a given initial elastic state.

The second part of the thesis is about thin films made of Te. Te-based materials were heavily studied in the 1980’s due to their applications in data storage, and are now experiencing a revival mainly because its potential application in electronic and optic devices. Due to the chain-like nature of the crystalline Te structure, this material's properties are highly anisotropic, with the conductivity, for example, being greater in the direction parallel to the chains. Because of this anisotropy, high-quality devices require large areas of single-crystalline Te.

Here, we explore the crystallization process of vapor-grown amorphous Te under different temperatures and, using tools from classical nucleation theory, investigate the nucleation and growth rate of crystals in an amorphous matrix. As a low nucleation rate will necessarily result in slow growth, another mechanism to grow Te single crystals is needed. An alternative route is offered by growing Te upon WTe2, a substrate with two-fold symmetry that favors chain alignment along its high-symmetry direction. Crystals nucleating on top of WTe2 are found to have single crystal-like texture, and thus be suitable for device applications.

A model of pulsed laser melting of embedded nanoparticles is introduced. Pulsed laser melting (PLM) is commonly used to achieve a fast quench rate in nanoparticles; this model enables a better understanding of the influence of PLM on the size distribution of nanoparticles, which is crucial for studying or using their size-dependent properties. The model includes laser absorption according to the Mie theory, a full heat transport model, and rate equations for nucleation, growth, coarsening, and melting and freezing of nanoparticles embedded in a transparent matrix. The effects of varying the laser parameters and sample properties are studied, as well as combining PLM and rapid thermal annealing (RTA) processing steps on the same sample. A general theory for achieving narrow size distributions of nanoparticles is presented, and widths as narrow as 12% are achieved using PLM and RTA.

Recently, embedded binary eutectic alloy nanostructures (BEANs) have drawn some attention. A previously calculated equilibrium structure map predicts four possible nanocrystal alloy morphologies: phase-separated, bi-lobe, core-shell and inverse coreshell

governed by two dimensionless interface energy parameters. The shape of the bilobe nanoparticles is obtained by nding the surface area of all interfaces that minimizes the overall energy, while also maintaining mechanical equilibrium at the triple point.

Two representative alloy systems displaying eutectic phase diagrams and negligible solid solubility were chosen: GeSn and AuGe. GeSn samples were prepared by sequential implantation of Ge and Sn into SiO2. AuGe samples were prepared by implanting Ge within Au-doped silica lms. Transmission electron microscopy images revealed bi-lobe nanocrystals in both samples. Therefore, the interface energies in both systems must be such that the dimensionless parameters lie in the region of bi-lobe stability.

Careful analysis of the bi-lobe structure leads to the determination of two dimensionless length scales, which describe the bi-lobe independent of the size of the nanoparticle. These two parameters, eta 1 and eta 2 can be used to calculate contours of equal eta 1 and eta 2 over the entire range of bi-lobe stability. Experimental measurement and comparison to predicted structures leads to determination of acting dimensionless interface energies. Experimentally available wetting data is then used to calculate the remaining interface energies in the system. gamma Ge(s)/SiO2 was found to be between 0.82-0.99 J/m2 . gamma Ge0.22Sn0.78(l)/SiO2 and gamma Au0.53Ge0.47(l)/SiO2 are determined to be 1.20 and 0.94 J/m2 , respectively.

To investigate the possibility of size eects at the nanoscale, size dependent phase diagrams for the AuGe and GeSn system are determined. This is done by the theoretical approach rst outlined byWeissmueller et al., which takes into account the energy contribution of the various morphologies listed above. Results from this calculation are compared to those using the tangent line construction approach. The composition dependent surface energies of binary alloy liquids required in this calculation are determined using Butler's equation.

α-Ti and α-Ti alloys are of technological interest as high specific strength, corrosion resistant, nonmagnetic, and bio-compatible materials. However, they are costly to process and require strict control of the presence of interstitial impurities that cause significant strength gains, but also loss of ductility. This work uses atomistic simulations to examine the properties of dislocation cores, i.e. the regions in a material surrounding a dislocation that has been deformed beyond it’s ideal strength in α-Ti and α-Ti alloys. Particular attention is paid to the interactions between these dislocations and solute atoms. It is shown that dislocation core structure affects the interaction with interstitial oxygen, and that solute atoms may be used to influence the dislocation core structure of screw dislocations through the so-called Cottrell atmosphere.

In recent years it has been shown that it is possible to design materials with strengths approaching their theoretical ideal limit. This is an intriguing development; materials typically fail at stresses that are several orders of magnitude below their theoretical limits of strength. The development of engineering alloys with usable strengths near the ideal limit would have profound technological implications.

The most common approach used to increase a material's strength, is grain refinement. This method has been used to produce nanograined hollow nanospheres of CdS. Under nanoindentation these spheres show remarkable strength and deformation properties. The stresses and strains in the shells are studied with linear elastic finite element analyses and from this a failure criterion is developed. The stresses predicted by the failure criteria are 2.2 GPa, which is very large for an inherently brittle material. We compare the failure stress to the calculated ideal strength for CdS, calculated using density functional theory. Comparing the stress predicted by the failure criteria to the ideal strength shows that the hallow nanospheres approach 70% of their ideal strength.

In 2003 a new Ti, Nb based alloy "Gum Metal" was introduced by Toyota Research Corp. This alloy has strength approaching the ideal limit even in bulk form. Moreover, the material deforms in a novel fashion without the obvious participation of dislocations. A Ti-V alloy has been chosen to study the properties of this type of alloy. The BCC ideal yield surface is examined as a function of composition. Dislocation core structures are also examined as a function of composition. The results explain some experimental observations in this novel system.