Switchable Intrinsic Defect Chemistry of Titania for Catalytic Applications

: The energy crisis is one of the most serious issue that we confront today. Among different strategies to gain access to reliable fuel, the production of hydrogen fuel through the water-splitting reaction has emerged as the most viable alternative. Speciﬁcally, the studies on defect-rich TiO 2 materials have been proved that it can perform as an efﬁcient catalyst for electrocatalytic and photocatalytic water-splitting reactions. In this invited review, we have included a general and critical discussion on the background of titanium sub-oxides structure, defect chemistries and the consequent disorder arising in defect-rich Titania and their applications towards water-splitting reactions. We have particularly emphasized the origin of the catalytic activity in Titania-based material and its effects on the structural, optical and electronic behavior. This review article also summarizes studies on challenging issues on defect-rich Titania and new possible directions for the development of an efﬁcient catalyst with improved catalytic performance.


Introduction
Some of the world's technologies are currently due to the manipulation of defects. For example, defects can transform a hard white solid α-Al 2 O 3 (corundum) to colored gems like ruby and sapphire [1]. Thus, the intentional creation of defects in materials with control over their concentration, type, spatial distribution, and location can drastically modify their functionalities. In particular, defect engineering serves as a platform to tailor the intrinsic electrons of materials and, hence, to tune their properties, reactivity, and catalytic activity [2][3][4][5][6][7][8][9][10][11][12][13]. The past centuries have witnessed significant progress towards commercialization of water-splitting technologies predominantly due to the intentional creation of defects in various catalytically in-active materials [14][15][16][17][18][19][20][21][22], but still, we are distant from the basic understanding of structural defects and the critical parameters which play an essential role in water-splitting applications. The grand challenge lies in the development of an improved catalyst for water-splitting applications. A stream of research focuses only on the effect of intrinsic defects on the solid-state properties of the material [23][24][25][26][27][28][29][30][31][32][33][34][35]. Few other groups concentrate on improving the electronic, optical properties of materials and discussing issues related to water-splitting reaction [36,37]. However, the progress of water electrolyzer technology requires combining these two research areas in order to address the challenges in developing an enhanced catalyst for water-splitting. Hence, it is a desperate need to fully understand the role of defect disorder on water-splitting in order to enhance the performance of electro/photocatalyst for water-splitting reaction.
To understand the scientific origin of catalytic activity on the disordered structures herein, we focus our interest on: (i) defects and defect chemistry; (ii) standard experimental approaches to To understand the scientific origin of catalytic activity on the disordered structures herein, we focus our interest on: (i) defects and defect chemistry; (ii) standard experimental approaches to generate point defects; (iii) the effect of having defects on their structural, electrical, optical behavior and, hence, catalytic activity; (iv) role of defects associated with the electrocatalytic production of hydrogen and photo-oxidation of water; and (v) challenges and applications of defect-rich Titania. Along with this, we have included perspectives and outlook on the future of the defect engineering. Several reports and reviews exist summarizing various statements on defect-engineered catalyst for water-splitting reaction [38][39][40][41][42]. Hence, in this review, we attempted to articulate the impact of defects on the structural, optical and electronic properties, which are critical factors for defining the catalytic activity of a material. We believe that a fundamental understanding of the defect engineering and combination of optimization strategies would be the bottleneck for finding the appropriate candidates for water-splitting reaction. Notably, we collectively discussed intrinsic defect engineering (self-doping) of futuristic catalyst 'Titania' for water-splitting reaction. The striking characteristics of Titania such as strong oxidizing power, earth abundance, non-toxic, chemical, physical and thermal stability, easy availability and excellent photoactivity supports this material as the best option for water-splitting reaction. It is also a ninth earth abundant material, obtained from the mineral ilmenite [43,44], and its phase diagram ( Figure 1) shows various stable phases at different Ti/O stoichiometry. Figure 1. Phase diagram of the Ti-O system. The region Ti2O3-TiO2 contains Ti3O5, Ti2O3 and seven discrete phases of the homologous series TinO2n−1 (Magneli phase) and TiO2. Reproduced from [35]; Copyright 2003, Elsevier.

Defects in Titania
In general, four common native-point defects ( Figure 2) exist in Titania: (i) Oxygen vacancies (Vo)-Missing of oxygen ion from the lattice site; (ii) Titanium vacancies (VTi)-Ti ion is missing from its lattice site; (iii) Titanium interstitials (Tii)-Ti ion is located in an interstitial site; and (iv) Oxygen interstitials (Oi)-Oxygen ion is located in an interstitial site.
General characteristics of point defects in Titania/Defect chemistry of Titania: (i) Point defects preferably gather as clusters rather than distributed randomly on the crystal structure and, hence, lead to line defects, planar and volume defects [45]. (ii) Depending on the location of defects in the crystal structure, the activity varies as tabulated in Table 1. Table 1. Behavioral difference of defects in the bulk and the surface [46].

Bulk
Surface Interstitial atom Adatom

Defects in Titania
In general, four common native-point defects ( Figure 2) exist in Titania: (i) Oxygen vacancies (V o )-Missing of oxygen ion from the lattice site; (ii) Titanium vacancies (V Ti )-Ti ion is missing from its lattice site; (iii) Titanium interstitials (Ti i )-Ti ion is located in an interstitial site; and (iv) Oxygen interstitials (O i )-Oxygen ion is located in an interstitial site.
General characteristics of point defects in Titania/Defect chemistry of Titania: (i) Point defects preferably gather as clusters rather than distributed randomly on the crystal structure and, hence, lead to line defects, planar and volume defects [45]. (ii) Depending on the location of defects in the crystal structure, the activity varies as tabulated in Table 1. (iii) Point defects are generally represented using Kroger-Vink notation ( (V) Intuitively, ionization of these ionic defects leads to the formation of electronic defects in the crystal system, which are called color centers [50,51]. There are two types of color center-based on their charge (i) electron center (F) and (ii) electron-hole center (V) and classified further as F, F + , F ++ and V, V + , V ++ , respectively.

Electron (F, F + , F ++ ) center
This center occurs due to the absence of a negatively charged ions (i.e., oxygen vacancy) in Titania. As a result of charge imbalance, it possess positive charge and, hence, attracts, traps electron and comprises F centers [52,53].

F center
The vacancy of oxygen (Vo) is compensated by a pair of unpaired electrons from Ti 3d orbitals, resulting in a (double) positive charged vacancy (F center). It has four Ti 4+ ions in the neighborhood with no unpaired electrons.

F + center
One of the electrons from F center tends to occupy the neighborhood Ti 4+ ion, so it is positively charged with respect to the lattice, yields center (F + center). It possesses one unpaired electron.

F ++ center
Both electrons from F center tend to occupy the neighboring Ti 4+ ion, so it is positively charged with respect to the lattice and yield center (F ++ center). The formation mechanism and defect equilibria are shown below ( Figure 2): (V) Intuitively, ionization of these ionic defects leads to the formation of electronic defects in the crystal system, which are called color centers [50,51]. There are two types of color center-based on their charge (i) electron center (F) and (ii) electron-hole center (V) and classified further as F, F + , F ++ and V, V + , V ++ , respectively.

Electron (F, F + , F ++ ) center
This center occurs due to the absence of a negatively charged ions (i.e., oxygen vacancy) in Titania. As a result of charge imbalance, it possess positive charge and, hence, attracts, traps electron and comprises F centers [52,53].

F center
The vacancy of oxygen (Vo) is compensated by a pair of unpaired electrons from Ti 3d orbitals, resulting in a (double) positive charged vacancy (F center). It has four Ti 4+ ions in the neighborhood with no unpaired electrons.

F + center
One of the electrons from F center tends to occupy the neighborhood Ti 4+ ion, so it is positively charged with respect to the lattice, yields center (F + center). It possesses one unpaired electron.

F ++ center
Both electrons from F center tend to occupy the neighboring Ti 4+ ion, so it is positively charged with respect to the lattice and yield center (F ++ center). The formation mechanism and defect equilibria are shown below ( Figure 2): (V) Intuitively, ionization of these ionic defects leads to the formation of electronic defects in the crystal system, which are called color centers [50,51]. There are two types of color center-based on their charge (i) electron center (F) and (ii) electron-hole center (V) and classified further as F, F + , F ++ and V, V + , V ++ , respectively.

Electron (F, F + , F ++ ) center
This center occurs due to the absence of a negatively charged ions (i.e., oxygen vacancy) in Titania. As a result of charge imbalance, it possess positive charge and, hence, attracts, traps electron and comprises F centers [52,53].

F center
The vacancy of oxygen (Vo) is compensated by a pair of unpaired electrons from Ti 3d orbitals, resulting in a (double) positive charged vacancy (F center). It has four Ti 4+ ions in the neighborhood with no unpaired electrons.

F + center
One of the electrons from F center tends to occupy the neighborhood Ti 4+ ion, so it is positively charged with respect to the lattice, yields center (F + center). It possesses one unpaired electron.

F ++ center
Both electrons from F center tend to occupy the neighboring Ti 4+ ion, so it is positively charged with respect to the lattice and yield center (F ++ center). The formation mechanism and defect equilibria are shown below ( Figure 2): (V) Intuitively, ionization of these ionic defects leads to the formation of electronic defects in the crystal system, which are called color centers [50,51]. There are two types of color center-based on their charge (i) electron center (F) and (ii) electron-hole center (V) and classified further as F, F + , F ++ and V, V + , V ++ , respectively.

Electron (F, F + , F ++ ) center
This center occurs due to the absence of a negatively charged ions (i.e., oxygen vacancy) in Titania. As a result of charge imbalance, it possess positive charge and, hence, attracts, traps electron and comprises F centers [52,53].

F center
The vacancy of oxygen (Vo) is compensated by a pair of unpaired electrons from Ti 3d orbitals, resulting in a (double) positive charged vacancy (F center). It has four Ti 4+ ions in the neighborhood with no unpaired electrons.

F + center
One of the electrons from F center tends to occupy the neighborhood Ti 4+ ion, so it is positively charged with respect to the lattice, yields center (F + center). It possesses one unpaired electron.

F ++ center
Both electrons from F center tend to occupy the neighboring Ti 4+ ion, so it is positively charged with respect to the lattice and yield center (F ++ center). The formation mechanism and defect equilibria are shown below ( Figure 2): (V) Intuitively, ionization of these ionic defects leads to the formation of electronic defects in the crystal system, which are called color centers [50,51]. There are two types of color center-based on their charge (i) electron center (F) and (ii) electron-hole center (V) and classified further as F, F + , F ++ and V, V + , V ++ , respectively.  Table 2. Kroger-Vink notation and their meaning [47].

Electron Holes
It is an antimorph of F center [54], consisting of Titanium vacancy and holes, which gives p-type conductivity to Titania as shown in Figure 3.

Electron (F, F + , F ++ ) Center
This center occurs due to the absence of a negatively charged ions (i.e., oxygen vacancy) in Titania. As a result of charge imbalance, it possess positive charge and, hence, attracts, traps electron and comprises F centers [52,53]

F + Center
One of the electrons from F center tends to occupy the neighborhood Ti 4+ ion, so it is positively charged with respect to the lattice, yields Ti 3+ lattice center (F + center). It possesses one unpaired electron.

F ++ Center
Both electrons from F center tend to occupy the neighboring Ti 4+ ion, so it is positively charged with respect to the lattice and yield Ti 2+ lattice center (F ++ center). The formation mechanism and defect equilibria are shown below ( Figure 2):

Electron Holes
It is an antimorph of F center [54], consisting of Titanium vacancy and holes, which gives p-type conductivity to Titania as shown in Figure 3.

Electron Holes
It is an antimorph of F center [54], consisting of Titanium vacancy and holes, which gives p-type conductivity to Titania as shown in Figure 3. These point defects possess distinct energy and, therefore, have different formation energies [55]. Recently, formation energy of various defects in Titania has been calculated as a function of fermi energy since fermi level of a material is based on their charged defects, electron and hole carriers (Figure 4a,b) [56]. According to them, the formation of the surpassing defect type in Titania depends upon their non-stoichiometry level. At Ti-rich conditions, titanium interstitials and oxygen vacancies are formed, and they behave as weak donors. While the formation of titanium vacancy is favored at O-rich growth conditions, they act as deep acceptors. M. K. Nowotny et al. attempted methods to derive the defect disorder diagram of Titania as a function of oxygen partial pressure ( Figure 4c) including illustrating the concentration of specific defects at different oxygen partial pressure [57]. Under low oxygen pressure/ activity, a considerable reduction of Titania leads to the formation of titanium interstitials (Ti excess: O2) and electrons. While at prolonged oxidizing conditions, titanium vacancies with electron holes (acceptors) may become as most dominant defects. Hence, the predominant defect in Titania over a wide range of stoichiometry (under strongly reduced, reduced and oxidized conditions) is oxygen vacancies (donors) and it is compensated by ionic charge (electrons). It is also supported by Kofstad, 1972 (Figure 5d). Thus, oxygen vacancies and titanium interstitials mostly dominate the defect chemistry of Titania due to their lower formation enthalpies and it leads to n-type conductivity in Titania. Formally, titanium vacancies are thermodynamically reversible defects (theoretically); hence, they are usually obtained by quenching to make it as an irreversible defect [58][59][60][61][62][63]. These point defects possess distinct energy and, therefore, have different formation energies [55]. Recently, formation energy of various defects in Titania has been calculated as a function of fermi energy since fermi level of a material is based on their charged defects, electron and hole carriers (Figure 4a,b) [56]. According to them, the formation of the surpassing defect type in Titania depends upon their non-stoichiometry level. At Ti-rich conditions, titanium interstitials and oxygen vacancies are formed, and they behave as weak donors. While the formation of titanium vacancy is favored at O-rich growth conditions, they act as deep acceptors. M. K. Nowotny et al. attempted methods to derive the defect disorder diagram of Titania as a function of oxygen partial pressure ( Figure 4c) including illustrating the concentration of specific defects at different oxygen partial pressure [57]. Under low oxygen pressure/activity, a considerable reduction of Titania leads to the formation of titanium interstitials (Ti excess: Ti 1+x O 2 ) and electrons. While at prolonged oxidizing conditions, titanium vacancies with electron holes (acceptors) may become as most dominant defects. Hence, the predominant defect in Titania over a wide range of stoichiometry (under strongly reduced, reduced and oxidized conditions) is oxygen vacancies (donors) and it is compensated by ionic charge (electrons). It is also supported by Kofstad, 1972 (Figure 5d). Thus, oxygen vacancies and titanium interstitials mostly dominate the defect chemistry of Titania due to their lower formation enthalpies and it leads to n-type conductivity in Titania. Formally, titanium vacancies are thermodynamically reversible defects (theoretically); hence, they are usually obtained by quenching to make it as an irreversible defect [58][59][60][61][62][63].  [57,58]. Reproduced from [57], Copyright 2008, American Chemical Society.
Based on the above discussion, it is understood that an appropriate growth condition is required to incorporate the required defects in Titania. It is also a challenge to integrate particular defects, since various complexities involve in the formation of defects.
In general, the sequence of reduction of TiO2 is: TiO2→TinO2n−1 (n > 10)→TinO2n−1(4< n < 10)→Ti3O5→Ti2O3→TiO→Ti2O Hence, defect formations and their concentration, as well as the properties depend on the preparative conditions. The design of synthesis with defects also has a significant effect on the intrinsic properties such as structural, electrical, optical behavior and, in turn, their catalytic activity. Based on the above discussion, it is understood that an appropriate growth condition is required to incorporate the required defects in Titania. It is also a challenge to integrate particular defects, since various complexities involve in the formation of defects.
In general, the sequence of reduction of TiO 2 is: Hence, defect formations and their concentration, as well as the properties depend on the preparative conditions. The design of synthesis with defects also has a significant effect on the intrinsic properties such as structural, electrical, optical behavior and, in turn, their catalytic activity.

Effect of Defects on Crystal Structure of Titania
Point defects in Titania will induce lattice relaxation and ionic polarization effect, and, hence, affect the surface geometries (i.e., atomic arrangement and coordination) [84][85][86]. Upon removal of the O atom, the nearest Ti-Ti bonds tend to relax away from the vacancy in order to reinforce their bonding with rest of the lattice. Simultaneously, the neighboring Ti-O bonds displace slightly inwards due to the electrostatic attraction induced by oxygen vacancies. This internal modulation induced by oxygen vacancy defects result in the rearrangement of atomic positions and decreases the overlap between Ti dangling bonds closer to the vacancy, and consequently leads to a reduction in Ti-O bond length [87][88][89]. This defect creates uneven internal stress/strain and leads to distortion in TiO 6 octahedra, which diverges with the concentration of defects and constitutes the material with different octahedral packing and crystal symmetry [90] as depicted by E. Stoyanov et al. (Figure 5).

Effect of defects on crystal structure of Titania
Point defects in Titania will induce lattice relaxation and ionic polarization effect, and, hence, affect the surface geometries (i.e., atomic arrangement and coordination) [84][85][86]. Upon removal of the O atom, the nearest Ti-Ti bonds tend to relax away from the vacancy in order to reinforce their bonding with rest of the lattice. Simultaneously, the neighboring Ti-O bonds displace slightly inwards due to the electrostatic attraction induced by oxygen vacancies. This internal modulation induced by oxygen vacancy defects result in the rearrangement of atomic positions and decreases the overlap between Ti dangling bonds closer to the vacancy, and consequently leads to a reduction in Ti-O bond length [87][88][89]. This defect creates uneven internal stress/strain and leads to distortion in TiO6 octahedra, which diverges with the concentration of defects and constitutes the material with different octahedral packing and crystal symmetry [90] as depicted by E. Stoyanov, et al. (Figure 5). As the concentration of oxygen vacancy defects increases, ordering of vacancy occurs, and it leads to the formation of new phases of titanium oxide, (i.e., Structural condensation happens to avoid having entire layers of vacant sites and form extended planar defects [crystallographic shear (CS) planes] with random or regular spacing) [91,92]. The number of CS planes increases thickness of the blocks as well between adjacent CS planes decreases with an increase in vacancy [90].

Crystal Structures of Various Titanium Oxides
Stoichiometric Titania (TiO2) exists as a well-known phase such as rutile (tetragonal-P42/mnm), anatase (tetragonal-I41/amd) and brookite (orthorhombic-Pbca). Whereas the structure of non-stoichiometric Titanium oxide varies with O/Ti stoichiometry as summarized in Figure 6 and Table 3.  As the concentration of oxygen vacancy defects increases, ordering of vacancy occurs, and it leads to the formation of new phases of titanium oxide, (i.e., Structural condensation happens to avoid having entire layers of vacant sites and form extended planar defects [crystallographic shear (CS) planes] with random or regular spacing) [91,92]. The number of CS planes increases thickness of the blocks as well between adjacent CS planes decreases with an increase in vacancy [90].
Whereas the structure of non-stoichiometric Titanium oxide varies with O/Ti stoichiometry as summarized in Figure 6 and Table 3.
Crystal structures of some well-known Ti oxides are discussed below: Titanium dioxide (TiO 2 ): The crystal structure of TiO 2 is considered as a two-dimensional chain of edge-sharing TiO 6 octahedra with individual chains linked at a corner oxygen atom to form the 3D lattice. Each octahedron is made up of titanium atom at the center and oxygen at each corner.
Magneli phase − Ti n O 2n−1 (n = 4-10) (e.g., Ti 4 O 7 , Ti 5 O 9 , Ti 6 O 11 . . . ) The crystal structure of Magneli phases is made of TiO 2 octahedra blocks with an oxygen vacancy at every n th layer, which leads to shear planes in the structure as illustrated in Figure 7. The TiO 2 octahedra blocks are coupled via edges and corners while shear planes have face-sharing octahedral. This atomic arrangement leads to titanium-atom positions in one block which matches with the interstitial or unoccupied positions in the next block. This organization ultimately decreases the symmetry of the crystal system from tetragonal to triclinic as the size of the unit cell increases.  Crystal structures of some well-known Ti oxides are discussed below: Titanium dioxide (TiO2): The crystal structure of TiO2 is considered as a two-dimensional chain of edge-sharing TiO6 octahedra with individual chains linked at a corner oxygen atom to form the 3D lattice. Each octahedron is made up of titanium atom at the center and oxygen at each corner.
Magneli phase − TinO2n−1 (n = 4-10) (e.g., Ti4O7, Ti5O9, Ti6O11…) The crystal structure of Magneli phases is made of TiO2 octahedra blocks with an oxygen vacancy at every n th layer, which leads to shear planes in the structure as illustrated in Figure 7. The TiO2 octahedra blocks are coupled via edges and corners while shear planes have face-sharing octahedral. This atomic arrangement leads to titanium-atom positions in one block which matches with the interstitial or unoccupied positions in the next block. This organization ultimately decreases the symmetry of the crystal system from tetragonal to triclinic as the size of the unit cell increases. Crystal structures of some well-known Ti oxides are discussed below: Titanium dioxide (TiO2): The crystal structure of TiO2 is considered as a two-dimensional chain of edge-sharing TiO6 octahedra with individual chains linked at a corner oxygen atom to form the 3D lattice. Each octahedron is made up of titanium atom at the center and oxygen at each corner.
Magneli phase − TinO2n−1 (n = 4-10) (e.g., Ti4O7, Ti5O9, Ti6O11…) The crystal structure of Magneli phases is made of TiO2 octahedra blocks with an oxygen vacancy at every n th layer, which leads to shear planes in the structure as illustrated in Figure 7. The TiO2 octahedra blocks are coupled via edges and corners while shear planes have face-sharing octahedral. This atomic arrangement leads to titanium-atom positions in one block which matches with the interstitial or unoccupied positions in the next block. This organization ultimately decreases the symmetry of the crystal system from tetragonal to triclinic as the size of the unit cell increases.

♦
The structure of magneli phase can be regarded as made of stacked alternating shear slabs and the family members of magneli phase differ in many shear planes. Thus, they also diverge in length of the pseudo-rutile chain segments.

♦
Magneli phases with higher n value possess greater shear plane interval. The shear planes provides a pathway for electrons transport, and hence, magneli oxides are an excellent electrical conductor [93].
♦ Magneli phase is a mixed valence compound of (n−2) Ti 4+ (3d 0 ) and two Ti 3+ (3d 1 ) configurations. The presence of both Ti 3+ and Ti 4+ ions offer several possible configurations of Ti in the crystal, leading to various charge-ordered states and viewed as electron-doped (oxygen deficient) TiO 2 [94].

♦
The value of n assures the crystal structure as well the electronic structure of the Magneli phase. It possesses more antiphase boundaries and stacking faults [108][109][110][111].
Based on the above discussion, it infers that striking changes in the crystal structure of titanium oxides have occurred due to the relatively small structural alterations through defects.

Effect of Defects on Optical Behavior of Titania
Stoichiometric TiO 2 is a wide bandgap semiconductor (3.3 eV), and, hence, it absorbs UV light, while reduced Titania absorbs visible light and behaves as a semiconductor or metal depending on their oxygen vacancy ( Figure 8) [74,[112][113][114][115][116][117][118][119].  Magneli phases with higher n value possess greater shear plane interval. The shear planes provides a pathway for electrons transport, and hence, magneli oxides are an excellent electrical conductor [93].  Magneli phase is a mixed valence compound of (n−2) Ti 4+ (3d 0 ) and two Ti 3+ (3d 1 ) configurations. The presence of both Ti 3+ and Ti 4+ ions offer several possible configurations of Ti in the crystal, leading to various charge-ordered states and viewed as electron-doped (oxygen deficient) TiO2 [94].  The value of n assures the crystal structure as well the electronic structure of the Magneli phase.
Ti3O5: The unit cell includes two Ti 3+ ions and one Ti 4+ ion with a different significant Ti-O distance leading to a distorted octahedron [95,96].
Ti2O3: The stoichiometry of Ti2O3 extends from TiO1.49 to TiO1.51 and comprises pairs of Ti 3+ ions in octahedral sites as a fundamental component in the unit cell [97,98]. TiO: ∆ TiO has a defective NaCl structure (space group Fm3m) and possesses 10-15 at.% vacancies at both Ti and O sites [99]. Owing to higher structural vacancies in titanium monoxide, they are considered as strongly non-stoichiometric and has a broader homogeneity region from TiO0.70 to TiO1.25 [100,101]. ∆ TiO has two polymorphs based on the vacancy distribution. If the vacancies are randomly distributed it leads to disordered cubic phase, and the other polymorph has ordered vacancies with monoclinic symmetry [83,[102][103][104][105][106]. ∆ It is metallic in nature due to the high content of vacancy channels [107].
Based on the above discussion, it infers that striking changes in the crystal structure of titanium oxides have occurred due to the relatively small structural alterations through defects.

Effect of Defects on Optical Behavior of Titania
Stoichiometric TiO2 is a wide bandgap semiconductor (3.3 eV), and, hence, it absorbs UV light, while reduced Titania absorbs visible light and behaves as a semiconductor or metal depending on their oxygen vacancy ( Figure 8) [74,[112][113][114][115][116][117][118][119]. According to crystal field splitting (Figure 9), Ti (3d, 4s, 4p) orbitals are linearly coalesced with O (2s, 2p) orbitals to form molecular orbitals as depicted in Figure 9 [90]. The upper t2g* and, eg* are primarily of Ti 3d character and configure conduction band, while the lower t2g and, eg are mainly of O 2p character and form valence band, respectively [90]. According to crystal field splitting (Figure 9), Ti (3d, 4s, 4p) orbitals are linearly coalesced with O (2s, 2p) orbitals to form molecular orbitals as depicted in Figure 9 [90]. The upper t 2g * and, eg* are primarily of Ti 3d character and configure conduction band, while the lower t 2g and, e g are mainly of O 2p character and form valence band, respectively [90]. he defects and non-stoichiometry in reduced Titania will induce alterations in T ancies and directly control the local structure of t2g and, eg orbitals due to Jahn-Teller e ollowing difference in the splitting of t2g and eg levels in different distorted environmen ia are illustrated in Figure 10 [90]. s an outcome, the incorporated modifications in the crystal field as a function of increa n vacancy content are: he systematic decrease in crystal field splitting between t2g and, eg levels he covalent bonding between Ti and O becomes ionic. he degree of electron occupancy in the t2g level increases. TiO2 has none, Ti2O3 has one iO has two t2g electrons. The defects and non-stoichiometry in reduced Titania will induce alterations in Ti 3d occupancies and directly control the local structure of t 2g and, e g orbitals due to Jahn-Teller effect. The following difference in the splitting of t 2g and e g levels in different distorted environments of Titania are illustrated in Figure 10 [90].
As an outcome, the incorporated modifications in the crystal field as a function of increasing oxygen vacancy content are: • the systematic decrease in crystal field splitting between t 2g and, e g levels. • the covalent bonding between Ti and O becomes ionic.

•
The degree of electron occupancy in the t 2g level increases. TiO 2 has none, Ti 2 O 3 has one and TiO has two t 2g electrons. The defects and non-stoichiometry in reduced Titania will induce alterations in Ti 3d occupancies and directly control the local structure of t2g and, eg orbitals due to Jahn-Teller effect. The following difference in the splitting of t2g and eg levels in different distorted environments of Titania are illustrated in Figure 10 [90].
As an outcome, the incorporated modifications in the crystal field as a function of increasing oxygen vacancy content are:  the systematic decrease in crystal field splitting between t2g and, eg levels  the covalent bonding between Ti and O becomes ionic.  The degree of electron occupancy in the t2g level increases. TiO2 has none, Ti2O3 has one and TiO has two t2g electrons. Besides the above-described changes in crystal symmetry and coordination number, the extent of mixing of Ti 3d and O 2p orbitals is also affected, and, hence, their electronic band structure and band gap vary on titanium oxide polymorphs. It is also known that the oxygen vacancy and titanium interstitial behave as donor states since their energy level is closer to the conduction band; while Besides the above-described changes in crystal symmetry and coordination number, the extent of mixing of Ti 3d and O 2p orbitals is also affected, and, hence, their electronic band structure and band gap vary on titanium oxide polymorphs. It is also known that the oxygen vacancy and titanium interstitial behave as donor states since their energy level is closer to the conduction band; while titanium vacancy forces the Fermi level towards the valence band, to accept electrons from their surrounding O atoms and act as an acceptor state [49,[120][121][122][123][124][125]. The distinct energy levels of various defect states in titanium oxide are shown in Figure 11 [86].  Figure 11. Various defect levels of Titania. The numbered letters a1, a2, a3, a4, b1, b2, c1, c2, c3, c4, d1 and d2 represent the defect levels VTi With these continuous formations of defect states, localized midgap states in between the bandgap will enrich and ultimately narrow the band gap of TiO2. Thus, the formation of vacancies results in shifts of average band energies, change of band widths and position of the Fermi level with the creation of new "vacancy states" in the bandgap. It also formulates an accumulation layer in the near-surface region that leads to a downward band bending [126].
The structural model of certain reduced Titania with their characteristic optical behavior and preparation methods are illustrated in Figure 12 [127]. As seen in Figure 12, Ti and O reside in their lattice and give rise to a colorless compound in case of stoichiometric Titania (TiO2). While on heat treatments under the H2 atmosphere, the surface oxygen vacancies are created and spread into bulk, which resulted in a pale blue color of a crystal. On continuing the heat treatment further, some oxygen vacancies co-exist with the conduction electrons in dark blue and dark green crystals, whereas, the conduction electrons completely migrate to the oxygen vacancy site on extensive heat treatment under the N2 atmosphere, so that the crystal appears yellow in color. Thus, different defect concentration in reduced titanium oxide forms colorful titanium oxide.
With these continuous formations of defect states, localized midgap states in between the bandgap will enrich and ultimately narrow the band gap of TiO 2 . Thus, the formation of vacancies results in shifts of average band energies, change of band widths and position of the Fermi level with the creation of new "vacancy states" in the bandgap. It also formulates an accumulation layer in the near-surface region that leads to a downward band bending [126].
The structural model of certain reduced Titania with their characteristic optical behavior and preparation methods are illustrated in Figure 12 [127]. As seen in Figure 12, Ti and O reside in their lattice and give rise to a colorless compound in case of stoichiometric Titania (TiO 2 ). While on heat treatments under the H 2 atmosphere, the surface oxygen vacancies are created and spread into bulk, which resulted in a pale blue color of a crystal. On continuing the heat treatment further, some oxygen vacancies co-exist with the conduction electrons in dark blue and dark green crystals, whereas, the conduction electrons completely migrate to the oxygen vacancy site on extensive heat treatment under the N 2 atmosphere, so that the crystal appears yellow in color. Thus, different defect concentration in reduced titanium oxide forms colorful titanium oxide.

Effect of Defects on Electrical Behavior of Titania
Defects turn Titania from semiconductor to metallic depending on the intensity or level of structural deformation. Usually, lower oxides of titanium are metallic conductors while higher oxide content is semiconductor or insulator. This transition of conductivity from electronic conduction in titanium to a hopping mechanism in Titania is due to the presence of oxygen. At lower oxygen content, the corresponding Ti atoms are under great proximity and interact electronically, which leads to good conductivity [128,129]. Besides, the shear planes in magneli's phase offer easy access for the charge transport and hence improvement in the conductivity as shown in Figure 13a [130]. The relative variation in conductivity of magneli's phases due to the variation in oxygen vacancy content (shear planes) is shown in Figure 13b

Effect of Defects on Electrical Behavior of Titania
Defects turn Titania from semiconductor to metallic depending on the intensity or level of structural deformation. Usually, lower oxides of titanium are metallic conductors while higher oxide content is semiconductor or insulator. This transition of conductivity from electronic conduction in titanium to a hopping mechanism in Titania is due to the presence of oxygen. At lower oxygen content, the corresponding Ti atoms are under great proximity and interact electronically, which leads to good conductivity [128,129]. Besides, the shear planes in magneli's phase offer easy access for the charge transport and hence improvement in the conductivity as shown in Figure 13a [130]. The relative variation in conductivity of magneli's phases due to the variation in oxygen vacancy content (shear planes) is shown in Figure 13b [92].

Effect of Defects on Electrical Behavior of Titania
Defects turn Titania from semiconductor to metallic depending on the intensity or level of structural deformation. Usually, lower oxides of titanium are metallic conductors while higher oxide content is semiconductor or insulator. This transition of conductivity from electronic conduction in titanium to a hopping mechanism in Titania is due to the presence of oxygen. At lower oxygen content, the corresponding Ti atoms are under great proximity and interact electronically, which leads to good conductivity [128,129]. Besides, the shear planes in magneli's phase offer easy access for the charge transport and hence improvement in the conductivity as shown in Figure 13a [130]. The relative variation in conductivity of magneli's phases due to the variation in oxygen vacancy content (shear planes) is shown in Figure 13b Table 4) [131]. The change in electrical properties at different oxygen proportions is due to the dissimilarity in electron occupancy, bond type, strength of interplay between Ti 3d orbitals and interaction between Ti 3d and O 2p orbitals (i.e., the complex interaction of charge order, orbital order). Subsequently, the electrons delocalization on different Ti ions or localized onsimilar Ti ions, which eventually leads to enhanced conductivity.

Effect of defects on the catalytic activity of Titania
Point defects in Titania act as catalytically active sites due to the vacancy-electron, vacancy-vacancy interactions, and vacancy-strain coupling. Furthermore, clusters of vacancy and associative vacancy voids behave as a transfer station for atom exchange or migration because of their associated 'conducting vacancy channels' and plays a governing role in the catalytic activity. Also, the vacancy-induced electrons on defective Titania are localized on the Ti atom and accelerate local lattice distortion, constituting a polaron [132]. These mobile polarons form movement with low activation energy and favor conductivity and catalytic activity [133]. Besides, a large number of donor/acceptor defect states and a large density of dangling bonds in reduced Titania cause high surface activities and provide cooperative electrical effects (e.g., improved electron transfer and transport) for catalytic activity [134]. Further, defects induce an internal stress/strain, which is crucial for faster kinetics and favorable reactivity [135,136]. Plus, point defects have a potential to stabilize the binding of surface adsorbed species and escort to stiffer molecule-surface interactions which enhance the activity. Thus, these defect-related interface effects and defect-mediated charge migration effects augment the catalytic activity towards water-splitting [70,[137][138][139][140][141][142][143].
7. Role of defects towards electro-catalytic water splitting  Table 4) [131]. The change in electrical properties at different oxygen proportions is due to the dissimilarity in electron occupancy, bond type, strength of interplay between Ti 3d orbitals and interaction between Ti 3d and O 2p orbitals (i.e., the complex interaction of charge order, orbital order). Subsequently, the electrons delocalization on different Ti ions or localized onsimilar Ti ions, which eventually leads to enhanced conductivity.

Effect of Defects on the Catalytic Activity of Titania
Point defects in Titania act as catalytically active sites due to the vacancy-electron, vacancy-vacancy interactions, and vacancy-strain coupling. Furthermore, clusters of vacancy and associative vacancy voids behave as a transfer station for atom exchange or migration because of their associated 'conducting vacancy channels' and plays a governing role in the catalytic activity. Also, the vacancy-induced electrons on defective Titania are localized on the Ti atom and accelerate local lattice distortion, constituting a polaron [132]. These mobile polarons form movement with low activation energy and favor conductivity and catalytic activity [133]. Besides, a large number of donor/acceptor defect states and a large density of dangling bonds in reduced Titania cause high surface activities and provide cooperative electrical effects (e.g., improved electron transfer and transport) for catalytic activity [134]. Further, defects induce an internal stress/strain, which is crucial for faster kinetics and favorable reactivity [135,136]. Plus, point defects have a potential to stabilize the binding of surface adsorbed species and escort to stiffer molecule-surface interactions which enhance the activity. Thus, these defect-related interface effects and defect-mediated charge migration effects augment the catalytic activity towards water-splitting [70,[137][138][139][140][141][142][143].

Role of Defects towards Electro-Catalytic Water Splitting
Point defects in reduced Titania build a lattice strain in the material, which induces hydrophilicity on their surface than that of (defect-free) Titania without strain [140]. Hence, water molecules are dissociatively adsorbed on the defect sites, and consequently, the number of bridging/terminal hydroxyl groups increases with increasing concentration of structural defects in reduced Titania. This hydroxyl group depresses the O + yield (Knotek−Feibelman mechanism) and favors lateral long-range redistribution of defect-electrons on the surface [144]. Thus, surface chemistry and electrical behavior of Titania are modified by electrons associated with oxygen vacancy defect sites and hence catalytic activity. The mentioned K-F process inversely decays with the oxygen vacancy content (Figure 15). Point defects in reduced Titania build a lattice strain in the material, which induces hydrophilicity on their surface than that of (defect-free) Titania without strain [140]. Hence, water molecules are dissociatively adsorbed on the defect sites, and consequently, the number of bridging/terminal hydroxyl groups increases with increasing concentration of structural defects in reduced Titania. This hydroxyl group depresses the O + yield (Knotek−Feibelman mechanism) and favors lateral long-range redistribution of defect-electrons on the surface [144]. Thus, surface chemistry and electrical behavior of Titania are modified by electrons associated with oxygen vacancy defect sites and hence catalytic activity. The mentioned K-F process inversely decays with the oxygen vacancy content (Figure 15). Similarly, titanium vacancy offers favorable active sites for water-splitting as it possesses strong electron affinity, which allows effective charge transfer for oxygen evolution reaction [57]. Hence, overall water-splitting is possible with n-and p-type defective Titania.

Role of defects towards photoelectrochemical water splitting
In principle, efficient photoelectrochemical watersplitting requires proficient separation of photo-generated charge carriers (photon activation) and subsequent faster transportation to the semiconductor interface for water ionization [145].
Similarly, titanium vacancy offers favorable active sites for water-splitting as it possesses strong electron affinity, which allows effective charge transfer for oxygen evolution reaction [57]. Hence, overall water-splitting is possible with n-and p-type defective Titania.

Role of Defects towards Photoelectrochemical Water Splitting
In principle, efficient photoelectrochemical watersplitting requires proficient separation of photo-generated charge carriers (photon activation) and subsequent faster transportation to the semiconductor interface for water ionization [145].
Photon activation: TiO 2 + hν → e − + h + Water ionization: H 2 O + h + → OH − + H + Since many reactive oxygen species are generated as an intermediate during the photoelectrochemical watersplitting reaction (Figure 16), both bulk and surface characteristics of the semiconductor will significantly influence the mechanism and kinetics of charge separation and interfacial charge transfer. Sun et al. proposed the photoelectrochemical watersplitting reaction pathway in Titania ( Figure 17). According to them, water-splitting occurs by the formation of hydroperoxide intermediate. Later, Ti-OH and Ti-OOH groups are formed due to nucleophilic attack of water following the coupling process and O-O bond formation. Then, it collapses to produce oxygen with regeneration of TiO 2 [146]. Since many reactive oxygen species are generated as an intermediate during the photoelectrochemical watersplitting reaction (Figure 16), both bulk and surface characteristics of the semiconductor will significantly influence the mechanism and kinetics of charge separation and interfacial charge transfer. Sun et al. proposed the photoelectrochemical watersplitting reaction pathway in Titania ( Figure 17). According to them, water-splitting occurs by the formation of hydroperoxide intermediate. Later, Ti-OH and Ti-OOH groups are formed due to nucleophilic attack of water following the coupling process and O-O bond formation. Then, it collapses to produce oxygen with regeneration of TiO2 [146]. Thus, based on the overall reaction mechanism, the presence of O2˚− and OHon the   Thus, based on the overall reaction mechanism, the presence of O2˚− and OHon the semiconductor's surface are likely to be an active site for the photoelectrochemical water oxidation. The defective Titania is enriched with surface hydroxyl groups and as well, highly active species such as O2˚− and O2 2− will be produced on Ti 3+ site when it reacts with dissolved oxygen (Figure 18) [147,148]. Whereas pristine Titania will barely afford chemisorptions sites. Hence, point defects in reduced Titania act as a reactive center for photoelectrochemical water-splitting reaction. Thus, based on the overall reaction mechanism, the presence of O 2 •− and OH − on the semiconductor's surface are likely to be an active site for the photoelectrochemical water oxidation. The defective Titania is enriched with surface hydroxyl groups and as well, highly active species such as O 2 •− and O 2 2− will be produced on Ti 3+ site when it reacts with dissolved oxygen (Figure 18) [147,148].
Whereas pristine Titania will barely afford chemisorptions sites. Hence, point defects in reduced Titania act as a reactive center for photoelectrochemical water-splitting reaction. Apart from the surface phenomena, bulk characteristics of defective Titania like superficial and deep defect states offer a dominant pathway for charge transport [148][149][150][151][152][153][154][155][156][157][158]. Also, defective Titania absorbs visible light, and the defect concentration tunes their optical behavior [159][160][161][162]. Importantly, defective Titania possesses numerous dangling bonds and serve as a bridge to facilitate charge transfer once it is photo-excited. Thus, benefiting from the surface adsorption and bulk properties through point defects, reduced Titania could serve as an efficient photo-electrocatalyst and as a generic platform for other defective metal oxides.

Challenges in Reduced Titania
Point defects in reduced Titania are usually not stable in air, as Ti 3+ /Ti 2+ is easily oxidized and even susceptible to oxidation by dissolved oxygen in the water. Furthermore, the strategies to develop reduced Titania involve multiple steps, harsh synthesis conditions, or expensive facilities [69,[162][163][164][165][166][167][168]. Therefore, developing a simple and economic strategy to synthesize stable reduced TiO2 is still a great challenge. Besides, the control of the quality and quantity of defects during preparation is complicated. However, the optimal concentration of point defects in reduced Titania is essential for the best catalytic activity. At higher concentrations, it functions as an electron trap and in case of photo-electrochemical water-splitting it acts as a scatterer in electro-catalytic water-splitting [169]. Moreover, reduced Titania has mostly triclinic crystal symmetry with very similar lattice parameters. As a result, the formed material usually contains various sub-stoichiometries.

Applications
The diverse characteristics of reduced Titania such as robustness, electron richness, chemical inertness (stability), electrical conductivity, visible absorption makes them a suitable candidate for cathodic protection of steel in concrete, photodegradation of organic compounds, CO2 reduction, Oxygen Reduction Reaction, solar cells, fuel cells, coating for tribological improvement, remediation of aqueous waste and contaminated water, electronic and optoelectronic devices, field emission, supercapacitors, microwave absorbers, photoelectrochemical sensor etc. [12,68,. It is also used as a chemical catalyst for ethylene polymerization, production of chemicals such as pyrite, glyoxylic acid and oxidation of flue gases, trichloroethylene. The enhanced catalytic activity has been frequently attributed to the presence of oxygen vacancies, Ti 3+/2+ species, hydroxyl groups, mid-gap energy levels. It also acts as a promising catalytic support for platinum and shows performance comparable to carbon black in PEM fuel cell technologies. Apart from the surface phenomena, bulk characteristics of defective Titania like superficial and deep defect states offer a dominant pathway for charge transport [148][149][150][151][152][153][154][155][156][157][158]. Also, defective Titania absorbs visible light, and the defect concentration tunes their optical behavior [159][160][161][162]. Importantly, defective Titania possesses numerous dangling bonds and serve as a bridge to facilitate charge transfer once it is photo-excited. Thus, benefiting from the surface adsorption and bulk properties through point defects, reduced Titania could serve as an efficient photo-electrocatalyst and as a generic platform for other defective metal oxides.

Challenges in Reduced Titania
Point defects in reduced Titania are usually not stable in air, as Ti 3+ /Ti 2+ is easily oxidized and even susceptible to oxidation by dissolved oxygen in the water. Furthermore, the strategies to develop reduced Titania involve multiple steps, harsh synthesis conditions, or expensive facilities [69,[162][163][164][165][166][167][168]. Therefore, developing a simple and economic strategy to synthesize stable reduced TiO 2 is still a great challenge. Besides, the control of the quality and quantity of defects during preparation is complicated. However, the optimal concentration of point defects in reduced Titania is essential for the best catalytic activity. At higher concentrations, it functions as an electron trap and in case of photo-electrochemical water-splitting it acts as a scatterer in electro-catalytic water-splitting [169]. Moreover, reduced Titania has mostly triclinic crystal symmetry with very similar lattice parameters. As a result, the formed material usually contains various sub-stoichiometries.

Applications
The diverse characteristics of reduced Titania such as robustness, electron richness, chemical inertness (stability), electrical conductivity, visible absorption makes them a suitable candidate for cathodic protection of steel in concrete, photodegradation of organic compounds, CO 2 reduction, Oxygen Reduction Reaction, solar cells, fuel cells, coating for tribological improvement, remediation of aqueous waste and contaminated water, electronic and optoelectronic devices, field emission, supercapacitors, microwave absorbers, photoelectrochemical sensor etc. [12,68,. It is also used as a chemical catalyst for ethylene polymerization, production of chemicals such as pyrite, glyoxylic acid and oxidation of flue gases, trichloroethylene. The enhanced catalytic activity has been frequently attributed to the presence of oxygen vacancies, Ti 3+/2+ species, hydroxyl groups, mid-gap energy levels. It also acts as a promising catalytic support for platinum and shows performance comparable to carbon black in PEM fuel cell technologies.

Towards Commercial Development
Currently, certain companies like Atranova, Atraverda, are in the process of making batteries, fuel cells with an electrically conductive titanium suboxide (Ti 4 O 7 ) with the trade name Ebonex ® . Lithium-ion rechargeable battery shows excellent rate performance with reduced Titania due to the oxygen vacancies, which creates well-balanced Li + /e − diffusion and provides short lithium-ion diffusion path and reduced charge diffusion resistance. Besides, the disordered surface of reduced Titania improves pseudocapacitive lithium storage. Vector Corrosion Technologies use titanium suboxides for cathodic protection of concrete [39][40][41].

Conclusions
Without a doubt, titanium sub-oxides with different crystal structures and colors have attracted tremendous interest due to their outstanding, electrical, optical and catalytic properties. The controlled oxygen vacancies in Titania impose significant structural modifications and substantially vary the conductivity from n-type to p-type semiconductors, and even quasi-metallic conductors. It also turns a colorless, inert Titania to a colorful, reactive defect-rich Titania. Despite the excellent electrical conductivity and visible absorption, their catalytic activity is still far from the ideal expectation. Thus, managing and optimizing the defects and the spatial distribution for catalytic activity is a critical issue. Different synthesis methods usually lead to various properties of defective titanium oxides. Importantly, much efforts and optimization are required to control the defects (n/p-type), concentration, and their spatial distribution. It is practically difficult to introduce defects of specific types into the desired location and at a controlled proportion, which requires more in-depth investigations. Also, new methods and tools must be developed to precisely characterize the defects in Titania lattice. For example, the atomic scale understanding, dynamics of defect, migration, and reconstruction of defects in Titania are still unexplored. The authors feel that the theoretical investigations and simulation methods will help to understand the structure-property relationship of defect-rich Titania. Besides, the proposed mechanism of catalytic activity in reduced TiO 2 should be evidenced through a more specific way. Also, it is of dire importance to consider the overall changes of the chemical environment in Titania rather than to focus locally on the defects, such as Ti 3+ or V O . However, comprehensively the defect-rich Titania will be a futuristic catalyst for water-splitting applications with a combinatorial attempt from materials scientists, physicists, and chemists.