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Advances in Materials Science and Engineering
Volume 2018, Article ID 9086195, 10 pages
https://doi.org/10.1155/2018/9086195
Research Article

Simulation Calculation and Analysis of Electronic Structure and Electrical Properties of Metal-Doped SnO2

Province-Ministry Joint State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China

Correspondence should be addressed to Hui-Ling Kang; moc.361@95895122251

Received 25 March 2018; Revised 12 July 2018; Accepted 14 August 2018; Published 9 September 2018

Academic Editor: Fernando Rubio-Marcos

Copyright © 2018 Jing-Qin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

SnO2 is an almost insulated semiconductor material, which increases the contact resistance of the AgSnO2 electrical contact material. Therefore, by improving the electrical performance of SnO2, the electrical properties of the AgSnO2 can be optimized. The first principle method based on density functional theory is used to calculate the electronic structure, formation energy, band structure, density of states, and differential charge density of SnO2 doped with the metals Ti, Sr, Ge, Sb, and Ga. The results show that metal-doped SnO2 materials are still direct bandgap semiconductor materials, and the effect of the electronic states of the metallic elements enhances the localization of the energy band, decreases the bandgap, increases the carrier concentration at the Fermi level, and enhances the electrical performance of the materials, and the bandgap of Ga-doped SnO2 is the smallest, 0.041 eV. And the charge transfer between Sb, Sr, Ga, Ti, and Ge metal atoms and O atoms increases, especially between Ga atom and O atom; that is, the electrical performance of Ga doping is better.

1. Introduction

As a new type of pollution-free contact material, AgSnO2 is the most promising to replace the toxic AgCdO, and it is widely used in low-voltage electrical appliances such as relay and circuit breaker because of its good resistance to welding and erosion [1]. And the material is a mixture of Ag and SnO2, with Ag as the main component and SnO2 as the auxiliary material to enhance the viscosity of the silver liquid and prevent the splash of Ag droplets. However, SnO2 is a kind of the wide bandgap semiconductor material with a bandgap value of 3.6 eV [2, 3], which is the main reason for increasing the contact resistance of AgSnO2 material; therefore, improving the electrical performance of SnO2 has become an urgent problem to be solved. Studies have shown that the doping of metals, metal oxides, or rare earth elements in SnO2 can enhance the electrical performance of SnO2 [4, 5], thereby achieving the purpose of optimizing the electrical properties of AgSnO2.

In recent years, scholars have done a lot of research on the doping modification of SnO2. Shan Lin-ting et al. prepared Ce-Cu codoped SnO2 nanopowders by the sol-gel method and studied the influence of doping on the electronic structure and photoelectric properties of SnO2 by first principles; the results showed that the bandgap was reduced by Ce-Cu codoping, and the electrical properties of SnO2 were improved [6]; Liu calculated the band structure and state density of Bi-, Cu-, Ni-, Co-, and Ti-doped SnO2 by CASTEP software and showed that several doped elements can improve the electrical performance of SnO2, and the best doping element is Bi [7]; Liu et al. prepared SnO2-TiO2 powder by the sol-gel method and prepared Ag-SnO2-TiO2 contact material by electroplating and showed that the conductivity of the Ag-SnO2-TiO2 contact material was 66.9% IACS and the density was 9.63 g/cm3 which were higher than the national standard, indicating that TiO2 doping improved the electrical performance of AgSnO2 [8]; Wang et al. studied the electronic structure, band structure, and optical properties of Fe and Mn codoped SnO2 by first principles and concluded that after the Fe and Mn codoping, the material exhibited semimetallic properties [9]. However, at present, the theoretical calculation and analysis of Sr-, Ti-, Sb-, Ge-, and Ga-doped SnO2 are rarely reported.

In this research, a 2 × 2 × 2 SnO2 supercell model was built and the electronic structure, energy band structure, state density, differential charge density of Sr-, Ti-, Sb-, Ge-, and Ga-doped SnO2 were calculated by the supersoft pseudopotential method in the first principle, and the best doping element to improve the electrical performance of SnO2 was also analyzed. Then, the metal-doped SnO2 powder materials were prepared by the sol-gel method, and the metal-doped Ag-SnO2 contact materials were prepared by powder metallurgy. Finally, the conductivity of metal-doped Ag-SnO2 contact materials was tested. The research provides theory and data support for further study, and a feasibility method for the study of AgSnO2 contact material.

2. Crystal Cells and Calculation Method of Metal-Doped SnO2 Materials

Figure 1 shows the crystal structures of intrinsic SnO2. The intrinsic SnO2 derived directly from the structure library of Materials Studio is a tetragonal rutile structure with the lattice constants of a = b = 4.737 Å, c = 3.816 Å, and α = β = γ = 90° [1012], and it contains two Sn atoms and four O atoms. The two Sn atoms occupy the center and vertex of the tetrahedron. The four O atoms are located in the tetrahedron and the surface, respectively. In this research, a supercell model of 2 × 2 × 2 SnO2 was established, and in order to analyze the influence of Sb, Sr, Ga, Ti, and Ge doping on the electric performance of SnO2, the 2 × 2 × 2 doped models were established by using the Sb, Sr, Ga, Ti, and Ge atoms to replace a Sn atom so that the doping ratio is 6.25%, and this ratio has reached a relatively good doping ratio verified by the research group. Therefore, this doping ratio is directly adopted herein.

Figure 1: Intrinsic SnO2 model.

The electronic structure, formation energy, band structure, density of states, and differential charge densities of Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2 are calculated by using the CASTEP module in Materials Studio 7.0 software based on the density functional theory. And the calculation process is divided into two parts. Firstly, the supersoft pseudopotential algorithm is used to optimize the models of Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2 to obtain the structural parameters and the stable structure with the lowest energy. Then, the energy of the optimized structure is calculated by using the generalized gradient approximation (GGA), the interaction between the valence electron and the real ion is approximately described by the supersoft pseudopotential, and the band structure, density of states, and differential charge density are obtained.

In order to make Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2 calculation results comparable, the parameters used for the calculation are set to be consistent. The calculation parameters are set as follows: the energy cutoff of the plane wave is selected as 340 eV, the self-consistent field (SCF) convergence rate is 2.0 × 10−6 eV/atom, the number of self-consistent convergence is 200 times, and the Brillouin region k-grid is selected as 3 × 3 × 4, and the electron energy as 1.0 × 10−5 eV/atom. The calculation process is carried out in the reciprocal space [13, 14], and the valence-electron configurations are chosen as Sn:5s25p2, O:2s22p4, Sb:5s25p3, Sr:4p65s2, Ga:3d104s24p1, Ti:3p63d24s2, and Ge:4s24p2.

3. Analysis of the Calculation Results of Metal-Doped SnO2 Materials

3.1. Analysis of Crystal Structure and Formation Energy

Table 1 shows the crystal cell after the optimization of Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2. It can be seen from the optimized data that after Sb, Sr, Ga, Ti, and Ge doping, the lattice parameters a and c and the volume V are bigger than that of intrinsic SnO2, and this is because the ionic valence radii of the metals Sb, Sr, and Ti are both larger than that of the Sn ions [15, 16]. The common valence states and ionic radius of each metal are shown in Table 2. Although the ionic radii of the metals Ge and Ga are smaller than those of Sn ions, it can be seen from the change of the bond lengths between the atoms after doping the metal (x = Sb, Sr, Ga, Ti, and Ge), as shown in Figure 2(a), that the Ge-Sn bond and the Ga-Sn bond increase compared with the Sn-Sn bond, and the Sn-O bond is also increased compared with the Sn-O bond of pure SnO2, which is the primary cause for the growth of lattice parameters and volumes.

Table 1: Optimized unit cell parameters.
Table 2: Common valence states and ionic radii of doped metals.
Figure 2: (a) Bond length and (b) rate of change.

The Sr ionic radius is larger than that of Sn, and the ratio of bond length between atoms after Sr doping, as shown in Figure 2(b), is larger; therefore, the cell volume expansion is larger after doping the Sr metal element, and the cell volume expansion is relatively smaller after doping the remaining metal elements. The calculation results conform to the theoretical basis, indicating that the optimization results are effective, and the structure and method used to calculate are reasonable.

The formation energy Ef can be used to judge the difficulty of metal doping and the structural stability of metal-doped SnO2. And the larger the formation energy of metal doping is, the more difficult the metal doping is and the lower the stability is. Ef can be calculated by [17] the following equation:where is the total energy of the metal-doped SnO2 system, is the total energy of the pure SnO2 supercell system of the same size with the doping system, and and are the energies of each molecule of the stable metal phase; the calculation results of the formation energy Ef are shown in Figure 3. It can be seen that the formation energy Ef of Ti doping is the smallest (i.e., the stability is the best), followed by Ge, Sb, Ga, and Sr.

Figure 3: Formation energy of the metal-doped SnO2 system.
3.2. Analysis of the Energy Band Structure

Figures 4(a)4(e) show the band structure of Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2. The energy level above the Fermi surface (0 eV) is the conduction band, and the energy level below the Fermi surface is the valence band. It can be seen from the energy band structure of pure SnO2 in [18] that SnO2 belongs to the direct bandgap semiconductor material and the bandgap value of pure SnO2 is 1.003 eV. It is known from the semiconductor theory that the physical properties of materials are mainly determined by the energy bands near the Fermi surface; therefore, in this study, the energy bands near the Fermi surface are mainly analyzed. It can be seen from Figures 4(a)4(e) that after SnO2 is doped with Sb, Sr, Ga, Ti, and Ge metal elements, the top of the valence band and the bottom of the conduction band are still at point G; that is, Sb, Sr, Ga, Ti, and Ge metal element-doped SnO2 materials are still direct bandgap semiconductor materials. And compared with pure SnO2, the valence band near the Fermi surface is remarkably refined, and the number of energy levels in the valence band increases significantly, which increases the number of electrons that may transition in the valence band; the interaction between electrons is enhanced, and the electrical performance is enhanced. According to the studies of Jiang et al. [19], Lu et al. [20], and other scholars, we can see that the smaller the bandgap is, the better the electrical performance is; therefore, the electrical properties of Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2 are analyzed in detail from the bandgap.

Figure 4: Band structure of pure SnO2 and metal-doped SnO2. (a) Sb-doped SnO2. (b) Sr-doped SnO2. (c) Ga-doped SnO2. (d) Ti-doped SnO2. (e) Ge-doped SnO2.

As can be seen from Figure 4(a), after the Sb doping, the energy level of the conduction band shifts to the lower level and becomes denser than that of pure SnO2, mainly concentrated in the range of (0 eV∼5 eV) and the locality is enhanced, and the bottom of the conduction band moves downward crossing the Fermi surface. And the energy level of the valence band also becomes denser after Sb doping and moves slightly to the lower energy level. Therefore, after Sb doping, the bandgap between the valence band and the conduction band is reduced; that is, the bandgap value is smaller than that of pure SnO2. From Figures 4(b)4(e), it can be seen that after Sr, Ga, Ti, and Ge doping, the energy levels of the conduction band all move to the lower energy level, mainly concentrated in the range of (0 eV∼5 eV), and Ga doping causes the bottom of the conduction band cross the Fermi surface. And the valence band varies with the doping metal. After doping with Sr and Ga, as shown in Figures 4(b) and 4(c), respectively, the new energy levels appear in the valence band region of −15 eV∼−10 eV, and the Sr doping causes another new energy level to appear at −35 eV∼−30 eV, which makes the valence band broadened. After Ti doping, as shown in Figure 4(e), the new energy levels appear at −35 eV∼−30 eV and −60 eV∼−55 eV, making the valence band further broadened.

After the analysis of Sb, Sr, Ga, Ti, and Ge doping, the valence band levels become denser near the Fermi surface so that the locality is strengthened, and after Ti doping, the top of the valence band crosses the Fermi surface. Therefore, when SnO2 is doped with Sb, Sr, Ga, Ti, and Ge, the bandgap between the valence band and the conduction band is different; that is, the bandgap values are different. The calculated bandgap values are listed in Table 3.

Table 3: Metal-doped SnO2 bandgap parameters.

It can be seen from Table 3 that, in the given doped metal elements, the bandgap value after Ga doping is relatively smaller (i.e., the energy required for the electrons to be excited from the valence band to the conduction band is also smaller, and the electrical performance is relatively better), followed by Ge, Sr, Ti, and Sb.

3.3. Analysis of State Density

Figures 5(a)5(e) show the total state density and partial state density of Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2. As can be seen from the total state density of Figures 5(a)5(e), after Sb, Sr, Ga, Ti, and Ge doping, the peak value of the total state density becomes larger than that of pure SnO2 proposed in [18], indicating the localization of the energy band enhanced. And the energy levels of the conduction band move closer to the Fermi level, mainly concentrated in the region of 0 eV∼5 eV, and because of the doping of Sr and Ti, the new energy levels are formed; thus, the valence band is broadened.

Figure 5: State density of pure SnO2 and metal-doped SnO2. (a) Sb-doped SnO2. (b) Sr-doped SnO2. (c) Ga-doped SnO2. (d) Ti-doped SnO2. (e) Ge-doped SnO2.

It can be seen from Figure 5(a) that after the Sb doping, the contribution of the 2p electronic state of O and the 5p electronic state of Sn is reduced compared with pure SnO2; however, because of the contribution of the 5s and 5p electronic states of Sb, the bottom of the conduction band crosses the Fermi surface, and the 5s electronic state of Sb and the 5s electronic state of Sn occur orbital hybridization at the Fermi surface. And in the region of the valence band, because of the contribution of 5s and 5p electronic states of Sb, the peak value of the total state density increases; therefore, the localization of the energy band is enhanced and the energy band becomes denser, especially the energy band near the Fermi surface. Therefore, after Sb doping, the movement of the valence band and the conduction band makes the bandgap value decrease. It can be seen from Figure 5(b) that after the Sr doping, the conduction band moves correspondingly closer to the Fermi surface because of the contribution of the 5s electronic state of Sr, and in the region of −1.8 eV∼0.2 eV, the 2p orbital of O hybridizes with the 5s, 4p orbitals of Sr; as a result, the concentration of carriers here increases. And because of the contribution of the 5s electronic state of Sr, the valence band region (−30 eV∼−31 eV) has a new energy level, which makes the valence band to broaden, and another new energy band appears in the region of −11.6 eV∼−13.2 eV because of the contribution of the 4p electronic state of Sr; the valence bands near the Fermi surface become denser, and the top of the valence band is closer to the Fermi surface because of the contribution of 5s and 4p electronic states of Sr; as a result, the bandgap is decreased. It can be seen from Figure 5(c) that after the Ga doping, the conduction band also moves closer to the Fermi surface because of the 4s and 4p electronic states contribution of Ga, and the movement is relatively larger such that the bottom of the conduction band crosses the Fermi surface; the hybridization occurs between the 2p electronic state of O and the 4s and 4p electronic states of Ga in the conduction band region so that the concentration of carriers increases. And in the valence band, a new energy band appears in the region of −13.8 eV∼−12.3 eV because of the main contribution of the 3d electronic state of Ga, and the other changes are similar to those in Figure 5(a); in general, the doping of Ga enhances the localization of the energy band. It can be seen from Figure 5(d) that after the Ti doping, the conduction band also moves closer to the Fermi surface because of the contribution of the 3d electronic state of Ti, while the valence band has two new energy bands due to the 3p and 4s electronic states of Ti, which causes the valence band to broaden, and the valence band becomes denser near the Fermi surface because of the 3d electronic state of Ti; thus, the bandgap decreases. The total state density of the Ge doping is similar to that of the Sb doping, as shown in Figure 5(e); however, the bottom of the conduction band does not cross the Fermi surface after the doping of Ge, and the 4s and 4p electronic states of Ge are hybridized with the 2p electronic states of O in the conduction band region, so the concentration of carriers also increases accordingly.

From the above analysis of the state density, it is found that after SnO2 is doped with Sb, Sr, Ga, Ti, and Ge, the contribution of the doped metals electronic states makes the movement degree of the conduction band and valence band different; therefore, the bandgap value is decreased to a different degree, which is in accordance with the energy band analysis results.

3.4. Analysis of Differential Charge Density

Figures 6(a)6(f) show the differential charge density of pure SnO2 and Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2. In this study, the differential charge density of the (0.7, 0.7, 0) cross section is taken. Figure 6(a) shows the differential charge density of pure SnO2, and the red region indicates the increases in the charge density, and the blue, green, and yellow regions indicate the decreases in the charge density. The distribution of the differential charge density around the O atom appears directionality, and this is because that the coupling of the 5s orbit of Sn and the 2p orbit of O; the Sn atom and O atom form a semiconductor by hybrid mode, and the isolated electrons of Sn atom enter the hybrid orbit to form the coordination bond, which strengthens the combination of the Sn atom and O atom; the gains and losses of electron between Sn atom and O atom are more compact; therefore, the distribution of the differential charge density appears directionality. From the differential charge density of pure SnO2, it can be seen that surrounding the Sn atom mainly gains electron, while the center of the Sn atom slightly losses electrons, and the center of the O atom losses electrons seriously, and surrounding the O atom gains electron, indicating that between the Sn atom and O atom are mainly ionic bonds with a certain covalent bond.

Figure 6: Differential charge density of pure SnO2 and metal-doped SnO2. (a) SnO2. (b) Sb-doped SnO2. (c) Sr-doped SnO2. (d) Ga-doped SnO2. (e) Ti-doped SnO2. (f) Ge-doped SnO2.

Figure 6(b) shows the differential charge density of Sb-doped SnO2, and the red-yellow region indicates the increases of the charge density, and the blue-green region indicates the decreases of the charge density. Compared with the differential charge density of pure SnO2, the distribution of the differential charge around the O atom and the Sn atom appears directionality after SnO2 is doped with Sb, and the charge density in the Sn-O bond direction decreases slightly, while the charge density in the Sb-O bond direction increases, indicating that the doping of Sb has a certain influence on the electronic structure of SnO2. Figure 6(c) shows the differential charge density of Sr-doped SnO2. The charge transfer between the Sn and O atoms around the Sr atom is not obvious; the Sr atom gains electron, and the O atom around the Sr atom losses electron, indicating that the doping of Sr also has a certain influence on the electronic structure of SnO2 and making it a shallow acceptor. Figure 6(6) shows the differential charge density of Ga-doped SnO2. The distribution of the differential charge density of the Ga atom and its surrounding O atoms all appears directionality, and this is because of the hybridization between the 4s and 4p electronic states of Ga and the 2p electronic states of O, making the isolated electrons of the O atom to enter the hybrid orbital to form the coordination bond; thus the combination and the gains and losses of electron between the Ga atom and the O atom are more compact, so the distribution of the differential charge density appears directionality. However, the distribution of the differential charge density of the Sn atom does not appear the directionality, which indicates that the charge density in the direction of Ga-O bonds increases and the charge density in the direction of the Sn-O bonds decreases; that is, the charge transfer degree on the Ga-O bonds is larger, so the conductive property of SnO2 is enhanced. Figure 6(e) shows the differential charge density of Ti-doped SnO2. The distribution of the differential charge density of the Ti atom also appears directionality, and the center of Ti atom gains electron, while the center of O atom losses electron. And comparing the differential charge density around the Ti atom and the Sn atom, it is known that the charge density around the Ti atom is larger than that of the Sn atom, indicating that the charge transfer on the Ti-O bonds is stronger than that on the Sn-O bonds; the electrical performance is improved. Figure 6(f) shows the differential charge density of Ge-doped SnO2. The center of the O atom losses electrons, and its surrounding gains electron, while the center of the Ge atom gains electrons, and its surrounding losses electron, comparing the differential charge density around Ge and Sn atoms. The number of the Ge atom losing electron is more than that of the Sn atom, so the charge transfer between the Ge atom and the O atom is more intense, thus improving the electrical performance of SnO2.

From the above analysis, it can be seen that the electrical performance can be improved after SnO2 is doped with Sb, Sr, Ga, Ti, and Ge , and the degree of charge interaction between Ga and O atoms is the strongest, followed by Ge, Sr, Ti, and Sb.

4. Experimental Verification of Metal-Doped AgSnO2

In this study, firstly, the sol-gel method was used to prepare the powder materials of Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2; therefore, Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2 materials are more proximate to the built structures used in the simulation calculation. And the X-ray diffraction experiment of metal-doped SnO2 materials was carried out, and the Sr-doped SnO2 powder material prepared by the sol-gel method is taken as an example to carry out the XRD phase analysis and to illustrate that the sol-gel method can make the doping element into SnO2 structure. The XRD diagrams are shown in Figure 7. It can be seen that the diffraction peak is basically similar to that of pure SnO2, and the intensity of the diffraction peak is reduced, which indicates that the Sr2+ infiltrates into SnO2 structure. And the diffraction angle of the three diffraction peaks marked in the figure is basically similar to that of pure SnO2, indicating that Sr doping has almost no effect on the SnO2 crystal structure and achieves better gap doping.

Figure 7: X-ray diffraction experimental diagram of pure SnO2 and Sr-doped SnO2 powder.

Then, the metal-doped Ag-SnO2 contact materials were obtained by the powder metallurgy technology, and this technology will not change the phase structure; the material ratio is Ag : Sn0.9375X0.0625O2 = 88 : 12(x = Sb, Sr, Ga, Ti, Ge). And the preparation process is mainly divided into the following steps: mixing Ag powder and metal-doped SnO2 powder, initial pressing the mixed powder, initial sintering, second pressing, second sintering, and polishing treatment. Finally, the electrical conductivities of pure AgSnO2 and Sb-, Sr-, Ga-, Ti-, and Ge-doped AgSnO2 contact materials were measured by the conductivity tester, and the conductivity of each metal-doped system is tested five times, and then the average value is obtained. The data are shown in Table 4.

Table 4: Conductivity.

It can be seen from the data that the conductivity of AgSnO2 contact material is 50.36%IACS, which is basically consistent with the conductivity data 50.84 %IACS of AgSnO2 contact material measured by Wang et al. [21]. And comparing the above data with the national standard value 54% IACS of AgSnO2 contact material, it can be seen that Sb, Sr, Ga, Ti, and Ge doping can improve the electrical performance of AgSnO2 contact material, and the metal Ga doping has the best improvement effect, followed by Ge, Sr, Ti, and Sb, which further verified the accuracy of the simulation calculation. This study initially proves that the first-principles calculation method can be used to calculate the electrical performance of the materials and to guide the test results.

5. Conclusion

In this study, the first principles based on the density functional theory is used to calculate the energy band structure, density of states, and the differential charge density of pure SnO2 and Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2. And Sb-, Sr-, Ga-, Ti-, and Ge-doped SnO2 powders were prepared by the sol-gel method, and then the metal-doped AgSnO2 contact materials were prepared by the powder metallurgy technology; the conductivity was tested. The conclusion reveals that after SnO2 doping with the metals Sb, Sr, Ga, Ti, and Ge, the bandgap decreases and the energy bands are concentrated near the Fermi surface, thus the locality is enhanced. The number of electrons that may transition on the valence band increases, and the interaction between electrons is enhanced; that is, the energy required for the carriers to transition from the valence band to the conduction band is reduced, and the electrical performance is improved. The bandgap of Ga-doped SnO2 is the smallest, that is, 0.041 eV. And after the doping of the metals Sb, Sr, Ga, Ti, and Ge, the charge transfer between Sn and O atoms decreases, while the charge transfer between the metal atoms Sb, Sr, Ga, Ti, Ge, and O increases, especially between Ga and O atoms, so the electrical performance of Ga doping is relatively better. And the conductivity of metal-doped AgSnO2 is higher than the national standard, and the conductivity of Ga doped is the largest, that is, 59.30% IACS, which indicates that Sb, Sr, Ga, Ti, and Ge doping improves the electrical performance of AgSnO2, thus verifying the correctness of the simulation results. This research provides a feasible method and a reference for the study of AgSnO2 contact materials.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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