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

Authors: Ji-Kang Yan; Jun-Yu Chen; Guo-You Gan
Journal: Journal of Spectroscopy
 (2020)

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## Abstract

The purpose of this study is to investigate the influence of Cu on TiO2 phase transformation and regioselectivity. TiO2 samples doped with different amounts of Cu2+ ions were synthesized by the sol-gel method. The phase and vibrational mode were characterized by X-ray diffraction (XRD), Fourier infrared spectroscopy (FTIR), and transmission electron microscope (TEM). The 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. This indicated that the addition of Cu obviously promoted the transformation from anatase phase to rutile phase. The vibration frequencies were calculated based on the principle of electronegativity. All types of bonds were qualitatively and quantitatively analyzed. The 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, CuAi-O, and CuRi-O in the 2.5 mol%Cu-doped TiO2 samples is 21.23%, 18.56%, 7.34%, and 0.98%, respectively. For the 5 mol%Cu-doped TiO2 samples, the content of TiA-O, TiR-O, H-O, CuAi-O, CuRi-O, CuAs-O, and CuRs-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 2.5 mol% doped sample, but Cu was present in the 2.5 mol% 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. The 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. The Cu replaced Ti position and the Cu atoms mixed into interstitial sites in the TiO2 lattice. The theoretical calculation was consistent with the experimental results.


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## Body

## 1. Introduction

The 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, TiO2 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. The results show the formation of charge compensating oxygen vacancies and a Cu2+ oxidation state. D. M. Tobaldi [8] studied Cu–TiO2 hybrid nanoparticles exhibiting tunable photochromic behavior. This retards the anatase-to-rutile phase transition and titania domain growth through a grain-boundary pinning mechanism. These 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 TiO2. We will conduct a quantitative and qualitative analysis of Cu-doped TiO2 by electronegative principle. In our previous work, the (Fe, N) Co-doped TiO2 infrared spectrum is calculated by the principle of electronegativity [8] and demonstrated qualitatively that N enters the TiO2 lattice and substitutes O, forming the Ti-N structure; Fe iron enters the TiO2 lattice and substitutes Ti, forming the Fe-O structure. When both N and Fe substitutions occurred simultaneously, they resulted in the Fe-N structure. These 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 TiO2 samples were prepared with the sol-gel method. The crystalline phase and IR spectra of the samples were characterized by X-ray diffraction and Fourier infrared spectroscopy (FTIR). The 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.


## 2. Experimental Details

### 2.1. Sample Preparation

The 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. The formed solid was ground to make a powder.


### 2.2. Characterization

The Cu-doped and undoped TiO2 systems were characterized by FT-IR, XRD, and TEM, and the Instrument parameters as shown in Table 1.Table 1
Instrument parameters.
Equipment nameParametersFT-IR (Fourier transform infrared spectroscopy)Spectral range: 4000–400 cm−1Max resolution ratio: 0.0035 cm−1SNR (Signal to Noise Ratio): 50000 : 1XRDThe sample size:φ ≤ 350 mmExport: asc, raw, dat, and so on.TEMMagnification times: 80∼1000k timesResolution ratio: 0.15∼0.18 nmAcceleration voltage: 200 kV


### 2.3. Experiment Principles

The 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 [9–13]. For the convenience of calculation, the atoms of the bond can be regarded as the interaction between the particle points. The reduced mass μ could be expressed as follows:(1)1μ=1m1+1m2=m1+m2m1m2.In equation (1), m1 and m2 are relative atomic mass. The mTi is 47.87, mCu is 55.845, and mO is 16.00. In practice, nonharmonic motion is dominant. The 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]. The 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 [14–17]:(2)v=12πkμ.In equation (2), the unit of υ is cm−1. The 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. The 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 [18–21]. By calculating the simple harmonic motion in a single direction, Jun-yu Chen [13] proposed the following relationship between the force constants and electronegativity:(3)k=mNXaXbd23/4.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). The values of m are 1.84 for stable molecules [22–25]. The 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]: XTi = 1.54, XO = 3.44, and XCu = 1.90.


## 2.1. Sample Preparation

The 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. The formed solid was ground to make a powder.


## 2.2. Characterization

The Cu-doped and undoped TiO2 systems were characterized by FT-IR, XRD, and TEM, and the Instrument parameters as shown in Table 1.Table 1
Instrument parameters.
Equipment nameParametersFT-IR (Fourier transform infrared spectroscopy)Spectral range: 4000–400 cm−1Max resolution ratio: 0.0035 cm−1SNR (Signal to Noise Ratio): 50000 : 1XRDThe sample size:φ ≤ 350 mmExport: asc, raw, dat, and so on.TEMMagnification times: 80∼1000k timesResolution ratio: 0.15∼0.18 nmAcceleration voltage: 200 kV


## 2.3. Experiment Principles

The 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 [9–13]. For the convenience of calculation, the atoms of the bond can be regarded as the interaction between the particle points. The reduced mass μ could be expressed as follows:(1)1μ=1m1+1m2=m1+m2m1m2.In equation (1), m1 and m2 are relative atomic mass. The mTi is 47.87, mCu is 55.845, and mO is 16.00. In practice, nonharmonic motion is dominant. The 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]. The 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 [14–17]:(2)v=12πkμ.In equation (2), the unit of υ is cm−1. The 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. The 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 [18–21]. By calculating the simple harmonic motion in a single direction, Jun-yu Chen [13] proposed the following relationship between the force constants and electronegativity:(3)k=mNXaXbd23/4.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). The values of m are 1.84 for stable molecules [22–25]. The 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]: XTi = 1.54, XO = 3.44, and XCu = 1.90.


## 3. Results and Discussion

### 3.1. TiO2 Molecular Structure Model

Figure1 is the structural model of TiO2. 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. The basic unit in the structure of both rutile and anatase TiO2 is oxygen octahedral. The subscript of the element symbol represents the position of this atom. The number between the two atoms represents the bond length. For instance, TiA represents that Ti atom is in Titanium lattices of anatase TiO2.Figure 1
The structural model of TiO2; (a) the structural model of rutile; (b) the structural model of anatase.
(a)(b)


### 3.2. Cu-Doped TiO2 Structure Model

Figures2(a) and 2(b) show that in the anatase, Cu atoms replace Ti atoms in the substitutional sites or occupy the interstitial sites. Figures 2(c) and 2(d) show that in the rutile, Cu atoms are in the substitutional sites and interstitial sites. Doping substitutional and interstitial sites are constructed by using SDD (selection of configuration types in Gaussian optimization) configuration, GaussView, and Gaussian09w27. The information on bond length and the position of each atom is shown in Figure 2. The dashed line between Cu and O indicates that Cu can form O-Cu-O with two O atoms and can also form Cu-O with only an O atom. The lower right corner of the symbol indicated that atomic location number. The numbers between the two atoms indicate that the bond distance between two atoms (unit: Å).Figure 2
Cu-doped TiO2 structure model; (a) Cu replaced substitutional sites in the anatase; (b) Cu occupied interstitial sites in the anatase; (c) Cu replaced interstitial sites in the rutile; (d) Cu occupied substitutional sites in the rutile.
(a)(b)(c)(d)


### 3.3. X-Ray Diffraction Analysis

XRD patterns of undoped TiO2, 2.5 mol% Cu-doped TiO2, and 5 mol% Cu-doped TiO2 by the sol-gel technique are shown in Figure 3. The calcination temperature of Cu-doped TiO2 samples at 550°C. According to the standard diffraction cards [15], the results show that only existing rutile and anatase phases in the TiO2 and Cu-doped TiO2 samples, because brookite phase is unstable, there existed transition from brookite to anatase [27–29]. In Figure 3, four peaks corresponding to (101)A, (004)A, (200)A, and (211)A planes of TiO2 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. This 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. The lattice parameters of samples are calculated from the XRD patterns shown in Table 2. The addition of Cu cannot change the lattice parameters. This evidence is considered that a greater portion of the Cu2+ ions is well-incorporated into the anatase and rutile TiO2 lattice [17]. Through contact to bulk anatase and rutile TiO2, a small change in lattice constant has been observed for the Cu-doped TiO2 samples as shown in Table 2. The reason for this might be due to the tensile strain in the lattice [30].Figure 3
XRD patterns of the Cu-doped TiO2 samples with different doping concentrations at calcination temperature (550°C).Table 2
The lattice parameters of the Cu-doped TiO2 samples with different doping concentrations.
AnataseRutileCu2+ (mol%)d101 (Å)d004 (Å)d200 (Å)a = b (Å)c (Å)d101 (Å)d101 (Å)d101 (Å)d101 (Å)a = b (Å)c (Å)03.5172.3731.8913.7829.4933.7412.8692.4811.7844.5942.95333.5162.3741.8933.7879.4973.7442.8652.4871.7874.5972.95653.5142.3761.8943.7859.4963.7432.8612.4821.7884.5962.957


### 3.4. Full Wave Number Section of Infrared

#### 3.4.1. Spectroscopy

Figure4 shows the full wavenumber section of the infrared spectra of the undoped and Cu-doped TiO2 samples. TiA-O is Ti-O bonds in anatase. TiR-O is Ti-O bonds in rutile. CuAi-O is Cu replaced interstitial sites in the anatase. CuRi-O is Cu occupied interstitial sites in the rutile. CuAs-O is Cu replaced substitutional sites in the anatase. CuRs-O is Cu occupied substitutional sites in the rutile. Not all structures are symmetrical, and most of the TiO2 crystal structures are asymmetric. It caused the bond length to fluctuate within a range [31–33]. In the actual situation, the crystal structure of Cu-doped and undoped TiO2 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(b) indicates that the absorption peaks of TiA-O, CuAs-O, and CuAi-O are similar. When the doping amount of Cu is 2.5 mol%, the absorption peaks of TiA-O are narrower. Meanwhile, the absorption peaks of CuAi-O and CuAs-O appear in anatase lattice. Figure 4(c) indicates that when the doping amount of Cu is 5 mol%, the absorption peaks of CuRi-O and CuRs-O are to appear in rutile lattice. The transmittance of Cu-O bond decreased from T = 0.74 to T = 0.38. Meanwhile, the absorption peaks of TiR-O are also narrower. It is predicted that in the rutile and anatase phases, a part of Cu and O atoms by interstitial solid solution to form Cu-O bond, and another part of Cu replaces Ti atoms by substitutional solid solution to form Cu-O bond with O atoms in the TiO2 lattice. In the next part, we will quantitatively analyze and prove it.Figure 4
Full wave number section of the Infrared Spectra of the Cu-doped TiO2 samples with different doping concentrations at calcination temperature (550°C).(a) Undoped. (b) 2.5 mol%Cu. (c) 5 mol%Cu.
(a)(b)(c)Table 3
The vibration frequency range corresponding to the various bonds of undoped and Cu-doped TiO2 samples.
SampleTypes of the bondsThe bond lengthd (Å)Vibration frequency v (cm−1)Undoped TiO2TiA-O1.949 Å∼1.980450 cm−1∼67011001600TiR-O1.930 Å∼1.973710 cm−1∼8501410 cm−1∼15502.5 mol% Cu-doped TiO2TiA-O1.739 Å∼1.976440 cm−1∼68011001600TiR-O1.627 Å∼1.973680 cm−1∼8501370 cm−1∼1650CuiA-O1.327 Å∼1.527450 cm−1∼480CuiR-O1.284 Å∼1.428550 cm−1∼7205 mol% Cu-doped TiO2TiA-O1.729 Å∼1.966435 cm−1∼67511051605TiR-O1.627 Å∼1.973680 cm−1∼8501370 cm−1∼1650CuiA-O1.327 Å∼1.527450 cm−1∼480CuiR-O1.284 Å∼1.428550 cm−1∼750CusA-O1.276 Å∼1.958550 cm−1∼740CusR-O1.364 Å∼1.965450 cm−1∼820


### 3.5. Low Wave Number Section of Infrared Spectroscopy (400 cm−1∼1800 cm−1)

ThedA 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, the values of the vTiA−O (orange) are 454.25 cm−1, 508.54 cm−1, 548.17 cm−1, 580.35 cm−1, 620.9 cm−1, 670.1 cm−1, 1114.3 cm−1, and 1563.4 cm−1, respectively. The values of the vTiR−O (blue) are 716.7 cm−1, 765.65 cm−1, 823.66 cm−1, 1395.6 cm−1, 1459.5 cm−1, and 1513.7 cm−1, respectively. The values of the vH−O (green) were 1638.3cm−1and 1712.9 cm−1. 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 TiA-O, TiR-O, and H-O is 23.87%, 16.30%, and 7.41%, respectively. In the 550°C and undoped TiO2 sample, the number of TiA-O bonds is greater than that of TiR-O bonds.Figure 5
Infrared spectra of the undoped TiO2 samples at calcination temperature (550°C). (a) 400 cm−1∼1000 cm−1; (b) 1000 cm−1∼1800 cm−1.
(a)(b)Table 4
Infrared spectra of the undoped TiO2 samples with the content and vibrational frequency of valence bonds.
The type of bondsContent (%)Vibrational frequency (cm−1)TiA-O23.871563.4, 1114.3, 670.1, 620.9, 580.35, 548.17, 508.54, and 454.25TiR-O16.301513.7, 1459.5, 1395.6, 823.66, 765.65, and 716.7H-O7.411712.9, 1638.3Figure6 shows that the infrared spectra of the 2.5 mol%Cu-doped TiO2 samples. The fitting rate is 99.95%. The values of the vTiA−O (orange) are 458.99 cm−1, 509.79 cm−1, 541.21 cm−1, 574.02 cm−1, 623.11 cm−1, 666.94 cm−1, 1574.6 cm−1, and 1114.3 cm−1, respectively. The values of the vTiR−O (blue) are 710.29 cm−1, 748.65 cm−1, 796.48 cm−1, 848.4 cm−1, 1394.74 cm−1, 1458.5 cm−1, 1503.3 cm−1, and 1537.9 cm−1, respectively. The values of the vH−O (green) are 1633.4 cm−1 and 1680.9 cm−1. At the same time, there are two new bonds, the values of the vCuAi-o (dark cyan) are 489.74 cm−1 and the values of the vCuRi-o (pink) are 609.31 cm−1. In Table 5, the content of each peak was counted. It is indicated that there are five types of bonds. The content of TiA-O, TiR-O, H-O, CuAi-O, and CuRi-O is 21.23%, 18.56%, 7.34%, 0.98%, and 1.34%, respectively. By compared with the undoped TiO2, the content of TiA-O decreased by 2.64%, the content of TiR-O increased by 2.26%, and the content of the H-O bond is little changed. It quantitatively proved that the addition of Cu promoted the transformation of the anatase phase to rutile phase.Figure 6
Infrared spectra of the 2.5 mol%Cu-doped TiO2 samples at calcination temperature (550°C). (a) 400 cm−1∼1000 cm−1; (b) 1000 cm−1∼1800 cm−1.
(a)(b)Table 5
Infrared spectra of the 2.5 mol%Cu-doped TiO2 samples with the content and vibrational frequency of valence bonds.
The type of bondContent (%)Vibrational frequency (cm−1)TiA-O21.231574.6, 1114.3, 666.94, 623.11, 574.02, 541.21, 509.79, and 458.99TiR-O18.561537.9, 1503.3, 1458.5, 1394.74, 848.4, 796.48, 748.65, and 710.29H-O7.341680.9 and 1633.4CuiA-O0.98488.74CuiR-O1.34609.31The infrared spectra of the 5 mol% Cu-doped TiO2 samples in Figure 7. The fitting rate is 99.75%. The values of the vTiA−O (orange) are 454.71 cm−1, 489.7 cm−1, 509.93 cm−1, 533.05 cm−1, 579.11 cm−1, 586.76 cm−1, 628.09 cm−1, 671.26 cm−1, 712.85 cm−1, 797.43 cm−1, 843.36 cm−1, 1114.3 cm−1, and 1562.7 cm−1, respectively. The values of the vTiR−O (blue) are 876.86 cm−1, 922.88 cm−1, 1331.8 cm−1, 1371.2 cm−1, 1393.4 cm−1, 1414.9 cm−1, 1449.4 cm−1, 1478.7 cm−1, 1517.3 cm−1, 1604.6 cm−1, respectively. The values of the vH−O (green) are 1636.6 cm−1and 1673.7 cm−1. The values of vCuAi-O (dark cyan) are 549.23 cm−1 and 606.28 cm−1. The values of the vCuAs-O (purple) are 734.82 cm−1 and 1533.5 cm−1. The values of the vCuRs-O (dark yellow) are 745.97 cm−1 and 1287.6 cm−1. When the doping amount of Cu is 2.5 mol%, there are only CuAi-O and CuRi-O, which are interstitial sites. When the doping amount of Cu is 5 mol%, the doping of substitution position occurred. 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 TiO2 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%Cu-doped TiO2 samples of the content of all kinds of bonds. There are seven types of bonds; the content of TiA-O, TiR-O, H-O, CuAi-O, CuiR-O, CusA-O, and CusR-O is 18.75%, 20.11%, 7.47%, 2.56%, 3.9%, 1.55%, and 2.35%. By contrast, the 2.5 mol%Cu-doped TiO2, the content of TiA-O decreased by 2.48%, the content of TiR-O increased by 1.55%, the content of CuAi-O increased by 1.58%, the content of CuRi-O increased by 2.56%, and the content of H-O bond is little changed. Because the increase rate of TiR-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 CuR-O is always higher than that of CuA-O, and the content of Cui-O is more than Cus-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.Figure 7
Infrared spectra of the 5 mol% Cu-doped TiO2 samples at calcination temperature (550°C). (a) 400 cm−1∼1000 cm−1; (b) 1000 cm−1∼1800 cm−1.
(a)(b)Table 6
Infrared spectra of the 5 mol%Cu-doped TiO2 samples with the content and vibrational frequency of valence bonds.
The type of bondContent (%)Vibrational frequency (cm−1)TiA-O18.751562.7, 1114.3, 843.36, 797.43, 773.15, 712.85, 671.26, 628.09, 586.76, 579.11, 533.05, 509.93, 489.7 and 454.71TiR-O20.111604.6, 1517.3, 1478.7, 1449.4, 1414.9, 1393.4, 1371.2, 1331.8, 922.88, and 876.86H-O7.471673.7 and 1636.6CuiA-O2.56606.28 and 549.23CuiR-O3.9819.88, 696.61, 648.81, and 454.61CusA-O1.551533.5 and 734.82CusR-O2.351287.6 and 745.97The lattice parameters of undoped and Cu-doped samples are calculated from the XRD patterns. The lattice parameters remain unchanged, independent of Cu2+ content. This evidently considered that a greater portion of the Cu2+ ions is well-incorporated into the anatase and rutile TiO2 lattice. The content of rutile increased obviously after Cu doping. This is indicated that the addition of Cu obviously promoted the transformation from anatase phase to rutile phase.Figure8 is the TEM diagram of sintering at 550°C with 5%Cu-doped TiO2. According to Figure 8(a), the powder particles did not exceed 50 nm when the 5 mol%Cu-doped TiO2 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 TiO2 lattice. The Cu-doped TiO2 sample is characterized by FT-IR and TEM and calculated by electronegativity principle, and the theoretical calculation is consistent with the experimental results.Figure 8
The TEM images of 5 mol% Cu-doped TiO2.


## 3.1. TiO2 Molecular Structure Model

Figure1 is the structural model of TiO2. 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. The basic unit in the structure of both rutile and anatase TiO2 is oxygen octahedral. The subscript of the element symbol represents the position of this atom. The number between the two atoms represents the bond length. For instance, TiA represents that Ti atom is in Titanium lattices of anatase TiO2.Figure 1
The structural model of TiO2; (a) the structural model of rutile; (b) the structural model of anatase.
(a)(b)


## 3.2. Cu-Doped TiO2 Structure Model

Figures2(a) and 2(b) show that in the anatase, Cu atoms replace Ti atoms in the substitutional sites or occupy the interstitial sites. Figures 2(c) and 2(d) show that in the rutile, Cu atoms are in the substitutional sites and interstitial sites. Doping substitutional and interstitial sites are constructed by using SDD (selection of configuration types in Gaussian optimization) configuration, GaussView, and Gaussian09w27. The information on bond length and the position of each atom is shown in Figure 2. The dashed line between Cu and O indicates that Cu can form O-Cu-O with two O atoms and can also form Cu-O with only an O atom. The lower right corner of the symbol indicated that atomic location number. The numbers between the two atoms indicate that the bond distance between two atoms (unit: Å).Figure 2
Cu-doped TiO2 structure model; (a) Cu replaced substitutional sites in the anatase; (b) Cu occupied interstitial sites in the anatase; (c) Cu replaced interstitial sites in the rutile; (d) Cu occupied substitutional sites in the rutile.
(a)(b)(c)(d)


## 3.3. X-Ray Diffraction Analysis

XRD patterns of undoped TiO2, 2.5 mol% Cu-doped TiO2, and 5 mol% Cu-doped TiO2 by the sol-gel technique are shown in Figure 3. The calcination temperature of Cu-doped TiO2 samples at 550°C. According to the standard diffraction cards [15], the results show that only existing rutile and anatase phases in the TiO2 and Cu-doped TiO2 samples, because brookite phase is unstable, there existed transition from brookite to anatase [27–29]. In Figure 3, four peaks corresponding to (101)A, (004)A, (200)A, and (211)A planes of TiO2 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. This 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. The lattice parameters of samples are calculated from the XRD patterns shown in Table 2. The addition of Cu cannot change the lattice parameters. This evidence is considered that a greater portion of the Cu2+ ions is well-incorporated into the anatase and rutile TiO2 lattice [17]. Through contact to bulk anatase and rutile TiO2, a small change in lattice constant has been observed for the Cu-doped TiO2 samples as shown in Table 2. The reason for this might be due to the tensile strain in the lattice [30].Figure 3
XRD patterns of the Cu-doped TiO2 samples with different doping concentrations at calcination temperature (550°C).Table 2
The lattice parameters of the Cu-doped TiO2 samples with different doping concentrations.
AnataseRutileCu2+ (mol%)d101 (Å)d004 (Å)d200 (Å)a = b (Å)c (Å)d101 (Å)d101 (Å)d101 (Å)d101 (Å)a = b (Å)c (Å)03.5172.3731.8913.7829.4933.7412.8692.4811.7844.5942.95333.5162.3741.8933.7879.4973.7442.8652.4871.7874.5972.95653.5142.3761.8943.7859.4963.7432.8612.4821.7884.5962.957


## 3.4. Full Wave Number Section of Infrared

### 3.4.1. Spectroscopy

Figure4 shows the full wavenumber section of the infrared spectra of the undoped and Cu-doped TiO2 samples. TiA-O is Ti-O bonds in anatase. TiR-O is Ti-O bonds in rutile. CuAi-O is Cu replaced interstitial sites in the anatase. CuRi-O is Cu occupied interstitial sites in the rutile. CuAs-O is Cu replaced substitutional sites in the anatase. CuRs-O is Cu occupied substitutional sites in the rutile. Not all structures are symmetrical, and most of the TiO2 crystal structures are asymmetric. It caused the bond length to fluctuate within a range [31–33]. In the actual situation, the crystal structure of Cu-doped and undoped TiO2 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(b) indicates that the absorption peaks of TiA-O, CuAs-O, and CuAi-O are similar. When the doping amount of Cu is 2.5 mol%, the absorption peaks of TiA-O are narrower. Meanwhile, the absorption peaks of CuAi-O and CuAs-O appear in anatase lattice. Figure 4(c) indicates that when the doping amount of Cu is 5 mol%, the absorption peaks of CuRi-O and CuRs-O are to appear in rutile lattice. The transmittance of Cu-O bond decreased from T = 0.74 to T = 0.38. Meanwhile, the absorption peaks of TiR-O are also narrower. It is predicted that in the rutile and anatase phases, a part of Cu and O atoms by interstitial solid solution to form Cu-O bond, and another part of Cu replaces Ti atoms by substitutional solid solution to form Cu-O bond with O atoms in the TiO2 lattice. In the next part, we will quantitatively analyze and prove it.Figure 4
Full wave number section of the Infrared Spectra of the Cu-doped TiO2 samples with different doping concentrations at calcination temperature (550°C).(a) Undoped. (b) 2.5 mol%Cu. (c) 5 mol%Cu.
(a)(b)(c)Table 3
The vibration frequency range corresponding to the various bonds of undoped and Cu-doped TiO2 samples.
SampleTypes of the bondsThe bond lengthd (Å)Vibration frequency v (cm−1)Undoped TiO2TiA-O1.949 Å∼1.980450 cm−1∼67011001600TiR-O1.930 Å∼1.973710 cm−1∼8501410 cm−1∼15502.5 mol% Cu-doped TiO2TiA-O1.739 Å∼1.976440 cm−1∼68011001600TiR-O1.627 Å∼1.973680 cm−1∼8501370 cm−1∼1650CuiA-O1.327 Å∼1.527450 cm−1∼480CuiR-O1.284 Å∼1.428550 cm−1∼7205 mol% Cu-doped TiO2TiA-O1.729 Å∼1.966435 cm−1∼67511051605TiR-O1.627 Å∼1.973680 cm−1∼8501370 cm−1∼1650CuiA-O1.327 Å∼1.527450 cm−1∼480CuiR-O1.284 Å∼1.428550 cm−1∼750CusA-O1.276 Å∼1.958550 cm−1∼740CusR-O1.364 Å∼1.965450 cm−1∼820


## 3.4.1. Spectroscopy

Figure4 shows the full wavenumber section of the infrared spectra of the undoped and Cu-doped TiO2 samples. TiA-O is Ti-O bonds in anatase. TiR-O is Ti-O bonds in rutile. CuAi-O is Cu replaced interstitial sites in the anatase. CuRi-O is Cu occupied interstitial sites in the rutile. CuAs-O is Cu replaced substitutional sites in the anatase. CuRs-O is Cu occupied substitutional sites in the rutile. Not all structures are symmetrical, and most of the TiO2 crystal structures are asymmetric. It caused the bond length to fluctuate within a range [31–33]. In the actual situation, the crystal structure of Cu-doped and undoped TiO2 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(b) indicates that the absorption peaks of TiA-O, CuAs-O, and CuAi-O are similar. When the doping amount of Cu is 2.5 mol%, the absorption peaks of TiA-O are narrower. Meanwhile, the absorption peaks of CuAi-O and CuAs-O appear in anatase lattice. Figure 4(c) indicates that when the doping amount of Cu is 5 mol%, the absorption peaks of CuRi-O and CuRs-O are to appear in rutile lattice. The transmittance of Cu-O bond decreased from T = 0.74 to T = 0.38. Meanwhile, the absorption peaks of TiR-O are also narrower. It is predicted that in the rutile and anatase phases, a part of Cu and O atoms by interstitial solid solution to form Cu-O bond, and another part of Cu replaces Ti atoms by substitutional solid solution to form Cu-O bond with O atoms in the TiO2 lattice. In the next part, we will quantitatively analyze and prove it.Figure 4
Full wave number section of the Infrared Spectra of the Cu-doped TiO2 samples with different doping concentrations at calcination temperature (550°C).(a) Undoped. (b) 2.5 mol%Cu. (c) 5 mol%Cu.
(a)(b)(c)Table 3
The vibration frequency range corresponding to the various bonds of undoped and Cu-doped TiO2 samples.
SampleTypes of the bondsThe bond lengthd (Å)Vibration frequency v (cm−1)Undoped TiO2TiA-O1.949 Å∼1.980450 cm−1∼67011001600TiR-O1.930 Å∼1.973710 cm−1∼8501410 cm−1∼15502.5 mol% Cu-doped TiO2TiA-O1.739 Å∼1.976440 cm−1∼68011001600TiR-O1.627 Å∼1.973680 cm−1∼8501370 cm−1∼1650CuiA-O1.327 Å∼1.527450 cm−1∼480CuiR-O1.284 Å∼1.428550 cm−1∼7205 mol% Cu-doped TiO2TiA-O1.729 Å∼1.966435 cm−1∼67511051605TiR-O1.627 Å∼1.973680 cm−1∼8501370 cm−1∼1650CuiA-O1.327 Å∼1.527450 cm−1∼480CuiR-O1.284 Å∼1.428550 cm−1∼750CusA-O1.276 Å∼1.958550 cm−1∼740CusR-O1.364 Å∼1.965450 cm−1∼820


## 3.5. Low Wave Number Section of Infrared Spectroscopy (400 cm−1∼1800 cm−1)

ThedA 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, the values of the vTiA−O (orange) are 454.25 cm−1, 508.54 cm−1, 548.17 cm−1, 580.35 cm−1, 620.9 cm−1, 670.1 cm−1, 1114.3 cm−1, and 1563.4 cm−1, respectively. The values of the vTiR−O (blue) are 716.7 cm−1, 765.65 cm−1, 823.66 cm−1, 1395.6 cm−1, 1459.5 cm−1, and 1513.7 cm−1, respectively. The values of the vH−O (green) were 1638.3cm−1and 1712.9 cm−1. 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 TiA-O, TiR-O, and H-O is 23.87%, 16.30%, and 7.41%, respectively. In the 550°C and undoped TiO2 sample, the number of TiA-O bonds is greater than that of TiR-O bonds.Figure 5
Infrared spectra of the undoped TiO2 samples at calcination temperature (550°C). (a) 400 cm−1∼1000 cm−1; (b) 1000 cm−1∼1800 cm−1.
(a)(b)Table 4
Infrared spectra of the undoped TiO2 samples with the content and vibrational frequency of valence bonds.
The type of bondsContent (%)Vibrational frequency (cm−1)TiA-O23.871563.4, 1114.3, 670.1, 620.9, 580.35, 548.17, 508.54, and 454.25TiR-O16.301513.7, 1459.5, 1395.6, 823.66, 765.65, and 716.7H-O7.411712.9, 1638.3Figure6 shows that the infrared spectra of the 2.5 mol%Cu-doped TiO2 samples. The fitting rate is 99.95%. The values of the vTiA−O (orange) are 458.99 cm−1, 509.79 cm−1, 541.21 cm−1, 574.02 cm−1, 623.11 cm−1, 666.94 cm−1, 1574.6 cm−1, and 1114.3 cm−1, respectively. The values of the vTiR−O (blue) are 710.29 cm−1, 748.65 cm−1, 796.48 cm−1, 848.4 cm−1, 1394.74 cm−1, 1458.5 cm−1, 1503.3 cm−1, and 1537.9 cm−1, respectively. The values of the vH−O (green) are 1633.4 cm−1 and 1680.9 cm−1. At the same time, there are two new bonds, the values of the vCuAi-o (dark cyan) are 489.74 cm−1 and the values of the vCuRi-o (pink) are 609.31 cm−1. In Table 5, the content of each peak was counted. It is indicated that there are five types of bonds. The content of TiA-O, TiR-O, H-O, CuAi-O, and CuRi-O is 21.23%, 18.56%, 7.34%, 0.98%, and 1.34%, respectively. By compared with the undoped TiO2, the content of TiA-O decreased by 2.64%, the content of TiR-O increased by 2.26%, and the content of the H-O bond is little changed. It quantitatively proved that the addition of Cu promoted the transformation of the anatase phase to rutile phase.Figure 6
Infrared spectra of the 2.5 mol%Cu-doped TiO2 samples at calcination temperature (550°C). (a) 400 cm−1∼1000 cm−1; (b) 1000 cm−1∼1800 cm−1.
(a)(b)Table 5
Infrared spectra of the 2.5 mol%Cu-doped TiO2 samples with the content and vibrational frequency of valence bonds.
The type of bondContent (%)Vibrational frequency (cm−1)TiA-O21.231574.6, 1114.3, 666.94, 623.11, 574.02, 541.21, 509.79, and 458.99TiR-O18.561537.9, 1503.3, 1458.5, 1394.74, 848.4, 796.48, 748.65, and 710.29H-O7.341680.9 and 1633.4CuiA-O0.98488.74CuiR-O1.34609.31The infrared spectra of the 5 mol% Cu-doped TiO2 samples in Figure 7. The fitting rate is 99.75%. The values of the vTiA−O (orange) are 454.71 cm−1, 489.7 cm−1, 509.93 cm−1, 533.05 cm−1, 579.11 cm−1, 586.76 cm−1, 628.09 cm−1, 671.26 cm−1, 712.85 cm−1, 797.43 cm−1, 843.36 cm−1, 1114.3 cm−1, and 1562.7 cm−1, respectively. The values of the vTiR−O (blue) are 876.86 cm−1, 922.88 cm−1, 1331.8 cm−1, 1371.2 cm−1, 1393.4 cm−1, 1414.9 cm−1, 1449.4 cm−1, 1478.7 cm−1, 1517.3 cm−1, 1604.6 cm−1, respectively. The values of the vH−O (green) are 1636.6 cm−1and 1673.7 cm−1. The values of vCuAi-O (dark cyan) are 549.23 cm−1 and 606.28 cm−1. The values of the vCuAs-O (purple) are 734.82 cm−1 and 1533.5 cm−1. The values of the vCuRs-O (dark yellow) are 745.97 cm−1 and 1287.6 cm−1. When the doping amount of Cu is 2.5 mol%, there are only CuAi-O and CuRi-O, which are interstitial sites. When the doping amount of Cu is 5 mol%, the doping of substitution position occurred. 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 TiO2 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%Cu-doped TiO2 samples of the content of all kinds of bonds. There are seven types of bonds; the content of TiA-O, TiR-O, H-O, CuAi-O, CuiR-O, CusA-O, and CusR-O is 18.75%, 20.11%, 7.47%, 2.56%, 3.9%, 1.55%, and 2.35%. By contrast, the 2.5 mol%Cu-doped TiO2, the content of TiA-O decreased by 2.48%, the content of TiR-O increased by 1.55%, the content of CuAi-O increased by 1.58%, the content of CuRi-O increased by 2.56%, and the content of H-O bond is little changed. Because the increase rate of TiR-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 CuR-O is always higher than that of CuA-O, and the content of Cui-O is more than Cus-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.Figure 7
Infrared spectra of the 5 mol% Cu-doped TiO2 samples at calcination temperature (550°C). (a) 400 cm−1∼1000 cm−1; (b) 1000 cm−1∼1800 cm−1.
(a)(b)Table 6
Infrared spectra of the 5 mol%Cu-doped TiO2 samples with the content and vibrational frequency of valence bonds.
The type of bondContent (%)Vibrational frequency (cm−1)TiA-O18.751562.7, 1114.3, 843.36, 797.43, 773.15, 712.85, 671.26, 628.09, 586.76, 579.11, 533.05, 509.93, 489.7 and 454.71TiR-O20.111604.6, 1517.3, 1478.7, 1449.4, 1414.9, 1393.4, 1371.2, 1331.8, 922.88, and 876.86H-O7.471673.7 and 1636.6CuiA-O2.56606.28 and 549.23CuiR-O3.9819.88, 696.61, 648.81, and 454.61CusA-O1.551533.5 and 734.82CusR-O2.351287.6 and 745.97The lattice parameters of undoped and Cu-doped samples are calculated from the XRD patterns. The lattice parameters remain unchanged, independent of Cu2+ content. This evidently considered that a greater portion of the Cu2+ ions is well-incorporated into the anatase and rutile TiO2 lattice. The content of rutile increased obviously after Cu doping. This is indicated that the addition of Cu obviously promoted the transformation from anatase phase to rutile phase.Figure8 is the TEM diagram of sintering at 550°C with 5%Cu-doped TiO2. According to Figure 8(a), the powder particles did not exceed 50 nm when the 5 mol%Cu-doped TiO2 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 TiO2 lattice. The Cu-doped TiO2 sample is characterized by FT-IR and TEM and calculated by electronegativity principle, and the theoretical calculation is consistent with the experimental results.Figure 8
The TEM images of 5 mol% Cu-doped TiO2.


## 4. Conclusion

The 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. This 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 TiA-O bonds is decreased by 2.64%, the content of TiR-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 TiA-O decreased by a further 2.48%, the content of TiR-O increased by a further 1.55%, the content of CuiA-O increased by a further 1.58%, the content of CuiR-O increased by a further 2.56%, the content of CusA-O decreased by a further 0.57%, the content of CusR-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. The 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%. This is explained that Cu atoms were more easily to be doped into rutile phase. The efficiency is that the quoted values refer to increases in the percentage content of rutile.



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