Browsing by Subject "surfaces"

Now showing 1 - 2 of 2

Open Access
An Electronic topological picturebook
(1992) Arslan, Ahmet
An electronic topological picturebook is envisaged as a computerized version of A Topological Picturehook by George K. Francis, .Springer-Verlag, New York (1987). Francis’ book is full of complicated topological figures, mostly drawn manually. The main goal of the thesis is to automate the production of such illustrations and to obtain publication-quality hardcopy using assorted techniques of computer graphics. To that end, sweeping is discussed as a major surface modeling tool. Some interactive methods are given to produce interesting topological surfaces. The program Tb (which stands for ‘Topologybook’) is described and various pictures generated by this software are presented. Tl· is a free-form surface modeler and produces topological shapes with little effort. Central to the implementation of Tb is a paradigm of solid modeling in which computation of a shape is regarded as sweeping with some parametric variations, viz. shape = sweep + control.
Open Access
Titanium dioxide nanostructures for photocatalytic and photovoltaic applications
(2008) Çakır, Deniz
In this thesis, TiO2 nanostructures and their photocatalytic and photovoltaic ap- plications have been investigated by using the ¯rst-principles calculations based on density functional theory. We have concentrated on three di®erent systems, namely TiO2 clusters, nanowires and surfaces. TiO2 is widely used in various applications, since it is chemically stable in di®erent conditions, ¯rm under il- lumination, non toxic, and relatively easy and cheap to produce. Most of the technological applications such as photovoltaic and photocatalytic of TiO2 are mainly related to its optical properties. First of all, structural, electronic, and magnetic properties of small (TiO2)n (n=1{10) clusters have been studied. Various initial geometries for each n have been searched to ¯nd out the ground state geometries. In general, it has been found that the ground state structures (for n=1{9) have at least one dangling or pendant O atom. Only the lowest lying structure of n=10 cluster does not have any pendant O atom. In the ground state structures, Ti atoms are at least 4{fold coordinated for n ¸ 4. Clusters prefer to form three{dimensional and compact structures. All clusters have singlet ground state. The formation energy and HOMO{LUMO gap have also been calculated as a function of the number of TiO2 unit to study the stability and electronic properties. The formation energy increases with increasing size of the cluster. This means that clusters become stronger as their size grows. The interaction of the ground state structure of each (TiO2)n cluster with H2O has been investigated. The binding energy Eb of H2O molecule decreases and oscillates as the cluster size increases. The interaction of the ground state structure of n=3, 4, 10 clusters with more than one H2O molecule has also been studied. We have calculated Eb per adsorbed molecule and we have shown that it decreases with increasing number of adsorbed H2Omolecule (N). When N ¸ 2 for n=3 and N ¸3 for n=4 clusters, H2O molecules bind more strongly to n=10 cluster. The adsorption of transition metal (TM) atoms such as V, Co, and Pt on n=10 cluster has been studied as well. All these elements interact with the cluster forming strong chemisorption bonds, and the permanent magnetic moment is induced upon the adsorption of Co or V atoms. Second of all, structural, electronic and magnetic properties of very thin TiOx (x=1,2) nanowires have been presented. All stoichiometric TiO2 nanowires ex- hibit semiconducting behavior and have non{magnetic ground state. There is a correlation between binding energy (Eb) and the energy band gap (Eg) of these TiO2 nanowires. In general, Eb increases with Eg. In non-stoichiometric TiO nanowires, we have both metallic and semiconducting nanowires. In addition to non{magnetic TiO nanowires, we have also ferromagnetic nanowires. Three{ dimensional (3D) structures are more energetic than planar ones for both stoi- chiometries. The stability of TiOx nanowires is enhanced by the increase of the size and coordination number of Ti and O atoms which tend to possess at least four and two nearest neighbors, respectively. We have also studied the structural and electronic properties of rutile (110) nanowires obtained by cutting bulk ru- tile along the [110] direction with a certain cross section. The bulk nanowires are more energetic than the thin nanowires after a certain diameter. Like thin TiO2 nanowires, all bulk wires are semiconducting and Eg oscillates with the cross section of these (110) nanowires. Third of all, we have studied the interaction of perylenediimide (PDI){based dye compounds (BrPDI, BrGly, and BrAsp) with both the unreconstructed (UR) and reconstructed (RC) anatase TiO2 (001) surfaces. All dye molecules form strong chemical bonds with the surface in the most favorable adsorption struc- tures. The lowest binding energy is 2.60 eV which has been obtained in the adsorption of BrPDI dye on the UR surface. In UR{BrGly, RC{BrGly and RC{ BrAsp cases, we have observed that HOMO and LUMO levels of the adsorbed molecules appear within the band gap and conduction band regions, respectively. Moreover, we have obtained a gap narrowing upon adsorption of BrPDI on the RC surface. Because of the reduction in the e®ective band gap of the surface{dye system and possibly achieved the visible light activity, these results are valuable for photovoltaic and photocatalytic applications. We have also considered the e®ects of the hydration of surface on the binding of BrPDI. It has been found that the binding energy drops signi¯cantly for the completely hydrated surfaces.Fourth of all, we have considered the interaction of BrPDI, BrGly, and BrAsp dye molecules with defect free rutile TiO2 (110) surfaces. All dye molecules form moderate chemical bonds with surface in the most stable adsorption structures. The average binding energy of dye molecules is about 1 eV. Regardless of the type of dye molecules, HOMO and LUMO levels of the adsorbed dye appear within the gap and the conduction band region of defect free surface, respectively. The e®ect of the slab thickness on the interaction strength between the dye and the surface has also been examined. Unlike the four layers slab, BrGly and BrAsp molecules are dissociatively adsorbed on the three layers slab. The interaction between BrPDI and partially reduced rutile (110) as well as platinized surface has been also considered in order to ¯gure out the e®ects of O vacancy and preadsorbed small Ptn (n=1, 3 and 5 ) clusters on the binding, electronic, and structural properties of the dye{surface system. It has been found that BrPDI dye prefers to bind to the O vacancy site for the partially reduced surface case. Transition metal deposition on metal oxides plays a crucial role in various industrial areas such as catalysts and photovoltaic cells. Finally, an extensive study of the adsorption of small Ptn (n=1{8) and bimetallic Pt2Aum (m=1{5) clusters on partially reduced rutile TiO2 (110) has been presented. The e®ect of surface O vacancies on the adsorption and growth of Pt and bimetallic Pt{Au clusters over the defective site of the 4£2 rutile surface has been studied. Struc- tures, energetics and electronic properties of adsorbed Ptn and Pt2Aum clusters have been analyzed. The surface O vacancy site has been found to be the most active site for a single Pt monomer. Other Pt clusters, namely dimer, trimer and so on, tend to grow around this monomer. As a result, O vacancy site behaves as a nucleation center for the clustering of Pt atoms. Small Pt clusters interact strongly with the partially reduced surface. Eb per adsorbed Pt atom is 3.38 eV for Pt1 case and Eb increases as the cluster size grows due to the formation of strong Pt{Pt bonds. Pt clusters prefer to form planar structures for n = 1{6 cases. The calculated partial density of states of Ptn{TiO2 surface has revealed that the surface becomes metallic when n ¸ 3. In the case of bimetallic Pt-Au clusters, Aum clusters have been grown on the Pt2{TiO2 surface. Previously ad- sorbed Pt dimer at the vacancy site of the reduced surface acts as a clustering center for Au atoms. This Pt2 cluster also inhibits sintering of the Au clusters on the surface. The interaction between the adsorbed Au atoms and titania surface as well as previously adsorbed Pt dimer is weak compared to Pt{TiO2 surface interactions. Since charge state of the clusters adsorbed on the oxide surfaces iscrucial for catalysis applications of these clusters, total charge on each atom of the metal clusters has also been calculated. Charge transfer among the cluster atoms and underlying oxide surface is more pronounced for Ptn clusters. Furthermore, the absolute value of total charge on the clusters is greater for Ptn than that of bimetallic Pt{Au case.