Study on the Crystal Structure of Coal Kaolinite and Non-Coal Kaolinite: Insights from Experiments and DFT Simulations

: Coal is often coated by kaolinite in ﬂotation, leading to a decrease in the quality of clean coal. The structure of the mineral determines its properties and ﬂotation behavior. Therefore, to remove the kaolinite from coal e ﬃ ciently, the di ﬀ erence in mineralogical characteristics between non-coal and coal kaolinite were analyzed using advanced instruments. The experiment results showed that, due to the substitution of the C atom for Si atom, the interplanar spacing of the kaolinite (001) surface became small with C-O-C, Al-O-C, and C-O-Si covalent bonds formed instead of Al-O-Si and Si-O-Si bond. Based on this, the models of monolayer and bilayer coal kaolinite (001) surfaces were built and the structure di ﬀ erence was compared through DFT calculation. The calculation results showed that the silicon atom of the kaolinite Si-O-(001) surface was easier to be doped by carbon atoms with external energy as the interplanar spacing of the kaolinite (001) surface decreased with the increase in doped carbon atoms (7.15440 Å → 7.11859 Å → 7.10902 Å → 7.10105 Å). The structural di ﬀ erence between non-coal kaolinite and coal kaolinite were compared from the view of the experiment and quantum chemistry, which provides an important theory for subsequent research on the properties of coal kaolinite and its further processing and utilization.


Introduction
In the process of coal slime flotation, a large number of fine-grained coal clay minerals are mixed into the clean coal, whose composition is mostly kaolinite [1]. This limits the efficiency of flotation and reduces the quality of clean coal [2]. The surface properties of coal kaolinite are the key factors to determine its surface floatability [3] and the surface properties depend on the surface crystal structure [4]. The previous study found that the coal pyrite surface was substituted [5] and covered [6] by carbon atoms so that the structure and properties of coal pyrite were different from the non-coal pyrite [7]. Meanwhile, the formed sulfur after optimization enhanced the hydrophobicity of coal pyrite [8]. Therefore, it is very important to accurately obtain the crystal structure information of kaolinite for understanding the physical and chemical properties and flotation characteristics of kaolinite [9]. Coal kaolinite has formed special crystal structures in the long-term coal forming environment due to the lattice defect and surrounding rock symbiosis and has further significantly exhibited different surface properties from the non-coal kaolinite. Because the kaolinite and other clay minerals exist as microcrystalline or cryptocrystalline, it is difficult to measure the microstructure of coal kaolinite thoroughly and comprehensively by experimental means. Many scholars have studied

Experimental Equipment and Methods
The four samples were characterized using SEM, XRD, FTIR and XPS. The appearances of the samples were observed by the Hitachi SU8020 Scanning electron microscope, whose magnification was 30-800,000×. XRD were carried out with the Bruker D8 ADVANCE X-ray diffractometer and the samples were ground under a 200 mesh. The tube voltage and the tube current were 40 kV and 40 mA, respectively. A Cu target and a wavelength of 1.5406 Å was selected. The scanning scope is generally 10-90 • and adjusted according to the sample difference. The scanning speed was set up to 0.06 s/step. The step interval was 0.02 • /step. FTIR spectra were attained with a Thermo Fisher Scientific Nicolet-IS5 spectrometer. The sample and KBr (1:100), which were mixed and pressed into pellets, were scanned at the range of 4000-400 cm −1 . All samples were dried at 105 • C for 4 h before measurement. The XPS experiment was carried out with a Thermo Scientific Escalab 250Xi X-ray photoelectron spectroscope, made by Thermo Fisher Scientific. The Al target X-ray source with monochromator was used for testing in an ultra-vacuum environment. The vacuum degree of the analysis chamber was greater than 1 × 10 −9 mbar. The value of the pass energy, energy step and spot size was 20 eV, 0.05 eV and 900 um, respectively.

Computational Method
The optimized single-layer model of the kaolinite (001) surface was attained from Han [16,17] with the CASTEP of Materials Studio software [18]. The generalized gradient approximation (GGA), developed by Perdew-Burke-Ernzerhof (PBE), was selected as the exchange-correlation function. The interactions between valence electrons and the ionic core were represented using the ultra-soft pseudopotentials [19]. The cut-off energy was 400 eV. All the calculations were run until the energies were converged to within 2.0 × 10 −6 eV/atom in each self-consistency cycle and the forces on all ions were converged to within 0.05 eV/Å. The threshold values for the other convergence criteria were 0.002 Å for maximum displacement, 0.1GPa for maximum stress, 2.0 × 10 −5 eV/atom for energy and DFT-D correction was adopted [20,21]. The atomic positions were optimized by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [22]. In the geometric optimization process of bulk kaolinite, all atoms and unit cell parameters were relaxed so that the optimized primitive unit cell were close to the experimental values. We optimized the carbon atom, silicon atom, oxygen atom and water molecule by the 20 × 20 × 20 cubic cell whose Brillouin zone sampling was restricted to k-point, and the other parameters were consistent with the primitive unit cell optimization, reported above.

Surface Model
The model of the kaolinite (001) surface was cleaved from the kaolinite unit cell, which was exposed with a hydroxylated and a siloxane on each side of the surface. We used the periodic supercell (2 × 1 × 1), which had a vacuum thickness of 20 Å [23]. The slab was comprised of "H-O-Al-O-Si-O", six atomic "sublayers", which were optimized with three "sublayers" fixed. Two sides of the kaolinite (001) surface model were studied-Al-O-(001) surface and Si-O-(001) surface-as shown in Figure 1a.
The double-layer model of the kaolinite surface constructed in the paper is based on the single-layer model, as shown in Figure 1b. The double-layer model of kaolinite is optimized to get the optimal exchange-correlation function and cutoff energy, as shown in Table 2. The rationality of the double-layer was determined according to the error ratio, which is calculated as: where E r was the error rate, d e was the experimental value of the interplanar spacing, which was 7.1453 in the paper, consistent with the other experimental values of 7.19 [24], 7.15 [25,26], 7.17 [27]. d c was the calculated value of the interplanar spacing. The smaller the E r , the more rational the double-layer structure of kaolinite.   Table 2, we can see that the interplanar spacing of the kaolinite double-layer (001) surface in different exchange-correlation functions and cut-off energies were obtained and the error ratio was calculated. The error ratio of the interplanar spacing on the condition GGA-RPBE and 400 eV is minimal (0.00), which explained that the calculated interplanar spacing was closest to the experimental value. The double-layer model of the kaolinite (001) surface was the most reasonable. The model of subsequent coal kaolinite (001) surface was constructed based on the optimized kaolinite (001) surface.

The Impurity Substitution Energy
The model of the kaolinite surface containing defects was optimized by impurity substitution energy [28]. Its value represented the difficulty of the substitution, defined as: where △ E is the impurity substitution energy in this paper, meaning the energy needed for substitution, and Etotal/C is the energy of the kaolinite surface substituted by the carbon atom. Etotal/perfect is the energy of a perfect surface. EX and EC are the energies of the single Si atom (or O atom) and C atom. If the △E was positive, the substitution can occur with the external energy. The larger the value, the more the needed energy, which means it is more difficult to replace an atom.  From Table 2, we can see that the interplanar spacing of the kaolinite double-layer (001) surface in different exchange-correlation functions and cut-off energies were obtained and the error ratio was calculated. The error ratio of the interplanar spacing on the condition GGA-RPBE and 400 eV is minimal (0.00), which explained that the calculated interplanar spacing was closest to the experimental value. The double-layer model of the kaolinite (001) surface was the most reasonable. The model of subsequent coal kaolinite (001) surface was constructed based on the optimized kaolinite (001) surface.

The Impurity Substitution Energy
The model of the kaolinite surface containing defects was optimized by impurity substitution energy [28]. Its value represented the difficulty of the substitution, defined as: where ∆E is the impurity substitution energy in this paper, meaning the energy needed for substitution, and E total/C is the energy of the kaolinite surface substituted by the carbon atom. E total/perfect is the energy of a perfect surface. E X and E C are the energies of the single Si atom (or O atom) and C atom. If the ∆E was positive, the substitution can occur with the external energy. The larger the value, the more the needed energy, which means it is more difficult to replace an atom.

SEM
The surface morphologies of all kaolinite samples were analyzed by field emission scanning electron microscopy, and the results are shown in Figure 2. The non-coal kaolinite has a structure of stacked layers, some of which are rhombic and hexagonal and some of which are irregular due to fragmentation, and the surface is smooth and clean without impurities. The coal kaolinite (CK-2, CK-3, CK-4) is also structured with stacked layers, some of which have rough surfaces and impurities clearly attached to them. It is preliminarily concluded that the surface of coal kaolinite may contain carbon impurities that have not been fully dissociated and it may contain lattice defects which lead to the incomplete crystal structure.

Mineralogical Characteristics
The surface morphologies of all kaolinite samples were analyzed by field emission scanning electron microscopy, and the results are shown in Figure 2. The non-coal kaolinite has a structure of stacked layers, some of which are rhombic and hexagonal and some of which are irregular due to fragmentation, and the surface is smooth and clean without impurities. The coal kaolinite (CK-2, CK-3, CK-4) is also structured with stacked layers, some of which have rough surfaces and impurities clearly attached to them. It is preliminarily concluded that the surface of coal kaolinite may contain carbon impurities that have not been fully dissociated and it may contain lattice defects which lead to the incomplete crystal structure.

XRD
Atoms with a similar radius and charge or net polarity substitute the atoms of crystal, which is called lattice substitution. It may be either stoichiometric or nonstoichiometric. XRD is an effective technique to analyze the lattice defect state of the mineral surface. On the basis of the above surface morphology by SEM, the XRD test was carried out to analyze the characteristic peak offsets or the new peak presences of the samples. The phase composition can be determined and the interplanar spacing calculated. Furthermore, the lattice impurity can be determined [29]. The XRD results in Figure 3(a) show that : (a) Although non-coal and coal kaolinite belong to different types, the diffraction peak position and intensity of the XRD powder diffraction pattern are basically the same, and the peak position and intensity are consistent with the crystal diffraction data of the PDF standard card, as shown in Figure 3(a). Among them, the intensity of the diffraction peak (001) is the strongest, the peak (002) is the second, and the content of kaolinite (001) is the highest, which is the most easily dissociated (001) in the process of fragmentation.
(b) Further comparative analysis shows that the diffraction peak position of non-coal kaolinite (001), shown in Figure 4(b), is consistent with that of standard card kaolinite (001) (2θ = 12.362°). However, the peak position (2θ = 12.382°) of coal kaolinite from Datong (CK-2) is shifted to the right, and the peak position (2θ = 12.405°) of coal kaolinite from Huairen (CK-3) is shifted to the right with a larger angle. The peak position (2θ = 12.368°) of coal kaolinite from Huaibei (CK-4) is also shifted to the right. The characteristic peak offsets of the coal kaolinite may be attributed to isomorphism, including silicon atom doping by the carbon atom, aluminum atom, iron atom or other atoms.
where the was the interplanar spacing, was the angle between the incident X-ray and the corresponding crystal plane, was the wavelength of the X-ray and n was the diffraction series. According to the Bragg's law (2)

XRD
Atoms with a similar radius and charge or net polarity substitute the atoms of crystal, which is called lattice substitution. It may be either stoichiometric or nonstoichiometric. XRD is an effective technique to analyze the lattice defect state of the mineral surface. On the basis of the above surface morphology by SEM, the XRD test was carried out to analyze the characteristic peak offsets or the new peak presences of the samples. The phase composition can be determined and the interplanar spacing calculated. Furthermore, the lattice impurity can be determined [29]. The XRD results in Figure 3a show that: (a) Although non-coal and coal kaolinite belong to different types, the diffraction peak position and intensity of the XRD powder diffraction pattern are basically the same, and the peak position and intensity are consistent with the crystal diffraction data of the PDF standard card, as shown in Figure 3a. Among them, the intensity of the diffraction peak (001) is the strongest, the peak (002) is the second, and the content of kaolinite (001) is the highest, which is the most easily dissociated (001) in the process of fragmentation.
(b) Further comparative analysis shows that the diffraction peak position of non-coal kaolinite (001), shown in Figure 4b, is consistent with that of standard card kaolinite (001) (2θ = 12.362 • ). However, the peak position (2θ = 12.382 • ) of coal kaolinite from Datong (CK-2) is shifted to the right, and the peak position (2θ = 12.405 • ) of coal kaolinite from Huairen (CK-3) is shifted to the right with a larger angle. The peak position (2θ = 12.368 • ) of coal kaolinite from Huaibei (CK-4) is also shifted to the right. The characteristic peak offsets of the coal kaolinite may be attributed to isomorphism, including silicon atom doping by the carbon atom, aluminum atom, iron atom or other atoms.
where the d HKL was the interplanar spacing, θ was the angle between the incident X-ray and the corresponding crystal plane, λ was the wavelength of the X-ray and n was the diffraction series.
According to the Bragg's law (2) and the wavelength of the Cu target (λ = 1.5406Å), the interplanar spacing of the samples (001) are calculated as follows: It was found that, due to the long-term coal forming environment, the carbon atom with smaller atomic radius (0.077 nm) in the coal may replace the silicon atom with larger atomic radius (0.117 nm) in the coal kaolinite (CK-2, CK-3, CK-4), which leads to the contraction of the crystal (001) surfaces and a decrease in the interplanar spacing. On the X-ray diffraction peak, it moves towards a large angle.
Symmetry 2020, 12, x FOR PEER REVIEW 6 of 12 It was found that, due to the long-term coal forming environment, the carbon atom with smaller atomic radius (0.077nm) in the coal may replace the silicon atom with larger atomic radius (0.117nm) in the coal kaolinite (CK-2, CK-3, CK-4), which leads to the contraction of the crystal (001) surfaces and a decrease in the interplanar spacing. On the X-ray diffraction peak, it moves towards a large angle.

FTIR
The FTIR diffuse reflection spectra of kaolinites can be divided into high frequency (3700-3600 cm −1 ) and low frequency (1200-400 cm −1 ). Farmer [30] thinks that there existed four characteristic adsorption peaks around 3695, 3670, 3651 and 3620 cm −1 in the pure kaolinite. For the four samples, the wavenumber of the FTIR spectra and their corresponding bonds are same. Among them, the bands around 3695, 3670, 3650 and 3620 cm −1 were found in Figure 3(b), which were assigned to the inner-surface hydroxyls and the inner hydroxyl, respectively [31]. The adsorption peak around 1114 cm −1 was the symmetric stretching vibration and 1033 and 1010 cm −1 were the antisymmetric stretching vibrations of the Si-O-Si bond, as shown in Table 3. The adsorption peaks around 937 and 913 cm −1 were caused by the bending vibration of the inner-face and the inner hydroxyls, respectively. The translation vibration of hydroxyl was 790 cm −1 . The bands at about 755 and 697cm −1 were the stretching vibrations of the Si-O bond. Another peak band, located at 432 cm −1 , can be assigned to the bending vibration of the O-Al-O bond [32][33][34][35].
Compared with the non-coal kaolinite, there existed some differences between the vibration bands of coal kaolinite. It was found that 539, 468 cm −1 gradually shifted to 541, 471 cm −1 , which may be attributed to the CO stretching and OCO bending vibration, instead of SiO stretching and OSiO bending vibration. Meanwhile, a small new band at about 686 cm −1 appeared, which implies that C atoms enter into the structure, replace the Si of kaolinite and affect the vibration-rotation energy of kaolinite.    As the K-1 and CK-3 samples are both powders, their XPS spectra of C 1s are same before and after etching, as is clearly shown in Figure 5. Before and after etching, the C 1s spectrum of coal kaolinite shows a strong peak around 284.60 eV, which belongs to the C-C bond of aromatic carbon on the kaolinite surface, covered with incomplete dissociated impurity coal. Meanwhile, the curvefitting peaks around 283.50 and 288.90 eV appeared, which revealed that Al-O-C and C-O-Si bonds were formed instead of Al-O-Si and Si-O-Si bond. These results were attributed to the substitution of the carbon atom for silicon atoms in the kaolinite lattice in the process of coal formation, as is clearly shown in Figure 6. However, the contents of the latter two are relatively small.

FTIR
The FTIR diffuse reflection spectra of kaolinites can be divided into high frequency (3700-3600 cm −1 ) and low frequency (1200-400 cm −1 ). Farmer [30] thinks that there existed four characteristic adsorption peaks around 3695, 3670, 3651 and 3620 cm −1 in the pure kaolinite. For the four samples, the wavenumber of the FTIR spectra and their corresponding bonds are same. Among them, the bands around 3695, 3670, 3650 and 3620 cm −1 were found in Figure 3b, which were assigned to the inner-surface hydroxyls and the inner hydroxyl, respectively [31]. The adsorption peak around 1114 cm −1 was the symmetric stretching vibration and 1033 and 1010 cm −1 were the antisymmetric stretching vibrations of the Si-O-Si bond, as shown in Table 3. The adsorption peaks around 937 and 913 cm −1 were caused by the bending vibration of the inner-face and the inner hydroxyls, respectively. The translation vibration of hydroxyl was 790 cm −1 . The bands at about 755 and 697cm −1 were the stretching vibrations of the Si-O bond. Another peak band, located at 432 cm −1 , can be assigned to the bending vibration of the O-Al-O bond [32][33][34][35]. Compared with the non-coal kaolinite, there existed some differences between the vibration bands of coal kaolinite. It was found that 539, 468 cm −1 gradually shifted to 541, 471 cm −1 , which may be attributed to the CO stretching and OCO bending vibration, instead of SiO stretching and OSiO bending vibration. Meanwhile, a small new band at about 686 cm −1 appeared, which implies that C atoms enter into the structure, replace the Si of kaolinite and affect the vibration-rotation energy of kaolinite.

XPS
In order to further study the existence of elements, such as Al, Si, O and C, X-ray photoelectron spectroscopy was conducted as an effective analysis technique. According to the position of the photoelectron absorption peak (electron binding energy), it can identify the elements in the sample and the different forms of the same elements in the compound.  [37,38].
As the K-1 and CK-3 samples are both powders, their XPS spectra of C 1s are same before and after etching, as is clearly shown in Figure 5. Before and after etching, the C 1s spectrum of coal kaolinite shows a strong peak around 284.60 eV, which belongs to the C-C bond of aromatic carbon on the kaolinite surface, covered with incomplete dissociated impurity coal. Meanwhile, the curve-fitting peaks around 283.50 and 288.90 eV appeared, which revealed that Al-O-C and C-O-Si bonds were formed instead of Al-O-Si and Si-O-Si bond. These results were attributed to the substitution of the carbon atom for silicon atoms in the kaolinite lattice in the process of coal formation, as is clearly shown in Figure 6. However, the contents of the latter two are relatively small.

The Doping Mechanism and Impurity Substitution Energies
According to the isomorphism principle, the carbon atoms were most likely to substitute for the Si or O atoms of the kaolinite (001) surface, including the Si-O-(001) surface and Al-O-(001) surface, so that the substitution models, as shown in Figure 7b,c,e, represented the coal pyrite in the present study. For the coal kaolinite, the Si atom and O atom of both sides may be substituted. Therefore, the impurity substitution energies were calculated, as shown in Table 4.  For the Si-O-(001)-doped (Si) and Si-O-(001)-doped (O), the ∆E were 258.12 kJ/mol and 660.01 kJ/mol, respectively. This demonstrated that, whether the carbon atom substituted the Si atom or O atom, it was not spontaneous and a large amount of external energy was needed to induce this chemical reaction. The former was easier to in the coal-forming process because of its smaller impurity substitution energy, which may be due to the fact that the C atom and the Si atom belong to the same main element group and their properties are close. For the Al-O-(001)-surface, the ∆E was 469.92 kJ/mol after the O atom was substituted by the C atom. In summary, a minimum energy was needed if the Si atom of Si-O-(001) surface was substituted by the C atom, and the carbon atom was the easiest to substitute for the silicon atom and the most difficult to substitute for the oxygen atom of the Si-O-(001) surface. So, the models of Si-O-(001)-doped (Si) were used as the surface models to study the effect of the carbon atom-defect on the structure of kaolinite.

Interplanar Spacing of Kaolinite
The XRD and XPS results showed that the interplanar spacing decreased due to the substitution of silicon atoms by carbon atoms. So, the double-layer model of the coal kaolinite (001) surface, doped with different amounts of carbon atoms, was further optimized and the interplanar spacing was calculated as follows: where d is the interplanar spacing, ∆Z is the Z coordinate difference of Aluminum atomic number. Z U is the Z coordinate of the upper aluminum atom and is the Z L coordinate of the lower aluminum atom. The interplanar spacing of non-coal kaolinite is 7.15440, close to the experimental value of 7.1543, which explained that the selected model is scientific and reasonable. Compared with the non-coal kaolinite, the interplanar spacing of coal kaolinite becomes small after the Si atoms are substituted by the C atom and decreased gradually with the increase in the doping number of carbon atoms (7.15440 Å→7.11859 Å→7.10902 Å→7.10105 Å), as shown in Table 5. This shows that the crystal of coal kaolinite shrinks during to the substitution of carbon atoms for silicon atoms. It was found that, due to the long-term coal forming environment, the carbon atoms with smaller atomic radii (0.077nm) in the coal replace the silicon atoms with larger atomic radii (0.117nm) in the coal kaolinite, which leads to the contraction of the crystal surfaces and the decrease in the interplanar spacing, which is consistent with the experimental results of XRD and XPS.  The interplanar spacing of non-coal kaolinite is 7.15440, close to the experimental value of 7.1543, which explained that the selected model is scientific and reasonable. Compared with the non-coal kaolinite, the interplanar spacing of coal kaolinite becomes small after the Si atoms are substituted by the C atom and decreased gradually with the increase in the doping number of carbon atoms (7.15440 Å→7.11859 Å→7.10902 Å→7.10105 Å), as shown in Table 5. This shows that the crystal of coal kaolinite shrinks during to the substitution of carbon atoms for silicon atoms. It was found that, due to the long-term coal forming environment, the carbon atoms with smaller atomic radii (0.077nm) in the coal replace the silicon atoms with larger atomic radii (0.117nm) in the coal kaolinite, which leads to the contraction of the crystal surfaces and the decrease in the interplanar spacing, which is consistent with the experimental results of XRD and XPS.

Conclusions
The mineralogical characteristics of between non-coal kaolinite and coal kaolinite were compared. The doping of the carbon atom appeared to incorporate into the kaolinite instead of the silicon atoms of the layered stacking coal kaolinite surface. The Al-O-C, C-O-Si and C-O-C bonds were formed instead of the Al-O-Si and Si-O-Si bonds, resulting in a reduction in the interplanar spacing and the contraction of the crystal surface. The calculated interplanar spacing of coal kaolinite decreased with the increase in doping carbon atoms, which agreed well with the experiment. It provided an important theory for subsequent research on the properties of non-coal kaolinite and coal kaolinite and their further processing and utilization.

Appendix A
All nomenclature and abbreviations were explained in alphabetical order, as follows: BFGS: Broyden-Fletcher-Goldfarb-Shanno;

Conclusions
The mineralogical characteristics of between non-coal kaolinite and coal kaolinite were compared. The doping of the carbon atom appeared to incorporate into the kaolinite instead of the silicon atoms of the layered stacking coal kaolinite surface. The Al-O-C, C-O-Si and C-O-C bonds were formed instead of the Al-O-Si and Si-O-Si bonds, resulting in a reduction in the interplanar spacing and the contraction of the crystal surface. The calculated interplanar spacing of coal kaolinite decreased with the increase in doping carbon atoms, which agreed well with the experiment. It provided an important theory for subsequent research on the properties of non-coal kaolinite and coal kaolinite and their further processing and utilization.