ABSTRACT
Titanium dioxide (TiO2) is an abundant, chemically stable, non-toxic, and highly versatile material, with applications ranging from photovoltaics to catalysis. TiO2 rutile and anatase have band gaps of 3.0 eV and 3.2 eV, respectively, which is too large to absorb visible light, resulting in low photocatalytic efficiency. Efforts have been undertaken to generate a band gap suited for solar energy absorption in order to improve TiO2's photo-activity under visible light (400 nm to 700 nm). Nitrogen doping into TiO2 in particular has been able to narrow its band gap, resulting in an absorption tail in the visible-light region. However, TiO2 has limits to which it can be doped suggesting investigations of the oxygen-deficient corundum Ti2O3. Using the state-of-the-art density functional theory (DFT), in the Quantum ESPRESSO package, the properties of the oxides were studied and presented in this work. The structural and electrical properties of the oxides were computed using the generalized gradient approximation (GGA). Ti2O3 exhibited metallic properties, yet it has been reported to have semi-conducting characteristics experimentally leading an improved prediction of the bandgaps of the oxides using the DFT+U approach. On doping, the band gaps of N doped TiO2 structures were reduced as dopant concentration was increased. Mid gap states, having shallower energies in 4%N doping than 2%N cases, were observed in N: TiO2 structures. However, TinN2O2n-3, n=2, appeared to have a higher absorption threshold than other Ti-based oxides such as TiO2, N: TiO2, and Ti2O3. The most stable sample of the oxynitrides (Ti2N2O_P1) had a gap of 2.2 eV, this is clearly near the middle of visible light and did not have mid-gap states. This suggests that they are more efficient visible-light-driven materials for photocatalytic applications compared to TiO2, N: TiO2, and Ti2O3.
TABLE OF CONTENTS
DECLARATION ii
ABSTRACT iii
ACKNOWLEDGMENTS iv
DEDICATION v
TABLE OF CONTENTS vi
LIST OF TABLES ix
LIST OF FIGURES x
LIST OF SYMBOLS AND ABBREVIATIONS xii
CHAPTER 1: INTRODUCTION
1.1 : Background of the Study 1
1.2 : Electronic Structure Calculations using ab-initio Studies 2
1.3 : Statement of the Problem 3
1.4 : Objectives 3
1.4.1 : Main Objective 3
1.4.2 : Specific Objectives 3
1.5 : Justification and Significance of the Study 4
CHAPTER 2: LITERATURE REVIEW
2.0 : Introduction 5
2.1 Materials Modeling 5
2.2 Theoretical and Experimental Studies on Titanium Oxides 5
2.3 : Doping in Titania based Oxides 7
CHAPTER 3: THEORETICAL BACKGROUND
3.0 : Introduction 9
3.1 : Background of Density Functional Theory (DFT) Study 9
3.1.1 : Density Functional Theory 9
3.1.2 : The Hohenberg-Kohn Theorem 13
3.1.3 : Kohn-Sham Equation 13
3.1.5 : Approximation for the exchange-correlation energy 16
3.1.6 : Density Functional Theory with Coulomb Interaction (DFT + U) 17
3.1.7 : Pseudopotentials Technique 17
3.2 : Materials Properties 19
3.2.1 : Structural Properties 19
3.2.2 : Electronic Properties 19
CHAPTER 4: METHODOLOGY
4.0 : Introduction 21
4.1 : Computational Methodology 21
4.4: Band Structure Calculations 23
CHAPTER 5: RESULTS AND DISCUSSIONS
5.0 : Introduction 24
5.1 : Structural Properties 24
5.1.1 : Pristine Structures 24
5.1.2 : Nitrogen doped TiO2 Structures 27
5.2 : Electronic Properties 31
5.2.2: Projected density of states and Band structures for pristine and doped Anatase 35
5.2.2: Projected density of states and Band structures for pristine and doped Ritile ...............
5.3 : Band structure and Pdos for Corundum Ti2O3. 40
5.4 : Titanium Oxynitrides (Ti2N2O) 45
CHAPTER 6: CONCLUSION AND RECOMMENDATIONS
6.1 CONCLUSION 52
6.2 RECOMMENDATIONS FOR FURTHER WORK 53
REFERENCES 54
APPENDIX 60
APPENDIX A: Structural optimization 60
A1: Structural optimization 60
APPENDIX B: Pseudopotential files 67
B1: Oxygen pseudopotential file 67
B2: Ti Pseudopotential file 68
B3: N pseudopotential file 69
APPENDIX C: Band structures 70
APPENDIX D: Sample Input File 72
LIST OF TABLES
Table 5.1: Lattice parameters of rutile TiO2, anatase TiO2, and corundum Ti2O3. 26
Table 5.2: GGA-PBEsol calculated and experimental bond lengths (Å) and bond angles (degrees) for TiO2 (anatase and rutile) and Ti2O3 26
Table 5.3: DFT-GGA calculated bond lengths (Å) before and after 2%,4% and 6% doping of the two phases of TiO2 29
Table 5.4: DFT-GGA bond angles before and after 2%,4%, and 6% doping of TiO2 30
Table 5.5: Optimization of the U values for TiO2 (anatase and rutile) and Ti2O3 41
Table 5.6: Calculated lattice parameters in variation with the Hubbard values 44
Table 5.7: Summary of the calculated and experimental band gap for the structures 51
LIST OF FIGURES
Figure 1.1: The process of photocatalytic action 1
Figure 3.1: Schematic diagram showing the self-consistency scheme 15
Figure 3.2: Real and pseudo-wave-function at a defined cut-off radius 18
Figure 3.3: Conduction and valence band of a direct bandgap semiconductor 20
Figure 4.1: Brillouin zone of (a) anatase TiO2 (b) rutile TiO2, and (c) corundum Ti2O3, showing the origin at =0 22
Figure 5.1: Optimized structures for anatase TiO2, rutile TiO2. and Corundum Ti2O3 25
Figure 5.2: TiO2 doped with 2% N Rutile and Anatase structure 27
Figure 5.3: Rutile and Anatase phases of TiO2 after doping with 4% N… 28
Figure 5.4: Rutile and Anatase phases of TiO2 after doping with 6% N 28
Figure 5.5: Band structure and Pdos for (a) pristine Rutile TiO2 (b) 2% N doped
Rutile TiO2, (c) 4% N doped Rutile TiO2, and (d) 6%N doped Rutile TiO2 33
Figure 5.6: Band structure and Pdos for (a) pristine Anatase TiO2 (b) 2% N doped
Anatase TiO2, (c) 4% N doped Anatase TiO2, and (d) 6% N doped Anatase TiO2 37
Figure 5.7: Charge Density Maps for Pristine and doped TiO2 38
Figure 5.8: A plot of band gap with increasing dopant concentration 39
Figure 5.9: Band structure and Pdos for Corundum Ti2O3… 40
Figure 5.10: A plot of band gap vs U values for anatase rutile and corundum structures 42
Figure 5.11: Band structures for (a) CorundumTi2O3, (b) Anatase, and (c) Rutile calculated
by DFT and DFT+U methods 43
Figure 5.12: Different orientations of Nitrogen substitutions in Ti2O3 P-structure 45
Figure 5.13: Four different angles of projection of Ti2O3 convectional unit cell 46
Figure 5.14: Side views of seven modeled titanium oxynitrides (Ti2N2O) projected
in the direction of a+b 47
Figure 5.15: Energy vs lattice parameters of (a) Three orientations of nitrogen substitution into Ti2O3 structure (P-samples), (b)seven different orientations of nitrogen substitution into Ti2O3 hexagonal convectional cell (S-samples), and (c) energy per formula unit for P- and S- structures of nitrogen substitution into Ti2O3 48
Figure 5.16: Band structures and Pdos for Corundum-based Ti2N2O P-Structures using DFT+U (U=5eV) method… 50
Figure 6.1: Energy/cell versus cutoff energy of TiO2 anatase phase 60
Figure 6.2: Energy/cell versus cell dimension c/a of TiO2 anatase phase 61
Figure 6.3: Energy/cell versus cell dimension c/a of TiO2 anatase phase 61
Figure 6.4: Energy/cell versus k- points of TiO2 anatase phase 62
Figure 6.5: Energy/cell versus lattice constant of TiO2 rutile 62
Figure 6.6: Energy/cell versus c/a of TiO2 rutile 63
Figure 6.7: Energy/cell versus k points of TiO2 rutile 63
Figure 6.8: Energy/cell versus cell dimension (c/a) of Ti2O3 64
Figure 6.9: Energy/cell versus the lattice constant of Ti2O3 64
Figure 6.10: Energy/cell versus k-points of Ti2O3 65
Figure 6.11: Energy/cell versus cut off energy of Ti2O3… 66
Figure 6.12: Anatase TiO2 band structure 70
Figure 6.13: Rutile TiO2 band structure 70
Figure 6.14: Corundum Ti2O3 band structure 71
LIST OF SYMBOLS AND ABBREVIATIONS
In this thesis, the symbols and acronyms listed below have been used. a and c Lattice parameters /cell dimensions
B3LYP Becke, Lee-Yang-Parr BZ Brillouin Zone
CB Conduction Band
CBM Conduction Band Minimum
DFT Density Functional Theory
DFT+U Density Functional Theory with Coulomb interaction
DOS Density of states
Ecut Cut-off kinetic energy ecut’rho’ Cut –off charge density Etot Total Energy
GGA Generalized Gradient Approximation
GW Green’s function and dynamically screened coulomb interactions
H Hamiltonian operator.
H-F Hartree-Fock
H-K Hohenberg-Kohn Theorem
HSE Heyd-Scuseria-Ernzerhof
KE Kinetic energy
K-S Kohn Sham Theorem
LDA Local Density Approximation
me Mass of an electron
N :TiO2 Nitrogen doped Titanium dioxide
n(r) Electron density
NCPP Norm-conserving pseudo-potential
PBE Perdew–Burke–Ernzerhof functional
PBEsol Enhanced Perdew–Burke–Ernzerhof functional PBE0 for solids
Perdew-Burke-Ernzerhof hybrid
Pdos Projected density of states
PP Pseudo-potentials
PW91 Perdew-Wang functional
P-samples Samples of nitrogen substitution into Ti2O3
QE primitive cells
Quantum ESPRESSO
Ry Rydberg units (13.6 eV)
S- samples Samples of nitrogen substitution into Ti2O3 in SC hexagonal convectional cells
Self-consistence
SCF Self consistent field
T Kinetic energy
Ti2N2O Titanium oxynitride
Ti2O3 Titanium sesquioxide /Titanium (III) Oxide
TiO2 Titanium dioxide
USPP Ultra-soft pseudo-potential
VB Valence Band
VBM Valence Band Maximum
Ve-e Mutual electron-electron potential energy
Veff (r) Effective potential
Vext Exchange-correlation potential
Vext (r) External potential
VH Hartree term
Vn-e nucleus –electron potential energy
Vn-n nucleus-nucleus potential energy
Vxc Exchange Energy
XC Exchange –correlation.
XcrysDen X-Window Crystalline Structure and Densities
∇2 Laplace operator for nuclei
∇2 Laplace operator for electrons
many-body wave function,
The permittivity of vacuum
CHAPTER 1
INTRODUCTION
1.1 : Background of the Study
Titanium-based oxides have attracted considerable attention due to their widespread use in photovoltaics and photocatalytic water treatment (Wu et al., 2013), thus the need for a better understanding of their properties. Water is arguably the most important natural resource, accounting for around 70% of the surface of the earth (Cunningham and Saigo, 1995). Due to significant population growth, the demand for water has increased, resulting in a water shortage. Water contamination has also risen dramatically as a result of rapid industrial growth and urbanization, causing disease and death (Foundation, 2014). Photo-catalysis remains a potentially low-cost and effective water treatment mechanism (Asahi et al., 2001). Figure 1.1 displays the photo-catalyst process, in which solar energy interacts with a semiconductor to absorb a photon. The photon excites an electron that causes a redox reaction where the hydrogen ion reacts with water to produce hydroxyl radicals and the oxygen reacts with electrons to generate powerful super-oxides responsible for the degradation of pollutants.
Figure 1.1: The process of photocatalytic action (Gnanaprakasam et al., 2015).
Nanomaterials made of titanium dioxide (TiO2) have applications ranging from basic products like sunscreen to complex technology like photovoltaic cells, among others (Chen and Selloni, 2014; Le Bahers et al., 2014). Solar cells are recommended over fossil fuels such as gas and coal because they serve to counter global warming resulting from the combustion of fossil fuels (Guo et al., 2011).
TiO2 is an auspicious and highly versatile material, except for its wide bandgap which limits it to utilize only about 4% of the solar energy (Morikawa et al., 2001). Band gap reduction has proved to enhance the photo-activity of TiO2 for improved solar energy applications (Morgan and Watson, 2010). Doping has been suggested as a potential means of bandgap narrowing (Mahendra et al.,2019) . Doping is the process of adding impurities to a substance in order to change its characteristics. Nitrogen substitution into the TiO2 structure has demonstrated an improved optical absorption (Mahendra et al., 2019), but the probability of doping higher oxide phases of Titania has not been adequately investigated. In this work, ab-initio studies have been employed.
1.2 : Electronic Structure Calculations using ab-initio Studies
Numerical solutions to the Schrödinger equation (Schrödinger, 1926) are required for computing the electronic structure of a given system. These electrical structure computations differ from other modeling methods in that they are based on fundamental principles, also known as ab-initio (Muscat et al., 2002). That is, they do not have any external parameters apart from the most basic system definition. To study the properties of materials, first-principles measurement employs the fundamental laws of physics (Hohenberg and Kohn, 1964). Many investigations in the area of condensed matter have been made feasible thanks to the use of first-principle calculations in identifying newer materials and providing a complete explanation of experimental data.
Several theories have been developed in the study of the behavior of materials, from Hartree to Hartree-Fock (Kohn and Sham, 1965), which has no approximation except that it neglects electron- correlation, to Density Functional Theory (DFT) (Kohn and Sham, 1965). The growth of ab-initio- based computational work is also attributed to the rapid advancement of computer technology. Given this, the structural and electronic calculations of the Titania-based oxides, which have received both experimental and theoretical attention, as well as the least studied Corundum Ti2O3 and oxynitride Ti2N2O have been studied using DFT (Hohenberg and Kohn, 1964). In order to enhance band gap prediction from local GGA calculations, the Hubbard U term has been used. The U range has been chosen from 1 to 7 eV to investigate how these U parameters boost the energy band gap approximation of TiO2 and Ti2O3 within each exchange-correlation functional. The Hubbard U's major goal is to correct for self-interaction effects of the d and f states, which appear to be too close to the Fermi energy (Goh et al., 2017). On Ti-3d states, the U was applied. Nitrogen partial substitution in the parent Ti2O3 structure was used to model oxynitride (Ti2N2O).
1.3 : Statement of the Problem
Rutile and anatase phases of TiO2 have bandgaps which range from 3.0 to 3.2 eV (Asahi et al., 2001), these are too large to absorb visible light, necessitating the formation of an absorbance tail in the visible-light region in order to increase photoactivity. In search of Ti-based oxides with relatively narrow band gaps and better absorption thresholds, the theoretical predictions of the properties of pristine TiO2, N: TiO2, Corundum Ti2O3, and Oxynitride Ti2N2O have been investigated in this study. Adequate theoretical predictions are needed to promote a thorough understanding of these materials for appropriate applications.
1.4 : Objectives
1.4.1 : Main Objective
The main objective was to investigate the structural and electronic properties of Titanium Dioxide (TiO2), Nitrogen doped Titanium Dioxide (N: TiO2), Titanium Sesquioxide (Ti2O2n-1, n=2), and Titanium Oxynitride (TinN2O2n-3, n=2) using DFT.
1.4.2 : Specific Objectives
The specific objectives were:
a) To determine the lattice parameter, bond lengths, and bond angles of Titanium Dioxide (TiO2) and Titanium Sesquioxide (Ti2O3).
b) To determine the optimum doping level of nitrogen in TiO2.
c) To assess the impact of nitrogen substitution on the structures of TiO2 and Ti2O3.
d) To determine and analyse band structures and density of states of pristine and doped TiO2 and Ti2O3.
1.5 : Justification and Significance of the Study
As discussed in section (1.1) of this thesis, Ti-based oxides have a broad range of applications. It is important to carry out fundamental studies on their properties ( e.g. the effects of doping on their structures) to reduce the discrepancy between theoretical expectations and actual material properties. Theoretical predictions tends to guide experiments, especially in cases where sample preparation is a challenge or in novel materials (Sholl and Steckel, 2011). This has been made possible by the exponential growth in computing power (Pokluda et al., 2015). There is very scanty information from the first-principle calculations on the properties of higher-oxide phases of titania like Ti2O2n-1, n 2. This study provides information to complement the pristine TiO2, N:TiO2, Ti2O3, and Ti2N2O experimental studies.
Login To Comment