In this study we construct two new equations to describe the effective diffusivity in nanomaterials where diffusion proceeds via both the grains and the grain boundaries in comparable amounts. We analyze two very simple 2D grain configurations by Monte Carlo methods to test the validity of the equations. In addition, we also test the Hart and the recently extended Maxwell-Garnett equations. It is shown that one of the two new equations provides a very good description of diffusion in the grain models postulated.

In the present work, the recently established principle of correspondence between the elastic and the piezoelectric problems for the transversely isotropic materials has been applied to obtain the solution of the problem of interaction of two tangential forces and a penny-shaped crack. The problem under consideration is described as follows: a penny-shaped crack in the unbounded piezoelectric medium is interacting with two tangential forces of the same magnitude acting in the same direction and applied arbitrarily but symmetrically with respect to the crack plane, which is a plane of isotropy. Some further investigation of the principle of correspondence is made and the important limiting conditions are stated.

A stochastic model is proposed to study dislocation dynamics in metallic single crystals. A Langevin type thermal fluctuation is taken into account for the model to maintain thermal equilibrium. This approach works as Brownian motion of segmental dislocations. Additionally, a new model for implementing the cross slip mechanism in FCC metals is developed based on results obtained by atomistic simulations. This new model is capable of simulating realistic thermal processes such as thermally activated dislocation motion during easy glide or cross slip during cold working of metals.

γ– and θ–alumina are two metastable phases of aluminum oxide observed along the thermal dehydration sequence of boehmite before conversion to the final product α–alumina. The transformation from γ– to θ–alumina was studied by using Al16O24 cells. Motion of some Al atoms from their γalumina positions to new positions and no O motions result in an approximate structure that, upon relaxation by first-principles calculations, becomes the known θ–alumina structure. Total-energy calculations along the paths of the atomic motions have been used to map out transformation pathways. The model accurately predicts experimentally observed domain boundaries in θ–alumina and the γ– to θ–alumina conversion rate.

Using the Unrestricted Hartree-Fock method and supercells containing up to 160 atoms, we calculated the energy level positions in the gap and atomic geometry for the Fe4+ impurity substituting for a host Ti atom in SrTiO3. In agreement with experiment, the high spin (S=2) state is much lower in energy than the zero-spin state. The energy level positions strongly depend on the asymmetric displacement mode of the six nearest O ions which is a combination of the Jahn-Teller and breathing modes. A considerable covalent bonding between the Fe ion and four nearest O ions takes place.

Atomic level processes often play an important role in the way a material responds to an external field. Thus in order to model the behavior of materials accurately, it is necessary to develop simulation techniques which can effectively couple atomistic effects to the macroscopic properties of the model system and vice-versa. In other words, a multiscale methodology needs to be developed to bridge the different length and time scales. In this work we study the propagation of an elastic wave through a coupled continuum-atomistic medium. The equations of motion for the wave propagation through the continuum are solved using the Finite Difference Time Domain Method (FDTD). Simultaneously we use Molecular Dynamics (MD) to examine the effect of the wave packet on the atomic dynamics and the effect of atomic dynamics on the propagation of the wave. The handshaking between the FDTD region and the MD region is concurrent.

At long times the effective solute diffusivity can be described by the (modified) Hart-Mortlock and Maxwell-Garnett equations for diffusion parallel and perpendicular to the grain boundary respectively. In this paper we analyze for the first time the time dependence of the effective solute diffusivity for these conditions. We assume that there are local regions (delineated by the diffusion length) in the grains adjacent to the grain boundary where the solute is equilibrated with the grain boundary. We write equations for the effective solute diffusivity with this assumption. Comparison with Monte Carlo simulations shows that this is quite a reasonable approximation for solute diffusion parallel to the grain boundary. For diffusion perpendicular to the grain boundary it is only a fair approximation unless the segregation is weak.

Sintering distortions of two and three-layer composite powder structures are determined based upon the continuum theory of sintering implemented in a finite element computer code. The macroscopic constitutive parameters of the powder material are obtained on the basis of the meso-scale simulations of a realistic grain-pore structure. The model follows both the densification and the damage development during sintering using a new fracture criterion for the prediction of macroscopic strength in sintering.

The martensitic phase transformation from bcc to hcp underlies a number of curious effects, including shape-memory and superelasticity. The distinctive feature is the microscopic reversibility of the transition: at the atomic level, the position of each atom is uniquely related between phases. Moreover, this one-to-one relationship holds not only for the perfect crystal transformation mechanism, but also for the topological defects (such as twin boundaries) which are created in the transformation. Furthermore, for shape memory effect the microscopic relationship must be preserved by the deformation mechanism active in the material. In this paper, we examine the microscopic phenomena which allow these relationships to hold, and the consequences for shape-memory alloy design.