Fractional Operators and Variations Applied to Stefan Problems

In this thesis, we present a model for the free boundary Stefan problem. We begin with outlining the problem and its complexities, motivating the need for a numerical method. Then we introduce fractional operators, exploring various characteristics to narrow down the proper operator that will apply to the Stefan problem. We then outline our model, using the Caputo fractional derivative with a finite difference discretization and the SOR method to solve numerically. Our results are presented for different parameters such as latent heat and temperature. We end with suggestions for further work on our model

Atomistic Simulation of Radiation-Induced Amorphization of the B2 Ordered Intermetallic Compound NiTi

Amorphization of the B2 intermetallic compound NiTi under electron irradiation has been investigated using molecular dynamics. The effect of irradiation was simulated using two processes: (1) Ni and Ti atoms were exchanged, resulting in chemical disorder, and (2) Frenkel pairs were introduced, leading to the formation of stable point defects and also chemical disorder upon mutual recombination of interstitials and vacancies. After {approximately}0.4 exchanges per atom, the first process resulted in an energy increase of approximately 0.11 eV/atom and a volume increase of 1.91%. On the other hand, after introducing {approximately}0.5 Frenkel pairs per atom, the second process led to smaller increases of 0.092 eV/atom in energy and 1.43% in volume. The calculated radial distribution functions (RDFs) were essentially identical to each other and to the calculated RDF of a quenched liquid. The structure factor, however, showed that long-range order was still present after atom exchanges, while the introduction of Frenkel pairs resulted in the loss of long-range order. It was concluded that point defects are necessary for amorphization to occur in NiTi, although chemical disorder alone is capable of storing enough energy to make the transition possible. 18 refs., 3 figs

Radiation-induced crystalline-to-amorphous transition in intermetallic compounds of the Cu-Ti alloy system

Recent progress in molecular-dynamics studies of radiation-induced crystalline-to-amorphous transition in the ordered intermetallic compounds of the Cu-Ti system is discussed. The effect of irradiation was simulated by the generation of Frenkel pairs,which resulted in both the formation of stable point defects and chemical disorder upon defect recombination. The thermodynamic, structural and mechanical responses of the compounds during irradiation were determined by monitoring changes in the system potential energy, volume expansion, pair correlation function, diffraction patterns, and elastic constants. It was found that the intermetallics Cu{sub 4}Ti{sub 3}, CuTi, and CuTi{sub 2} could be rendered amorphous by the creation of Frenkel pairs, but Cu{sub 4}Ti could not, consistent with experimental observations during electron irradiation. However, the simulations showed that Cu{sub 4}Ti did become amorphous when clusters of Frenkel pairs were introduced, indicating that this compound may be susceptible to amorphization by heavy-ion bombardment. A generalization of the Lindemann criterion was used to develop a thermodynamic description of solid-state amorphization as a disorder- induced melting process

Calculation of defect properties of NiTi and FeTi

The energies and configurations of interstitials and vacancies in the B2 ordered compounds NiTi and FeTi were calculated using atomistic simulation. The stable configuration of a vacancy after the removal of an Ni atom was a vacant Ni site; similarly, the removal of an Fe atom in FeTi resulted in a vacant Fe site. Removal of a Ti atom in both compounds, however, resulted in a vacant Ni or Fe site and an adjacent antisite defect. The effective vacancy formation energies in NiTi and FeTi were calculated to be 1.48 and 1.07 eV, respectively. Interstitials in NiTi formed split {l angle}111{r angle} configurations consisting of a Ni-Ni dumbbell oriented in the {l angle}111{r angle} direction with one or two adjacent antisite defects. The Fe interstitial in FeTi had a similar configuration, except the dumbbell contained Fe atoms. The Ti interstitial in FeTi formed an {l angle}110{r angle} Fe-Fe dumbbell. 8 refs., 2 tabs