Multiscale modeling of oxygen and vacancy diffusion in dilute ferritic iron alloys

Iron-based ferritic alloys are used for a plethora of industrial applications. These alloys contain foreign atoms purposely employed to improve certain properties as well as some unwanted impurities introduced during fabrication. Materials properties are decisively influenced by diffusion processes. Very often diffusion cannot be avoided during fabrication and application. Therefore, many efforts are made to understand the underlying atomic-level mechanisms by both experimental and theoretical investigations. In this thesis work a multiscale modelling approach is used to study oxygen and vacancy diffusion in dilute ferritic iron alloys. Due to the extremely low solubility of oxygen the measurement of oxygen diffusion in iron is difficult. Only few experimental data are available. Experimental investigation of vacancy migration is still more complicated. The lack of reliable experimental data is therefore an important motivation for theoretical investigations. Gaining fundamental data on oxygen and vacancy diffusion in dilute iron alloys is essential for many applications. Oxygen plays a crucial role in the corrosion of iron-based alloys. Oxygen and the vacancy are also important in the formation and evolution of Y-Ti-O nanoclusters in oxide dispersion strengthened ferritic Fe-Cr alloys, which are considered as promising candidates for structural materials of future fusion and fission reactors. Furthermore, vacancies are formed during neutron and ion irradiation and their diffusion affects radiation-induced nanostructure formation in ferritic alloys. In the first part of this thesis work, the diffusion of interstitial oxygen under the influence of substitutional atoms or solutes (Al, Si, P, S, Ti, Cr, Mn, Ni, Y, Mo and W) in bcc Fe is investigated by the combination of Density Functional Theory (DFT) and Atomistic Kinetic Monte Carlo (AKMC) simulations. The substitutional atoms are assumed to be immobile because oxygen diffusion is much faster than that of the solutes. DFT is applied to gain data on binding energies between interstitial oxygen and the substitutional foreign atoms, and to calculate the migration barriers for oxygen in the environment of the solutes. Using the migration barriers obtained by DFT, the diffusion coefficient of oxygen is determined by AKMC simulation. It is found that Si, P, Ni, Mo, and W have negligible influence on the oxygen diffusion coefficient. Al, Cr, Mn, S, Ti, and Y cause a considerable reduction of oxygen mobility. In these cases, the temperature dependence of oxygen diffusivity shows deviations from Arrhenius behavior. This is explained in detail by the significant temperature dependence of the ratio between residence times in the respective states. In the second part of the work a method is presented which allows for an efficient calculation of the diffusion coefficient of oxygen and other interstitial atoms in dilute alloys. The method is applied to examples considered in the first part of the work. The calculation procedure is based on the separation of the diffusion path into a contribution related to migration in the interaction region between the mobile interstitial and the substitutional solute and another part related to diffusion in perfect bcc Fe. In this manner AKMC simulation must be performed only for one concentration of the substitutional solute, and the obtained results can be employed to obtain data for other concentrations using analytical expressions containing binding energies between the interstitial and the substitutional solute. The focus of third part of the work is on the mutual dependence of oxygen and vacancy diffusion in bcc Fe and dilute iron alloys. Here both O and v must be considered as mobile while the substitutional atoms are assumed to be immobile. DFT is applied to determine the binding energy between O and v for different distances, the migration barriers for O in the environment of v, and the corresponding barriers of v in the vicinity of O. In agreement with previous work O and v have a very strong binding at the 1st neighbor distance. On the other hand, the calculations show that the Ov pair at the 6th neighbor distance is instable. The newly found simultaneous or coupled jumps of both O and v compensate the lack of jump paths that would occur due to this instability. The DFT results are employed to determine the diffusion coefficient of O and v using the scheme of the AKMC-based calculation method presented in the second part of the thesis work. At first a model system with fixed O and v concentrations is studied. It is found that a small v content of some ppm can already lead to a strong reduction of the O diffusivity. A similar effect is obtained for v diffusion under the influence of O. Furthermore, investigations on the interdependence of O and v diffusion during thermal processing of oxide dispersion strengthened iron alloys are performed, and the influence of the substitutional atoms Y and Ti is studied. A simple thermodynamic model is employed to determine the concentration of O, Y, and Ti monomers as well as the total v concentration, for a typical total content of O, Y, and Ti. These results are used in calculations of the diffusion coefficients of O and v. Not only a strong mutual dependence but also a significant influence of Y on O diffusion is found. Finally, O and v diffusivities in a system with a total O content close to the thermal solubility are calculated. The monomer O concentration as well as the total v concentration was determined using two different models considering equilibrium of O and v with Ov, or equilibrium of O and v with Ov and O2v or Ov2. Despite the very small value of thermal solubility of O in bcc Fe, both the O and v diffusion coefficient are very different from that in pure iron. Even for such a low amount of O in the alloy the diffusion coefficients differ strongly from those in perfect bcc Fe. The results of the present work have important consequences for planning and performing new experiments on O and v diffusion in dilute iron alloys. In particular, a very precise knowledge of the concentrations of O and v, as well as of other foreign atoms and traps such as dislocations is required

A privacy-preserving fuzzy interest matching protocol for friends finding in social networks

Nowadays, it is very popular to make friends, share photographs, and exchange news throughout social networks. Social networks widely expand the area of people’s social connections and make communication much smoother than ever before. In a social network, there are many social groups established based on common interests among persons, such as learning group, family group, and reading group. People often describe their profiles when registering as a user in a social network. Then social networks can organize these users into groups of friends according to their profiles. However, an important issue must be considered, namely many users’ sensitive profiles could have been leaked out during this process. Therefore, it is reasonable to design a privacy-preserving friends-finding protocol in social network. Toward this goal, we design a fuzzy interest matching protocol based on private set intersection. Concretely, two candidate users can first organize their profiles into sets, then use Bloom filters to generate new data structures, and finally find the intersection sets to decide whether being friends or not in the social network. The protocol is shown to be secure in the malicious model and can be useful for practical purposes.Peer ReviewedPostprint (author's final draft

Efficient calculation methods for the diffusion coefficient of interstitial solutes in dilute alloys

In the example of oxygen diffusion in dilute ferritic iron alloys it is shown that the calculation of the diffusion coefficient can be separated into a contribution related to the migration in the interaction region between oxygen and the substitutional solute and a part related to diffusion in pure body centered cubic (bcc) Fe. The corresponding diffusion times are determined by analytical expressions using Density-Functional-Theory (DFT) data for the respective binding energies. The diffusion coefficient in the interaction region must be determined by atomistic kinetic Monte Carlo (AKMC) simulations with DFT values for the migration barriers as input data. In contrast to previous calculations, AKMC simulation must only be performed for one concentration of the substitutional solute, and the obtained results can be employed to obtain data for other concentrations in a very efficient manner. This leads to a tremendous decrease of computational efforts. Under certain conditions it is even possible to use analytical expressions where merely DFT data for the binding energies are needed. The limits of applicability of the presented calculation procedures are discussed in detail. The methods presented in this work can be generalized to interstitial diffusion in other host materials with small concentrations of substitutional solutes

Strong Convergence of Non-Implicit Iteration Process with Errors in Banach Spaces

The purpose of this paper is to study the strong convergence of a non-implicit iteration process with errors for asymptotically I-nonexpansive mappings in the intermediate sense in the framework of Banach spaces. The results presented in this paper extend and improve the corresponding results recently announced

Carrier Dynamics in Submonolayer InGaAs/GaAs Quantum Dots

Carrier dynamics of submonolayer (SML) InGaAs/GaAs quantum dots (QDs) were studied by micro-photoluminecence (MPL), selectively excited photoluminescence (SEPL), and time-resolved photoluminescence (TRPL). MPL and SEPL show the coexistence of localized and delocalized states, and different local phonon modes. TRPL reveal shorter recombination lifetimes and longer capture times for the QDs with higher emission energy. This suggests that the smallest SML QDs are formed by perfectly vertically correlated 2D InAs islands, having the highest In content and the lowest emission energy, while a slight deviation from the perfectly vertical correlation produces larger QDs with lower In content and higher emission energy.Comment: 12 pages, 5 figure