1.
Introduction
Titanium dioxide is a promising photocatalysis material, which also has wide applications in heterogeneous catalysis, solar cells, gas sensor, etc[1-5]. The surface of TiO2 has been extensively studied for many years due to its essential role in the applications. Especially, surface defects have been proved to be vital for surface reactivity. For instance, surface oxygen vacancies are reactive sites for water and other molecules[6]. It is desirable to use external field to control the surface properties in order to improve the surface reactivity of TiO2.
Strain field is unavoidable in fabrication of nanostructures and thin film[7, 8]. It has been demonstrated that the band structure of TiO2 can be changed by using strain[9]. Besides, the surface properties can also be engineered by strain. We have paid our attention on the strain effect on the surface of TiO2 since 2008, and found that the strain can change many aspects of the surface properties, such as the surface energy, the distribution of surface defects, surface adsorption and dissociation[10-15].
In this paper, we review our work on the strain engineering of the surface properties of TiO2. The following section is arranged as follows. In the second section, we will first introduce the simple theoretical background on the strain engineering. In the third section, we will discuss how the strain can be used to improve the relative percentage of the reactive surface. In the fourth and fifth sections, the thermodynamic and kinetic properties of oxygen vacancies under strain are reviewed, respectively. In the sixth and seventh sections, the effect of strain on the surface adsorption on stoichiometric and reduced TiO2(110) are reviewed, respectively.
2.
Elastic properties of TiO2 surface
The structure and thus the properties of a bulk material respond to the external strain differently according to its bulk elastic properties. The bulk elastic properties of TiO2 are described by six independent elastic constants. The bulk modulus and Young’s modulus can be further calculated by these independent elastic constants. The results are presented in Table 1, including our own calculations based on the density functional theory (DFT)[13].
Parameter | $C_{11}$ | $C_{12}$ | $C_{13}$ | $C_{33}$ | $C_{44}$ | $C_{66}$ | $B$ | $Y_c$ | $Y_r$ | $Y_a$ |
Rutile | ||||||||||
PW91[12] | 265 | 179 | 151 | 472 | 116 | 211 | 209 | 369 | 348 | 138 |
Phonon[16] | 269 | 189 | 166 | 506 | 105 | 217 | 219 | 386 | 349 | 130 |
PBE[17] | 261 | 132 | 137 | 456 | 117 | 204 | 187 | 360 | 311 | 182 |
Exp[18] | 268 | 175 | 147 | 484 | 124 | 190 | 212 | 386 | 354 | 147 |
Anatase | ||||||||||
PW91[12] | 331 | 144 | 141 | 189 | 46 | 59 | 173 | 105 | 264 | 219 |
Phonon[16] | 333 | 143 | 140 | 198 | 39 | 57 | 176 | 116 | 278 | 226 |
PBE[17] | 311 | 150 | 138 | 191 | 51 | 59 | 172 | 108 | 262 | 199 |
Table1.
The elastic constant
Table options
-->
Download as CSV
Parameter | $C_{11}$ | $C_{12}$ | $C_{13}$ | $C_{33}$ | $C_{44}$ | $C_{66}$ | $B$ | $Y_c$ | $Y_r$ | $Y_a$ |
Rutile | ||||||||||
PW91[12] | 265 | 179 | 151 | 472 | 116 | 211 | 209 | 369 | 348 | 138 |
Phonon[16] | 269 | 189 | 166 | 506 | 105 | 217 | 219 | 386 | 349 | 130 |
PBE[17] | 261 | 132 | 137 | 456 | 117 | 204 | 187 | 360 | 311 | 182 |
Exp[18] | 268 | 175 | 147 | 484 | 124 | 190 | 212 | 386 | 354 | 147 |
Anatase | ||||||||||
PW91[12] | 331 | 144 | 141 | 189 | 46 | 59 | 173 | 105 | 264 | 219 |
Phonon[16] | 333 | 143 | 140 | 198 | 39 | 57 | 176 | 116 | 278 | 226 |
PBE[17] | 311 | 150 | 138 | 191 | 51 | 59 | 172 | 108 | 262 | 199 |
Similar to the case of a bulk material, the response of a surface to the external strain depends on the surface elastic properties. Generally speaking, different surface structures also have different surface elasticity. Therefore, the thermodynamic equilibrium surface structures would adjust themselves according to the external strain, and the surface properties change with the strain correspondingly.
The surface elastic properties can be described mainly by the surface stresses and surface elastic constants, which are defined as follows[19],
$$ begin{array}{l} sigma_{alpha beta} = dfrac{1}{A_{ m{L}}}dfrac{partial (A_{ m{L}} gamma_{ m{L}})}{partial epsilon_{alpha beta}} = dfrac{partial gamma_{ m{L}}}{partial epsilon_{alpha beta}}, S_{alpha betaalpha' beta'} = dfrac{partial sigma_{alpha beta} }{partial epsilon_{alpha' beta'}} = dfrac{partial^2 gamma_{ m{L}}}{partial epsilon_{alpha beta} partial epsilon_{alpha' beta'}}. end{array} $$ | (1) |
Here
m{L}} $
m{L}} $
$$ begin{align} gamma(epsilon) =; & gamma(0)+ sigma_{11} epsilon_{11}+ sigma_{22} epsilon_{22} &+frac{1}{2}epsilon_{11}^2S_{1111}+frac{1}{2}epsilon_{22}^2S_{2222} +epsilon_{11}epsilon_{22}S_{1122}. end{align} $$ | (2) |
Under a certain strain, by comparing the surface energies of different surface structures, one can expect to investigate the effect of strain on the surface thermodynamic or kinetic properties.
The surface elastic properties of TiO2 are shown in Table 2, the calculation details of which can be found in Ref. [13]. The surface elastic constants
Parameter | $ gamma $ | $ sigma_{11} $ | $ sigma_{22} $ | $ S_{1111} $ | $ S_{2222} $ | $ S_{1122} $ |
Rutile | ||||||
(110) | 0.44 | 2.52 | 1.14 | –73.81 | –17.67 | –26.30 |
(100) | 0.70 | –1.74 | 1.28 | –20.64 | –2.88 | –9.75 |
(101) | 1.03 | –0.08 | 0.16 | –24.62 | –25.38 | –21.88 |
(001) | 1.30 | 1.27 | 1.27 | –8.27 | –8.27 | –15.80 |
Anatase | ||||||
(101) | 0.52 | 0.77 | 2.06 | 41.33 | –2.21 | 9.99 |
(100) | 0.59 | 1.90 | 0.82 | –1.31 | 4.40 | –5.06 |
(001) | 1.04 | 9.58 | –2.13 | 2.64 | 2.64 | –18.01 |
(110) | 1.10 | –2.09 | 1.31 | –27.74 | 16.07 | –2.17 |
Table2.
The calculated surface energy and surface mechanical properties of rutile and anatase phases.
Table options
-->
Download as CSV
Parameter | $ gamma $ | $ sigma_{11} $ | $ sigma_{22} $ | $ S_{1111} $ | $ S_{2222} $ | $ S_{1122} $ |
Rutile | ||||||
(110) | 0.44 | 2.52 | 1.14 | –73.81 | –17.67 | –26.30 |
(100) | 0.70 | –1.74 | 1.28 | –20.64 | –2.88 | –9.75 |
(101) | 1.03 | –0.08 | 0.16 | –24.62 | –25.38 | –21.88 |
(001) | 1.30 | 1.27 | 1.27 | –8.27 | –8.27 | –15.80 |
Anatase | ||||||
(101) | 0.52 | 0.77 | 2.06 | 41.33 | –2.21 | 9.99 |
(100) | 0.59 | 1.90 | 0.82 | –1.31 | 4.40 | –5.06 |
(001) | 1.04 | 9.58 | –2.13 | 2.64 | 2.64 | –18.01 |
(110) | 1.10 | –2.09 | 1.31 | –27.74 | 16.07 | –2.17 |
It is worthy to note that there is an odd–even oscillation of the surface properties of the relaxed TiO2 in the thin film slab. For instance, for rutile (110) surface, although the surface energy and the band gap converge in a slab within about ten trilayers, the surface stresses in the
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-1.jpg'"
class="figure_img" id="Figure1"/>
Download
Larger image
PowerPoint slide
Figure1.
(Color online) (a–c) Variations of surface energies and surface stresses, as well as (d–f) the electronic structure properties with the slab thickness. Black solid curves and red dashed curves are for the unrelaxed and relaxed surfaces, respectively. The valence band maximum (VBM,(e)) and the conduction band minimum (CBM,(f)) are referenced to the vacuum level. These figures are adapted from Ref. [14].
3.
Improving the percentage of reactive surfaces
Generally speaking, there is an intrinsic controversy between stability and reactivity in nature. The more reactive a surface is, the less stable it is, or the higher surface energy it is. According to the Wulff's theorem, it means that the percentage of a reactive surface is usually low. For example, in equilibrium anatase TiO2, the most reactive (001) surface has a surface energy much larger than the (101) surface, as shown in Table 2. As a result, the area proportion of anatase (001) surface is no more than 3%, which strongly limits the reactive efficiency of TiO2 in application as a photocatalyst[20-22].
Fortunately, the anatase (001) surface possesses the largest surface stress among all the surfaces, which is positive and occurs along the [100] direction. We therefore expect that the relative stability of (001) surface can be significantly improved by applying an compressive strain along the [100] direction, and thus its area percentage of anatase (001) according to Wulff construction. By first principle calculations, we have verified this[13]. As displayed in Fig. 2(a), under 5% biaxial compressive strain or compressive strain along [100], the area proportion of anatase (001) surface increases more than five times. In this way the external strain can be used to enhance the reactivity of TiO2 catalyst.
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-2.jpg'"
class="figure_img" id="Figure2"/>
Download
Larger image
PowerPoint slide
Figure2.
(Color online) (a) The area percentage of anatase (001) facets with variation of the applied strain. The inset displays the equilibrium shape of the anatase crystallite. (b –d) The surface energy ratio
4.
Formation of surface oxygen vacancies under strain
Oxygen vacancies are the most common defects in transition metal oxide. The reduced materials usually show different physical properties compared to the stoichiometric one. In TiO2, the oxygen vacancy (OV) has a low formation energy, and it has been experimentally found reactive in the surface reaction[23-30]. In order to investigate the influence of strain on the bulk and surface properties when different OVs are introduced, we first of all need to understand the responses of the formation of OVs to different external field[31, 32]. By using DFT calculations, we have found that external strain can modify the type of oxygen vacancy, which further influences the surface reactivity. Hereafter we refer the stoichiometric TiO2 as s-TiO2, while the TiO2 with oxygen vacancies as r-TiO2.
There are three types of oxygen atoms, bridging, in-plane and subbridging oxygen atoms, as shown in Fig. 3. Correspondingly, three different types of OV can be introduced by removing corresponding different types of oxygen atoms, namely BOV, IPOV and SBOV. We named different types of OVs to include the site of the defect. For example, 2-in-plane OV represents the OV formed by removing an in-plane oxygen atom in the second trilayer.
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-3.jpg'"
class="figure_img" id="Figure3"/>
Download
Larger image
PowerPoint slide
Figure3.
(Color online) Schematic of the rutile TiO2(110) surface. The bridging oxygen (BO), the subbridging oxygen (SBO) and the in-plane oxygen (IPO) atoms are indicated by the arrows.
m{o}} $
m{t}} $
The OV formation energy can be calculated as follows,
$$ E_{ m{OV}} = E_{ m{r}}-E_{ m{s}}+frac{1}{2} E_{{ m{O}}_{2}} , $$ | (3) |
where
m{O}}_{2}} $
m{r}} $
m{s}} $
The OV formation energy as a function of OV depth is shown in Fig. 4(a). Obviously the 1-bridging OV is the most easily formed OV defect because of the lowest formation energy. In addition, the in-plane OV formation energy remains almost constant at different depth, while the bridging and subbridging OVs formation energies appear a kind of odd-even oscillation behavior. With the position of OV going deeper, both of them tend to approach the formation energy of bulk OV[33, 34].
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-4.jpg'"
class="figure_img" id="Figure4"/>
Download
Larger image
PowerPoint slide
Figure4.
(Color online) (a) The formation energy of OV and (b) the changes of the surface stresses and surface elastic constants induced by the OV as a function of the OV depth. The depth is defined as the distance below the unrelaxed 1-bridging O atoms. The dashed horizontal line in (a) denotes the bulk vacancy formation energy. Solid or dashed curves in (b) are to guide the eyes.
To get the influence of oxygen vacancies on the surface elasticity, we also calculated the vacancy-induced change of surface energy,
$$ Delta gamma = frac{E_{ m{r}}-E_{ m{s}}} {A_{ m{L}}} = theta frac{ E_{ m{OV}} - frac{1}{2} E_{{ m{O}}_{2}}}{A_{ m L0}}, $$ | (4) |
where
m{L0}} $
m{OV}} $
m{OV}} $
The value of
Oxygen vacancy | $ Deltagamma $ | $ Deltasigma_{11} $ | $ Deltasigma_{22} $ | $ Delta S_{1111} $ | $ Delta S_{2222} $ | $ Delta S_{1122} $ |
1-bridging | 2.17 | 0.51 | –1.66 | –2.42 | –29.36 | –14.76 |
1-in-plane | 2.40 | –5.02 | –2.73 | –151.01 | –34.03 | –53.21 |
1-subbridging | 2.21 | 1.50 | –0.63 | –51.67 | –62.98 | –44.09 |
2-bridging | 2.58 | 0.43 | –0.88 | –8.38 | –12.66 | |
2-in-plane | 2.44 | –5.51 | –2.95 | –157.96 | –39.62 | |
2-subbridging | 2.52 | 0.18 | –0.41 | –3.99 | –81.19 |
Table3.
Changes of surface energy, surface stress and surface elasticity induced by different types of oxygen vacancies. The units are eV/
Table options
-->
Download as CSV
Oxygen vacancy | $ Deltagamma $ | $ Deltasigma_{11} $ | $ Deltasigma_{22} $ | $ Delta S_{1111} $ | $ Delta S_{2222} $ | $ Delta S_{1122} $ |
1-bridging | 2.17 | 0.51 | –1.66 | –2.42 | –29.36 | –14.76 |
1-in-plane | 2.40 | –5.02 | –2.73 | –151.01 | –34.03 | –53.21 |
1-subbridging | 2.21 | 1.50 | –0.63 | –51.67 | –62.98 | –44.09 |
2-bridging | 2.58 | 0.43 | –0.88 | –8.38 | –12.66 | |
2-in-plane | 2.44 | –5.51 | –2.95 | –157.96 | –39.62 | |
2-subbridging | 2.52 | 0.18 | –0.41 | –3.99 | –81.19 |
By substituting the data in Table 3 into Eq. (2), a phase diagram can be obtained for the most stable oxygen vacancy in the first trilayer[11]. As shown in Fig. 5, the sub-bridging OV and the in-plane OV are the most favorable surface OV under the compressive and tensile biaxial strain, respectively. In contrast, the bridging OV is most favorable when a tensile strain is applied along
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-5.jpg'"
class="figure_img" id="Figure5"/>
Download
Larger image
PowerPoint slide
Figure5.
Phase diagram of the type of the energetically most favorable OV as a function of the external strain
It is worthy to mention that we did not realize until recently that the incipient ferroelectricity of TiO2 is also quite important for its surface properties. Under tensile strain, it tends to be more stable in the ferroelectric polarization state with lower symmetry[35-37]. However, we calculated the surface elasticity of OVs without intentionally reducing the symmetry. Therefore only if an OV could automatically break the symmetry, the tensile strain may drive the system to a polarization state[15]. We recently found that this occurs only when introducing an in-plane OV, whereas in the other cases the polarization state cannot be spontaneously reached although it is thermodynamically more stable under tensile strain. Therefore in more accurate calculations of the surface elasticity, one should take the polarization state into account.
5.
Diffusion kinetics of oxygen vacancies
The distribution of defects can also be influenced by the diffusion kinetics. We have extensively studied the diffusion properties of OVs in TiO2 and the effects of strain on the kinetics[12]. We found that the barrier is very high for an OV to directly hop along [001] direction, therefore the global energy barrier for an OV to diffuse either along [001] or [110] is determined by the path from the base planes to the apex positions of the Ti-O octahedrons. As shown in Fig. 6, this barrier decreases with increasing density of OV in the [001] direction. It indicates that the interaction between neighboring OVs facilitates the mobility of OVs in the bulk of TiO2.
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-6.jpg'"
class="figure_img" id="Figure6"/>
Download
Larger image
PowerPoint slide
Figure6.
(Color online) Energy profiles of OV pathways within the primitive cell of rutile TiO
When a strain is applied along [001] direction or biaxially along [100] and [010], it would not break the symmetry. In this case, we found that the diffusion barrier is reduced by tensile strain and enhanced by compressive strain. If, however, the strain is just applied in [110] and
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-7.jpg'"
class="figure_img" id="Figure7"/>
Download
Larger image
PowerPoint slide
Figure7.
(Color online) (a) Schematic of bulk OV diffusion along the [110] and
The diffusion barrier of OV on the surface is much lower than that of bulk OV. However, a highest diffusion barrier of OV occurs between the second trilayer and the third one, which hinders the OVs in bulk from diffusing to the surface[12]. Externally applied tensile strain can reduce the energy barrier of the subsurface OV diffusion, and help to improve the diffusion of OVs from bulk to surface[12].
The diffusion of OVs within the (110) surface is also anisotropic. As shown in Fig. 8, the surface bridging OV diffuses more rapidly along
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-8.jpg'"
class="figure_img" id="Figure8"/>
Download
Larger image
PowerPoint slide
Figure8.
(Color online) The strain-dependent diffusion barrier of the surface OV along [001] (Path I) and along
6.
Water adsorption and dissociation energy on s-TiO2(110)
Since the hydroxyl ions and protons introduced by water dissociation play key roles in most relevant surface reactions, the adsorption and dissociation of water on TiO2 surfaces have been extensively studied in the past years. We have found that the adsorption and dissociation of water on stoichiometric rutile (110) surface depend on both the coverage and the thin film thickness[14]. The adsorption energy was calculated as follows,
$$ E_{ m{M(D)}} = (E_{ m{w}}- E_{ m{s}})/2 - E_{{ m{H}}_2{ m{O}}}, $$ | (5) |
where
m{w}} $
m{s}} $
m{H}}_2{
m{O}}}$
m{M}} $
m{D}} $
m{D}}-E_{
m{M}} $
As shown in Fig. 9, both the adsorption and dissociation of water are energetically more favorable when the thin film has an odd O–Ti–O trilayers. Especially, when the adsorbed water has no neighboring one along the [001] direction, the dissociative water is more favorable on the TiO2(110) surface of a thin film with three trilayer. This can be easily understood by referring to Fig. 1(a), since the slab containing an odd number of layers is less stable and thus more reactive than the one of even number of layers. With increasing thickness of the thin film or increasing coverage of the water, both the adsorption and the dissociation of water become less favorable.
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-9.jpg'"
class="figure_img" id="Figure9"/>
Download
Larger image
PowerPoint slide
Figure9.
(Color online) Adsorption energies per water molecule in (a) molecular state and (b) dissociative state on the surface with different supercell size and different thickness
The adsorption of water is more energetically favorable on thin films under tensile strain. Besides, the dissociation barrier of the water also decreases with increasing tensile strain[14]. Furthermore, the odd–even oscillation of the dissociation energy is enhanced by compressive strain, while reduced and even reversed by tensile strain. It means that under moderate tensile strain, the dissociation of water is more favorable on thin films containing even numbers of trilayers. This can be understood from the thickness-dependent surface stress. As shown in Figs. 1(b) and 1(c), the surface stress of the (110) thin film are positive. Therefore, tensile strain should increases their surface energy and thus their surface reactivity.
7.
Adsorption and dissociation on reduced TiO2(110): Effect of strain via polarization
As mentioned above, the rutile TiO2 is a well-known incipient ferroelectric material. Previous theoretical studies suggested that the transition can occur under negative pressure or uniaxial strain. For the most stable TiO2(110) surface, spontaneous in-plane polarization is predicted to occur under tensile strain. This strain-induced in-plane polarization is expected to play roles in the surface reactivity of the TiO2(110) surface, which we have just explored[15].
By studying the adsorption of a series of molecules on the reduced TiO2(110) surface under tensile strain, we found that the stabilities of the polarized structure relative to the non-polarized one are determined by the surface doping caused by the charge transfer between the adsorbates and the surface. The polarized structure favors the surface adsorption, and vice versa, if the adsorbate captures extra electrons of the reduced TiO2 surface and introduces no additional holes. It is because the free carriers would screen the long-range Coulomb interactions and suppress the spontaneous polarization. The electrostatic interaction between the polar molecule and the in-plane polarization is of less importance relative to the effect of the surface doping.
The adsorbates we calculated were a series of chalcogen-containing molecules, including H2O, H2S, O2 and CO2, in molecular state and dissociative state. Since the molecular adsorption of H2S is unstable against partial dissociation, we only considered the adsorption of H2S in a partial dissociative or complete dissociative state, denoted respectively as (D
We calculated the total energies of reduced TiO2(110) after surface adsorption. The energies are denoted as
m{a}}^{
m{pl}} $
m{a}}^{
m{np}} $
m{a}} = E_{
m{a}}^{
m{pl}}-E_{
m{a}}^{
m{np}} $
m a}$
m r} $
m{a}} $
m{s}} $
m{r}} $
m{s}} $
m{r}} $
m{s}} $
m{r}} $
m{s}} $
In order to understand the difference between the two different categories of adsorbates, the density of states (DOS) of r-TiO2(110) with different adsorbates were compared. We found that the structures have similar
m{a}} $
m{r}} $
m{s}} $
In order to further verify the conclusion, we charged the polarized and non-polarized s-TiO2(110) surface by simply adding and removing electrons, and then calculated the energy difference
m{s}} $
m{s}} $
m{r}} $
m{a}} $
m{r}} $
m{a}} $
m{r}} $
m{a}} $
m{s}} $
m{a}} $
m s}$
onerror="this.onerror=null;this.src='http://www.jos.ac.cn/fileBDTXB/journal/article/jos/2020/9/PIC/20060025-10.jpg'"
class="figure_img" id="Figure10"/>
Download
Larger image
PowerPoint slide
Figure10.
(Color online) The change of the total energy of the s-TiO2(110) surface induced by the in-plane polarization under strain along
8.
Summary
In this paper, we have reviewed our work within recent ten years on the strain engineering of TiO2 surface properties. We found that when suitable external strain is applied in specific directions, the surface and bulk properties undergo a significant change, due to the difference in the elastic properties of different surface structures. We thus propose that the external strain is a good way to engineer the physical and chemical properties of TiO2 and to further improve the catalytic reactivity. We hope our work will stimulate more experimental studies.
Acknowledgements
The numerical calculations were carried out at the High Performance Computing Center of Nanjing University. This work was supported by the National Natural Science Foundation of China (Grants No. 11974164).