The Vibrational Spectroscopy of the Valence Bonds of Cu-Doped TiO2 Using Electronegativity Principle Quantitative Calculations

*e purpose of this study is to investigate the influence of Cu on TiO2 phase transformation and regioselectivity. TiO2 samples doped with different amounts of Cu ions were synthesized by the sol-gel method. *e phase and vibrational mode were characterized by X-ray diffraction (XRD), Fourier infrared spectroscopy (FTIR), and transmission electron microscope (TEM). *e XRD phase analysis shows that the lattice parameters have not changed after Cu incorporation. In addition, the content of rutile increased obviously after Cu doping. *is indicated that the addition of Cu obviously promoted the transformation from anatase phase to rutile phase. *e vibration frequencies were calculated based on the principle of electronegativity. All types of bonds were qualitatively and quantitatively analyzed. *e content of TiA-O, TiR-O, and H-O in the undoped TiO2 samples is 23.87%, 16.30%, and 7.41%, respectively. In the same way, the content of TiA-O, TiR-O, H-O, CuA-O, and Cu i R-O in the 2.5mol% Cu-doped TiO2 samples is 21.23%, 18.56%, 7.34%, and 0.98%, respectively. For the 5mol%Cu-doped TiO2 samples, the content of TiA-O, TiR-O, H-O, CuA-O, Cu i R-O, Cu s A-O, and Cu s R-O is 18.75%, 20.11%, 7.47%, 2.56%, 3.9%, 1.55%, and 2.35%, respectively. Cu was not present at substitutional sites in the 2.5mol% doped sample, but Cu was present in the 2.5mol% doped sample. It is indicated that Cu was more likely to exist in the form of interstitial position in the TiO2 lattice, with the number of Cu atoms in the interstitial position reaching saturation, and this forced Cu to replace Ti. *e TEM shows that the stripes of different periods and orientations overlapped each other to form the Moiré patterns. In addition, the diffraction patterns of the Moiré image were slightly different from that of the matrix. *e Cu replaced Ti position and the Cu atoms mixed into interstitial sites in the TiO2 lattice. *e theoretical calculation was consistent with the experimental results.


Introduction
e advantages of titanium dioxide include nontoxic, stable chemical properties and high photocatalytic activity [1]. However, the low quantum yield and difficulty in separation and recovery under visible light irradiation limit its further development as a photocatalyst [2]. To improve the photo efficiency of the electronic process as well as the response into the visible part of the spectrum, TiO 2 doping with noble metal doping [3], composite semiconductors [4], and transition metal doping [5] have been widely employed. In addition, the effect of doping on the activity also depends on other factors, such as the method of doping and the concentration of dopant [6].
Recently, Cu-doping has been increasingly investigated as a dopant for titania. Byrne et al. [7] studied Cu-doped rutile and anatase. e results show the formation of charge compensating oxygen vacancies and a Cu 2+ oxidation state. D. M. Tobaldi [8] studied Cu-TiO 2 hybrid nanoparticles exhibiting tunable photochromic behavior. is retards the anatase-to-rutile phase transition and titania domain growth through a grain-boundary pinning mechanism. ese hybrid nanoparticles show tunable photochromic behavior under both UVA and visible light. However, there are few works of literatures about the qualitative and quantitative analysis of Cu-doped TiO 2 . We will conduct a quantitative and qualitative analysis of Cu-doped TiO 2 by electronegative principle. In our previous work, the (Fe, N) Co-doped TiO 2 infrared spectrum is calculated by the principle of electronegativity [8] and demonstrated qualitatively that N enters the TiO 2 lattice and substitutes O, forming the Ti-N structure; Fe iron enters the TiO 2 lattice and substitutes Ti, forming the Fe-O structure. When both N and Fe substitutions occurred simultaneously, they resulted in the Fe-N structure. ese valence bond structures and the original Ti-O bond structure in anatase and rutile together formed a wide band of IR absorption, which was consistent with the actual IR test results.
In this work, Cu-doped and undoped TiO 2 samples were prepared with the sol-gel method. e crystalline phase and IR spectra of the samples were characterized by X-ray diffraction and Fourier infrared spectroscopy (FTIR). e XRD phase analysis showed that the addition of Cu promoted the transformation of anatase phase to rutile phase, but only at the level of qualitative analysis. By infrared spectroscopy and combining the principle of electronegativity, the doping of Cu was further quantitatively analyzed.

Sample Preparation.
e formula A was prepared by mixing 0.982 g of copper acetate and 16 mL of distilled water, and the formula B was prepared by mixing 1.585 g of citric acid and 16 ml of distilled water. After stirring at 50°C for 5 min, formula B was dropped into the prepared formula A. 2 ml of Tetrabutyl titanate and 16 ml of 30 mol% sodium hydroxide solution was added to the mixture of formula A and B, which was stirred at 25°C for 1 hour. Finally, the solution was put into a vacuum drying oven for 60°C and 6 hours. e formed solid was ground to make a powder.

Characterization.
e Cu-doped and undoped TiO 2 systems were characterized by FT-IR, XRD, and TEM, and the Instrument parameters as shown in Table 1.

Experiment Principles.
e motion of two particles under interaction is the relative motion of one particle relative to another. At this point, the quality of the quality point should be changed to the reduced mass [9][10][11][12][13]. For the convenience of calculation, the atoms of the bond can be regarded as the interaction between the particle points. e reduced mass μ could be expressed as follows: In equation (1), m 1 and m 2 are relative atomic mass. e m Ti is 47.87, m Cu is 55.845, and m O is 16.00. In practice, nonharmonic motion is dominant. e anharmonic vibrational problem is usually solved by using second-order perturbation theory with a harmonic reference wave function, often with some treatment of Fermi resonances [10]. e geometrical component of anharmonic motion is considered as a combination of multiple simple harmonic motions. According to classical mechanics, the stretching force constant k and frequency υ satisfy the following relation [14][15][16][17]: In equation (2), the unit of υ is cm −1 . e VSCF (vibrational density of states) can easily quantize to a simple harmonic oscillator. In the VSCF method, the analysis of anharmonic interaction comprises coupling between different modes of vibration. e VSCF algorithm is based on the approximation of separability and the total vibrational wave function is described by a product of single mode wave functions [18][19][20][21]. By calculating the simple harmonic motion in a single direction, Jun-yu Chen [13] proposed the following relationship between the force constants and electronegativity: In equation (3), k is the stretching force constant, d is the bond length, N is the bond order, and Xa and Xb are the electronegativities of the atoms at both ends of the bond (k unit: dynes/cm10 −5 , d unit:Å). e values of m are 1.84 for stable molecules [22][23][24][25]. e bond order N could be calculated as follows: N� (total number of electrons in a stable structure -total number of valence electrons)/2; the calculation yields a bond order of 0.5. By looking up the electronegativity table, the following values are obtained [26]: X Ti � 1.54, X O � 3.44, and X Cu � 1.90. Figure 1 is the structural model of TiO 2 . From the periodic arrangement, it can be seen that it constitutes multiple oxygen octahedral structure units, and so only the model of a single cell structure needs to be discussed. e basic unit in the structure of both rutile and anatase TiO 2 is oxygen octahedral. e subscript of the element symbol represents the position of this atom. e number between the two atoms represents the bond length. For instance, Ti A represents that Ti atom is in Titanium lattices of anatase TiO 2 .

Cu-Doped TiO 2 Structure Model. Figures 2(a) and 2(b)
show that in the anatase, Cu atoms replace Ti atoms in the substitutional sites or occupy the interstitial sites. e numbers between the two atoms indicate that the bond distance between two atoms (unit:Å).

X-Ray Diffraction
Analysis. XRD patterns of undoped TiO 2 , 2.5 mol% Cu-doped TiO 2 , and 5 mol% Cu-doped TiO 2 by the sol-gel technique are shown in Figure 3. e calcination temperature of Cu-doped TiO 2 samples at 550°C. According to the standard diffraction cards [15], the results show that only existing rutile and anatase phases in the TiO 2 and Cu-doped TiO 2 samples, because brookite phase is unstable, there existed transition from brookite to anatase [27][28][29]. In Figure 3, four peaks corresponding to (101) A , (004) A , (200) A, and (211) A planes of TiO 2 anatase phase are observed (PDF #21-1272); the formation of the rutile phase is confirmed by matching five peaks corresponding to (110) R , (101) R , (111) R , (211) R , and (220) R planes which match with data card (PDF #21-1276). It can be found that the content of rutile increased obviously after Cu doping. is indicates that the addition of Cu obviously promoted the transformation from anatase phase to rutile phase. In the section of the infrared spectrum, we will use the electronegativity principle to analyze it quantitatively. e lattice parameters of samples are calculated from the XRD patterns shown in Table 2. e addition of Cu cannot change the lattice parameters. is evidence is considered that a greater portion of the Cu 2+ ions is well-incorporated into the anatase and rutile TiO 2 lattice [17]. rough contact to bulk anatase and rutile TiO 2 , a small change in lattice constant has been observed for the Cu-doped TiO 2 samples as shown in Table 2. e reason for this might be due to the tensile strain in the lattice [30].   [31][32][33]. In the actual situation, the crystal structure of Cu-doped and undoped TiO 2 is continuously optimized. According to the electronegativity principle [34], the calculation results of all vibration frequencies are calculated in Table 3. In this part, by conducting full-spectrum analysis and predicting the patterns of Cu doping, Figure 4 In the next part, we will quantitatively analyze and prove it.

Low Wave Number Section of Infrared Spectroscopy
e d A is the substituted value into formula (3), and the stretching vibration frequencies of Ti-O in anatase and rutile were calculated by electronegativity principle. In Figure 5, After the position of various bonds was determined, we would use the FTIR peak fitting method [35] to analyze it quantitatively. In Figure 5, the proportion of each peak was calculated, the red curve is the fractal fitting calculation, and the black curve is the actual measurement, and the fitting rate is 99.87%. Table 4 counts the content of bonds. It indicated that there were three types of bonds; the content of Ti A -O, Ti R -O, and H-O is 23.87%, 16.30%, and 7.41%, respectively. In the 550°C and undoped TiO 2 sample, the number of Ti A -O bonds is greater than that of Ti R -O bonds. Figure 6 shows that the infrared spectra of the 2.         It is shown that interstitial locations are more susceptible to Cu doping because Cu atoms are more inclined to form a spherical shell stable structure in the interstitial position of TiO 2 lattice. Moreover, with the increase of Cu doping content, the clearance position repulsive force increased; when the repulsion is increased to a certain value, Cu atoms of the interstitial position could replace the Ti atoms. Table 6 shows that infrared spectra of the 5 mol% Because the increase rate of Ti R -O is lower than that of 2.5 mol%Cu doping, so when Cu doping content is too high, the conversion efficiency of rutile from anatase to rutile would be reduced. In addition, whether the doping amount of Cu is 2.5 mol% or 5 mol%, the content of Cu R -O is always higher than that of Cu A -O, and the content of Cu i -O is more than Cu s -O. It is represented that in the anatase phase and rutile phase, Cu atoms are more likely to be mixed into interstitial sites and rutile phase.   e lattice parameters of undoped and Cu-doped samples are calculated from the XRD patterns. e lattice parameters remain unchanged, independent of Cu 2+ content. is evidently considered that a greater portion of the Cu 2+ ions is well-incorporated into the anatase and rutile TiO 2 lattice. e content of rutile increased obviously after Cu doping. is is indicated that the addition of Cu obviously promoted the transformation from anatase phase to rutile phase. Figure 8 is the TEM diagram of sintering at 550°C with 5%Cu-doped TiO 2 . According to Figure 8(a), the powder particles did not exceed 50 nm when the 5 mol%Cudoped TiO 2 samples were sintered at 550°C. In addition, the agglomeration samples were serious, which made many small particles formed into large particles. Figure 8(b) shows that the stripes of different periods and orientations overlapped each other to form the Moiré patterns [36,37]. In addition, the diffraction patterns of the Moiré image were slightly different from that of the matrix. It explains that the stretching vibration frequencies were changed by the Cu replaced Ti position and the Cu atoms mixed into interstitial sites in the TiO 2 lattice. e Cu-doped TiO 2 sample is characterized by FT-IR and TEM and calculated by electronegativity principle, and the theoretical calculation is consistent with the experimental results.

Conclusion
e XRD phase analysis shows that the lattice parameters have not changed after Cu incorporation. In addition, the content of rutile increased obviously after Cu doping. is is indicated that the addition of Cu obviously promoted the transformation from anatase phase to rutile phase. By all and low wavenumber section of infrared spectroscopy, we find that when the doping amount of Cu is 2.5 mol%, the content of Ti A -O bonds is decreased by 2.64%, the content of Ti R -O is increased by 2.26%, and the content of H-O bond is slightly changed. When the doping amount of Cu is 5 mol%, the content of Ti A -O decreased by a further 2.48%, the content of Ti R -O increased by a further 1.55%, the content of Cu i A -O increased by a further 1.58%, the content of Cu i R -O increased by a further 2.56%, the content of Cu s A -O decreased by a further 0.57%, the content of Cu s R -O increased by a further 1.01%, and the content of H-O bond is slightly changed. It quantitatively proved that the addition of Cu promoted the transformation from anatase phase to rutile phase. e incorporation of Cu has no effect on H-O bonds. When the doping amount of Cu is 2.5 mol%, the conversion efficiency is 2.26%. When the doping amount of Cu is 5 mol%, the conversion efficiency is 1.55%.
is is explained that Cu atoms were more easily to be doped into rutile phase. e efficiency is that the quoted values refer to increases in the percentage content of rutile.

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

Conflicts of Interest
e authors declare that they have no conflicts of interest.